[Surveying]
[From the U.S. Government Publishing Office, www.gpo.gov]
WAR DEPARTMENT
TECHNICAL MANUAL
SURVEYING
NON-CIRCULATING
Document Reserve
kTM 5-235
NTSU UBRARYi
TM 5-235
c 1
TECHNICAL MANUAL
SURVEYING
Changes! WAR DEPARTMENT,
No. 1 | Washington 25, D. C., 18 September 1944.
TM 5-235,1 October, 1940, is changed as follows:
52. Handling1 level.
*******
e. Steps in leveling.
*******
(2) Example.-—Assume the level * *• * or 259 feet. This sight taken on a rod held upon a point of known elevation is termed a “backsight” (B. S.), so the equation can be written: El+B. S.=H. I. The line of * * * H. I.-F. S.=El.
55. Profile leveling.
* * * * * * *
e. Profile and grade lines.—Profile and grade * * * on the plot. For a detailed discussion of setting grade stakes and slope stakes, etc., see paragraph 188.
*******
57. Barometric elevations.
* * * * * * *
d. Procedure (Superseded).—With a calibrated aneroid barometer, take the aneroid barometer readings at two stations whose heights are to be compared. Also take the temperature (Fahrenheit) at the two stations. Assume that the following data have been obtained:
Station Barometer Temperature
A Beach (at sea level)---- 29.98 78° F.
A Top___.__________:______ 23.66 70° F.
To compute the difference of elevation between these two stations, obtain from table VII, TM 5-236, the difference of elevation between A Beach and ATop and interpolate to the nearest 0.1 foot, as shown
here :
A Beach Barometer 29.98 Elevation________________________________ 18
A Top Barometer 23.66 Elevation_____________,____________________6,469
First difference=6,451
Next obtain coefficient (C) from table VIII, TM 5-236, for (£+£') the sum of the thermometer readings, (78°+70°) = 148°. Interpolating from the table, C = 0.0554. This multiplied by the first difference
AGO362C 598803°—44
TM 5-235
C 1
SURVEYING
(6,451 X 0.0554) =357. The latter added to the first difference (6,451 + 357) gives a final corrected difference of 6,808 feet. Assuming that the true elevation of A beach is 14.0 feet, the elevation of A top is 14.0+6,808=6,822 feet.
57.1 Surveying altimeter (Added).—a. Description.—The surveying altimeter (fig. 20.1) is an aneroid-barometer type instrument used to determine differences in elevation. There are two classes of altimeters, one with 10-foot divisions and a maximum range of 6,000 feet of elevation, the other with 20-foot divisions and a maximum range of 15,000 feet.
5. Use.—Altimeter leveling is more accurate than barometric leveling (par. 57) and less accurate than differential leveling (par. 54). With the proper corrections applied, altimeter leveling gives results accurate enough for vertical control of multiplex topography (TM 5-240 and 5-244). It is a particularly useful method of providing vertical control over terrain areas within a radius of 8 miles of a starting point when differential-leveling accuracy is not required.
c. Reference.—For detailed descriptions and instructions for using the surveying altimeters, see TM 5-9420 for the 6,000-foot altimeter, and TM 5-9418 for the 15,000-foot altimeter.
65- Transit.
*
l>. Verniers.
*
*
*
*
*
= 20 seconds.
*
77z^38 -37 27"C9 ’29
"31 —30
x32 6823
55 tO
89 52 53 66
-59
-45 x41 .42 70x
Figure 12.—Component parts of K. and E. dumpy level.
4^'
23 22 67
—8
•—9 710
i
4412
-24
-25
8
13-
JI
"20 19
66g
3—TtT§
18
10-*21
20 22
26-
36 F35
28-
81—
33^ 32^84-
47
48
65
1 Tripod head
2 “ bolt
8 “ " nut
4 “ " washer
5 “ " lockscrew
6 “ leg
7 ‘ plate
8 Leveling head
9 " screw
10 •* " shoe
11 Half ball
12 “ “ lock screw
13 Center
14 “ cap
15 “ spring
16 “ nut
18 Level bar
19 Level bar clamp
20 “ “ “ gib
21 “ “ " screw
22 “ “ “spr’gbox
23 “ " "tangent
screw
24 *' "plunger
25 ........spring
26 “ '* " cap
27 Adjustable Y
28 Fixed Y
54
f
I
,51 p—50
54 }1 40 51 72 58 63 72
RLAfhfai I ..IJ------
TM 5-235
51-52
SURVEYING
used more frequently than the target rod. The target must be used for third-order leveling but need not be for less accurate work.
(2) Other accessories for level work are the Abney level (fig. 13 @), used for obtaining vertical angles or percentage of slopes for reconnaissance purposes and chaining; the hand level (fig. 13 @), used for leveling the tape in chaining, etc.; and the steel turning pin (fig. 13 ©), used as a temporary turning point on level lines.
(3) Figure 13 ® shows a level rod target with vernier which permits readings on the rod to the nearest 0.001 foot.
52. Handling level.—a. Function of level.—When a level is properly set up the line of sight is perpendicular to the line of gravitation and revolves in a horizontal plane. The line of sight is the basis of determining elevations and of establishing points at desired elevations.
In all surveys the elevations are referred to some common datum which is designated as zero elevation. The elevation of any point not in the datum plane is secured by the addition or subtraction of its vertical distance above or below that plane.
b. Setting up level.—Set tripod legs firmly in the ground so as to leave only a slight adjustment of instrument to be made by the leveling screws. Turn the telescope until it is directly over two diagonally opposite leveling screws and bring the bubble approximately to the center of the tube by turning these screws. The leveling screws should be worked at the same time and in opposite directions. A helpful rule to remember is that the bubble always moves in the direction in which the left thumb is turned. Now turn the telescope until it is over the other pair of screws and bring the bubble exactly to the center. Turn the telescope back over the first set of screws, level carefully, and turn again to the second set to check the position of the bubble. If the instrument is in adjustment, and has been properly leveled, the bubble will remain in the center of the tube through an entire revolution of the telescope about the vertical axis (par. 53). On a slope, set two tripod legs downhill. Make sure that the line of sight will come within the limits of the rod before completing the leveling of the instrument. An approximate determination can usually be made by sighting along the horizontal center line of the telescope.
c. Steps in leveling.—(1) After the level has been set up, the next step is to determine the elevation of its horizontal plane of sight, called the height of instrument measuring up to this plane by reading the vertical distance on the rod from some point (a bench mark, B.M.f of which the elevation is known. Then the elevation of any point is found by subtracting the rod reading at that point from the ILL. (par. 54).
>
I
A z
55
TM 5-235
52 CORPS OF ENGINEERS
(2) Example.—Assume the level to be set up so that a sight can be taken on the rod held on a bench mark with a known elevation {El) of 255 feet. It is found that the line of sight of the level cuts the rod at a distance of 4 feet above the bench mark, so that the rod
with target. target. ® Level rod target. © Turning pin (steel).
Figure 13.—Level rods and accessories.
reading is 4 feet. Then the elevation of the horizontal plane of sight or the height of instrument is equal to 255 plus 4 or 259 feet. This sight taken on a rod held upon a point of unknown elevation is termed a “backsight” {B.S.), so the equation can be written: El-\-B.S.=H.I. The line of sight is now directed at the rod, held on a point of unknown elevation; assuming rod reading 8 feet, the elevation of the unknown
56
@ Abney level.
® Hand level.
TM 5-235
52
SURVEYING
point is equal to 259 minus 8 or 251 feet. This sight taken upon a rod held on a point of unknown elevation is termed a “foresight” (F.S.). The second equation thus can be written: H.I.—F.S.—El.
d. Reading rod.—The rod is held vertically on the station with its face toward the level, the rodman squarely behind it and facing the levelman so that he can see any signal from the latter, directing the movement and setting of the target. When necessary, the levelman indicates movement of the rod to right or left until it coincides with the vertical wire in his telescope. The rod is vertical when it shows the minimum reading; this is readily noted through the telescope when the rod is swung through a small arc in the line of sight. The levelman should note the accuracy of the telescope bubble before giving the signal for the rod target to be read if the target is being used,
6
5 — _
o
5
® Rod vernier, reading 5.16 feet.
® Construction of vernier scale.
Figure 14.—Vernier scale.
or before and after reading the rod when it is being used as a selfreading rod. The target vernier is read by the rodman, who reports the reading to the note keeper, who checks the setting before making the records. The self-reading rod lends itself to more rapid work than the target rod, and gives nearly as accurate results.
e. Rod vernier.—A rod vernier is an auxiliary scale, used in connection with the target rod, by means of which the rod scale can be read one decimal place beyond its smallest division. The use of the vernier depends on the fact that it is easier to determine coincidence of two lines than to estimate fractions of a scale interval. A vernier is constructed by laying off a distance equal to nine of the main scale divisions and dividing it into ten equal parts, placing it edge to edge along the main scale. (See fig. 14®.) After the vernier starts to move, no lines are coincident until the vernier has moved one-tenth of a main subdivision, at which time the first division line of the ver-
57
TM 5-235
52-53
nier coincides with a line of the main scale. The position of the zero on the vernier is the reading desired. In figure 14@, the zero lies between 5.1 and 5.2, and the sixth subdivision of the vernier is coincident with a subdivision of the main scale; hence the reading is 5.16.
/. Use of hand level.—The hand level, having no tripod, is held to the eye by hand and the forward end is raised or lowered until the bubble is in the center of the tube. The levelman may stand erect, in which case he must know the distance that his eye is above ground, or the level may be fastened to the top of a staff of known height, usually 5 feet. In the first case the height of instrument is found by adding the height of eye above ground to the elevation of the ground. In leveling uphill any point where the line of sight cuts the ground is the same elevation as the height of instrument. By moving up to this point, a new height of instrument is established. In leveling downhill the levelman moves downhill until the line of sight cuts a point of known elevation; then the elevation where the levelman is standing is found by subtracting the height of eye from the known elevation. If a staff is used to support the level, the method is the same, but is more accurate as the height of eye is definitely fixed for every shot. Level rods may also be used with the hand level, the level being used in the same manner as a tripod level. No shots over 75 feet should be taken, or errors may become excessive.
g. Use of Abney level.—The Abney level is a modification of the hand level with a supplementary telescope and a graduated arc for reading vertical angles or percentage of slope. A sight is taken through the tube as with the hand level while the bubble of the pivoted level tube, to which is attached the graduated arc, must remain in the center. The vertical angle or percentage of slope is then read from the graduated arc which has a direct vernier enabling the levelman to take readings to 10 minutes, or even less, depending on the markings of the arc and vernier.
53. Adjustments of dumpy level.—a. Equipment.—Dumpy level, leveling rod, stakes, hatchet, adjustment pins, note paper, pencil.
b. Adjustment of horizontal wire.—To make the horizontal wire horizontal when the instrument is level and parallax, if any, has been eliminated:
(1) Level the instrument and sight on some sharply defined point which is covered by the horizontal wire.
(2) Turn the telescope with the slow motion screw about its vertical axis so that the point appears to traverse the field of view. If the point remains on the horizontal wire the adjustment is correct. If not, turn the wire reticle slightly after loosening the capstan screws until the condition is satisfied.
58
CORPS OF ENGINEERS
TM 5-235
53-54
SURVEYING
(3) Sighting at a plumb line with the vertical hair is an alternative method.
c. Adjustment of the spirit level.—To make the axis of the spirit level perpendicular to the vertical axis—
(1) Set up the instrument and level it over one pair of leveling screws.
(2) Turn the instrument on its vertical axis through 180° or halfway around. The bubble should remain in the center of the tube. If not, move it halfway back to the center by means of the spirit level adjusting nuts.
(3) Repeat until the bubble remains in the center of the tube for any position of the instrument.
d. Direct or “peg” adjustment.—To make the line of sight parallel to the axis of the spirit level—■
(1) Drive stakes (at A and B) about 300 feet apart.
(2) Set up midway between them and take a rod reading at each. Their difference will be the true difference of elevation between them.
(3) Set up so that when the rod is at A the eyepiece will be about one-fourth of an inch from it.
(4) Look through the telescope from the objective to the eyepiece and note the reading on the rod opposite the center of the field. (The location of the point on the rod may be determined by setting a pencil point at the center of the small field of view.)
(5) To this reading add or subtract (depending on whether B is lower or higher than A) the difference obtained in (2) above and set the target at the result.
(6) Sight on the rod at B and move the horizontal wire until it cuts the center of the target.
(7) Check the adjustment of the horizontal wire.
e. Exercise II.—Make the adjustments of the dumpy level as described above.
54. Differential leveling.—a. General description.—Differential leveling has for its object the determination of the difference of elevation between two stations, or the establishment of the elevation of a new station with reference to a known elevation, irrespective of the distance or the profile of the terrain between them. The level is set up and a backsight taken on the rod at the first station. The rodman paces the distance to the instrument and an equal distance beyond, if possible, to the second rod point, so as to equalize the lengths of backsights and foresights and thus to eliminate errors of instrumental adjustment. The level notes should show these distances, and, if it is not possible to equalize related backsights and foresights, allowance
59
TM 5-235
54 CORPS OF ENGINEERS
should be made later so as to have the sum of all backsights and all foresights equal upon completion of the level circuit. At the second rod point the rodman selects or prepares a suitable turning point (T.P.\ This may be a well defined summit of a solid boulder, a spike driven into the spreading root of a tree, or an iron pin driven firmly into the ground, (see fig. 13 ©). After reading this foresight the levelman picks up his instrument, goes by in the direction of the second station, and makes a new set-up. The operation continues in this manner until the final foresight is taken on the second station, the elevation of which, referred to the first, is desired. To check the arithmetical work, compare the difference between the sum of the backsights and foresights with the difference in elevations between the first and second stations. If the results are alike, the computations in the notebook check.
b. Field notes.—Figure 15 ® shows a standard form of differential level notes. The small encircled numbers (in the upper right corners) are not recorded; they are used here only to show the progression of entering the notes as obtained from the example of the field work shown in figure 15 ®.
c. Field method.—Figure 15 ® shows the first part of a differential level line, assumed to be run from B.M. 35, the elevation of which is 133.163 (all figures referring to elevations here are in feet). The first set-up shows the B.S. to be 6.659, which added to the elevation of B.M. 35 gives an H.I. of 139.822. The first F.S. on O 16 was 4.971, which subtracted from the H.I. gives an elevation of 134.851 for O 16. The lengths of B.S. (220) and F.S. (220) shown opposite the H.I. were determined by pacing, and were recorded together with the other readings as indicated in figure 15 ®. The instrument was then set up halfway between 016 and 017, and the operations (B.S., H.I., F.S., etc) repeated, after which it was moved between succeeding stations until the leveling was completed. (Caution.—The rodman must never remove a temporary turning point (T.P.) until he gets a definite signal from the observer.) The levelman must never quit work on a temporary turning point but must continue until he comes to the next permanent B.M. or station where he will observe and record an F.S.
d. Checking methods.— (1) To check the accuracy of the level notes, add all backsights together (see fig. 15 ®); add all turning-point foresights together; the difference between these two sums should equal the difference between the elevations of the first and last stations. The foresight on the last station must be included in the sum of foresights although there is no corresponding backsight. The last station
60
TM 5-235
54
SURVEYING
is a turning point in the sense that, if work should be continued, a backsight would be taken on it. It is good practice to make this check for every page of the field notes before recording or computing subsequent work; this avoids the carrying over of computed errors to the next page. It must be remembered that this check enables one to detect only numerical mistakes made in computing for heights of instrument and elevations of turning points, and does not disclose mistakes in using the level, reading the rod, or recording rod readings; nor is it a check on the computed elevations of intermediate station (side shots) because no backsights are taken on such stations.
(2) Successful leveling requires a thorough knowledge of the sources of errors and of the methods of eliminating them. They are—
(a) Instrumental errors, due to imperfect adjustments of the level, sluggish bubble, irregularities in the movement of the object glass slide, errors in rod graduations, and defective rod joints on extension rods.
(6) Mistakes in manipulating equipment in setting up the level, including unnecessary clamping of the spindle, unequal backsights and foresights, not centering the bubble, resting the hand on the tripod or telescope, holding the rod improperly, or allowing dirt to accumulate on the base of the rod.
(c) Mistakes in reading the rod, as dropping a zero from the reading (like 5.170 for 5.017), etc.
((/) Errors in sighting by not having the cross hair coincide with the center of target, or using one of the stadia wires for the (center) horizontal hair.
(e) Errors due to changes in position of level or rod, as settling of instrument between backsight and foresight, disturbance of the level by passing traffic, and settling of a turning point between foresighting and backsighting.
(/) Errors due to natural sources, such as effects of sun or wind, changes in length of rod from variations in temperature, and, for very precise work, failure to consider corrections for curvature and refraction if backsight and foresight are not equal.
(g) Mistakes in recording and computing, by entering the reading with figures interchanged, recording backsights and foresights in the wrong column, neglecting to enter a reading, etc. Errors in computing are usually discovered by the check described in (1) above.
(A) Personal errors arising from causes peculiar to the individual.
(3) The only method to check the field work is by rerunning the line if it fails to tie within the required allowable error. If the line is of considerable length it is better to use two rodmen and obtain two
61
TM 5-235
54
CORPS OF ENGINEERS
L EV EL C/R OU IT Leveler Rod mar FRO. : Sgt. M3 ■Sgt C.L. M B.M. Todd Miller 35 7 B& B D Level 3! ) B.M. rmpy 757 19
5ta B.S. 7*- th ts. E lev. Slgt fl S. ts FS Rerr arhs
April L t, 1940 '3 hours^ C/oudy, moder a te.
B.M. 35 6.659 139.822 133.163 220 Cone re te mor ament
0 !6 4.968 139.819 4.97/ 134851 250 220 Peg
0 /7 4.508 136.875 7.452 J32367 3/0 250 u
0 /8 L4I2 132.430 5.857 131.018 100 3/0 u
TP / 7.073 138.242 1.261 131.169 190 too Turning Point
B.M. !9 1.785 136.457 190 Concre le morn men!
24.620 21326 133.163 1070 K)7O Actual e leva Hot 1 of 0 9 =136.4 42 ft.
24620 J3.294 1070 Pern- issible rror = O. ■>5Y2T4C 7=0.032 ft.
3.294' 'Chech. 2140 Actual rror of closure = 328C 0.0/5 ft.
y
® Notes.
Figure 15.—Differential leveling.
62
TM 5-235
54
SURVEYING
0 17
132. 367
(?) Method.
Figure 15. Differential leveling.
/ TP I 131.169
O 18 131.018
---190+ 7.073
136.875
-310-------------------------310
+ 4.508
I - 5.857 |
132.430 —ioo--y--loo-+ 1.412 \-1.26l _
-7.452
139.819
--250 ------------y-----------250
-4.971 ' + 4.968
0 16 134.851
139.822
--220--------------4------------220-
I j+ 6.659
S 35 133.163
O 05
138.242
—y----------190-----
\ -1.785
□ 19 136.457
TM 5-235
54
CORPS OF ENGINEERS
sets of readings from every set-up, each rodman using different positions for turning points. This method is more economical of time than to rerun a long line.
e. Adjustment of level lines.—(1) In the adjustment of level lines (or circuits), the notes or a transcript of the notes are first examined for errors (see d(l) above). Single lines that close within the allowable error are adjusted by distributing the closing error in proportion to the distance for intermediate points along the line. If a level net embracing several long lines, some of which perhaps cross each other, is to be adjusted, the general procedure given in (2) below should be followed.
(2) A diagram or plat showing the approximate location of all the lines, including previously adjusted lines or stations forming the base of the net or system, is made first. On each line an arrow head is placed to show the direction in which it was run. The field notes are checked and elevations for the various stations, which may be mean results of two or more runnings, listed. Before proceeding further, the rod and orthometric corrections, if large enough to affect final results, should be applied. Rod corrections are normally not to be considered if wooden rods are used and foresights and backsights are balanced. However, on long lines at high elevations a correction, called orthometric correction, is required to take account of the fact that level surfaces at different altitudes are not parallel except at the equator and at the poles. This correction, applied negatively to points going northward, is found from the formula:
p_hm — sin (,,+ ,)
659,000
in which
C=correction in feet.
Am=mean height of line in feet.
(„-|-0S) = the latitudes of the north and south ends of the line. (0„—0s)= difference of latitude in minutes of arc.
After all adjustments and corrections to the individual values for each separate line are made, level lines associated with one another are considered at one time and the remaining closing errors removed by a final adjustment based on the principle that the probable error of each point to be adjusted is to the distance between each two points as the total error is to the total length of the line.
f. Exercise III.—Run a line of levels over an established traverse starting and closing on assigned bench marks, the closing error not to exceed 0.05 -ydistance in miles. Record and compute all data as
64
TM 5-235
54-55
SURVEYING
shown in figure 15®, and make adjustments, if necessary, as explained in e (1) above.
55. Profile leveling.—a. Purpose.—The object of profile leveling is to find the elevations of points at known distances apart and thus obtain the profile on the ground surface along a given line. A profile shows all elevations and depressions along the line that would be seen in section from the side.
b. Description — Profile leveling is similar to differential leveling except that distances between stations, if not already established, must be located and measured. In profile leveling it is customary to let the number of a station indicate its distance from the starting point, the latter being marked 0+00 and succeeding stations as 1+00, 1+50, 2 + 50, 14 + 00, 123 + 50, etc., meaning that they are 100, 150, 250, 1,400, and 12,350 feet, respectively, from the first station. Since a number of foresights from the same set-up are often taken on intermediate stations, it is good practice after backsighting on the last turning point to foresight immediately on the next turning point before the level bubble has a chance to “get out,” after which the foresights on the intermediate stations between the two turning points are taken. Foresights and backsights on turning points are taken with the level rod on the top of the station, usually to the nearest 0.01 foot. Foresights on intermediate stations with the level rod on the ground next to the stake are usually taken to the nearest 0.1 foot only. This method will insure the same degree of accuracy for the line of levels as a whole without wasting time on readings for ground elevations on intermediate stations. Very often it is desirable to obtain the ground elevations at turning points, which at the same time are numbered stations along the line. In this case an additional reading on the ground, to the nearest 0.1 foot, is taken after the backsight or foresight at the top of the stake serving as turning point is completed.
c. Field notes.—Figure 16 is a form for recording field notes for profile levels along a short line, showing a check on the notes as for differential leveling. The computed elevations for intermediate stations and those for turning points are kept in separate columns as shown. Readings on turning points were taken to the nearest 0.01 foot, and for ground elevations to the nearest 0.1 foot.
d. Field method.—Examine the ground and set intermediate stakes as required for a good profile. Take rod readings to the nearest 0.01 foot on turning points and bench marks; but take ground rod readings on intermediate stations to the nearest 0.1 foot. In calculating elevations, preserve the same degree of exactness in the results as observed in the rod readings; that is, when the rod readings are taken
262341°—40--5 65
TM 5-235
55
CORPS OF ENGINEERS
to the nearest 0.1 foot, use only the nearest 0.1 foot in the height of instrument to calculate the elevations. When a station stake is used as a turning point, the notes should show the ground elevation at this stake to the nearest 0.1 foot on the line preceding the more precise turning point record. Check-levels by the same parties should not differ more than 0.1 foot into the square root of the length of circuit in miles. Backsights and foresights should be balanced, and no sight longer than 350 feet should be taken. In order to secure a
PROFILE: LEVELS
\Leve/er: Cp7. LC- Mahon Rodman. Cp!. M. f\Bear
B. & B. Bumpy No. 330//
5ta.
Q2 0+70 I +00 2+00 3+00
4+00 5+00 6+00 7+00 8+00 8 +56
9 + 00
MT VERNON HIGHWAY
FROM ®2
TO 0 7
E/ev.
7.23
964
3.65
20.58 - 226 + 78.32
138.21
747.65
74924
730.92
4/8.32 Check
7.8
6.6
0.20
8.4
7.4 '
3.6
4.4 '
2.2 '
2.6
2.06
6.8
2.26
730.4
129.7
133.1
131.6
139.2 740.2 /44.0 7432
745.4 745.0
E/ev. T.P\_______________ ...
________fpnl 2a 7940 । '2 hours ) Cleary
730.92\7"iron pipe near road.___________
________Road crossing.____________________
138.01 ^ron pin.
''Road crossing.
I45.59\lron pin.______
\Edge of road.
Rema
rks
modera.
fif,
-
Checked.
Figure 16.—Field notes for profile levels.
representative profile, ground rods should be taken not only at every station stake, but also at every important change of slope between station points, and appropriately recorded. The notes should be frequently checked and other safeguards taken to prevent blunders. Keep all records and notes as shown in figure 16.
e. Profile and grade lines.—Profiles and grade lines are plotted by the draftsman from the field notes obtained by the surveyor. Methods of plotting from these notes are explained in section X, TM 5-230. A profile (sec. X, TM 5-230) is a line plotted to a certain scale from known elevations and distances showing the configuration of the
66
TM 5-235
55-56
SURVEYING
ground surface along the measured line. A grade line is determined from the plotted profile and indicates the finished (graded) line in relation to the profile. A comparison of elevations between the profile and grade line will show how much higher (fill) or lower (cut) the ground must be graded at any point along the line to correspond with the grade line on the plot. For a detailed discussion of setting grade stakes and slope stakes, etc., see paragraph 197.
/. Exercise IV.—Run profile levels over an assigned line, placing stakes 100 feet apart, taking all necessary readings and recording and checking same. Follow methods outlined in this paragraph.
56. Cross sections and cross sectioning.—a. Cross sections for earthwork.—(1) For the construction of roads, railroads, or similar projects it is often necessary to estimate or determine the amount of earth to be moved to bring the road, etc., to the predetermined grade throughout its width. Estimates for earthwork are obtained by calculations necessitating the use of cross sections.
(2) Cross sections (see sec. X, TM 5-230) are taken perpendicular to the center lines usually at each 100-foot station. The number of cross sections to be made depends on their interval and on the length of the project. So-called cross levels are taken to determine the ground heights on either side of the main line and at right angles thereto.
(3) Cross levels to obtain the necessary data for cross sections may be run in conjunction with profile levels for the main line, or separately after the main line has been staked and run. The latter method is to be preferred, since it will avoid confusion in the work and in recording the readings. Figure 17 shows a set of cross level notes pertaining to the cross sections plotted in section X, TM 5-230. The second column in figure 17 contains the elevations of the profile transcribed from the profile level notes (sec. X, TM 5-230), the remaining columns the foresights to the points (and their elevations) along the cross levels, 15 feet apart in this case.
(4) The plotting of cross sections from field notes is explained in section X, TM 5-230. Cross sections (and profiles) are sometimes plotted from contoured maps. This too is explained in section X, TM 5-230.
(5) Volume computations for estimating earthwork are made from the cross sections as described in section X, TM 5-230.
b. Cross section levels.—In connection with drainage and irrigation work, the grading of earthwork, location and construction of buildings, etc., it is often desirable to obtain the shape of the surface of a piece of land. This may be done by dividing the area into a system of squares, and then determining the elevations of the corners and other points
67
TM 5-235
56
CORPS OF ENGINEERS
where changes of slope occur. The length of the sides of the squares are from 100 feet to 50 or 25 feet. The squares are laid out with the tape or transit, distances measured by the tape or stadia, and elevations determined with the engineer’s level. Stakes are set at the corners of the square and marked A-l, A-2, B-l, etc. The data obtained by this method are frequently used in the construction of a contoured map, or to plot cross sections of any portion of the area. Figure 18 shows a page of field notes for cross section levels. The notes
M/Z G TERTOIA 'AH elev. ROSS N HIGH it ions a LEVS WAY 0 i t top of IS ■50 To ground \Leveier: 4+50 \Rodman 1 Cpi. M. F. Pvt.A.i. Sear Muir B.& B L No. 330 lumpy H
Sta Center Elev Left 30' Left 15' Right 15' Right T JO' ' Remc rks
□ W/7 156.73 B5.+4.I HI. 160.8 1
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Surface Elev Grade Elev. Crc Base 44. ss-Sectk Slope /£ to / 1
O ±50 151.5 150.7 29.0 -0.8 22.4 1
-6.0 .1
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-4.8 -3.3
/ ±-50 150.6 149.4 26.0 -1.2 25.5 J
-4.2 -3.7 1
2 ±OO 150.1 146.7 25.1 -1.4 1 22-5 ।
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2 ±50 149.4 148.0 25.1 -f-4- 22.4 i
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3 ±00 149.2 147.3 24.8 -19 22.0 _j
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3+50 149.0 /46.6 24.5 -2.4 21.8 1
-2.9 -1.3 |
4 +OO 148.6 145.9 23.9 -2.9 21.7 !
-1.4 -1.2
4+50 147.2 145.2 23.0 -2.0 1 21.5 I
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69
TM 5-235
57
CORPS OF ENGINEERS
70
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83
TM 5-235
65 CORPS OF ENGINEERS
Figure 26.—Other transit graduations.
84
® Vertical arc.
@ Beaman stadia arc.
® Compass box and variation plate.
TM 5-235
65
SURVEYING
(5) Vertical arcs on engineer transit are graduated usually in degrees and half degrees, with verniers reading to minutes or to 30 seconds. Figure 26® shows a vertical arc with vernier reading plus 9°30'.
(6) Some instruments are now equipped with an additional graduation known as the “Beaman Stadia arc” or simply “stadia arc.” This (par. 138/) is a graduation based on percentage of slope. Compare in figure 26® the vertical arc reading of + 10°34' with the Beaman arc reading at the index of +18. A scale at the left, opposite the H index, gives —3 as the percentage factor to be subtracted from the measured distance to obtain the horizontal distance.
(7) A type of graduation similar to that of the vertical arc will be found on the compass box ring. This enables the observer to read magnetic bearings, usually within 30 minutes of arc and sometimes within 15 minutes. On most transits the box containing the graduated ring can be rotated to set off the magnetic declination for a reading of the true bearing. This is useful when running a needle traverse.
c. Accessory equipment.—As a rule each transit is equipped with a reading glass for verniers. It is best to carry this on a string around the neck. In addition each transit is normally equipped with a plumb bob, sunshade, screw driver, adjusting pins, waterproof cover, and sometimes with a prismatic eyepiece with dark glass slide. The plumb bob is used for centering the transit accurately over the station mark: the sunshade to replace the cap on the objective during work; the screw driver and adjustment pins to adjust the transit; and the prismatic eyepiece which is attached to the regular eyepiece, for observing objects of high altitude, the dark glass being employed whenever the sun is observed.
d. Handling transit in field.—(1) When setting up the transit, place two of the tripod legs in approximately the correct position with reference to the station mark; then manipulate the third leg so that the plumb bob is brought over the point, at the same time keeping the tripod head approximately level. On hillsides, one tripod leg should be uphill, the other two downhill. Keep the tripod bolt nuts sufficiently tight so that they will just sustain the weight of the legs when the instrument is lifted. Press the tripod shoes firmly into the ground to aid rigidity. If the plumb bob is nearly over the point, final centering may be made by moving the shifting plate after loosening the leveling screws.
(2) When leveling the instrument, turn the plates so that each plate level is parallel to a pair of diagonally opposite leveling screws. Great care should be exercised when leveling up; the screws must be snug to avoid tipping of the plates and possibly causing a horizontal shift of
85
TM 5-235
65-67
CORPS OF ENGINEERS
the plumb bob. The screws must not be too tight, on the other hand, as this injures the instrument and causes errors due to strains in the metal. To level, grasp a pair of opposing screws between the thumb and forefingers and turn so that the thumbs move toward or away from each other, thus tightening one screw and loosening the other. After one bubble has been brought nearly to the center of its tube the other bubble is centered in a similar way. Instead of getting one bubble centered exactly, it is better to get both bubbles approximately level, after which one bubble and then the other may be exactly centered. After the instrument has been leveled, check the plumb bob to see that it has not been moved from the point during the leveling process.
66. Repeating theodolite (vernier type).—a. Comparison with transit.—The repeating theodolite (fig. 27) is similar in general design to the ordinary engineer’s transit but of larger size and superior workmanship. The circle is usually 7 or 8 inches in diameter, and the verniers read commonly to 10 seconds. Figure 27 shows a 10-second repeating theodolite with striding level and individual magnifying (reading) glasses for each vernier. Usually no compass needle is found on these instruments.
b. Handling theodolite in field.—The theodolite should be carried in the box provided for each instrument. In order to obtain the best results the following rules should be carefully observed:
(1) Adjust and level the instrument carefully before proceeding with measurements.
(2) Keep away from tripod when making measurements.
(3) Turn plates gently, taking hold of plates or limbs and not the telescope.
(4) Work steadily and carefully; do not speed.
(5) Do not screw tripod legs too tightly.
(6) Do not turn clamps or leveling screws too tightly.
(7) When setting instrument up over stations, place two of the legs in their approximate positions. Then manipulate the third leg until the plumb bob is approximately centered over the station. Complete centering by loosening leveling screws and moving instrument on tripod head; finally level instrument carefully.
c. Accessory equipment.—The accessory equipment of the repeating theodolite consists of the same items as those listed in paragraph 65c except a reading glass.
67. Direction theodolite.—a. Comparison with repeating (vernier type) theodolite.—The direction instrument (fig. 28) is distinguished by having only one vertical axis so that angles cannot be measured by repetitions; also, it has two or more micrometer microscopes for read-
86
TM 5-235
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SURVEYING
Figure 27.—Repeating theodolite.
87
TM 5-235
67
CORPS OF ENGINEERS
Figure 28.—Direction theodolite.
mi
88
TM 5-235 67
SURVEYING
Figure 29. Micrometer microscope.
eter lies ordinarily between two circle graduations. To determine the fractional part of the space between two graduations, the wire or wires are moved with the thumbscrew until they coincide with a scale division and the micrometer head is read. The direction to the object is found by combining the micrometer reading and the scale reading. Sometimes the micrometer is read on each of the two graduations between which the index lies. The micrometer may usually be read to the nearest second, and by estimation to the nearest one-tenth second.
On the left of figure 29 is shown the apparent arrangement in the field of view of the comb, wires, and circle graduations; on the right, the center notch and the micrometer head which furnish direct readings to seconds and by estimation to tenths of seconds. The reading as shown by the movable wires and comb is 74°58', which, added to the drum reading of 29.5", gives a reading of 74°58'29.5".
ing the angles. Vertical angles are read as on a transit except that the arc and vernier are graduated on the better class of instruments to read to 10 seconds.
b. Description of micrometers and microscopes.—Precision in measuring parts of the graduated circle is secured by means of the micrometer microscope, two or more of which are equally spaced around the circle. The device consists of a microscope focused on the graduated circle, having in the focal plane a wire, or two closely spaced parallel wires, mounted on a movable slide. In the field of each microscope two or more graduations of the circle can be seen (fig. 29). The slide is moved by a milled thumbscrew carrying a graduated drum called the micrometer head. When the telescope is pointed at an object and the horizontal motion is clamped, the index or fiducial line of the microm-
-40
-30
-20
89
e d
’ 5
TM 5-235
67-68
CORPS OF ENGINEERS
— Vertical circle
Illuminating mirror for the diaphragm
— Knob for coincidence setting
Illuminating mirror for the vertical circle
Clamping screw for vertical circle
— Ring for focussing telescope
— Inverter knob
Eyepiece for reading
— microscope
— Eyepiece of telescope
— Horizontal level
Tangent screw for altitude
Tangent screw for azimuth
Reflector for collimation level
Circular level
Illuminating mirror for horizontal circle
Eyepiece for optical centering
One of the 3 levelling screws
Tightening screw
Figure 30.—Universal theodolite, Wild T2.
c. Accessory equipment.—The accessory equipment for the direction theodolite consists, with the exception of a reading glass, of the same items as those listed in paragraph 65c.
68. Wild type theodolite.—-a. Description.—The Wild type theodolite is a direction instrument. Because of its ingenious design and ease of handling it may be considered one of the best instruments for general use. It is manufactured in several sizes. The “Wild T2” being perhaps the most satisfactory for military work is here described, together with preliminary instructions for handling it.
(1) Setting up instrument.—Set up the tripod over the station point. The central fixing screw, which holds the instrument down to the
90
SURVEYING
TM 5-235
68
91
tripod, remains always on the tripod, and thus cannot be lost or mislaid. A hole is bored lengthwise through this screw, and serves to receive the plumb line which is carried in a leather pouch on the lower part of the tripod. The tag at the upper end of the plumb line fits accurately into the bore of the central fixing screw; insert it into place from below, giving it a slight turn to secure it (bayonet joint). After setting up the tripod firmly and plumbing it over the mark to within about half an inch, take the plumb line off again. Then loosen the two locking levers of the theodolite casing by firmly pulling outward both ends of the leather strap and lift the sheet steel hood carefully from the base plate. Loosen the three black screws which secure the theodolite to the base plate and withdraw the three slides thus set free; the theodolite is now ready to be lifted from the base plate. Move the telescope from its steeply inclined position to a horizontal one, then take up the instrument by grasping the right hand support (the upper part of which carries the seconds drum), place it on the tripod, and screw up the central fixing screw moderately tight. When handling the instrument, never grasp it by the left hand support (which carries the collimation level and its adjusting arrangement), as this might disturb the adjustment. The theodolite should be so placed on the tripod that the illuminating mirror of the horizontal circle can receive sufficient light.
(2) Removal of star-shaped base plate.—If automatically controlled centering is desired in the case of polygon and similar measurements, a small screw is loosened at the bottom of the base plate. Only after loosening this screw can the spring plate, which holds the foot screws, be turned far enough as to permit removal of the theodolite. Owing to the spring system the plate cannot turn by. itself even if the safety screw is open.
(3) Centering and leveling instrument.—For shifting the instrument on the tripod head in centering over the mark, a play of 2 inches is available. The centering of the instrument is normally done by means of the optical plummet. First bring the bubble of the circular level to center by working the three foot screws. On looking through the eyepiece of the optical plummet, on the lower part of the theodolite (see fig. 30), and focusing, the circular adjusting mark and the ground point will be seen. Move the theodolite about on the tripod head until the ground point appears in the middle of the adjusting mark. Now level the instrument exactly, making use of the horizontal level which is situated between the two supports, and rectify any remaining divergence of the optical plummet by further movement of the instrument on the tripod head. The central fixing
TM 5-235
68 CORPS OF ENGINEERS
screw should be slightly slackened before every shift of the instrument on the tripod head, and then tightened up again as soon as the centering has been accomplished. In calm weather, the theodolite might be centered over the ground mark by the use of the plumb line alone. The centering can be done before leveling the instrument, because the point of suspension of the plumb line lies in the same plane as the points of the foot screws. For refined measurements, the instrument and the entire tripod should be protected from the direct rays of the sun by the use of a sunshade. Before beginning measurements, the theodolite should be rotated a few times about its vertical axis, and the telescope moved up and down about the horizontal axis. After being centered and carefully leveled, the instrument is ready for taking measurements.
(4) Focusing.—Direct the telescope toward the sky and turn the milled black dioptric collar on the eyepiece until the cross lines appear sharp and black. Note the setting of the dioptric collar on the numbered scale because this will be nearly constant for the same observer. Focusing for a sharp image of the object to be sighted is accomplished by turning the nickeled focusing collar (testing for absence of parallax between image and cross lines by movement of the eye). To focus the reading microscope, turn the small milled black collar of the eyepiece, which is alongside the eyepiece of the telescope, until the graduation marks of the circles appear perfectly sharp.
b. Measurement of angles.—On the front and back of the right-hand support will be found the change-over knobs on the same axis for the two circles. To make the horizontal circle visible, the black lines on the change-over knobs are to be set horizontally. For reading the vertical circle the lines should be set nearly vertical.
(1) Reading of circles with 360° graduation, horizontal circle.—(a) First set the black line of the change-over knob horizontally, so that the two images of the horizontal circle are visible in the reading microscope.
(6) To obtain the brightest and most uniform illumination possible of the two images of the circle divisions, turn the illuminating mirror on the tribrach below into the most favorable position. When measuring angles the illumination should not be changed.
(c) Then focus the reading microscope by turning its milled black collar until the graduation marks of the circle appear sharply defined in the images.
(d) Two separate images are now seen in the reading microscope.
1. Above.—The double image, divided by a fine horizontal line, of the diametrically opposite parts of the horizontal
92
TM 5-235
SURVEYING 68
circle, for reading off the degrees and tens of minutes (fig. 31).
2. Below.—The small image of the scale of the seconds drum, for reading off the individual minutes and the seconds.
The reading itself is accomplished in the following manner: After making the pointing by bringing the telescope exactly onto the object, look at the image in the reading microscope before making the coincidence. In the middle of the field of view, on the lower half of the image of the circle, there will be seen a fixed vertical line which does not serve for taking the reading, but only to mark the middle of the field of view, and to form a pointer. The coincidence adjustment of the graduation lines of the two images of the circle should be made in this vicinity by turning the knob of the coincidence adjustment until in the middle of the field of view the graduation lines of the upper half-image appear to be in exact prolongation of those of the lower half-image. The final turning movement of the coincidence adjustment should always be in a clockwise direction. In figure 31 the image of the scale is depicted as it appears after the coincidence adjustment has been made, since the reading of the circle is only taken when the graduation lines exactly coincide: In figure 31® the nearest upright figure to the left of the center line gives the degree division 285°. Now, starting from 285, count the graduations to the division 105 (which lies diametrically opposite to the division 285 on the horizontal circle). In the example, there are 5 intervals, that is, 5 tens of minutes, or 50'; thus from the upper image the reading is 285°50'. In the lower image of the scale of the seconds drum 1 minute is read off on the lower series of numbers and 54.6 seconds on the upper series of numbers and graduations; thus reading 1'54.6" on the drum. The complete reading is therefore 285°51'54.6".
(2) Vertical circle 360°.—Graduation and numbering of the vertical circle are the same as for the horizontal circle. With telescope direct, the zenith distances can be read directly. Observing in both telescope positions and according to the readings Ax and A2 the zenith distances are given by the formula
z==i8o°-4^—=^(A+360°-A2)
The vertical angles are obtained by the formula
= (90o-A+A2-270°)
The following procedure is indicated:
93
TM 5-235
68
CORPS OF ENGINEERS
Circle ....
Drum ....
Complete reading
Figure 31.—Reading horizontal and vertical circles on Wild T2 theodolite.
6° 30'
0' 03",3
6° 30' 03",3
105 106 10
285 286 28
94
I 1 1 I 1 1 I 1
73 274 275
CO
* CO IO
■ OO
Telescope direct Telescope reversed
Circle'.............0° 0'
Drum.................. 9' 48",8
Complete reading . 0° 9' 48",8
« I" 0
9_________»_________10
359 0 1
I I I
179 180 181
186 187
6 7
io 1 o'7777')
H 1 1 * j
3 94l 95
265 I 266
r\' 40 5' 7'
I 3° 2 2
1._____________
f\" ' 20 ' 3>D‘"U
Ho 7 7
I 7
94° 12' 43", 7 265° 47' 23", 6
Reading with telescope direct — 4° 12' 43",7
Reading with telescope reversed — 4° 12' 36",4
Mean = correct vertical angle — 4° 12' 40",0
/Ti
TM 5-235
68
SURVEYING
(a) The black line of the change-over knob is set vertically, so that the image of the vertical circle becomes visible in the reading microscope.
(6) Turn the illumination mirror at the end of the tilting axis toward a clear part of the sky, so that the image of the vertical circle appears bright.
(c) Focus the circle image sharply by turning the milled black collar on the reading microscope.
(d) Bring the bubble of the collimation level to center by turning the fine adjustment screw of the level until the two ends of the bubble coincide as seen in the level prism. Then check the pointing of the telescope on the object and take the reading in the same manner as for the horizontal circle.
c. Setting horizontal circle.—If angular measurement is to start from 0° (or any other desired graduation point of the circle), the telescope is first directed to the initial object, and then the milled head which serves to rotate the circle (and which is situated on the tribrach and covered by a protecting cap) is turned until the desired initial circle reading appears in the reading microscope. If, for example, the first pointing is to read 0°0'0", the seconds drum must first be set to zero, then the pointing must be made, and then the circle rotated by the lower milled head until the 0° graduation line coincides exactly with the 180° graduation line in the double image seen in the reading microscope, after which the protecting cap is closed. For other precise angular measurements where it is required to begin with a certain number of degrees, the pointing is first made, then the circle turned by the lower milled head to the desired graduation mark with approximate coincidence; the protecting cap is closed, and exact coincidence of the required graduation lines (0° and 180°, 45° and 225°, 90° and 270°, 180° and 0°, etc.) made by the seconds drum, after which the seconds reading is taken, as for example 0°2'36".
d. Returning instrument to case.—Withdraw the three slides of the ground plate of the metal hood. Open the clamps of the theodolite and hold the instrument by grasping the right-hand support. Turn the cone with the free hand to set the instrument into the ground plate, taking proper care that the three lugs are placed correctly on the three rests. Now, push in the slides and firmly drive home the three black screws. Move the telescope to a vertical position and tighten moderately the vertical and horizontal clamps. Then put the metal hood on and lock it.
e. Supplementary equipment.—(1) Electric illumination.—Take out the two illuminating mirrors and replace by the corresponding lamp
95
TM 5-235
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CORPS OF ENGINEERS
holders. Hang the battery case on the tripod, put the switch in the holder provided for it on one of the tripod legs, and place the plug in its socket on the instrument. For changing the bulbs, the lamp holders can be withdrawn from the illumination supports. The brightness of the illumination can be varied by turning the collar on the switch to change the resistance. The illumination of the tele-
Figure 32.- Universal theodolite, Wild T2, with electric illumination and hand lamp.
scope diaphragm can be regulated by turning the milled head on the center of the telescope.
(2) Diagonal eyepieces.—Remove the eyepieces from the telescope and reading microscope, replacing same by pushing in the diagonal eyepieces. They make it possible to observe angles of elevation up to the zenith.
(3) Striding level.—The striding level is placed on the bright rings of the horizontal axis which are ground exactly concentrical. The striding level is used almost exclusively for astronomical observations.
96
TM 5-235
68-69
SURVEYING
For the usual terrestrial measurements the alidade level is more convenient and of sufficient accuracy.
(4) Horrebow level.—The Horrebow level is used for astronomical observations, especially for refining the methods of corresponding zenith distances. This level is screwed on the vertical clamp.
/. Accessory equipment.—In the ground plate of the metal hood the following accessories are located: adjustment pins, screw driver, brush, oil bottle, and illumination plugs. The parts belonging to the tripod, such as plummet and hexagonal spanner, are kept in the tripod pocket. The central fixing screw is mounted firmly on the crossing of the tripod head.
Section XI
ADJUSTMENTS OF TRANSIT AND THEODOLITES—THE STADIA
Paragraph . 69
_ 70
_ 71
_ 72
. 73
. 74
in
General_____________________.•__
Stadia__________________________
Adjustment of transit___________
Adjustment of repeating theodolite..
Adjustment of direction theodolite. Adjustment of Wild type theodolite..
69. General.—a. A damaged instrument should not be repaired the field unless required in an emergency. If any parts have been injured, the instrument should be turned in, through proper channels, for repair by expert instrument repairmen. Such repairs can be made with less trouble and less cost if no attempt has been made to turn the various parts to determine the extent of the damage.
b. The adjustment of surveying instruments requires extreme care and good judgment. No man should be allowed to attempt the adjustment of an instrument until he has had several weeks’ experience in its use and has become thoroughly familiar with its construction and operation.
c. Before commencing the adjustment of an instrument be sure that it is firmly set up and carefully leveled. An instrument may appear to be out of adjustment when some minor part is loose, therefore it should be looked over carefully before commencing the adjustments. After completing the various adjustments, always make all the tests again before using the instrument. AU the adjusting screws should be screwed tight enough to hold, yet not so tight as to injure the threads or put an undue strain on any other part.
d. Adjustments should be made in the order given, as some depend on the accuracy of others previously made, and a change in one may
262341°—40——7
97
TM 5-235
69-70
CORPS OF ENGINEERS
affect the others. If an instrument is badly out of adjustment it is better not to adjust one part completely at once, but to bring the instrument as a whole gradually into adjustment. Nearly all adjustments of instruments depend on the principle of reversion. It should
be understood that by reversing the position of the instrument the effect of an error is doubled.
70. Stadia .—a. Description.—The stadia is a device for measuring distances by reading an intercept on a graduated rod. For this purpose two additional horizontal hairs called stadia hairs are carried in the transit telescope on the same reticle as the cross hairs and are placed equidistant from the horizontal hair. By reading the amount of intercept on a rod between the upper and lower wires, multiplying this by a constant, usually 100, and then adding a second constant, expressed (c+/), the distance from the center of the instrument to the point on which the rod is held is fairly accurately determined.
98
® ® ®
Figure 33.—Stadia rods.
TM 5-235
70
SURVEYING
@ Horizontal.
It is a folding rod hinged at the 6-foot mark and when opened for use is 12 feet long. Figure 33® is similar to a standard level rod without target, usually about 3 inches wide and may be of the folding type as the one described above or a single board. Figure 33® is a flexible pocket rod which can be carried rolled up in the pocket. It is about 3% inches wide and can be tacked through eyeleted holes to any piece of light board.
c. Theory oj the stadia.— (1) Horizontal sights (fig. 34®).—The stadia wires, spaced a distance i, are shown at a and b; AB is the space on the rod intercepted by the stadia wires, and 00' is the objective
The theory involves the relation between the sides and altitudes of similar triangles.
b. Stadia rods.—Figure 33 shows parts of three types of stadia rod graduations, ® being the most commonly used type in the Army.
(R), before making use of slide rule, diagram, or table.
TM 5-236 contains stadia tables for the reduction of readings.
d. Stadia constant (K).— It is extremely difficult to place the stadia hairs so they will exactly intercept the proportional part on the stadia rod which when multiplied by 100 should give the true distance between the instrument and the rod; therefore, it will be found by testing that many instruments will read long or short. For this reason a stadia constant, called K is determined, which when multiplied by the reading of the stadia hairs will give the true distance.
e. Exercise VI. Determination of stadia constant (K), and (c-\-f).— (1) Equipment.—Complete transit, stadia rod, steel tape, chaining pins, foot rule, notebook, pencil.
(2) Method.— (a) Set up transit and set ten chaining pins in line about 100 feet apart on level ground.
(6) Plumb stadia rod by side of first pin.
(c) Set lower hair on an even footmark keeping telescope nearly level, and read intercept.
(d) Record same (line 1, column 2, fig. 35).
(e) Read intercept on rod at remaining pins and record same (column 2).
(f) Measure distance from center of transit to each pin with steel tape and record same (column 3).
(<7) Focus objective on a distant object, measure f (the distance from the plane of the cross hairs to the center of the objective) and c (the distance from the center of the objective to the center of the instrument). Record same (column 6).
(A) Calculate the value of stadia constant K. Enter in column 4 the recorded values of column 3 minus c-\-f (1.4 in this case). Obtain K, column 5, by dividing each value in column 4 by the corresponding
TM 5-235
70-71
CORPS OF ENGINEERS
stadia distance, column 2. Add values in column 5 and obtain mean by dividing the sum by the number of values in that column. The result will be the stadia constant of the instrument used. In recording, etc., follow the form in figure 35.
f. The stadia constant should be frequently checked during the progress of a survey and must always be determined after cross hairs have been replaced in an instrument.
g. Use of stadia.—The transit is set up over a station of known elevation and oriented as outlined in paragraph 80e. Measure the
DETE RMINATI )N OF S FADIA \lnstrumer Viead Chair \Rear Chair .—Possible relations between grid north, true north, and magnetic north.
magnetic GRID DECLINATION OR GISEMENT
purposes, azimuths are angles reckoned clockwise from 0° at magnetic, true, or grid north through 360°. Thus, there are three different azimuths for a given line—magnetic azimuth, true azimuth, and grid azimuth. Consequently, the necessity for specifying the kind of azimuth expressed is obvious.
(1) The magnetic azimuth of a given line is the angle measured clockwise from magnetic north to the line.
114
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• Y
Y T M
®
°6
°7
Y M
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°4
°3
°2
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M Y T
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T M Y
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Y T MT T M M T TM
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TM 5-235
76
SURVEYING
•GRID AZIMUTH
TRUE AZIMUTH
■MAGNETIC AZIMUTH
(2) The true azimuth of a given line is the angle measured clockwise from true north to the given line.
(3) The grid azimuth of a given line is the angle measured clockwise from grid north to the given line.
(4) Grid, true, and magnetic azimuths.—The relation between grid, true, and magnetic azimuths is shown in figure 37. From the informa-
/0
X” APPROXIMATE MEAN DECLINATION 1935
ANNUAL MAGNETIC CHANGE INCREASE 3'
tion contained in the margin of the map (fig. 38 ®), in the case illustrated in the year 1935, the mean magnetic declination at Washington, D. C., was 6°40' west with an annual change of O'. The average grid declination was 2°25' east and does not change. The grid azimuth is in consequence less than the true azimuth by 2°25' and in 1935 was less than the magnetic azimuth by 9°05' (i. e., 6°40' plus
\ _______-----------------GRID BACK AZIMUTH
"" __________K X------------TRUE BACK AZIMUTH
'----MAGNETIC BACK AZIMUTH
Figure 37.—Example of relationship between three base directions on a map, showing corresponding azimuths and back azimuths of line OA.
1 t;/
1 —12° 25
6“40'V-----
x\ J a
o ? zl z a
$21 5
ujl or '—.
Z H_______
--------_____
A
A1
115
TM 5-235
76 CORPS OF ENGINEERS
2°25'). The true azimuth was, in 1935, 6°40' less than the magnetic azimuth and 2°25' greater than the grid azimuth. In order to determine the interrelationship of the azimuths for the year 1937, account must be taken of the annual change, if any, of magnetic declination. For instance, the increase in 2 years, if the annual change is +3', would be 6' (i. e., 2 times 3'). Any confusion or uncertainty in the mind of the student when converting from one type of azimuth to another on a particular map may be quickly cleared up by drawing a rough diagram similar to that shown in figure 37.
(5) Back azimuth.—The back azimuth of a line is the azimuth of the line extended in the opposite direction. It is the azimuth plus or minus 180°. Thus in figure 37 it may be noted that the azimuth of the line from 0 to A (or OA) differs from the azimuth of the line from 0 to A' (or OA') by 180° and the azimuth of the line OA' is equal to the back azimuth of the line OA.
b. Bearings.—Bearings are used to express directions as determined by means of the service watch compass or any compass without an azimuth circle. The bearing of a given line is the angle and direction which the line makes with respect to the north or south base direction line. Bearings are stated by quadrants and never exceed 90°. Figure 38@ shows how bearings are measured and expressed and indicates the relationship between bearings and azimuths. Figure 38@ illustrates the expression of a typical direction in each quadrant both as an azimuth and as a bearing. The reverse bearing of a line is the bearing of the line extended in an opposite direction and differs from the bearing by 180° of arc. Bearings are not as convenient for military purposes as azimuths. Even though some instruments and sources of information may give directions as bearings, the angles so expressed are usually converted to azimuths which are less subject to error in recording, transmission, and plotting. Confusion in converting azimuths to bearings or bearings to azimuths may be quickly cleared up by resort to a simple diagram of the four quadrants roughly constructed with two lines crossing at right angles.
c. Exercise IX.—(1) Find the bearings of the following azimuths:
1. 132° 7. 91°57' 13. 17°01'01"
2. 217°40' 8. 219°51' 14. 349°59'59"
3. 101°35' 9. 269°59'30" 15. 73°14'15".5
4. 343°01' 10. 179°59'30" 16. 143°17'59".3
5. 67°14' 11. 271°00'15"
6. 271°57' 12. 300°00'15"
116
@ Lines of equal magnetic declination and of equal annual change in the United States for 1935.
Figure 38.—Magnetic declination and azimuths and bearings.
262341°—40 (Face p. 117)
TM 5-235 76
SURVEYING
W-90‘
Arrows indicate the direction of measurment of the bearings in each quadrant from O* to 90'
Azimuths are measured in a clockwise direction from 0° (north point) to 36(T
@ Relations between bearings and azimuths.
■BEARING N45*B
BEARING N40°W-
AZIMUTH 48'
AZIMUTH 320'
AZIMUTH 108°
BEARING S75’E
AZIMUTH 210'
BEARING S 30°W
@ Typical directions expressed as azimuths and bearings.
AZIMUTH = BEARING
BEAR I NG’AZIMUTH
S-----°-----W
AZIMUTH = I8O°+BEARING
BEARING=AZIMUTH-I8O’
S----------E
AZIMUTH’I8O°-BEARING BEARING = 180-AZIMUTH
Figure 38.—Magnetic declination and azimuths and bearings—Continued
N----------W
AZIMUTH =360°- BEARING
BEARING=360°—AZIMUTH
E
I
j-90°— E
n
in
wl
0°
S
117
N
wi
w
TM 5-235
76-77
CORPS OF ENGINEERS
(2) Find the azimuths of the following bearings:
17. S. 43° E.
18. N. 17°50' W.
19. N. 43°54' E.
20. S. 55°17' W.
21. S. 43°43' E.
22. N. 43°43' W.
23. S. 17°15' E.
24. N. 89°59'59" E.
25. S. 29°30'30" W.
26. S. 29°30'30" E.
27. N. 49°59'15" W.
28. N. 49°59'51" E.
29. S. 73°17'14" W-
30. N. 62°13'20" E.
31. N. 52°52'52" W.
32. S. 29°31'59".7W
77 . Measuring angles.—a. To measure a horizontal angle.—With the instrument set up over the station at which the angle is to be read, set the zero of the vernier opposite the zero of the horizontal circle, using the upper clamp and tangent screw to bring them to coincidence. Turn to the first object by touching the lower plate only and point at it approximately by looking over the top of the telescope. Move the telescope until the vertical cross hair is very nearly on the point, clamp the lower plate by means of the lower clamp thumbscrew, and set exactly on the point by the lower motion tangent screw. The line of sight is now on the first object. To measure the angle, loosen the upper clamp, turn the telescope to the second point, set nearly on the point, clamp the upper plate, and set the vertical cross hair exactly on the point by the upper tangent screw. The angle is then read on the vernier which originally was set at zero. As a check on this reading, read the other vernier and subtract 180°; the results should be the same.
b. Angles by repetition.-—The mean of a number of measurements of an angle gives a value for the angle more nearly accurate than any single measurement. Where considerable accuracy is required, therefore, it is customary to repeat the measurements, using methods described in paragraph 79.
c. To measure a vertical angle.—(1) The angle between two intersecting lines in a vertical plane is a vertical angle. In surveying, one of these lines is assumed to be horizontal, and the vertical angle to a point is the angle in a vertical plane between the line to that point and the horizontal plane. An angle above the horizontal is positive, or one of elevation; if below it is negative, or an angle of depression.
(2) Set up and level the transit, and sight upon the distant point; turn telescope approximately horizontal, clamp and with the slow-motion screw center the telescope bubble accurately. If the vertical arc vernier reads zero, there is no index error; if not, read and note the angle for the index correction, which must be applied with proper sign to the observed vertical angle. Next sight on the distant point and read the vertical angle. To determine the angle of elevation (or depression) between two points, it is necessary to take into account the height of instrument and the height of target at the distant point.
118
TM 5-235
SURVEYING 77
d. To run or prolong a straight line.—(l) To run a straight line between two points which are intervisible, set up over one point as A and sight on the other point B. This establishes the line and any number of intermediate points may be set in this line of sight.
(2) If the two points between which a straight line is desired are not intervisible, set up as nearly as possible on the line between them and at such a point that both are visible from the instrument. Sight on one point, plunge the telescope, note how much this trial line varies from the second point, and estimate the next position for the transit. A point in the line is finally found by successive approximations. This is a slow process and one must have considerable practice in order to become adept in it.
(3) To prolong a line from two points, the method of (1) above can be used if the prolongation of the line is visible from A. If the prolongation of the line is not visible, from A, set up over B, sight at A, and plunge the telescope. The vertical wire will now produce the straight line if the instrument is in adjustment, and additional points may be set in on the continuation of the line.
e. To run a traverse.—(1) The following method for running an azimuth traverse, is recommended: Assume that the aximuth AE (fig. 39) is known to be 112°. Set up at A. Set the A vernier, which becomes the controlling vernier for station A, to read 112°. The B vernier then reads the back azimuth AE, or the forward azimuth EA, 292°. Sight on E, using the lower motion, and clamp. Now unclamp the upper motion and sight on B. Read the A vernier, which gives the azimuth of course AB, 40°. Next, leaving the upper motion clamped, unclamp the lower motion and advance to B. Set up at B and sight on A, using the lower motion. Since, at A, the B vernier recorded the back azimuth of the line AB and has not been reset, it must now record the azimuth of the line BA, and therefore becomes the controlling vernier for station B. Sight on C, using the upper motion, and read the azimuth of course BC, 82°, from the B vernier. Continue in this manner with the lower motion free and the upper motion clamped when changing station. Make all backsights with the lower motion and all foresights with the upper motion. Remember that the A and B verniers are alternately the controlling verniers. It is advisable, particularly for inexperienced transitmen, to read and record compass bearings as a check. Both vernier readings for each course should be recorded as a check. Distances are measured by tape or stadia (par. 80).
(2) In connection with reconnaissance work, or when a moderate degree of accuracy is acceptable, only alternate traverse stations need be occupied by the transit in running a compass or needle traverse. At
119
TM 5-235
77-78
CORPS OF ENGINEERS
each station occupied, the transit is oriented by the compass needle. Referring to figure 39, set up at A and set verniers to zero and 180°, leaving lower motion free. Orient limb of transit by compass needle so that transit points to magnetic north and clamp lower motion. Sight on E and B successively, reading the respective back and forward azimuths or bearings. The next set-up is made at C, following the same procedure. Distances are usually determined by stadia
making back and forward measurements from each transit station. See paragraph 81.
78. Prevention of errors.—a. General.—To come within a given limit of error in transit surveying both linear and angular errors must be within required limits. The most important points may be summarized as follows:
(1) The true error of any measurement is never known but can be estimated from duplicate measurements.
(2) Accidental or compensating errors, as a rule, are less important than constant or cumulative errors.
In transit surveying two classes of errors, both of which can be avoided or minimized, are the usual cause for unsatisfactory work, namely—
120
True azimuths, O°ot north.
Figure 39.—Running a traverse.
TM 5-235
78-79
SURVEYING
personal errors and instrumental errors. The first named, caused by haste or carelessness, may be called mistakes and should be guarded against at every step of the work. The second named can be avoided with ait otherwise undamaged instrument by a proper program of observation (see par. 79e (12)).
b. Instrumental errors.—The instrumental errors which most adversely a fl eet the accuracy of final results are that the plates are out of level and that the line of collimation is out of adjustment. The plates and line of collimation should be frequently and carefully checked.
c. Avoidable errors.—All errors, with the exception of those caused by faulty construction or condition of an instrument, are avoidable and can be eliminated if the work is performed as described in the paragraphs following.
79. Traverse with transit and tape.—a. Organization of party.— Assuming that distances are to be measured (with an accuracy of at least 1 :5,000) using a calibrated steel tape and that angles are to be obtained by repetition, the party should include:
I chief of party.
1 instrument man.
1 recorder.
2 chainmen.
2 rod men (with range poles).
1 or more helpers to clear lines, etc.
b. Equipment.—Thirty-minute transit, reading glass, notebook, pencil, 2 range poles, steel tape, 2 chaining plumb bobs, 11 steel arrows, stakes, 8d nails, copper tacks, crayon, brush hook, hatchet, and signal cloth.
c. Form of notes.—Figure 40 shows a standard page of notes on which is recorded part of a traverse showing the mean distance of two measurements between stations and the mean angle as calculated from three readings, for instance: The mean distance from 3 to 16 (216.32) is the mean of the two measurements or % (648.94 + 649.00) reduced to yards, and the mean angle (186° 01' 50") is the mean of th e angle at 03 between A Top and 016, the latter being the first station of the new traverse. Assuming that the azimuth from 03 to A Top is given, the first angle at 03 is read (186° 02' 00") and recorded as shown in the notes opposite 03 of the diagram. The measurement of the angle then is repeated until three readings are obtained on the horizontal circle, in this case the final reading being 198° 05' 30". Since the first angle reading was over 180° (but less than 240°), 360° must be added to the final reading, which gives a total of 558° 05' 30". This divided by three gives a mean angle of
121
TM 5-235
79
CORPS OF ENGINEERS
186° 01' 50", as shown in figure 40. The notes must show a diagram including witness marks for all new stations and their distances from the traverse station. The recording is usually done from the bottom of the page toward the top. For the method of reading angles by repetition, see e below.
d. Control (starting and closing) data.—AW traverses of the types described in this and paragraphs 80 and 81 must start at some fixed point (triangulation or traverse station) previously located and ter-
CONTRC L TRA\ ’ERSE — .... . Instrume Recordet FR ntiCp/MJ ■: Cpt.J.C L 7M 3 Bear ee TO Rod man Rodman., 19 Nt.J.L.Mk. ’vtA.t Mui
By d/re :t horizc ntai me asure me it (3 repe. titions) 4/th tele. cope dir ect.
5ta. /& Dist 2^ Diet Mean (in yds ) Mean Angle Azimuth\ Ren larks
'April 15, 1940(4 ? hours) C/ear, cc £>/
\/OO ft. z ufkin 5 'eei Tape No. T58 7
!9 _ 8 oak
q/5'oak
/45'1 16' 00 75*4 7’ 00
5J 360* OO' OO’ 435*47' OO* •7/ side 7/0 on east of road.
745‘ !5'40
/BO* 25' 00' 181° !4' JO'
t\360*00 OD* 3)\54! 14' 3d
180° 24' 50' to
12' Oak \ P 12" s famp
191* 33'30' 2/4° 4l‘ 00
+ \36O* OO'00" 3)\574* 41’ OO' 4 oak o-
191*33 4d
186*02' 00
t 198’ 05 3O' 360* OO ' 00'
18 — 19 345.22 545.29 181.75 145° 1540 558*05' 30* /869 O/' 50" ~93
/7~/8 594/3 594.2! 198.06 180'24 50
/6-/7 4-76.18 476.32 758.75 191 33 40
3-/6 648.94 649.00 2/6.32 1860!30 4 'decked: We 8 £ N
Mop J
tf an accuracy of greater than /in 2,500 is required,
2 direct and 2 reversed repetitions should be taken.
Figure 40.—Control traverse notes.
minate at another fixed point, or in the case of a closed traverse, at its starting point. See paragraph 83.
c. Field work.—The measurement of distances is identical with the method described in paragraph 47, except that the recorder here records the horizontal angles and transcribes distances from notes made by the head chainman. To measure angles by repetition, proceed as follows:
(1) Send rear rodman (with range pole) to rear station of azimuth line, unless said station is a triangulation station or other point marked with a signal. Send front rodman to first new station of traverse.
122
TM 5-235
79
SURVEYING
(2) Set the transit over the starting point, center, and level. This is called “setting up.”
(3) Set A vernier to read zero, sight at the left hand (rear) station approximately, clamp the lower motion, and make an exact bisection with the lower tangent movement.
(4) Unclamp the upper motion, sight at the right hand (front) station approximately, clamp, and make an exact bisection with the upper tangent movement.
(5) Read A vernier to the nearest 30 seconds and record. This is the trial measurement of the angle sought.
(6) Unclamp the lower motion and sight again at the rear station approximately, clamp the lower motion and make an exact bisection with the lower tangent movement.
(7) Unclamp the upper motion and sight at forward station approximately and make an exact bisection with the upper tangent movement. (This is the second measurement of the angle.)
(8) Without reading any vernier, unclamp lower motion, sight at rear station, clamp lower motion, and make an exact bisection with the lower- tangent movement.
(9) Unclamp upper motion and sight at forward point approximately, making an exact bisection with the upper tangent movement. (This is the third measurement of the angle.)
(10) Read A vernier to the nearest 30 seconds and record. One-third of this reading will be the angle.
(11) M easure and record the other angles of the traverse in like manner.
(12) Three direct repetitions are described above. Reversing the telescope for half the observations of an angle eliminates many errors due to imperfections of the instrument and its adjustment. Observing two direct and two reversed clockwise repetitions with a 20-second transit should yield third-order traverse angles. The A, B, and mean of the verniers are recorded on the initial setting and the fourth (second reversed) repetition, and only the A vernier need be read on the first angle, thus:
00° 00' 00"
186° 02' 00"
24° 07" 20"
744° 07'
20"
20"
10" (initial setting)
(1st angle)
20" (4th repetition)
10" (4th—initial 360X (1st angles-90°))
186° OF 48" (above-^-4)
/. Special notes on boundary traverse - Distances and angles for a boundary traverse are usually obtained by the same methods as described above, distances taped and angles by repetition. Due to the
123
* TM 5-235
79-80 CORPS OF ENGINEERS
peculiar nature of a boundary survey, usually involving properties of several parties, complicated by possible boundary disputes, the surveyor should be familiar with interpreting the descriptive part of deeds conveying property from one owner to the next. Descriptions in some deeds are often vague and ambiguous and the surveyor must frequently reconcile smaller differences between contending parties, based on honest and conscientious interpretations of his findings. Copies of deeds, or that part of deeds containing description (metes and bounds) of property, can be obtained from the land records of the county court of the county in which the property is situated. These land records are usually well indexed and cross indexed and the officials supervising the records will be found most willing to cooperate.
g. Exercise X.—Measure the angles of an assigned traverse by the repetition method described in e above and record and calculate the mean angle for each set-up as shown on the form in figure 40.
80. Azimuth traverse with transit and stadia.—a. Organization of party.—A transit party which is given the task of establishing stations by an azimuth traverse with transit or stadia, such traverse also being termed stadia control traverse, should consist of
1 instrument man and chief of party.
1 recorder.
2 rodmen.
1 or more helpers to clear lines, etc.
b. Equipment.—A 1-minute transit, 2 stadia rods, stadia computer or stadia reduction table (see table VI, TM 5-236), H.I. stick (about 6 feet long and graduated to tenths of feet), stakes, hatchet, brush hook, notebook, and pencil. Figure 41 shows a Cox stadia computer, with an example.
c. Form of notes.—Figure 42 shows some notes with all measurements reduced to their proper values. The methods of observing and recording them are explained in e below.
d. Control {slarHn9 and closing} data.—In addition to the azimuth from the starting point of the traverse to some other established point the elevation of the starting point should be known. In this case (fig. 42) the known azimuth© 16 to03 was given as 330°15' and the known elevation of 016 as 135.0 feet. Also, an azimuth from the terminal station of the traverse to some other established point must be known as well as the elevation of the last point of the traverse occupied by instrument, so that the degree of accuracy of the work can be calculated and a reasonable amount of closing error adjusted.
e. Field work.—To run an azimuth traverse by the method outlined in paragraph lie (1), proceed as follows:
124
SURVEYING
o f
Id
Figure 41.—Cox stadia computer.
center
125
(1) Set up on the starting point (016, fig. 42) and measure the H.I. with the H.I. stick or stadia board. Unclamp needle.
(2) Set A vernier at the azimuth (330° 15') to the known point (03), and signal rear rod “Edge.”
(3) With lower motion and telescope direct, sight on rear rod and clamp. Read needle “North (or south) so many degrees and minutes east (or west),” which is recorded in the notebook (N. 30°00' W.). Signal rear rod “Down” and front rod “Face.”
TM 5-235
80
Directions for Use
Set the arrow marked zero on the disc, opposite the reading of the rod on the cuter scale.
Opposite the vertical angle of the transit telescope find the Difference of Elevation, and opposite the same angle on the Distance Scale find the Horizontal Distance.
EXAMPLE:
Vertical angle 12° 30', reading of the Rod 537 feet. Set the zero of the disc opposite 537, and opposite 12° 30' of the scale at the left read 1 I 3 J feet Difference of Elevation, and opposite 1 2 30', of the Scale at the right read 5 12 feet Distance.
(4) Unclamp upper motion, reverse telescope, and set horizontal hair on front rod (017) at the H.I. with upper motion.
(5) Read vertical vernier, calling, “Reversed, plus (or minus) so many degrees and minutes,” to the recorder, who repeats and records on scratch paper (—O°1U).
Copyright, 1899, by
W. & L. E. Gurley. Troy. N. Y., U. S. A.
TM 5-235
80 CORPS OF ENGINEERS
(6) Plunge telescope and with upper and vertical motions set the lower stadia wire on one of the hundred-foot divisions, if possible, so that the center wire will be at about the H.l. Count the graduations from the lower to the upper wire and call, “Distance, so many feet,” to the recorder, who repeats and records (475) in the notebook.
(7) Set middle wire at the H.l. Signal “Edge.”
(8) With the upper motion, set on the edge of the rod and signal front rod “Down” and rear rod “Come in.” 9 10
f 5 From 5 to 1AD/A !6 To c Dist CONTR 22 Azu OL TR noth AVERS Ft. Be/v c \Chief.of ~ Observer O/Tj Vd. \Recorder \Rodman brty 5gZ MJ. Blair . .M. Toe '.ee 4 Roe Date-Af. /nsT 'Bet K = C + f ‘ rit 17,194 ■ger 1322 tot 105 0
From - To STADIA D/5T CORR 0/5T Control Check VA. Diff £/ev\ 6lev. Needle Rerr arks
16-3 648 *330°t5 I5O°I5 1 135.0 N30°00W 0 3- wood >n peg wt fb coppet ■ tack on
17 475 138°4! 3l8’4l' -o°n' 1 54l’30‘6 5.E cc rner of -.oncrete. 3etvoir
Mean 48! -0°H 30° t.6 1 133.4 Rd ct id 23rds treet.
17 - /6 475 B O ! 318 41 I38°4l‘ t0°/2‘ 1 N4l'o6w o/6-Same ■ as 03 at put t5 Belvoir Hi
IB 595 138°!6 3/8° 16'30 -0°3l‘ 1 541°3O'6 oH-same <5 5 03, aboui /5Vt.of b M "35
Mean 602 -o’si'rd1 5.5 | 127.9 o/8-same 15 oJj abou ’ 30 6 of L end in
18 - 17 595 "318’16'30 138° 16 t0°32‘ 1 N4l°30‘w //< road'
t9 545 172 59 30 352°59 30 r!°03' r~ 5 7 00 6 4 !
Mean 55! tl°O3‘ 10.1 1 138.0
19 - 18 545 B35259 '30 172°59 30 -!°03‘ 1 N7°OO'W o/9 same y ■ ■ as c>3
20 250 200° 13 20° t3' + 2° 12' 1 520° 30 W o20- san- e as o3. c ybout 10 14 of road
Mean 254 t2°12 9.8 1 147.8 and 7N of s cyamope tree
20 - 19 250 *20° 13' 200° 13 -2°A 1 M20 002
2/ 513 !65°oi30 345’oi3O fO°34 1 5/4°30E o2l- copp. W side
2t - 20 513 a345°0l 30 165°0l'3d' -O'36 1 NI5°00\N
22 430 208° 23 28° 23' -3°I7 1 1 5 28°30 \N \ (vG 22 same < IS 03
Mean 1 Top or*
I
1
1
1
i
1
1 1 Checked: ms bJ
Figure 42.—Field notes, stadia control traverse.
(9) Read A vernier and call, “Azimuth, so many degrees, etc.” to the recorder, who repeats and records (138°41') as “Control.” Read B vernier to the recorder, who checks it against the A reading and records (318°41'), repeating and adding “Check.” Read and record needle (S. 41°30' E.). Clamp needle. Call in rear rodman.
(10) Read vertical vernier, calling, “Direct, plus (or minus) so many degrees, etc.,” to the recorder, who repeats (—0°l 1'), and checks against the reversed reading (see (5) above). If the instrument is in adjustment, they agree; if not, their mean is correct and is recorded in the notebook (—0°ll').
126
TM 5-235
. SURVEYING 80
(11) Make sure that the rear rodman knows the location of this station, unclamp below, and move to next station. Set up and measure H.I. Send front rodman forward.
(12) Check vernier settings (B vernier should read 318°41') and reset if necessary. Signal rear rod “Face,” reverse telescope, and with lower and vertical motions, set on rear rod at H.I. Read V.A. to recorder, who repeats and records ( + 0°12') on scratch paper as in (5) above. Plunge telescope, set on the rod with lower motion, read and record distance (475). Set on H.I. and signal rear rod “Edge.” With lower motion, set on edge and signal rear rod “Down.” Read B and A verniers to recorder, who checks and records (318°41' and 138°41', respectively). Read needle and record. Read V.A., calling, “Direct, plus (or minus) so many degrees, etc. (+0°12')” to the recorder, who repeats and checks against the reversed reading recorded on scratch paper. The recorder now records the V.A. (see (10) above). Signal front rod “Face.” Proceed as in (4) to (11) above, substituting B for A vernier and A for B. (They alternate at each change of station which is shown in the notes.) Occupy, read, and record the data for the remaining stations on the traverse.
(13) Bear in mind that only the lower motion is used while sighting on the rear station, and only the upper motion while sighting on the front station.
(14) As the data are obtained the recorder reduces the mean stadia distances to true horizontal distances by applying K, (c+/), and horizontal corrections when necessary; he also calculates the difference of elevation between stations and deduces the elevation of each.
(15) For example, on the first line marked “Mean” he will enter the mean distance, corrected for K and (c+/), in this case 475XF-f (c+/) or 475X 1.01 +1.05= (480.8) 481 feet corrected distance. On the same line, column V.A., he will enter the mean vertical angle or —0°ll'30". With the Cox stadia computer (or stadia reduction table) the difference of elevations for a distance of 481 feet and the mean vertical angle of —0°ll'30" equals 1.4. which is entered in the “Diff. Elev.” column. This subtracted (the sign of the V.A. is —) from 135.0, the elevation of 0 16, gives 133.6, the elevation of 0 17.
(16) The corrected distances and elevations for the remaining stations of the traverse are obtained in a like manner.
(17) Horizontal corrections (always to be subtracted) are seldom applied to distances if the V.A. between the two corresponding stations is less than 5°. These corrections also are obtained with the Cox stadia computer or, more accurately, from stadia reduction tables.
/. Exercise XI.—Run a stadia traverse between two assigned points
127
CORPS OF ENGINEERS
Figure 43.—Field notes, needle traverse.
TM 5-235
80-81
by the method described in e above and record and calculate corrected distances and elevations for all stations. A diagram, similar to the one in figure 42, must show the location of each station to facilitate easy recovery.
81. Compass traverse with transit and stadia.—a. Organization oj party.—The party usually consists of—
1 instrument man, who acts as chief of party.
1 recorder.
2 rodmen.
1 or more helpers to clear lines, etc.
b. Equipment.—A 1-minute transit, 2 stadia rods, stadia computer or stadia reduction table, H.I. stick, stakes, hatchet, brushhook, notebook, and pencil.
c. Form oj notes.—Figure 43 shows notes with all observed data reduced to their correct values as the traverse progresses. The method of recording is explained together with the method of observing, etc., in e below.
d. Control (starting and closing) data.—This method does not require that the first and last stations occupied with the instrument must be
128
C needle Traverse \Chief of dorfy: L.B. brown \kodman\5hortl Lcing ..—
Frnm TrTa/3/ CRelvnir !/n ''Observer MN. Brack Inst Berger *37/40 (/V\
from oOf fo O/JI Ft De/votr, l/a. \Recorder C.B.Black K-099
ora. D/st Azi. math_______________________\Sketcher.___LB t rown c ef = LO 7_________________
From-To Torrdist Control Check /A Diff.Llev. I E/ev. Need/e_______________________ Rerr arks____________
' 375 « < . , . , । . > r/ev 06/=129.3
t - 67 372 \/20 77 300 !7 -O 03 t 0.3 I 129 6 S 60 00 £_____________________________________
620 O * O • 0 • I 0 <
______2 6/5 313 // 133 H \to // t 2.0 I 131.6 N46 30 W______________________________________
_____________________________________________I__________________;__________________________._________________ 3-2 429 130° t6 3/0° !6 -7° 13_______________e 9.0 I 740.6 S50N>0£_ _______________________
______4 €626 293°!4 113*14 11° 2/' t !5,7 I 156.3 N67’00W____________________________________________
________ ____________________ I ■ ' __________________________________________ 52 / o ' o * __/ 1 o’
5 - 4 5/7 124 3t 304 3t -2 03 r 184 I 774.7 355 00£ ° 5 is T.t!.M. 92 ._______________
______6 527 307°47' I27°47' t3°0t‘ + 27.3 I 202.0 N52°00W___________________________, _________
____________________,_________________________________I_______________________________________________________
7-6 2/J 145°35 325’35 + 0° II' - 0.7 } 20/3 3 34°30 £____________ '_______________________
395 ‘ 1 ‘ , • i • • 4
______8 392 33! 43 151 43 - 0 43 - 4-8 \ 196 5 N&OOW 08 is T.L'M 96__________________________
550 0 t « / o> I- " ® •
g - 8 546 133 79 313 19 7 2 0/ - !9,2 1 177.3 346 30£______________________________________
______/0_ 323 323°02 143’02' -2*3/' ‘ - /4.0 163.3 N37°odw ■ 630 i 7 I . \ : '
II - 70 625 762 // 342 II -0 03 ____0.5 163.8 577 30 £ OH is ^rc ss, cut in cone ret,. ■. Surface
420 . 1 I- . > of rac'd. intersSction of .SeFvoir
______72 477 340 38 760 38 ±J_[3_ t___6 6 । 172.6 n79 30 W Rd. ar.d 9th str, et._______________
/ ________ . j Checked: L-B- B- y
TM 5-235
81
SURVEYING
the starting, respectively terminal, points of the traverse, nor that an azimuth be known. However, knowing the azimuth and occupying these stations will serve as a check of the magnetic declination when in doubt. The elevation of the starting point and terminal point must be known.
e. Field work.—When running a compass traverse, the transit, as a rule, is set up at the first new station of the traverse, usually 01, then at every other station, namely—03, 05, etc. The work, with reference to the example recorded in figure 43, is done as follows:
(1) Set up and “orient” the transit at (01) the first new station on the traverse. Set off on the instrument, if possible, the magnetic declination of the locality in which the work is done. This setting-should not be disturbed as it remains the same for all subsequent set-ups. Have rodmen at rear station (067) and forward station (02).
(2) Set A vernier to read 0° and clamp upper motion. (A vernier is the control vernier on all set-ups.)
(3) Measure H.I. with the H.I. stick. Unclamp lower motion and turn transit until the north end of the compass needle rests at 0°, and clamp.
(4) Now azimuths, together with their corresponding compass bearings may be taken in any direction. All sights are taken to the “face” of the rod. Unclamp upper motion and sight at rear station (0 67), bisecting the face of the rod with the vertical wire. Read stadia distance (375) and record in small figures, leaving room for correct distance. Set center horizontal hair at the H.I. on the rod and signal rear rodman in. Read A vernier (120°17') and B vernier (300°17/) as a check and record. Read needle (S. 60°00' E.), check same against azimuth, and record.
(5) Read V. A. (—0°03') and record. Send rear rodman to establish new stations (03 and 04).
(6) Unclamp upper motion, turn telescope to front station (02), signal front rodman, and read distance (620).
(7) Set horizontal center hair on rod at H.I. and signal rodman down. Read A vernier (313°11') and B vernier (133°llz) as a check and record. Read needle (N. 46°30' W.), check same against azimuth, and record.
(8) Read V.A. (+O°ll') and record.
(9) Move transit to new station, passing observed forward station which becomes the rear station, and set up and “orient” the instrument (at 03).
(10) Observe from this station and every alternate station for distance, azimuth, and vertical angles as described in (1) to (9) above.
262341°—40--9 ^29
TM 5-235
81-82 CORPS OF ENGINEERS
(11) The recorder will reduce the notes in the field obtaining the values shown in figure 43 as follows: Here K=0.99, (c+/) = 1.07. Multiply first recorded distance (375) by K and add c+/, which equals 375X0.99 +1.07= (372.3) 372. When K is less than one, it is simpler to deduct (fi—K) X stadia distance from the latter than it is to multiply by K (in the present example 375 — 3.75 + 1.07 = 372.3). Compute difference of elevation for 372 feet distance and 0°03'V.+., which is 0.3 foot. As the elevation of the starting point (0 67) given was 129.3 (see “Remarks” column), and the V.A. (from 0 1 to 067) was minus, the difference of elevation must be added, which makes the elevation of the first station (01) 129.3 + 0.3 = 129.6 feet and is so recorded. The remaining notes are similarly reduced and the values recorded as indicated in figure 43.
/. Exercise XII — Run a compass traverse between two assigned points by the method described in e above and record and calculate corrected distances and elevations for all stations. A diagram showing the location of each station should accompany the notes.
Section XIII
COMPUTATION AND ADJUSTMENT OF TRAVERSES
Paragraph
General___________________________________________________________ 82
Traverse between two separate points, and closed (loop) traverse__ 83
Computation and adjustment of azimuths____..._____________________ 84
Magnification of scale____________________________________________ 85
Computation, adjustment, and checking of coordinates—taped traverse. _ 86
Computation and adjustment of elevations__________________________ 87
Computation and adjustment of stadia traverse_____________________ 88
Area computation by double meridian distance method (D. M. D. method). 89
82. General.—a. Purpose.— (1) This section treats in detail the use of field notes in the computation and adjustment of rectangular coordinates (horizontal position), azimuths, and elevations pertaining to traverse stations.
(2) Rectangular coordinates are computed from adjusted azimuths and corrected distances in yards. Sec b below.
(3) Adjusted azimuths are obtained as explained in paragraph 84.
(4) Elevations are computed and adjusted as explained in paragraph 87.
b. Rectangular coordinates.—(1) Rectangular coordinates are distances from an assumed or fixed point, called the “origin”, to any other point within the boundaries of any one particular rectangular coordinate system. These distances are measured parallel to two
130
TM 5-235
82-83
SURVEYING
lines intersecting at right angles at the “origin,” one line running south-north and the other line west-east. The location of any point in a system of rectangular coordinates is always expressed by two values, latitude and departure.
(2) In order to avoid duplication and confusion the values of the grid coordinates of the Grid System of the United States, described in section XI, TM 5-230, and given in Special Publication No. 59, United States Coast and Geodetic Survey, should be used for all computations of rectangular coordinates. As grid coordinates are expressed in yards and nearly all military maps have superimposed on them their corresponding grid by rectangular lines, computations for rectangular coordinates of traverse stations should be made in yards. Hence, all measured, corrected distances on a traverse must be converted into yard equivalents, unless they were originally obtained in yards.
(3) Figure 44 shows the standard grid coordinates for zone B, one of the nine grid zones, into which the Continental United States is divided (see Special Publication No. 59, referred to above). The position of the area covered by figure 45 is indicated by the small black square in figure 44.
(4) Figure 45 shows the rectangular coordinates (conforming to the grid coordinates in fig. 44) of a small part of zone B, together with the stations of a short, closed traverse, illustrating the relation of coordinates, distances, azimuths, and bearings between the different stations. In figure 45 AF—differences of latitude, AX=difference of departure, a = azimuth and /3=bearing. The coordinates for 02 are X= 1,000,000, F=l,000,000; distance 2 — 3 = 896.76 yards; and the azimuth between them is 156° 18', making the bearing S. 23° 42' E. In the computation (par. 86), AF is obtained from the distance times the cosine of the bearing, and AX from the distance times the sine. After computing (and adjusting) AF becomes — 821.10 and AX, +360.47 making the coordinates of 03: X= 1,000,000+360.47= 1,000,360.47 and F= 1,000,000-821.10 = 999,178.90. Similar relations for the remaining stations of the traverse may be seen by comparing figure 45 with the results of the computation shown in figure 47.
83. Traverse between two separate points, and closed (loop) traverse.—a. To compute and adjust positions of stations on a traverse starting and terminating at two separate points, the grid coordinates and elevation of both points, as well as the grid azimuth for both ends of the traverse, must be known.
131
TM 5-235
83
CORPS OF ENGINEERS
3,000,000
2,500,000
MICH
2,000,000
W VA
zone: "o'
ZONE "A
1,500,000
1,000,000
500,000
Area represented by figure 45 —
Figure 44.—Grid coordinates, zone B.
132
^76°30‘
49’10'
40°r
44’
PA
N Y.
- VA
j KY
N C.
SO.
GA
36°
28° *■
32°
o o o 6" o
TENN.
24°
1,000,000
TM 5-235
83-84
SURVEYING
b. When running a short closed traverse, the coordinates, elevation, and azimuth at the point from which the traverse starts, need only be known, as such traverse closes at the starting point.
84. Computation and adjustment of azimuths.—a. General.— To compute grid coordinates, the azimuths of the different courses of a traverse must be first calculated and adjusted. Ordinarily, azimuths are obtained from observation of angles by repetition (see par. 79), or from the method employed in running an azimuth traverse (see par. 80). In the first case, azimuths must be calculated and adjusted
1,001,000
1,000,000
999,000
-Ax !7
I ;-ay
J-J--------
rAY
N
;-ax •
998,000 ____
998,000
999,000 1,000,000
Figure 45.—Rectangular (grid) coordinates.
1,001,000
if necessary; in the second case, the azimuths obtained in the field must be adjusted if there is a discrepancy between the check azimuth (recorded in the field) at the end of the traverse and the known or given azimuth.
b. Calculation and adjustment of azimuths from angles by repetition.— (1) To calculate the azimuths of the courses of a traverse add the observed (mean) angle recorded in the field notes, plus or minus 180°,
133
TM 5-235
84-85 CORPS OF ENGINEERS
to the back azimuth (given azimuth minus or plus 180°) of the known course and to the calculated azimuth of each course for each succeeding course. Referring to figure 46 (Form 1), azimuth 02-A top was given as 14°10,52"; this is a closed traverse and hence the check azimuth on closing should be the same. The back azimuth is 14°10'52" +180° or 194°10'52" (see third line of form). As the forward azimuth is required in each case, the mean angle plus or minus 180° must be added to each preceding azimuth to obtain the forward azimuth. If the recorded mean angle is 180° or less, add the angle plus 180°, and if the recorded mean angle is more than 180° add the angle minus 180°. In the figure, the recorded angle at ©2 is 142°07'12". Add 142°07T2" + 180° to the azimuth a top-©2 (194°10'52"), which gives 516°18'04". However, since an azimuth becomes 0° as soon as it reaches 360° we must subtract 360° from 516°18'04", thus obtaining an azimuth of 156°18'04" for ©2-©3. Add the recorded angle at ©3, corrected for 180° (271 °16'34"—180°) to 156°18'04", which gives 247°34'38", the azimuth from ©3 to ©4. We now’ add the recorded mean angle at ©4, corrected for 180°, or 192°50'54" —180°= 12°50'54" to 247°34'38", getting an azimuth of 260°25'32" for the azimuth from ©4 to ©5. The calculation is continued similarly until the last recorded angle has been applied, giving 14°ll'2O" for the azimuth ©2-Atop.
(2) Angles, as well as other measurements, cannot be expected to agree within certain small amounts. So in this case, we find that the last azimuth, 02-ATop is 14°ll'2O", when it should be the same as the starting azimuth 14° 10'52", an error of —28". Assuming that this is a cumulative error, we distribute the excess ( — 28") equally among the courses of the traverse by subtracting a proportional part of the total error from each azimuth. Since there are seven courses on the traverse, we subtract # of 28" or 4" from the azimuth of the first new course (azimuth 02-03), % of 28" or 8" from the azimuth of second new course (azimuth 03-04), etc., getting for the final adjusted azimuths of the traverse 156°18'00", 247°34'30", etc., as shown in the column “Correction, adjusted azimuths” on the form in figure 46.
c. Exercise XIII.—Calculate and adjust the azimuths for a taped traverse, with angles obtained by repetition, as described in this paragraph and illustrated in figure 46. If a regular form 2 is not available a form similar to form 1A, squared paper, may be used for this and other computations.
85. Magnification of scale.—a. Rectangular coordinates computed from azimuths and distances of a traverse between two points more or less widely separated may vary by a small amount from the
134
TM 5-235
85-86
SURVEYING
standard grid coordinates of these points due to the fact that the Y coordinates based on the poly conic projection contain an error known as the magnification of scale. This error is due to the simple reason that a spherical or spheroidal surface cannot be projected to a plane surface without some sort of distortion, which in the polyconic projection appears as magnification of scale in the Y coordinates, the enlargement varying from zero on the central meridian of the grid zone to 2 yards per thousand yards and over at 4° east or west of the central meridian. The corrections to Y coordinates for magnification of scale are found on pages 31 and 32, Special Publication No. 59, United States Coast and Geodetic Survey.
b. An azimuth between two points computed from their grid coordinates differs from the true grid azimuth by a certain amount due to the magnification of scale error. Corrections for the reduction of geographic azimuths to grid azimuths, or vice versa, are found on page 33, Special Publication No. 59, United States Coast and Geodetic Survey. See paragraph 117.g, for instructions for reducing azimuths referred to above.
c. For an application of magnification of scale correction for taped traverses see paragraph 118c. In many cases, especially for traverses run by stadia, magnification of scale is not considered.
86. Computation, adjustment, and checking of coordinates— taped traverse.—a. Computation.—The actual computation of coordinates for control traverse stations is made on a form usually provided for that purpose. Figure 47 shows form 2, considered excellent for this work. The method of computation is as follows:
(1) In the second column enter the station numbers, beginning with the starting point, as 2-3, 3-4, etc.
(2) In the third column enter all horizontal distances, as 896.76, 665.93, etc. Enter the adjusted azimuths (156-18-00, 247-34-30, etc.) leaving space for the bearings. Check distances and azimuths against the original record. Compute bearings and enter same between distance and azimuth, as S. 23-42-00 E., S. 67-34-30 W., etc. Check bearings.
(3) In fourth and fifth columns take out logarithms, 5-place or 7-place, of distances and write them in their proper places. Take out log cos and log sin of bearings and enter them under the log distance in the proper column. Add log distance to log cos or log sin of the bearing in each course and check the two completed columns.
(4) In the sixth and seventh columns inspect bearings and mark with a cross the space not to be used; that is, if bearing is S. W., put a cross in the N. and a cross in the E. column, etc. This is necessary,
135
TM 5-235
86
CORPS OF ENGINEERS
CALCULATION Control Project. XTTT AND ADJUSTMENT OF AZIMUTH Traverse, from 02 to 0 2 from Notebook No.
Courses, etc. First values Correction Adj azimuth Courses, etc First values Correction Adj. azimuth
a. 02 -Atop /4° !0 52 O 1 " a
A ATop-02 !8O 00 OO Z
a. Atop-02 194 10 52 a
L 02 142-07-12 322 07 12 -4" Z
a 0 2 - 03 156 /8 04 156 !8 00 a
Z 0 3 27/-Z6-34 9/ !6 34 -8" Z
a 03 - 04 247 34 38 247 34 30 a
Z 04 /92 -50 -54 /2 50 54 -/2" Z
a 04 - 05 2.60 25 32 260 25 20 a
Z 05 26O-4/-54 80 4/ 54 -/6" Z
a 05 - 06 34/ 07 26 34/ 07 IO a
Z 06 286-57-04 106 57 04 -20" Z
a 06 - 07 88 04 30 88 04 IO a
Z 0 7 228-49-24 48 49 24 -24" Z
a 07 - 02 136 53 54 136 53 30 a.
Z 02 57-/7-26 237 17 26 -28" Z
a 02 - CTop !4 // 20 !4 !O 52 a
Z Z
a a
z Z
a a
Z Z
a a.
Z Z
a a
Z Z
a a
Z Z
a. a
Z Z
a a
Z Z
a a
Z Z
a a
Z Z
a a
Z Z
a a
Z Z
a a
Calculated azimuth 02 fo AJpjo LL?fi' Correct azimuth 74-° /O 52 Error + +28'' No of courses 7 Correction first course + -4" Correction for all other courses = No. of course X (±.) -4" Date: April 26, 194 <9 Computed by: RR Checked by. (RX R FORM 1
Figure 46.—Calculation and adjustment of azimuth.
136
SURVEYING
TM 5-235
86
FORM IA
Figure 46.—Calculation and adjustment of azimuth—Continued.
137
TM 5-235
86
CORPS OF ENGINEERS
TRAVERSE SHEET
Control ____ TRAVERSE
FROM: 5 to.2(ii - ra,rfa.*.)
TO: 5ta2 (B-Fairfax")
. • **• । ,v- v Vl vn. vm.
. DISTANCE LOG DISTANCE LOG DISTANCE I
I STATION ; BEARING I LOG COS BEARING LOG SIN BEARING |j LATITUDE DEPARTURE ' COORDINATES
II + AY -AY ’ FAX -AX Y ~ X~
.ZiHUTH LOG LATITUDE LOG DEPARTURE || NORTH SOUTH | EAST j WEST NORTHINGS EASTINGS
““T I a96 76 ^W®17[6p*^;sb + I^FIA/lo |lJl6|o;v|7 pkj I IP' io[ol0'0l010[dm/0'0l0 0106W
----5 23'42 00 E +961 73 55\+p0 4 ! 6 9^. >4 --[o 3 >4_NLfLLdJl f's+fcl
/_ 3 _!56-ja_:00__ 2,9144 II 7 2'5 56 '8 45 8+( | 3 6&j45\ + 9 9 9-1 7 8,9 0 1M0 3 6 0^4 7
P T ~ 665.93 2'82'3 42'86+8 23 4+8 6ij^ + ' " 2~5~4\0 T x 4 6 I + 4_■_।_।_
,-iP--5 67-34-30 H +58 ! 4 64 7 9|p|5 5 8 504] >4_■ -|<7 /_ I >J I_-|l7 3 _-2 5_4\03__-6 l\5\5 4
_____4 247_-3413O_ 1?MM8_9[33 £i7&,9? 790t4_ ' \ 254+4]+ “TJ 61 7 9\9 8J 2'4'8 7(19.947 4 4<9'3 " 1"_~ 258.52 2'4l24 947++i24 94lty T4 j " T ’ X X 25 4lS 0"_ j I ’
4t —-5 80-25-20 V! 9R2 ! / / 7 6[9i9 9390 3 611 >4_|_I >4 "^2 \-4+0 ! -254\9C
+____5\_260-25RQ_ t'6 3 36 l7T2'4O 6 3 9 7 tr E '■ j _4 3'0/]. ' i_ J_25 tj> .= 9 9 8 fl 8 / 8 6 9 9 9 4 0.0 1
’ T 1622.87 J270 28 3 8''3\2l'0 2 8~3 8\l 5 3 5'6 0^^ F^lT' 4 | 3 2 '5i!'2 ~ ~~ J ' X__I_
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AT___? 34bO7-±O__ Ji+zVyW +(+o'2 8t4+536++Y+ r J fit! '+7oW04_ / 7j76|9939«<9 >
" ~~ 624.95^ 2'7958453 2'79 5845.3l\ J -- __ZLZ' 1 J L_
1-2--N88-04-10 E 8i52 7 4 775+999 753m !_>4_t<0 J >4 >?7]o/ [7624'63
kA ___7 _88_494tp__ (3233228 Z/95j59,PjX 2 (O_ i <+_ _ C >. _? ■? ++d\+’_ _ J/OO 0 4 3 8'4 7 9 9 958 9^5 4
1 ~ 600.6! 2\778 5926~?O7 8\5^~++'Z"+Z 4 3 7 T 4 / _|~j 1 _
„14---5 43-06-30E 9[8 6 3[3 6+3 9[83 4 6 6 221 _-'0 L\ 4'0 ^<1 - 4 3 8'4 zj LZ4/9J46
dP I 2 136-53-30 2647 95 29 2613+5++++ 4-3+48 4iO-44\..'" (.J/o.0,6 06 O'p 0\/0 0 OOOPP 0
~ ~ ~____-r’i__+Jr ~ 1 n । 1 | 1 1 __2j_LZ
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** __2----: ””’1 rl
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--------1-----4----J| ' [ 1 1 1 ___:__|___i__l__
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--------------1------J----U '-------------I 1 4- - -! 1—
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—______________________________________________________ -::r-
1 I II I I I I 1 I I 1 1
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> 1 T । T1 । | 1 । i T
COLUMNS I. fl. III. COPIED BY_<5/7^ M. G. /_______DATE pt'll 2___________. 194^ COMPARED AND FINAL CHECK
columns iv. v. vi. vii. computed by 5^/ M.GBedell_DATE April 2__. i94.. by ^9^ T.R. Gar rod _
COLUMN VIII COMPUTED BY___5^/, M G Bedell_________ DATE April 2_194
IN___L___ SHEETS SHEET MO--FORM 2
® Control.
Figure 47.—Computation and adjustment of traverse
138
TM 5-235
SURVEYING 86
TRAVERSE SHEET
......... Stadia ______________TRAVERSE
FROM: A Lacey (Fairfax) ro: RCamp (Fairfax) . ....
I- II. III. i IV. V. I VI. I VII. VIII.
DISTANCE j LOG DISTANCE LOG DISTANCE- '
ELEV STATION; BEARING* . LOG COS BEARING LOG SIN BEARING 1 LATITUDE DEPARTURE ' COORDINATES
H + ay -ay n Tax' Tax “" I y x '
. AZIMUTH LOG LATITUDE LOG DEPARTURE I I___
( '[I NORTH SOUTH || EAST WEST | NORTHINGS EASTINGS
tatZ/ZZZZ /67i9 gxaM'i _uhsi it n/wurnwr urrt 'E/xm/w eswe
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, ~ 238.0 2*3 7 6.58 ^37658 | |X TT ’"Z:3 5z"T " ‘u^LL______E___________1 -
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163,2 222840 2g2g1 i ............................. : ■ 1.1 .■
CONTROL NET
ADJUSTED AND UNADJUSTED
300
262341
(Face p. 153)
THE UNITED STATES OCTOBER 1,1938
Figure 52.—Map of areas in United States covered by first- and second-order control.
SHOWING FIRST AND SECOND ORDER TRIANGULATION AND TRAVERSES BY THE VARIOUS US.
GOVERNMENT DEPARTMENTS
STATUTE MILES
100 200
TM 5-235
SURVEYING 95
of accuracy. Starting with an isolated base line involves the determination of the geographic position (par. 90), azimuth, and elevation, and the utilization of a base net. Figure 52 indicates the distribution of completed and adjusted triangulation of first- and second-order accuracy in the continental United States as of 1938. The United States Coast and Geodetic Survey publishes in tabular form descriptive data on the triangulation systems in various regions. These tables give the latitude and longitude of each point on the North American datum of 1927 and the azimuth and back azimuth of each line observed between triangulation points. The table also gives lengths of these lines in feet and meters and the logarithms of the distance in meters. The above and also unpublished data may be secured through the office of the Chief of Engineers. The first precaution in the use of these data is to make certain that all figures have been adjusted to the 1927 North American datum. Station descriptions, which include the description of the station mark, azimuth, and reference marks, and a good route to the site, should be procured before recovery is undertaken. Outside of the continental United States, similar control data and station descriptions may be procured from the department engineer or the chief engineer of the expedition.
b. After a study of the adjusted control data in the region of the project, it is almost invariably most convenient to utilize lines of existing triangulation as bases and check bases, and the resulting data are the more useful on account of being adjusted to the national control system. In starting from or connecting with existing triangulation it is advisable that the connection be made to a line of proper strength, and also that observations be made from the two ends of that line upon a third point of existing triangulation. If the new and old angles upon the third point agree closely, exact recovery of old stations is then assured. Connection in position alone (to a single point) or in position and azimuth (to a single point but with a direction observed from that point to another old station) may sometimes be advantageously made at intervals between the connections in length just described.
c. Grid triangulation will usually be started from stations of higher order, but the results may be needed before further connections can be made. Check bases by the method of paragraph 106 may be useful in such circumstances.
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Section XV
TRIANGULATION RECONNAISSANCE AND SIGNALS
Paragraph
Purpose of reconnaissance___________________________ _ _ _ _____ 96
Organization of party and equipment_______________________________________ 97
Station and base line selection and construction______________ ___________ 98
96. Purpose of reconnaissance.—Modifications applicable to grid triangulation are described in paragraph 98o.
a. The success of triangulation depends upon an intelligent reconnaissance. This reconnaissance should select station locations forming the strongest and most feasible figures for the triangulation and locate the base lines and public roads and other routes. The lengths of sights will often be fixed by the nature of the topography, but where this is not the case there must be a decision as to the average length desirable. The lower limit of length of line is fixed by two considerations. On very short lines it is difficult to get observations of the degree of accuracy necessary to close the triangles within the required limit. Extreme caution is required in centering and plumbing the signals and the theodolite to avoid the errors due to eccentricity. Very short lines also multiply the number of stations and increase the danger of cumulative errors. On the other hand there is no advantage, insofar as accuracy is concerned, in using very long lines. Long lines are apt to introduce delays due to signals not being visible. With long lines, supplementary stations to reach required points in all portions of the area covered are much more apt to be needed than with short lines. In third-order triangulation the sights may range between 3 and 10 miles in length.
b. Experienced surveyors should be assigned to reconnaissance, since much depends on the proper selection of stations. The form of the triangles, the amount of clearing necessary, possible damage to private property, accessibility and cost of stations, the avoidance of possible sources of atmospheric disturbances, and many similar subjects have to be considered in determining the location of stations. The line of sight should not “graze” the ground or any other object so closely as to make lateral refraction possible.
c. The chief of the reconnaissance party must bear in mind that he is selecting points which are to be marked permanently and to serve not only for the work immediately in contemplation but possibly for other surveying projects. The net result of a geodetic survey is a number of scattered monuments and a data sheet showing their locations and elevations. The importance of selecting a place for the station where the mark will be least exposed to disturbance is
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evident. If consistent with other considerations, the station should be at a picture point. (See sec. XXVII of this manual and sec. XV, TM 5-230.) The reconnaissance party should keep full notes regarding station locations; these will be supplemented by notes of the signal-building and angle-measuring parties, as their operations afford additional data.
d. Duties of reconnaissance party.
(1) The selection of well conditioned figures.
(2) Making sure that stations are intervisible, without grazing rays.
(3) Siting, flagging, and marking each point temporarily.
(4) Laying out sites and nets for any base lines required.
(5) Directing attention to possible intersection stations.
(6) Preparing an adequate description of the location of each point and the route thereto.
(7) Determining the kind of signal or observing platform, and the clearing required.
(8) Securing the written consent of the property owner for the above. If any clearing is necessary, the value of the timber to be cut should be definitely fixed and agreed upon with the owner before cutting is begun.
(9) Furnishing a plat of the system, and a record of any angles and azimuths as roughly determined by the party.
e. The plat of the triangulation system is copied and used in the field by the construction and observation parties and in the office by the computing section. Another copy in the office is marked with various colors to indicate the progress of station erection, observation, and computation.
97. Organization of party and equipment.—a. A chief of party and instrument man, a recorder, and two or more laborers are generally sufficient for the reconnaissance party proper with such additional personnel as necessary for supply, transportation, etc. The triangulator should act as chief of reconnaissance, or his recorder should be a member of the party, thus becoming familiar with the region, the control net, and its stations.
b. The reconnaissance party will find the following instruments useful:
Protractor. Steel tape.
Pocket sextant. Plane table or sketching
Prismatic compass. board.
Clinometer. Alidade with folding sights.
Aneroid barometer. Notebook and pencil.
Field glasses. Blank forms for station deScale. . scription.
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Description of existing stations Saw.
and bench marks. Nails.
Best maps of country available. Wire.
Lineman’s climbers, short and long Signal cloth.
spur, complete with straps. Crayon.
Ax. Light line.
Hatchet.
c. A close study should be made of all available maps. All established stations and bench marks should be plotted on the most suitable medium scale map. A provisional scheme including intersection stations and base line sites, if required, should be lightly penciled on the map, to be revised during the field reconnaissance. Lacking a suitable map, a plane table sheet of suitable scale is prepared showing all existing control, and the new system plotted by intersection and resection during the reconnaissance.
d. The field glasses are needed for picking up distant flags, and for studying remote summits so they may be recognized from other locations. A good prismatic compass supplemented by a pocket sextant in case of local attraction is very valuable for obtaining azimuths and angles from tree tops to distant points. The rays are plotted on the map or sheet and the azimuths and deduced angles are recorded in the notebook. The observations from each point are kept on a separate page. As the scheme progresses some of the figures may be diagrammed on other pages. The latter will be done especially for lines difficult to observe or which are concealed by forest growth. (See par. 98c.) As these notes and the station descriptions will be needed for station construction and also by the observing party, the records must be clear and complete.
e. The tools will be needed for minor clearing and for erecting flags. The flags should be varied in size and color if there is any chance of confusion from a distance.
/. Clinometer and barometer notes may aid in the identification of summits. They will be of some use in preliminary determinations of intervisibility on lines that have to be cleared.
98. Station and base line selection and construction.—Special methods applicable to grid triangulation are described in o below.
a. General.—(1) Triangulation stations, as far as practicable, should be placed on the crests of ridges and on the highest points of hills and mountains. In a mountainous country it is not necessary to place the stations on the highest peaks, but each one should be on the highest point of the peak selected, and this peak should be the highest one in the immediate vicinity in order that there may be an unobstructed
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view in all directions. The most favorable ground for a line of triangles is a valley of proper width, with bold banks or slopes on either side. Stations can then be selected giving well conditioned triangles, with little or no clearing out of lines. In wooded country, clearing must be resorted to or tall stations built, preferably the former if it can be accomplished at reasonable expense. A careful study of the maps will indicate the general lay of the country, the direction of drainage, the approximate location of the highest points, and the route which apparently offers the least resistance. In the actual examination of a region it is necessary to consider only the topographic features that may come within range of the work in hand, such as the crests of the highest ridges, hills, and peaks, which may serve as observation points in laying out the scheme.
(2) When visiting one of these commanding points, the first step is to locate its approximate position on the map or sketch. Trained powers of observation and a habit, natural or acquired, of self-orientation, by which is meant the faculty of knowing at any point visited for the first time just where to look for other points requisite to the work in hand, will best help the observer to secure a full knowledge of the country and will suggest the best method of laying out the work.
(3) The next step is to study closely with the aid of binoculars the prominent objects that may come within the area of the scheme for the purpose of fixing them in the memory and estimating their appearance from other directions. The positions of objects observed may be closely determined by magnetic compass bearings and by estimating the distances. Each point should be plotted on the work sheet or map in the position fixed by the bearings and estimated distances. Any distinctive features of the objects observed which will assist in identifying them when seen from other points should be noted.
(4) If in wooded country the observer, having selected from the ground what appears to be the best location, must assure himself by climbing trees or otherwise that previously located stations are visible, or can be made so by reasonable construction or clearing, and that there is a proper field of view in the direction of progress of the system. If maps are not available, the man on reconnaissance must from each located station pick out points in advance which appear to be suitable for stations, determine their location as nearly as possible by intersection, and proceed thereto as best he can. Certain natural landmarks are apparent in any landscape which will determine some of the locations; others will be more difficult.
b. Selection of base sites and nets.—The necessity for any base line measurement should be foreseen, if possible, so that a suitable site
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may be chosen, and a net of comparable strength arranged for the connection to the main systems. A material part of the accuracy of the base measurement may be lost through a very weak base net. A base may be measured with tapes with the required accuracy over fairly rough ground and moderate slopes. It is of more importance to locate the base so as to secure well conditioned figures in the base net than to locate it in the smoothest place.
c. Direction of stations not intervisible.—As to intervisibility of stations, the man on reconnaissance must recognize that sometimes one station will be concealed from another merely by forest growth which can be cleared out. He must, before extending his system in such manner as to depend upon a doubtful station, assure himself that it is practicable to render it visible at reasonable expense. In
A
Figure 53.—Determination of direction of stations not intervisible.
some cases ground reconnaissance along direction lines determined approximately from one or both stations will suffice. In other cases it may be necessary to determine the direction from one station to another by some method such as the following, which is applicable if two other points can be found from each of which both stations are visible: In figure 53, AB is the line to be cleared, and C and D are two points from which both stations A and B can be sighted. Call CD unity. Measure angles from C and D. Solve triangle BCD for side BC and triangle ADC for side AC. Two sides and included angle of triangle ABC are now known. Solve for other angles (par. 119<7). These angles will give the direction for line AB from either A or B using C and D as reference points. In such cases, additional personnel and additional equipment, such as a transit, may be temporarily required. •
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d. Height of stations.—(1) The height that it is necessary to build a station for observation between two points depends on the relative heights of the ground at the stations and of the intervening ground. Two factors enter into the problem: The curvature of the earth’s surface and the refraction of light by the earth’s atmosphere. These factors involve corrections of opposite sign.
(2) Curvature equals the ratio of the square of the distance to the . f K2 3
mean diameter of the earth, or 2^> where K and R are, respectively, distance and the earth’s radius, in the same units. Refraction equals the ratio of the square of the distance to the semidiameter of the earth . K2
times a coefficient m, or m. The value of m is taken as 0.07. The
formula for the combined effect of curvature and refraction is the
. K2
difference of the two expressions, or (1 — 2m) Calling the height of the station in feet h, and the distance in statute miles between two stations K, the following approximate formulas result:
h=0.574 K2 and K=1.32V^
The. values of h may be obtained from table XVI, TM 5-236. However, the values of A=0.574 K2 are so close to the tabular values that reference to the table is unnecessary if the formula is at hand.
(3) The calculated heights of stations should be increased by at least 10 feet in order to avoid grazing rays, unfavorable refraction, and other atmospheric disturbances.
e. Intervisibility of stations can be determined from the above formula or table, which gives the height of one station for visibility when observed from another at the ground level in open, level country. Some examples are given.
(1) In figure 54®, two stations are at the water level on opposite shores of a lake 8 miles wide. The line of sight should be at least 10 feet above the water. At 8 miles h—0.574X8X8 = 36.7 feet. The tripod heights will be 10 feet at A and 47 feet at B.
(2) In figure 54®, if the towers can be made of equal height, the line of sight would meet the 10-foot height above the water halfway 36 7
between C and D. At 4 miles h——— =9.2 feet. It is seen that 4
both tripods need be only 19 feet high.
(3) In figure 54®, two stations D and F, respectively, at 100 and 200 feet elevation, are 8 miles apart. A bare ridge E at an elevation
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CORPS OF ENGINEERS
of 120 feet is 2 miles from D on line toward F. What is lowest tripod that can be used if the target at the other station is 8 feet? As the obstruction at E is 2 miles from D, the effective elevation at D is reduced by curvature and refraction, 0.574X2X2 = 2.3 feet, to 97.7 feet. Similarly at F, 0.574X6X6 = 20.7 feet deducted from 200 gives an effective elevation of 179.3 feet. Adding 10 feet to avoid grazing ray at E, the elevation becomes 130 feet. In figure 54® the three
points are considered as based on a plane surface, with all elevations corrected as above for curvature, refraction, and grazing. The height of the necessary tripod may be found by proportion. A target 8 feet above the ground at F' would have 187.3 feet elevation. Then
187.3-130 187.3-(97.7 + z) 1O o ,
------------------------——- or z=13.2 feet, O 0
which is the height of tripod necessary at D. Inspection of figure 54® shows that a higher tower would be required at F. Other things being equal, it is always more economical to build at the station nearest the obstruction, for the height necessary to clear the obstruction increases in direct proportion to the distance from it.
160
Figure 54.—Intervisibility of stations above the ground.
f/zOO’
EH20'
~6mi.
®
100
2
d\
/o'
8 mi.
Line of sight
4
8/
C
8 mi.
D
O)
F'
187. 3
97.7
0.0
E'
130’
D
6mi.
>-2
X'
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SURVEYING
64'.50
Figure 55.—Side views of scaffold and tripod for 60-foot signal.
responding accuracy. Traverses were formerly employed in heavily wooded, almost flat country, due to the expense and time consumed in the construction of high wooden towers. The Bilby steel towers 262341°—40--------11 161
f. Types of stations.—(1) Triangulation, because of the constant availability of the checks described in section XVI, and because its stations are usually better distributed and more advantageously located for most purposes, is generally preferred to traverses of cor-
rf
V1
if) / \
\ i9.
\
. I. - 2->—4—30‘
V)/ / ।
'in \ \
*z \ \
I \
\/ •• \\ E-------2’ x.C-----N44’
3" X 4" M
K---------- ... --------—---- go
cut 18 \
------- t - — j m -
2*'x A " •
I-----0 Stand for lights
N 4-(--13' Top floor
I 7 .25 cut I gr
—2-——10 Lower floor
2" X 4" ^22'
k——V'35’
"in I / I
i \
x\. I
k-——k50.
■" \ _________3" X 4"__66.
I cut 22' I
' '70'. 50
TM 5-235
98 CORPS OF ENGINEERS
are extensively utilized by the United States Coast and Geodetic Survey. In the Army the steel towers are less common, since they have to be procured beforehand, and they occupy considerable truck or trailer capacity. The use of a steel tower near the front would be ill-advised, as a couple of intersecting rays and a “pin-point” photograph might make the tower most useful to the enemy.
o f I
I -» <0 *2 So I
F A—Top of Derrick
C I00’
\ i z -
ir x I /
'' I /
/ । 18^ Z .
/ * Tg
/ I 22*90 2\ \
r' / i \ ^>0.
•/ I x
J [ 'tr.
1 I
R I I bU a*t
Figure 56.—Ground plan for 60-foot signal.
(2) In hilly or mountainous country it is seldom necessary to build high observing towers to elevate the instrument, as it is only necessary to select prominent intervisible points that satisfy the requirements of a strong scheme that will give proper control over the area covered.
(3) Rolling country requires very careful reconnaissance, if towers are avoided while strong figures are laid out. Occasional selection of
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a church spire, flagpole, or other similar object which cannot bo occupied may help in advancing the system without much construction. The use of towers for instrument supports should be avoided wherever possible because of the expense and delay, and because usually the station cannot be used for future work without rebuilding the tower.
(4) Station construction.—Instrument stations which arc over 20 feet high are classed as high tower, all others as low tower stations. High tower stations are expensive and require considerable time to construct and their use should be avoided if possible. The following governing considerations apply to both high and low tower stations. The station should consist of two entirely separate structures—one for supporting the instrument and the other for sustaining the platform on which the observer stands. These two structures should be entirely of wood and should not touch each other. In high towers the outer structure is usually carried higher than the inner and the target fastened to the apex of the outer structure. The upper framework will also serve to support an awning to shade the instrument from the sun.
(5) Figure 55 shows working drawings of the instrument tripod and the observation scaffold for a 60-foot signal. During construction a slight bow is given all of the legs, which puts the legs and horizontal ties under a moderate initial strain, adding greatly to the stiffness of the structure and somewhat to the strength. It is not advisable to employ a wooden-frame instrument stand over 60 feet above the ground because of the effect of the wind. The high tower station will require the services of an experienced construction party, including 1 foreman carpenter, 2 carpenters, 1 rigger, and 2 to 10 laborers. The frame members should be built up by spiking together 2-by-6-inch or 2-by-4-inch lumber. There is little loss in rigidity or strength if joints are properly broken. The tripod legs and one side of the tripod are framed with all the material lying on the ground. The holes for the foundation are laid out and staked according to the ground plan in figure 56. If possible, the orientation of the signal should be such that no line of sight from the head of the tripod will be obstructed by a scaffold leg. The footplates are 2 by 12 inches and 3 feet long. The holes for the tripod and scaffold legs are all made 3 by 3% by 3% feet deep. One or more sections of a leg of the scaffold may be used as a gin pole for raising side No. 1 of the tripod. The gin pole should be about two-thirds the height of the tripod. Four-inch posts for attaching guys should bo set as shown at A, B, C, D, and E in figure 56. G represents the foot of the gin pole. When the tripod is completed, spike the feet to the footplates and put on anchors, making the anchor platform about 3 feet square. Fill the
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CORPS OF ENGINEERS
hole to the top, keeping the earth well tamped. Opposite sides of the scaffold are framed completely and all four legs are cleated before raising. In the case of an obstructed line on which the obstruction is not discovered until the towers have been built, the difficulty can be overcome by building a superstructure on the signal at each end of the line.
(6) The low tower tripod and a scaffold, as shown in figure 57, can readily be constructed by a carpenter and two helpers.
(7) Another type of instrument support is a tree trunk cut off at a suitable height and stripped of all branches. This will save building a tripod at least, and may save much clearing. A separate platform should be built for the observer. The tripods furnished with the
modern instruments are rigid enough for any but the most accurate work. If the ground is soft or spongy, the tripod shoes should be supported on 2- by 4-inch stakes driven solidly into the ground.
g. Targets.—(1) A good target should be clearly visible against all backgrounds, readily bisected, rigid, capable of being accurately centered over the station, and so constructed that the center of the visible portion, whether in sun or in shade, shall coincide with its vertical axis.
(2) To make a target visible against both light and dark backgrounds it should be painted in alternating black and white belts. For ready bisection it should be as narrow as possible without sacrificing distinctness. This is accomplished by making the width subtend an angle of from 2 to 4 seconds of arc. Since the arc of 1 second is 0.3 inch for a mile radius, an angle of 4 seconds would re-
164
E/e^ation
Figure 57.—Low tow’er station.
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SURVEYING 98
quire a target 0.1 foot in diameter for 1 mile distance, or 1 foot in diameter for 10 miles distance. A flag or panels of appropriate size should be added so that the signal may be readily picked up through the telescope.
(3) When the signal must be seen from a distance, and especially when it is to be used also for topographic or hydrographic purposes, a tripod signal is used of the type shown in figure 58®. As there is space for observer and instrument below the braces, this signal does not have to be disturbed during occupation. One objection to this type is that it is difficult to plumb over a mark already in place. The upper portion of the legs will often be covered with cloth or painted boards to attract attention. Each leg should be secured to the ground by a stake or other means. Wire guys to hold the center poles are necessary if the pole has a considerable length. The largest tripods usually have a height of about 20 feet to the apex of the tripod and from 30 to 35 feet to the top of the center pole. Where cut lumber is available, timbers 4 inches square are generally used for the legs and center pole of large signals and 2- by 4-inch lumber for those of smaller tripods.. Ordinarily the center pole should be large enough in diameter to be visible through the theodolite from the adjacent stations, as otherwise observations will be made upon the tripod or banners and errors due to phase and eccentricity will develop. One-inch boards are ordinarily used for dressing signals and should be rough or should have only one side planed, as a rough surface is superior for holding whitewash.
(4) A convenient method of constructing a large tripod signal is indicated in figure 58®. The drawing shows the legs and center pole as assembled on the ground. An identifying letter is placed at the lower end of each part. This assembly is arranged so that the lower ends of the legs A and C are in the approximate positions they will occupy when the signal is completed. The tripod is then erected by using leg B as a lifting pole and prop. When the tripod is erected and secured in the proper location the lower end D of the center pole, which pivots on the bolt, is brought within reach by means of a line attached at D, and the pole is then adjusted to a vertical position and secured by cross braces to each leg of the tripod. The targets on the center pole may be attached before or after this operation. The sides of the tripods are then boarded up as desired. The spaces between boards need not be less than the width of the boards, and wider spacing may be desirable in order to cover as much surface as possible with a limited amount of material.
(5) Figure 58® shows a pole signal held in a vertical position by wire guys with the foot of the pole resting on a low bench. The
165
CORPS OF ENGINEERS
@ See paragraph 98o(5).
Figure 58.—Types of targets.
166
Wood wedges
l"or IVz" pipe 30" long,one end pointed
Zz or l" diom. electric conduit (alternate feet white and black)
Small holes and wire for securing flog
Wood guard I stake 4
and nailed to them. The foot of the pole should have a spike driven at its center projecting about an inch, and when the pole is erected
bench may be made of two stakes driven in the ground on either side of the station mark, with a piece of scantling placed across on top
TM 5-235
98
2- l"><8" x 2'-0"
I - l"x4"x 2-6" 2-2"x4"x 2'-6" 90 feet lOgage wire
4 stakes
Centerpole Cross bracing
r3/4 bolt and washers
Target of cloth on wooden cross pieces
TM 5-235
SURVEYING 98
this spike should be placed in a hole bored in the crosspiece of the bench directly over the station. Each set of guys should consist of four wires of No. 12 smooth galvanized wire. The number of sets depends upon the height of the pole. The pole is easily lowered when the station is occupied by loosening the guy or guys on only one side. The guys on the other three sides are not loosened from their anchors. To replace the pole it is only necessary to stand it up on the bench and fasten the loosened guy or guys on the one side. The centering of the pole or that part on which observations are made should be tested after the pole has thus been replaced, but it will usually be found that it has not been disturbed.
(6) While a target should be comparatively narrow at the part on which the pointings are made, something more conspicuous is desirable at longer distances or wherever the background may be unfavorable. A white flag might be satisfactory if the wind always exposed it. A flag attached to a bar of wood or metal at the top of the pole, and with a tack or two to the pole near the bottom, allowing the lower corners to flutter, is very good. The cloth should be slashed if the station is near a settlement. If the background makes a pole difficult to distinguish, a piece of white signal cloth hung behind the pole will make it easy to bisect, especially if the pole is dark in color.
h. Heliotropes and signal lamps.—(1) Either of these types has to be procured in advance, and requires a group of trained light tenders to set and keep them adjusted for good observation. The opaque targets as described above are best for daylight work if they are clearly visible.
(2) A heliotrope (fig. 59®) is an instrument to reflect the sun’s rays by a mirror from the station sighted on to that occupied by the observer. The heliotrope should rarely be used as a signal for distances less than 20 miles, unless the atmosphere is very smoky or hazy, or because it is difficult to make an opaque signal visible in a dense wood; nor should it be used at a greater distance if an opaque signal can be seen. Opaque signals give relatively good definition, while the beam from the heliotrope is too large at short range and it is difficult to arrange satisfactory understanding between the observer and the distant heliotroper.
(3) An emergency heliotrope, shown in figure 59®, may be made by driving two nails vertically about 2 feet apart into a board, the heads of the nails to be used as sighting points for the beam of reflected sunlight. Place the board on the stand and aline the heads of the nails with the station of the observing party. Next fit a narrow strip of paper to the front side of the forward nail, the strip
167
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CORPS OF ENGINEERS
projecting slightly above the nailhead. With a common mirror a few inches in diameter throw the reflected rays of the sun along the line of the nailheads. This will be accomplished when the shadow of the head of the rear nail falls on and exactly covers the head of the forward nail. The paper strip mentioned above enables one to make this exact contact. The center of the mirror should be held approximately in line with the nailheads to avoid eccentricity of the light shown the observer. If the direction to the observer is nearly opposite the direction to the sun. it may be necessary to use an auxiliary mirror to reflect the sun’s rays onto the mirror which is in line with the nails.
(4) When daytime observation between two stations is impeded by dense smoke, fog, or haze, signaling at night gives the best results. Electric signal lamps operated on dry cells are now used by the United States Coast and Geodetic Survey almost exclusively. Aside from the electric connections, only two adjustments are needed for the electric lamp, one for focus and the other for the sighting devices. The focusing adjustment is made by the screw socket into which the bulb fits. Since it frequently differs for different bulbs of the same apparent size, it should be made each time a new bulb is used. It is best done by directing the light upon a flat surface, such as a tarpaulin about 100 feet or more away, and varying the adjustment until the brightest part of the disk is but little larger than the lens of the lamp. After this has been done the sighting device should be adjusted to point exactly above the center of the brightest part of the illuminated surface and as far above it as the sighting tube is above the center of the lens of the lamp. As the transportation of the lamp from station to station is apt to disturb both of these adjustments, they should be tested before the lamp is posted at a new station.
(5) For azimuth shots around a mile, a flashlight bulb, after removing the lens and reflector, is suitable. The bulb is pointed toward the instrument and secured while plumb over the mark. If the light seems too bright at the shorter distances, some partially exhausted cells should be employed. If it is pointed exactly toward the instrument, a flashlight with lens and reflector may be observed at distances considerably over a mile.
i. Searchlight stations.—A truly vertical searchlight beam makes a fairly good substitute for a highpole signal, and can be observed over 20 miles with a telescope of large objective. These beams are excellent for intersecting crossroads from high towers in level, heavily wooded country. They can be used to advantage in resection. Past results indicate that they will not yield close enough figure closures for advancing even third-order work. Close to the front lines, they
168
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might afford the enemy the opportunity of obtaining intersection points in inaccessible territory.
j. Station marks.—(1) Stations of either first-, second-, or third-order accuracy on triangulation and traverse should be marked by tablets of some noncorrodible metal set firmly in posts of concrete or in large boulders or outcropping bedrock, but where a station is on a building suitable marks of a different character may be used. The tablets (see fig. 8) may be set in place by means of cement, sulphur, or lead. The Corps of Engineers survey control mark shown in figure 8 may be appropriately stenciled to serve as bench mark, triangulation or traverse station, or reference or azimuth mark. The concrete posts should be not less than 8 inches in diameter and should extend 30 inches below the surface of the ground. They should have the shape of a truncated prism or cone, in order that the lower end may be larger than the upper and thus better able to resist the lifting effect of frost action. For the same reason the post should be smoothly molded for the upper 10 or 12 inches of the part beneath the surface. Particular care should be taken to insure that the materials used in making the concrete are clean and well mixed. The top 12 or 15 inches of the post should be at least equivalent in strength to a 1-2-3 mixture of cement, sand, and stone; the base may be made of a somewhat leaner mixture. Where a boulder is used it should be at least as large as the concrete post prescribed and should extend to a similar depth beneath the surface. Where the tablet is to be set in bedrock care should be exercised in selecting rock that is of suitable durability, and also to make sure that what is apparently bedrock is not a small detached mass of rock.
(2) Special marks.— Under certain conditions special marks may be used. Where no larger boulder or bedrock is available at a station and where by its location it would be unduly expensive to construct a concrete mark, a metal pipe of suitable size and of noncorrodible material may be used. The base of this pipe should be so shaped as to resist extraction of the pipe and should preferably be set in concrete. In swamps a long metal pipe set inside a drain tile filled with hydraulic cement may be used. Where a station mark must be set on land subject to cultivation it is better to have the top of the post entirely below the depth which can be reached by a plow; that is, about 12 inches below the surface. Where a mark of this type is set it is necessary that measurements to the center of the roadways, section lines, blazed trees, corners of buildings, etc., be made in sufficient number to enable one seeking to recover the mark in the future to determine its location within a few feet. The mark itself can then be found by digging or by prodding with an iron rod.
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® Heliotrope, box type.
® Emergency heliotrope.
Figure 59.—Heliotropes and signal lamps.
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® Signal lamps.
Figure 59.—Heliotrope, and signal lamps—Continued.
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(3) Subsurface marks.- Where a concrete post is used, a subsurface mark should be set if possible. This mark should preferably be made of concrete, not less than 6 inches thick and 10 inches in diameter, with the station point marked by a metal tablet, copper bolt, or other durable substance. The subsurface mark should be 4 or 5 inches below the base of the concrete post, and extreme care must be taken that the subsurface mark is directly underneath the surface mark.
(4) The procedure in making the standard concrete mark is as follows: A hole is dug to a depth of 3% feet or more. It should be 16 inches in diameter for the first 2% feet, and 10 inches in diameter at the lower end. Concrete made of good cement, sand, and gravel or broken rock is placed in the lower part of the hole to a depth of 6 inches. A standard tablet station mark is then set in the concrete, with the top of the tablet slightly depressed. This completes the underground mark. A layer of from 4 to 6 inches of sand or dirt is then put into the hole. The hole is then enlarged about 2 inches in radius near the bottom in order that the lower end of the block of concrete for the surface mark will be mushroomed, and then the hole is filled with concrete to within 9 inches of the surface of the ground. Next a mold or frame 12 inches on a side at the top, 13 inches at the bottom, and 12 inches in depth is set in the hole on top of the concrete and filled in around the outside with dirt tamped firmly. The frame is then filled with concrete level with its top and a standard tablet station mark is set in the center of the concrete, with the top of the tablet slightly depressed. The tablet must be centered exactly over the underground mark. The top of the concrete should be smoothed with a trowel and the frame should be left in place to protect the concrete until it becomes firmly set. Care must be taken not to disturb the position of the tablet in the underground mark when placing the layer of sand or dirt and when pouring the concrete for the surface mark. A piece of thin board should be placed over the lower mark or other suitable means used to insure against any horizontal movement of the tablet due to the impact or pressure of the material above.
(5) Selection of names.—The name of a triangulation or traverse station should be stamped upon the metal tablet, preferably before it is set into the concrete or stone. The name should not be duplicated within the confines of a State if duplication can be avoided. Names for triangulation and traverse stations should have a geographic significance wherever possible. Care should be taken by the chief of party to ascertain the name which is most prevalent for a particular geographic feature, for frequently a mountain or stream will have
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different names in the same region. Station names should be short, for it is important that the same name be used for the same station throughout the records and computations.
(6) As an aid to a reconnaissance party in the recovery of established stations from the United States Coast and Geodetic Survey descriptions, their standard notes (extract from pages 112-114, Special Publication No. 145) on the marking of stations are given below. Their descriptions do not describe the marking used at a station but simply give the numbers of the standard notes which describe the station, underground, reference, and witness marks. The notes were made as genera] as possible in order that it might not be necessary in the field to describe small and unimportant variations.
DEPARTMENT OF COMMERCE
U. S. Coast and Geodetic Survey, 1929
MANUAL OF SECOND AND THIRD ORDER TRIANGULATION AND TRAVERSE” (If a later edition is available it should be used instead)
Surface marks
Note 1.—A standard disk triangulation station mark set in the top of (a) a square block or post of concrete, (b) a concrete cylinder, (c) an irregular mass of concrete.
Note 2.—A standard disk triangulation station mark wedged in a drill hole in outcropping bedrock (a) and surrounded by a triangle chiseled in the rock, (b) and surrounded by a circle chiseled in the rock, (c) at the intersection of two lines chiseled in the rock.
Note 3.—A standard disk triangulation station mark set in concrete in a depression in outcropping bedrock.
Note 4.—A standard disk triangulation station mark wedged in a drill hole in a bowlder.
Note 5.—A standard disk triangulation station mark set in concrete in a depression in a bowlder.
Note 6.—A standard disk triangulation station mark set in concrete at the center of the top of a tile (a) which is embedded in the ground, (b) which is surrounded by a mass of concrete, (c) which is fastened by means of concrete to the upper end of a long wooden pile driven into the marsh, (d) which is set in a block of concrete and projects from 12 to 20 inches above the block.
Underground marks
Note 7.—A block of concrete 3 feet below the ground containing at the center of its upper surface (a) a standard disk triangulation station mark, (b) a copper bolt projecting slightly above the concrete, (c) an iron nail with the point projecting above the concrete, (d) a glass bottle with the neck projecting a little above the concrete, (e) an earthenware jug with the mouth projecting a little above the concrete.
Note 8.—In bedrock (a) a standard disk triangulation station mark wedged in a drill hole, (b) a standard disk triangulation station mark set in concrete in a
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depression, (c) a copper bolt set in cement in a drill hole or depression, (d) an iron spike set point up in cement in a drill hole or depression.
Note 9.—In a bowlder 3 feet below the ground (a) a standard disk triangulation station mark wedged in a drill hole, (6) a standard disk triangulation station mark set in concrete in a depression, (c) a copper bolt set with cement in a drill hole or depression, (d) an iron spike set with cement in a drill hole or depression.
Note 10.—Embedded in earth 3 feet below the surface of the ground (a) a bottle in an upright position, (b) an earthenware jug in an upright position, (c) a brick in a horizontal position with a drill hole in its upper surface.
Reference marks
Note 11.—A standard disk reference mark with the arrow pointing toward the station set at the center of the top of (a) a square block or post of concrete, (6) a concrete cylinder, (c) an irregular mass of concrete.
Note 12.—A standard disk reference mark with the arrow pointing toward the station (a) wedged in a drill hole in outcropping bedrock, (6) set in concrete in a depression in outcropping bedrock, (c) wedged in a drill hole in a bowlder, (d) set in concrete in a depression in a bowlder.
Note 13.—A standard disk reference mark with the arrow pointing toward the station, set in concrete at the center of the top of a tile (a) which is embedded in the ground, (b) which is surrounded by a mass of concrete, (c) which is fastened by means of concrete to the upper end of a long wooden pile driven into the marsh, (d) which is set in a block of concrete and projects from 12 to 20 inches above the block.
Note 14-—A conical mound of earth surrounded by a circular trench.
Note 15.—A tree marked with (a) a triangular blaze with a nail at the center and each apex of the triangle, (b) a square blaze with a nail at the center and each corner of the square, (c) a blaze with a standard disk reference mark set at its center into the tree.
k. Reference marks.—At least one and preferably two reference marks should be set at each station. They should be metal tablets set in concrete posts, boulders, or bedrock. The metal tablets used for the reference marks should have a different inscription upon them than the station tablets and preferably should bear an arrow pointing toward the station. Where more than one reference mark is used at a station, they should be stamped and numbered serially, clockwise as viewed from the station. Particular care should be taken in selecting sites for these reference marks where they will not be subject to disturbance. Fence lines or section lines are suitable sites. The azimuths and distances from the station mark are accurately determined. Witness marks are used primarily to recover the general locality of a station. They may be indefinite, such as a stream junction, fence corner, blaze on tree, etc. The distances and directions to witness marks need be only moderately accurate.
I. Azimuth marks.—At each station where a high or low tower is needed to enable the observer to see the adjacent stations of the scheme an azimuth mark should be established. This mark should
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be placed over 1,000 feet away, at some point visible from an instrument mounted on an ordinary tripod set on the ground over the mark. An engineer recovering the station will then not only have a geographic position but will be able to obtain an azimuth as well. The azimuth mark should be of the same size and character as a reference mark. Azimuths should also be obtained to several other objects, such as water tanks, stacks, and church spires if they are in view from the ground.
m. Intersection stations (see par. 107d) are of two kinds—features of the terrain, such as towers, finials, flagpoles, sharp peaks, etc.; and ground stations, which have to be monumented. For the latter, a pole signal or flag has to be erected plumb over the station mark. The terrain features are preferable, as no mark or signal has to be constructed, and the object remains in view long after the triangulation party has moved on. It is essential that the records of observations on any intersection station from several occupied stations should have the name of the intersection station exactly the same. For example, in case of a church spire, the name and denomination of the church should be given. Either the reconnaissance or erection party should measure accurately and report the vertical distance from the top of an intersection station to the ground, as such stations need not be visited by the observation party.
n. Description of station.-—(1) The description furnished by the reconnaissance party contains all information needed for construction such as route, exact location, height of signal, necessary clearing, etc. and also any items which might be useful during observation. The construction party adds the details and measurements of the station and other marks and pertinent items. The observation party checks the description, makes necessary changes, and adds the prescribed distances and directions to reference and azimuth marks, etc., using a main scheme station as the initial direction (par. 108). As soon as the above data have been obtained, form 4, Description of Station (fig. 60), is prepared, forwarded to, and filed at the headquarters of the organization making the survey. A copy should be retained for field use.
(2) The purpose of the description is to enable one who is unfamiliar with the locality to find the exact point determined as the station, and to know positively that he has found it. The essential information which should be included in a description is as follows:
(a) Locality (general and particular).
(6) Flow marked.
(c) Distances (by tape) and directions (by theodolite) from center of station to reference and witness marks.
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(3) If a feature of the terrain is intersected, and the name is sufficiently descriptive (see m above), no further description need be furnished. However, the “Description of Station” should be filled out showing the elevation of the top and the elevation of the ground or station mark, if any.
(4) Where search is made for a triangulation or traverse station established in a previous year, a note to that effect must be entered on an appropriate form. If the station is found, the recovery note should state the condition in which the mark was found and should give any modifications or additions to the description which would make the station more easily found in the future. If the station is not found, the note should indicate the thoroughness of the search made and give recommendations as to whether or not the station should be marked “lost” in the records.
(5) Report of recovery of any Federal survey mark.—Member organizations of the Board of Surveys and Maps should instruct their field officers to report upon the condition of station and bench marks visited by them which were established by another member organization. If a properly equipped field party of a member organization finds in poor condition a Federal triangulation or traverse station mark of a third or higher order of accuracy and if its proper location can be determined with certainty and accuracy, either by a recovered underground mark or by measurements from two or more reference marks, the party should re-mark the station if practicable. If the tablet marking the original station is recovered, it should be reset. If an underground mark exists, due care must be exercised to insure that the new surface mark is exactly centered over the subsurface mark.
o. Grid triangulation, special methods.—(1) Those who are concerned with grid triangulation should be thoroughly familiar with the specifications and methods of executing triangulation of higher accuracy, which are designed for extending more precise control over considerable distances. Grid triangulation is intended only for the most rapid fulfilment of two urgent needs as follows:
(a) To establish horizontal and vertical control which will aid in the preparation or revision of battle maps. (See sec. XIX, TM 5-230.)
(5) To furnish control for the combat troops, more particularly for the Field Artillery, who have their own survey organizations, whose duties include the adaptation of the grid triangulation data to the needs of the firing batteries and the Field Artillery intelligence service. Echelons of the Engineer survey organization should cooperate with the Field Artillery whenever practicable without neglecting other assigned missions.
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3 i—6 <3
pu. SlA^- <3-^. aj-c-u-cCa- aV If. N°^AM i a
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FORM 4
Figure 60.—Description of station.
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262341°—40------12
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(2) Reconnaissance for grid triangulation is a specialty requiring continual practice over varied terrain. The deliberate triangulator can reconnoiter the ground, select stations, and erect signals before he starts observing. The grid triangulators have to try to fix points in inaccessible territory and to prepare for the rapid extension of their system with the advancing forces. The solution of map and terrain problems without troops is helpful. Most valuable of all arc practical exercises and maneuvers in which control schemes are actually worked out and rapidly extended as the combat units move forward. The survey troops should receive notice of such problems early enough to permit the collection of data and the establishment of stations in the concentration area. This provision is entirely justified, as reconnaissance proceeds continuously in actual operations.
(3) Some stations must be marked before observations are begun. Time permitting, the reconnaissance should be conducted with a plane table, rays being drawn from each station to several likely points where other stations might be located. As each station is marked, the lines to be observed from it are drawn in. If time is too short for the above procedure, the tentative positions of the stations are marked on a map or diagram, and the lines drawn in as they are found to be feasible. However brief the reconnaissance, each station to be occupied must be visited to make sure that the points to be observed from it are visible from the height of the instrument. In suitable terrain, several observers may accompany the reconnaissance and begin observing the first triangle as soon as a few stations have been selected. To avoid confusion each net or series of grid triangulation stations may be assigned a letter, and each station name composed of the sign for grid triangulation station (V) the number of the organization, the letter designating that particular system of stations, and the number as established in that series, thus: V64D12. At the conclusion of the reconnaissance definite orders should be made out for the observers, as described in paragraph 113e. A diagram of the scheme is furnished the computing section so that their work may be started on receipt of the first data from the field.
(4) Grid triangulation must be executed so rapidly that clearing is limited to a small amount of brush-cutting at the station site, and not even low towers can be built. The sights should not average under 2 or 3 miles in length or observing will take too long. All considerations emphasize the importance of skill in reconnaissance. The simple triangles are easier to locate than any figure having more lines of sight, and other requirements are reduced in order to speed the progress. Occasionally some form of intersection or resection may
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have to be used in advancing. In such cases a check must be made on other work in order to detect possible gross errors. Frequently the signal will be a flagged pole above a house or tree, necessitating an eccentric station for the instrument. The reduction to center (par. 109) is quite simple, provided the eccentricity is minimized, and the record shows its amount and direction so clearly that misinterpretation is impossible. Ideally, all stations should be located at picture points (see sec. XXVII), on the highest ground in the vicinity, convenient for Field Artillery use, but away from command or observation posts and defensive works, and should be in a position protected from traffic of any sort. While choosing the exact spot for the station mark, consideration should be given the utilization of any station mark already established in the vicinity. Confusion may thus be avoided, and a valuable tie to other work may be made. Two witness marks should be blazed, or witness stakes 3 inches out of ground should be set for each station and the direction and distance to nearest tenth of foot recorded.
(5) Concrete monuments will not be established by grid triangulation. A 3-inch stake, 30 inches long, may be used in an emergency. All station marks should be driven flush with the ground, no matter how sheltered, and a substantial guard stake, 6 inches out of ground, will be driven 1 foot away from the station. A 1-inch pipe, 30 inches long and pointed at one end, would be the most suitable station mark. If the troops disturb the driven pipes, 2-inch pipes with two /(-inch steel rods, each 1 foot long, inserted at right angles through holes drilled through the pipe near the bottoms will be more difficult to extract, if the earth is well tamped over the rods. The use of pipes is advised as a piece of 1- or )(-inch round electric conduit, with alternate feet painted black and white, with a small flag or red and white panel fastened to the top through small drilled holes, would make a good signal if the conduit were secured in a vertical position with several wooden wedges at the rim of the pipe (fig. 58®).
(6) Perhaps the best type of signal for grid triangulation would be a quadrupod or tripod (fig. 58® and @) which permits observing at the station without disturbing the signal, but even a light frame would require lumber and a carrying party. A fairly high guyed pole might have to be used in some cases. Flag poles on buildings or in trees should be fastened in a truly vertical position. In grid triangulation all elevations are deduced from vertical angles. Any party erecting a signal or flag must measure and report the vertical distance to the nearest tenth of a foot from the ground to the top, and to any other part on which a vertical angle might be observed. Should a
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signal have to be lowered during observation, the adjacent observers may point at the instrument if the recorder and others keep out of the way. Night observations are easily made and give good accuracy if the light tenders are well trained.
(7) Reconnaissance never ceases. Before the observations for one net are completed, preparations must be under way to move on. In war, the most forward stations have to be located out of enemy view, often so situated as to make forward extension impracticable. Larger signals should be prepared for several of the rear stations located on high ground so that they may be quickly erected as the advance begins, and resected on from the new stations which become available in the forward areas. One or two observers might remain in rear long enough to observe on the new signals and so simplify the computations and minimize the possibility of error.
(8) The Field Artillery will need new grid triangulation points as they move into new positions. Every effort must be made to press the fringe of advance intersection points further into inaccessible territory. If the advance should develop so rapidly that the grid triangulation lags, one or two observers may be assigned to carry an azimuth forward with the artillery, as it is highly important that they know grid azimuth on going into position. To assume an azimuth (par. 137) necessitates great delay and labor in converting all of the data to the correct grid azimuth. With the proper azimuth from the start, the coordinates may be corrected by simple addition or subtraction. Astronomic azimuths are quickly obtained, weather permitting, but unfavorable conditions have to be expected.
(9) The engineer survey troops should maintain liaison with similar organizations in their own sector and on the flanks. Frequent ties help to keep all of the engineer surveys on a common datum.
Section XVI
CHECKING METHODS—TRIANGULATION DATA
Paragraph
General_______________________________________________________________ __ 99
Closing on measured or established bases___________________________________ 100
Triangle closures__________________________________________________________ 101
Horizontal angles. ________________________________________________________ 102
Checks in grid triangulation_______________________________________________ 103
99. General.—a. Though triangulation is the preferred method of establishing control, there are sources of large and small errors, almost too numerous to mention, including—-
(1) Base line not accurate.
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(2) Basic data erroneous.
(3) Established station not truly recovered.
(4) Poorly conditioned figures.
(5) Too many figures between cheeks.
(6) Signal not centered over station mark.
(7) Instrument not plumbed over mark.
(8) Poor condition of instrument.
(9) Rough handling of instrument.
(10) Instability of instrument support.
(11) Too much sun or wind on instrument.
(12) Instrument unsuited for program of observation.
(13) Parallax of cross hairs.
(14) Plate levels out of adjustment.
(15) Failure to turn tangent screws against the springs.
(16) Too much time between pointings.
(17) Too few observations for the accuracy sought.
(18) Poor visibility.
(19) Observing on false station.
(20) Careless bisection of target.
(21) Lateral refraction.
(22) Crooked signal poles.
(23) “Phase” of target.
(24) Errors in reading micrometers or verniers.
(25) Partiality to previous readings or to expected results.
(26) Mistakes in recording.
(27) Unjustifiable alteration of notes.
b. Remedies for many of the above items are obvious. Some of them are governed by the order of accuracy which is prescribed. Others are difficult to detect or recognize even when the results are materially affected. Increasing the number of observations might reduce the effect of some conditions but could not correct an error in centering over the mark, or faulty bisection of the target due to the imperfect construction or design of the latter, etc. Prevention of error, resulting from constant care and attention to detail, makes possible maximum speed in obtaining triangulation data of the required accuracy with the minimum of men, material, and equipment. Strict compliance with instructions, the employment of standard methods, and the formation of orderly habits in every procedure will limit the amount of work which has to be repeated. The persistent elimination of conditions likely to cause errors will make their occurrence so rare that the causes can be isolated and remedied as soon as the effects become apparent.
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100. Closing on measured or established bases.—The principal criterion in classifying the accuracy of a triangulation system is that the discrepancy between the measured length of a base line and its length as computed through the scheme from the next preceding base, after the usual adjustment of the angles and sides, shall not exceed the small ratios given in paragraph 92a for each order of accuracy. The word “base” implies either a base line measured to the proper order of accuracy as described in section XVII, or a monumented line of previously adjusted triangulation of an equal or higher order of accuracy.
101. Triangle closures.—Coupled with the above gage of the length agreement on bases and almost coordinate in importance are the requirements limiting the error of angle measurements, for the limits imposed on angular errors serve to maintain a uniform accuracy along the chain of triangles. The triangle closures allowed for each of the orders in paragraphs 92a are the amounts the sums of the three angles (mean values after deduction of spherical excess, if any) may differ from 180°. As soon as observations have been completed at the three corners of a triangle, this check is applied. The difference should usually be much less than the maximum so that the average of all triangle closures in the scheme will be within the prescribed limit. In order to maintain the required accuracy through an extensive system, the specifications make use of other criteria, such as the number and strength of the geometrical figures between adjacent bases, the observation of an astronomic azimuth at specified intervals, and the accuracy of measurement of base lines. In the triangulation generally executed by the Army, keeping the distance angles over 30° and securing average triangle closures within the prescribed allowance of error should bring about the requisite agreement of the computed lines with the measured bases, or lines previously established. Thus it is that triangle closure is the first and only reliable check which can be applied during the observations. Any unusual differences, or upward trend of the average error of closure, should be at once investigated and corrective measures applied. To insure that the necessary accuracy is maintained throughout the triangulation, it is essential to give careful consideration to the instrumental equipment and the methods of observing, in order that the systematic and accidental errors may be kept within the prescribed limits and that no part of the system will exhibit undue weakness.
102. Horizontal angles.—a. Agreement.—The close agreement of different measurements of an angle is not a check on the triangulation. In the direction method (par. 1075) any readings which give values materially different from the other values for the same line indicate
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errors in pointing or reading, but uniform results are no proof that the system will finally close. With the repetition method (par. 107c) close agreement between the first angle and the mean of the set, between the two halves of the set, or between sets of the same angle is no assurance that the triangles adjacent to the station will have good closures. Even the horizon closure, the difference of the sum of all the mean angles at a station from the correct 360°, is no check to prove that the angles are correct. A difference more than that allowed for a single triangle might indicate some sort of error, but an exact horizon closure of 360° might be made without a single angle’s being close to its correct value.
b. Astronomical azimuth checks.—These should be made between bases of extensive systems in order to detect any “swing” or deviation from true aximuth. See paragraph 92a for the allowable probable error of the check azimuth. The observations for second and third order are usually made on Polaris at any hour (par. 177), making about 50 percent more observations than would ordinarily be taken on triangulation with the same class of instrument. The observed value is not corrected for the deflection of the vertical before being used in the adjustment of the triangulation. In regions with no high mountains and no great differences in the density of the nearby subsurface geological structures, the error in the observed azimuth due to the deviation of the plumb line will not usually exceed 1 or 2 seconds of arc, but in other regions may reach several times that amount.
103. Checks in grid triangulation.—Under peace conditions such checks are similar to those for the higher orders, but with the larger allowances given in paragraph 92a. Such practice is good training, as the relative speed and accuracy of the various methods may be tested by frequent closures on more accurate work. In maneuver and war, the work must bo pressed forward so rapidly that little time can be spent on cheeks. Usually the grid triangulation will be somewhat ahead of the main triangulation, and the data must be published as soon as obtained. Circumstances will seldom be favorable for check base measurement, even by the short base methods. Advancing through a double chain of triangles, or ties with colateral chains might afford a check or merely show a disagreement. During lulls in the advance, and whenever personnel can be spared from more urgent work, provision must be made for checks. Every opportunity must be made for securing intersections on conspicuous features on high ground everywhere they may be found, in inaccessible territory, on both flanks and in the rear. Especially favorable points which are
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out of enemy view should be provided with better signals than are needed for the immediate purpose. If all of the observers are trained to observe on and describe such prominent marks as can be identified, checks by resection and intersection should be obtained at such intervals that check base measurement becomes unnecessary.
Section XVII
BASE LINES
Paragraph
Types of base lines________________________________________ 104
Base lines with invar tapes___________________________________________________________ 105
Base lines with steel tapes___________________________________________________________ 106
104. Types of base lines.—a. General.—The measurement of an accurate base may occasionally become necessary. Base lines for triangulation of the first and second orders should be measured with a ' probable error (see par. 105d(12)) not greater than one part in
500,000, instead of 1,000,000 as shown in paragraph 92a. For military purposes, the gain in accuracy is not worth the additional time spent in securing the lower limit. Special Publication No. 145 of the United States Coast and Geodetic Survey gives complete details and some special tables, which are not included in TM 5-236.
b. Base lines with invar tapes.-—The same methods are used in measuring second- and third-order bases, and the precautions against error are the same. The only differences are in the permissible errors. The allowances mentioned in paragraph 105 are for third-order accuracy. Invar tapes (“invar” from invariable) are made of an alloy of nickel and steel, characterized by a coefficient of expansion which is one-tenth or less that of steel. This low coefficient is of great advantage as temperatures of the tape are difficult to obtain exactly. If steel tapes have to be used for this class of work, the measurements should be made either at night, or when the sky is heavily overcast. An invar tape should not be reeled or unreeled rapidly or under a heavy tension, or wound upon a reel having a small diameter, or dragged over the ground, or shaken violently, or stretched beyond its yielding point, nor should it be subjected to sudden large changes in temperature. When reeling an invar tape, the marked side should be inside or outside, whichever it was originally. Kinking a tape may render it useless as a precise measuring instrument for whether the tape is allowed to remain kinked or is straightened, its effective length will be different from its previous standardized length. In fact, invar tapes require such good care that they are not used for third-order traverses and such purposes.
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1
Strips, copper, for stake tops, of same thickness as tape, 20 per kilometer.
tape, steel, 30-meter (standardized or tested in field), for measuring set-ups and set-backs, tape, steel or invar. 50-meter unstandardized, for marking out base.
3 tapes, invar, 50-meter, standardized.
1 theodolite.
3 thermometers, backed, for tapes.
1
c. The base lines with steel tapes (par. 106) are of much higher probable error, as the special equipment employed with the invar tapes will not be available. However these steel tape bases are intended only for grid triangulation.
105. Base lines with invar tapes (third order).—a. Apparatus.— (1) The following instruments and appliances will be useful:
2 awls, marking. 2 dividers, pairs. 1 level, with rod. 2 plumb bobs. 2 range poles.
2 scales, one-tenth meter, boxwood, reading to millimeters.
1 stretcher apparatus for tape, complete, consisting of two staves with loops and tape attaching clips, two balances, and an apparatus for testing balances.
Tools for staking line, as follows: hammer, hatchet, hand saw, 2 mauls, 2 machetes, lOd nails, posts and stakes, and movable tripods or chaining bucks if ground is so rocky that stakes cannot be driven.
(2) All new invar tapes should be calibrated at the United States Bureau of Standards, and a copy of the certificate should be issued with the tape. As the length of an invar tape seems to change in course of time, one of them should be sent each year to the Bureau of Standards for recalibration. The Bureau certificate states the absolute length of the tape under standard conditions of temperature, tension, and support, in addition to the coefficient of expansion per degree centigrade, and the weight in grams per meter. Great care must be exercised to use a tape under the conditions of tension and support for which its standardization equations are given. One of the three tapes is used exclusively as a reference tape with which the two field tapes are compared both before and after measuring each base (d(3) and (4) below). The base should be measured in sections about 1 kilometer in length, with the exception of one section which may be longer or shorter than this. Each section should be measured at least twice, one measurement being made forward, and the other backward. If the discrepancy in millimeters between two measurements of a section exceeds (where K is the length of the section in kilometers), additional measurements of that section should be made until two values made in
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opposite directions are secured which agree within this limit. The two field tapes will be alternated in use.
(3) Tape-stretching apparatus is shown in figure 61. It consists essentially of two staves of steel tubing, pointed at the bottom and with wooden tops. A loose-fitting leather loop with an attachment to receive the looped end of the tape slips over the staff used at the rear end of the tape. The leather loop can be easily slipped up and down on the staff according to the height of the rear stake. A frame for holding the spring balance is attached to the forward staff by means of a spring friction grip. The tape is fastened to the balance by the attachment shown. There is a finger bar by which the forward contact man carries the end of the tape when moving forward.
Figure 61.—Tape stretcher and spring balance.
(4) The spring balance is also shown in figure 61. The counterpoise shown in the figure may be so adjusted as to prevent any drag of the frame of the balance on the drawbar when tension is applied. Errors in base measurements have frequently been due to spring balances which do not read correctly. For this reason a testing apparatus for the spring balances is sent with the balances. This should be used in testing before and after each day’s work. The form of tester is usually a weight which is applied to the balance held vertically, after which the pointer is adjusted exactly to 15 kilograms. When this is done the balance will indicate true tensions when it is used in a horizontal position. In other words, the weight is of 15 kilograms mass, as weighed by the spring of the balance at the Bureau of Standards, minus the weight of the drawbar and other movable parts of balance below the spring. The most common injury to a spring balance used on base measurement results from the tension being suddenly released,
186
Staff-
Counterpoise
Spring Balance
Friction Grips
K -----
xFmger Bar of Tape Clip
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allowing the drawbar to snap back. This may change the position of the dial pointer by several hundred grams and even result in injury to the spring. For this reason the tension on the tape should always be released gradually. If through accident the drawbar of the balance is allowed to snap back, the balance should be tested before measuring is resumed.
(5) Thermometers.-—These are special and rather expensive thermometers, correct to within 0.5° C., within the ordinary range of temperature. They are tested at the Bureau of Standards before being sent to the field. Field computations need not take into account the graduation errors of the thermometers found by the standardization. The glass tube is supported in a metal holder to prevent the breaking of the tube when the tape is being handled or flexed. During standardization a thermometer of the type described above is fastened at each end of the tape, at a point 1 meter toward the center from the terminal mark, the distance being measured from the mark to the nearer end of the thermometer. On base measurement the thermometers should always be fastened in this same position by narrow bands of adhesive tape. When moving the tape, care will be taken to keep these thermometers on the upper side and thereby avoid getting any twist in the tape.
b. Preparation oj base.—(I) The first step is to clear the base line so that the ends will be intervisible and the work of making the measurements will not be impeded. All grass, weeds, and brush should be cut close to the ground so that there is no possibility of any touching the tape. Set up a transit at one end of the base and arrange pole at the other; also set intermediate range poles if necessary. Now drive 4- by 4-inch posts on the line accurately spaced 50 meters between centers. Before staking is begun, the extra tape used for spacing the posts should be compared with a standard tape, so that intervals may be correct and frequent set-ups or set-backs avoided. If a steel tape is used, it may save time to make an approximate allowance for the change in length due to temperature. The 25-meter point of the tape may be marked by a strip of adhesive tape to make it readily recognizable while staking. The tops of the posts should be not less than 10 inches nor more than 24 inches above the surface of the ground. Each post should be driven to a firm bearing. Halfway between posts drive a 2- by 4-inch stake offset from the line of sight so that the face of the stake nearest the line of sight will be about 1 inch from it. All stakes should be offset on the same side of the line of sight. Sighting along the tops of each two of the 50-meter posts, locate and drive a tenpenny nail horizontally into the face of the
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intermediate stake so that the nail will be on line with the tops of the posts. These nails serve as intermediate supports between the 50-meter posts during measurements. The tape is brought into position with its rear mark in contact with the mark on the base station or on the bench above it, and the proper tension is applied, with the edge of the tape touching the final alining mark on the forward stake. A copper strip is then nailed in position flush alongside the tape on the alining side, and at the same time a pencil mark is made on the top of the stake opposite the forward mark on the tape. This mark is used as a rear contact mark in setting the stakes for the next tape length. The tape is then moved forward and the process repeated. All posts at kilometer ends should be braced. If for any reason the intermediate support between the tape ends cannot be placed so it will be
Figure 62.—Chaining bucks.
down to grade with the terminal posts, it should be numbered with colored chalk and marked with a piece of cloth so it may be noticed and touched upon by the levelman. All stakes are numbered with colored crayon as they are driven, and intermediate supports above grade should be given a fractional number. An intermediate support which is not on grade makes what is known as a broken grade. At ravines or streams it is frequently necessary to place a stake on the edge of the bank and begin a tape length from that point. If it is less than half a tape length from the previous tape-end post, the number of which, for instance, is 34, the fractional-length post should be numbered “34 set-up”, the next terminal post being numbered 35. If the fractional-length post is more than half a tape length from the next preceding tape-end post, a 2- by 4-inch stake should be driven in at the half-tape mark and be given the number 34%, and the post on the edge of the obstruction should bo numbered “34% set-up.” By
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following this system there will be no uncertainty in the interpretation of records. Where the ground is so rocky that stakes cannot be driven, “chaining bucks” may have to be utilized. See figure 62.
(2) Base and monuments.—The concrete monuments at the ends of the base have their copper hubs hair-lined in the direction of the base and at right angles thereto, accurately marking the base-end points. If the permanent mark at an angle station is low, a bench should be built over it and a scratch made on a copper strip fastened to the bench directly over the station mark to which the measurements may be made.
c. Procedure for measurement.—(1) When prepared to begin the actual measurement of the base, check the alinement of the stakes by means of the engineer transit and range poles. If any of the stakes are out of line, aline them before proceeding further. Next a line of levels should be run over the line to determine the relative elevations of all 50-meter posts and broken grade stakes. (See fig. 64.) x
(2) Organization of party.—Six men are ordinarily required, as follows:
Front contact man.
Rear contact man.
Recorder.
Front stretcher man.
Rear stretcher man.
Middle man.
The chief of party makes the forward contact unless there is another experienced front contact man, in which case the chief may act as recorder. If any of the men are inexperienced, it is better to measure 1 or 2 practice kilometers before the recorded measurements are begun.
(3) Method of measuring.—(a) The middle man carries the middle of the tape high off the ground when moving forward, places the tape on the middle support when the tension is to be applied, sees that the tape is not in contact with weeds, brush, or other obstructions, notifies the recorder of all middle supports marked “broken grade,” carries and places the tape so that there is no twist in it, and each time makes sure that the middle support is not more than 10 centimeters distant from the middle mark on the tape. If a nail is used as a middle support for the tape, he must rapidly and lightly tap the under side of the tape near the support with a stick somewhat larger than a pencil until the front contact man calls, “Ready,” in order to lessen the friction over the nail.
189
(&) The rear stretcher man (fig. 63) with the rear tape stretcher holds the tape in position during the time the tension is on, so that the rear terminal mark on the tape is opposite to, or slightly forward of, the mark on the copper strip on the rear stake. As he comes up to the rear stake he must place the rear staff firmly in the ground at the proper distance back of the rear stake directly in line with the stakes, and at the same time he must slip the leather loop bearing the tape link to the proper height on the staff so that when the full tension is applied the tape will be a few millimeters above the top of the stake. The tape must not drag over the top of the stake at any time. In order to maintain a steady position of the staff, the rear stretcher man should have the top of the staff back of one of his shoulders, his body being forward of the staff. As soon as the front
Figure 63.—Making contact with tape, rear end.
contact man calls, “Mark,” and the thermometers are read, the tension is slackened off. The tape is then carried forward without being detached from the rear stretcher, the rear stretcher man maintaining just enough tension on the tape to keep it from touching the ground.
(c) The front stretcher man applies the proper tension to the tape as measured by the spring balance attached to the front stretcher. In moving forward he carries the front stretcher and balance detached from the tape. As the tape is brought forward into position the front stretcher man with one hand holds the balance out horizontally with the hook in such position that the tape can be quickly attached. As the tape is attached he places the staff in line with the stakes at the proper distance from the front stake and applies the tension smoothly, rapidly at first, but gradually more slowly as the 15-kilogram point is neared. Jerking motions must be avoided as they may injure the balance or tape. With the staff held in the same manner as described
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for the rear stretcher man, and with one hand steadying the balance so the drawbar swings free, the front stretcher man can quickly bring the tape into equilibrium under the proper tension, at which time he informs the front contact man that the tension is correct. When under tension the tape must just clear the top of the forward stake and must not drag over it, otherwise the full tension will not be transmitted throughout the tape. Care must be taken that the stretcher staff is moved in the vertical plane through the stakes, for otherwise the balance will be twisted and friction exerted on the drawbar. The tension must be kept constant at 15 kilograms and watched closely, for if the dial pointer indicates more than 100 grams from 15 kilograms when the front contact man calls, “Mark,” the front stretcher man should immediately tell the front contact man in order that the marking may be repeated. If the tension is satisfactory at the call of “mark”, the tension is quickly but smoothly slackened off while the front contact man is reading the forward thermometer, the balance is held out for the detachment of the tape by the front contact man in the same manner as for its attachment, and the advance begun to the next position.
(cZ) The recorder should be an experienced man. If he is not, the chief of party must frequently inspect the record, especially where broken grades or set-ups and set-backs are to be recorded. It is the duty of the recorder to be sure that no blunders are committed, such as the dropping or adding of a tape length, or recording a half tape length as a full one, or a set-up as a set-back. He should check the chalked numbers on each stake as it is reached and make all notes necessary to a definite and correct interpretation of the record.
(e) The rear contact man (fig. 63) makes the rear contact and reads the rear thermometer. As the tape is brought up to a new position he steadies the tape as the rear staff is being placed in position and the tension applied, taking care that the tape does not drag over the rear stake. As the tension is applied he advises the rear stretcher man whether to ease off or take up on the tape. Standing directly opposite the mark on the copper strip nailed to the top of the stake, with one hand he firmly grasps the tape between the staff and the mark and with the other hand he lightly touches the tape on the opposite side of the stake to steady it. He can then flex the tape with his rearward hand and bring exactly opposite each other the marks on the tape and copper strip. Before flexing the tape it is necessary, of course, that the mark on it shall be slightly forward of the mark on the strip. The marks are thus held in coincidence until the front contact man calls, “Ready,” when the rear contact man calls, “Right,” and the front
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contact man answers, “Mark,” denoting the completion of the marking of the tape length. Immediately following the call, “Mark,” the rear contact man reads the rear thermometer and the tape moves forward to the next position, unless someone at the forward end of the tape calls, “Hold,” or “Tension.”
(f) The front contact man must decide when all the conditions which affect the tape as a measuring unit are complied with, satisfying himself that the tape is in proper equilibrium under proper tension and support before he makes the forward mark. He also carries the forward end of the tape when moving forward and thus to a large extent sets the pace for the entire operation. The sequence of his movements during the measurement of a single tape length is as follows: As the forward stake is reached he lowers the front end of the tape from its position above his shoulder and attaches the link to the hook of the balance, grasping and guiding the hook to make sure that the attachment is made with a single movement. He then steps quickly back to a position alongside the forward stake, where he steadies the tape into its proper position just clear of the top of the stake, alongside the copper strip and between him and the strip. As the tension is perfected and the tape approaches equilibrium he places the point of the sharp, symmetrically pointed awl on the edge of the copper strip next to the tape and keeps it opposite the terminal mark on the tape until he is satisfied that conditions are right. After glancing at the balance to check the tension and down the tape to check the alignment he calls, “Ready,” as above described. When he hears the response, “Right,” from the rear contact man, he marks the copper strip with the awl, calling, “Mark,” as the marking is completed. In making the mark several precautions must be taken. The awl must be very sharp; it should at no time touch the tape in the region of the terminal mark; the eye of the man making the forward contact, the terminal mark of the tape, and the axis of the awl should be kept in approximately the same vertical plane; and the mark should be made by the contact man’s moving the awl away from him in order to keep constant any error due to parallax. The mark should begin at the very edge of the copper strip in order to make it easier for the rear contact man to make contact. Immediately following his call of “Mark” the front contact man reads the forward thermometer as the tension is released, then detaches the front tape link from the balance as he starts to pull the tape forward to the next position. If the tape is always carried in the hand which is toward the rear when making the contact, there is no danger of causing a half twist in the tape, for when detaching the tape from the balance
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the finger clip is caught in the rear hand, fingers pointing down, then the end of the tape is elevated above the shoulder without changing the grip, and at the next position is again attached with the hands in the same relative position.
0) Sometimes it will happen that when the tape is advanced 50 meters its forward end will fall short of the next metal strip. When this occurs, make a scratch on the rear metal strip as close as possible to its forward end and make the rear contact there. Then measure with a pair of dividers and millimeter scale the distance between the two scratches on the rear metal strip and add this to the length of the base line. This operation is known as setting forward. The opposite condition obtains when the forward graduation overshoots its post when a set-back becomes necessary. The set-backs and set-ups should be recorded in special columns and their algebraic sum (set-backs are minus) should be added to the length of the base line. Small set-ups and set-backs should be measured with an error not greater than 0.1 or 0.2 millimeter. As an additional safeguard the recorder may check the measurement of set-ups and set-backs and have the contact man in turn check his entry in the record book.
(Ji) Upon arriving at the end of the base, if the distance from the last 50-meter stake is less than 25 meters, measure this distance by means of the steel tape. If the distance is greater than 25 meters, proceed as follows: Determine approximately the 25-meter point on the 50-meter tape and mark it on the tape; place a stake approximately 25 meters from the last 50-meter stake, aline it, and nail a copper strip on it. Now stretch the 50-meter tape and mark on the strip the point where this approximate 25-meter point comes. Then reverse the tape end for end and mark where the 25-meter point comes again. If the distance between the two approximate 25-meter points is then bisected, the resulting point will be 25 meters from the last 50-meter stake regardless of the accuracy with which the 50-meter tape was bisected. The distance forward from this 25-meter point to the end of the base may then be measured with the steel tape. Setbacks of more than 10 centimeters should never be used. This method will avoid in large measure the possibility of a large error in length due to an error in the sign of a partial tape length distance on both measurements. Some base tapes have marks at approximately 5-meter intervals along the tapes, the lengths of the intermediate intervals having been determined with secondary accuracy. Where such tapes are available long set-ups are sometimes so staked as to enable the invar tape to be used for the greater part of the set-up— that is, for some multiple of 5 meters, the remainder of the set-up being measured with a standardized steel tape.
262341°—40--13 193
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(i) In order to avoid confusion, the marks placed on the copper strips during the second measurement are usually distinguished from the first markings by a bar across the scratch, while a third measurement would have a second bar. On the first measurement of each kilometer section the end mark of the section is given a distinguishing mark on the copper strip. On the second measurement, as the stake marking the end of each section is reached, a set-up or set-back is taken to the original section mark on the strip, and the measurement
r LEVELING FOR EASE L From Z E Base to T.E. 2C Forward INE Back- Obs Sgt R Roe Rec Opt T Crane Inst Berger Dumpy ward Ju/y5J/924-2PM. Clear and ho! (n\ "8923 Gent/e breeze \~z
POST B.S Meters Meters DtFF Meters DIFF Feet B. 5. Feet E5f DIFF.' Feet DISTANCE Meters MEA/J.D/FF Feet fNCUN CORA mm ELEV. Feet
AEB 2 754- 9.035 77976
AEB Sup 2 438 + 0.3/6 +1.037 7.999 + /.036 20 + 1036 25
/ 2004 + 0.434 + 1.424 6.575 + 1.424 50 + /4Z4 /.8
2 1.937 + 0.067 + 0.220 6.354 + 0.22/ 50 + 0.220 00
3 1540 + 0.397 + E302 5.052 + 1.302 50 + /.302 !6
4 1309 + 0.23/ + 0.758 4.290 + 0.762 50 + 0.760 05
5 25H t. no + 0399 + 0.653 8.270 3.648 + 0642 50 + 0.648 0.4
6 2.438 + 0.073 + 0.240 8005 + 0.265 50 + 0252 0/ 785.40
S^BS.) 2 440 - 0002 -0.007 8.005 + OOOO 25 - 0004 00
7 04-7/ 2.779 - 0.339 - u/z E55O 932/ - U/6 25 - 1.114 2 3
8 0 799 - 0328 -1.076 2.625 - /.075 50 - /.076 /./
9 0.976 -0377 -0.58/ 3.202 - 0.577 50 - 0.579 03
!0 1.273 - 0.297 -0.974 4/76 - 0.974 50 - 0.974 09
to SET-UP / 300 - 0.027 - 0.089 4.265 - 0.089 4.66/9 - 0089 O1
// / 647 1.738 -0.438 -1.437 5.404 5.7/2 - /.447 50 - 1.442 / 9
12 1.962 - 0.3/5 - 1033 6.437 - /.O33 50 - / 033 !0 779.09
/3 1437 + 0525 + 1.722 4.7/4 + 1.723 50 + 1.722 2.8
14 0.537 + 0.900 + 2.953 1.765 + 2.949 50 + 2.95/ 8./
15 1.734 - 1397 -3927 _J 5.692 - 3.927 50 - 3.927 14 3
!6 1247 1.469 + 0.265 + 0.869 4.100 4820 + 0.872 50 + 087/ 0.7
/7 E837 - 0.590 - 1936 6.03/ - 1931 50 - 1.933 3.5
18 2.004 - 0/67 - 0548 ■■ 1 6575 - 0.544 50 - 0.546 0.3
/9 2.540 - 0.536 - E759 j 8.330 - 1.755 50 - 1.757 2.9
20 2 486 + 0.054 + 0377 | 8349 + 0/8/ 50 + 0./79 0.0 776.65
\Checke d by &U Cot vputed b Checked by ■£ F Mean £. 'evation - ■^473 780.2)
Figure 64.—Leveling for base line.
of the next section is begun at the section mark. By this method a comparison is obtained between the forward and backward measures of a section.
(4) Record data will be recorded in a separate field notebook for each base line measured. One double page or more will be devoted to each of the following:
Leveling for base line (fig. 64).
For each kilometer section.
Comparison with reference tape (fig. 65).
For each field tape before measurement.
For each field tape after measurement.
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Measurement of base line.
For each kilometer section, forward.
For each kilometer section, backward.
A base of 3 miles (about 5 kilometers) would require a total of 19 pages if no work had to be repeated.
(a) Leveling for base line.—The sample form (fig. 64). shows the level record when using a rod graduated in meters on one side and feet on the other. When such a rod is used the levels are run in only
(COMPARISON W/TH REFERENCE TAPE \r™' ^nfact. r%fsLc>oe ~fF\\
Iff ear Contact- 5g t. n roe \ R }
I Field Tape ■ *2916 Invar
Cloudy and Still________________________Ref. Tape R 366! Invar _____ _____________
March t, 1940__________________________ ________________________________________
Before . st measui e___________________ _______________________________________
t 2TC________________________________।_________________________________________
204 mm
§ | ' —f------------------------------------------------------------------------—
--IQ_____--------------—--------------__1----------------------------------___ -------------------------------------------------------------------------------*-I-
K-_______g/6___________________________I____________________________________
2.92 mrh ,
- । _ ——
is 2.8 2ZZZ | 2 _ ZZZ2 ZZZZ_______________
2.4 32___________________________I__________________________________________
a.4 J. 4________________________ | ___;_____________________________
2.0 2.6__________________________| ___________________________
/.6 2.6___________________________।______________________________________
5) 102 5 )/4.6__________________________‘_________________________________________
2.04 2.92_________________________|__________________________________________
ET&2G 5°C 2HZZ ZZZZ | ~ ZZZ —— ——-
0.88 mm________________________________I ______________
longer 1 han____________________________|___________________________
R.T. @213°C ~__________________________j_________________________________________
Computet i ^ .£>.______________________!__________________________________________
Checked R R._______________________________________________________________________
Figure 65.—Comparison of notes with reference tape.
one direction, but both sides of the rod are read at each rod point, the reading in meters being recorded as the forward running and the reading in feet as the backward running. If the rod used is graduated on only one side, forward and backward running is necessary. The numbering of the stakes in this record should correspond to the numbering on the “measurement of base line” form (fig. 66). Extreme care should be taken to get readings on all broken grades and partial tape lengths, and these should be plainly indicated in the record. All columns must be marked meters or feet, whichever is applicable.
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(6) Before measurement is begun, a pair of posts on especially favorable ground are selected and braced for utilization in all comparison of the field tapes with the reference tape. To avoid possible confusion, the metal strips on these two posts will have to be renewed from time to time. The mean of five separate measurements should be obtained by taking set-ups or set-backs of about a centimeter each. (See fig. 65.)
(c) Measurement of base line (fig. 66).—In recording the tape measures two thermometer readings indicate a full 50-meter tape length and one thermometer reading a half tape length or a set-up. Each half tape length or large set-up should bo recorded on a separate
Figure 66.—Measurement of base line.
line, and not on the same line with a full tape length. The numbering of the stakes should plainly indicate the full tape lengths and the partial lengths. (See 6(1) above for method of numbering.) Notes in the “Remarks” column should clearly explain any unusual conditions. At the beginning of the day’s work, and as often as changes occur, an entry should be made in the “Remarks” column giving the names and duties of the chief of party, recorder, and the two contact
196
z MEASUREMENT OF BASE LINE From Z) E. Base to Station TE. 20 Forward FRONT CONTACT-T SGT J DOE REAR CONTACT ■■ SGT R ROE READ TAPE ■ SGT J. ADAM REAR TAPE'■ CPL.T CANE RECORDER- 5GTL VANE JULY 7,1924 X CLOUDY, NO WIND C7k\ TAPE NA 922 \ /2) BALANCE Ne.302 —' THERMOMETERS Na 51518 E 33260
Sec bon temp. °C Set-up Set-back Tape
Fr om Tl 1 Forward Bear meters meters Supports Remarks
4 EB Z) EB set-up 20.0 20.0000 2 0-20 8/0 AM.
Z) EB. set-up / 21.3 2/.0 3
/ 2 212 21.0 3
3 20.6 20.0 0.07/4 3
J 4 212 21.0 3
4 5 2/.0 20.5 3
5 6 20.0 19.8 3
6 7 202 20.0 0.02/4 3 BG. at s-r
7 8 20.2 20.0 3
8 9 20.4 20.5 3
51 /0 20.6 20.6 3
/0 to set-up \ (2/3) 4.7000 0.038/ 2 —5tee/ Tape 87
o set-up II 20.7 2/.0 2 -Cross/ /g Gully
// Z? 20.8 2/.0 0.0027 3
12 13 20.8 210 0.0732 3
!3 !4 2/.0 21.0 3
15 21.0 20.0 4 Supp. 0- '21-25- 50
15 16 20.8 20.5 3
!6\ n 20.5 20.3 3
n IB 20.7 20.5 3
18 19 20.8 20.4 3
Z9 20 21.0 20.5 3
Mean = 20.7 20.5
Com/ ■>uted by. £2/ Ch •eked by
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Figure 67.—Computation of base line.
Each part of the computation should be labeled so
197
men, also a statement as to the results of the comparison of the balances and the dial reading being used on the balances. All marginal notes and entries at the top of the page should be made as measurement progresses. The insertion of notes after leaving the section is very dangerous to accuracy.
d. Computations.—(1) General.—Figure 67 is compiled from the field records (figs. 64, 65, and 66) shown on earlier pages of the notebook, and also from subsidiary computations performed on later pages of the notebook, where a double page should be allotted for each single measurement of a kilometer section. The circled numbers
in figure 67 indicate from what page of the notebook the data above it were taken. The same system should be followed on the subsidiary pages, marking a circled number opposite each item from another page.
that the work can be readily checked by another.
In this manner the entire record of the work and computations, with the names of the computer and checker of each item, is kept in one place. The only inconvenience is that only one pair of computers can use the book at one time. To aid the explanation, the columns of
X 1 A COMPUTATION OF .....Exemplar. BAST LINE 1
SECTION ME DIR. OF TAPE TAPE LENGTHS TEMP COR REC- [ TION5 REDUCED ADOPTED V V*
MEAS. NO. NO. METERS TEMP TAPE AND 1 SET-UP CATENARY \5ET-BACK INCLINATION SEA-LEVEL LENGTH LENGTH
LEB. TO TE. 20 7/7 fr 922 'c 20.0 METERS - 0.0001 METERS 1 METERS - 0 0009 \+20.0000 METERS - 0.04-1! METERS - 0.0382 METERS 1024.4-744 METERS
922 20 1000 20.6 - 0.0064 -0.0756 - 00586 \
* 872. - — 21.5 0.000 + 0.00/3 14.7000 j COMPUTED CHECKED fr U
P46£© © © © ® ® ® 1 © © ® ®
|
i
1 1
1
I-
“T“
1
1
1
1
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1
1
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(2) (O 15) (U (7) (8) M 1 (70] (n) 1/3} 04) 05] (!6i)
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figure 67 have been numbered in parentheses at the bottom. The corrections commonly applied to base line measurements are as follows:
Temperature (8).
Tape (9).
Catenary (9).
Set-ups and set-backs (10).
Inclination (11).
Mean sea level (12).
Tension.
Alinement.
The results show the adopted length of each kilometer section, length of the base line, and the probable error. Columns (1) to (7), inclusive, of figure 67 are obtained from figure 66, “Measurement of base line,” 20.6 in column 7 being the mean of all the temperatures for the 20 whole tape lengths.
(2) The “Leveling for base line” form should be completed as shown in figure 64, the distances in column (9) are obtained from the “Measurement of base line” form (fig. 66). If the rod readings are in both meters and feet, the differences of elevation of one of the columns are converted to either unit by table IX or X, TM 5-236, and written in column (8) and the mean differences are put in column (10). Column (11) is for the inclination corrections in millimeters with the sum at the bottom. For 50-meter tape lengths and measurements made with the intermediate 5-meter marks these corrections can be obtained from table XIV, TM 5-236. These tables are made out for differences of elevation in both feet and meters, so either feet or meters may be used in column (10). The corrections for other lengths and also for differences of elevations outside the limits of the tables must be computed. If I is the inclined length and h the difference of elevation of the two ends, the correction is
_____ A2 14 A6
Cv=-(l-^-TV = --.27-8/3-1^5- .
A4 .
Since for a 50-meter tape length the second term is less than 0.1
millimeter where h is less than 3.1 meters, on ordinary grades the correction will vary directly as the square of the difference of elevation. Since the correction varies inversely as the distance, fractional tape lengths are likely to a larger error in the grade correction. It is very important that all broken grades and partial tape lengths be indicated on this form and that the grade correction be computed for the corresponding distance. The most frequent mistake made in computing
198
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105
SURVEYING
grade corrections arises from using a 50-meter length instead of the real length. In column (12) several of the elevations are computed and the mean elevation of the section, correct within 100 feet, is written at the bottom.
(3) Standardization.—The data secured from the “Comparison with reference tape” (fig. 65) are used to derive new standardization data for each of the field tapes, invar or steel. Assuming that the certificate gives 49.99595 meters at 26.4° C., when supported at the 0-, 25-, and 50-meter points, and a coefficient of expansion of 0.00000104 per degree C. for the reference tape No. 3861, and a coefficient of expansion of 0.00000110 and a weight of 25 grams per meter for the field tape No. 2916, the length of No. 3861 at 21° C. is 49.99595 — 5.4X0.00000104X50 or 49.99567 meters. No. 2916 at 20.5° C. was 0.00088 meters longer or 49.99655 meters. At 26.4° C. (assumed as the temperature of standardization for No. 2916) it would be 49.99655 + 5.9X0.00000110X50=49.99687 meters, which should agree closely with the original calibrated length of No. 2916, and will be used as the length of tape until another comparison with the reference tape.
(4) Temperature correction is computed as follows: The correction = ( T— Ts) X coefficient of expansion X 50 Xnumber of tape lengths, in which T is the mean temperature for the section and Ts is the temperature of the tape at standardization. The value of Ts is given in the standardization data for the tape. (See (3) above.) The coefficient of expansion may be considered as the change in length per meter for each degree centigrade change in temperature and is given with the standardization data. The number of tape lengths is given in the column headed “Tape lengths” and is the number of full tape lengths recorded in (5) in figure 67. For tapes with a positive coefficient of expansion the temperature correction is, of course, +or—, according to whether the mean temperature is greater or less than the standard temperature. There are a few tapes which have negative coefficients of expansion, and for these corrections would have the opposite signs.
(5) Tape and catenary corrections are combined in column (9). The correction is obtained from the standardization data (see (3) above) for the tape or by computing the catenary correction when the tape is supported in an unusual manner. The tape correction per tape length is the difference between 50 meters and the length of the tape as given for the proper method of support. For instance, in the sample form (fig. 66) there are 18 tape lengths supported at three points, 1 at four points, and 1 at two points. The correction for a tape
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CORPS OF ENGINEERS
supported at three points is obtained directly from the standardization values, and this is multiplied by 18 for the 18 tape lengths. Referring again to the data on the form, the correction for the one tape length supported at four points is obtained by combining the proper fractional parts of the corrections for the three- and the two-point supports. The correction for the tape supported at two points may be computed by the catenary formula below. The algebraic sum of these corrections is entered in the column headed “Tape and catenary,” the sign depending on whether the length of the tape is greater or less than 50 meters. The effective length of the tape when suspended between supports under tension is affected by the shortening due to the sag and to the stretching due to the tension. The correction due to the sag is given by the formula
r = -2Lf^Y/3 s 24\tJ
where 9i=number of sections into which the tape is divided by the equidistant supports.
Z=length of each section in meters.
w= weight of tape in grams per meter.
t= tension in grams.
To illustrate by an example: For tape No. 2916, supported at 2 points under a tension of 15 kilograms,
n— 1
Z=50
w=25
and
Cs — — X 252 X 503 X j 5 qqq2 =—0.01447 meters.
(6) Set-ups and set-backs.—In the column headed “Set-up and set-back” is entered the algebraic sum of the set-ups and set-backs recorded on the form in figure 66, the set-ups being plus and the setbacks minus. In the sample shown in figure 67 the two large set-ups and the corrections to them are recorded separately. All set-ups, however, could have been combined, and also the temperature, tape, and catenary corrections for the large set-ups could have been combined with the same corrections for the full tape lengths, and then the entire computation of a section would have been on one line. It simplifies the checking of the computation somewhat, however, to enter each large set-up on a separate line, as shown on the sample form.
(7) The inclination correction, always negative, is the sum at the bottom of column 11, “Leveling for base line,” figure 64.
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(8) Reduction to mean sea level.—Since the lines of a scheme of triangulation are reduced to their equivalent lengths at sea level, the length of any base must be likewise reduced to sea level before it can be used in adjusting the triangulation to which it is connected. This requires the connection of the base line levels to a bench mark and the computation of the elevation above sea level of the tape supports in order to obtain a mean elevation for the base. The formula used in reducing a base to sea level is
6 h2 h3 C=-S- + S-2-S^+..........
in which C is the correction to reduce to sea level a section of length S, of a mean elevation h, with r the radius of curvature of the earth’s surface for that section. Only the first term of the formula need be used for any field reduction.
The computation of the sea level correction, shown on sample in figure 67, is given below, assuming a value for log r (mean radius of curvature in meters) of 6.80421. The mean elevation as obtained from “Leveling for base line” (fig. 64) is 780.2 feet.
log 1,024.5005 meters=3.01051
log 780.2 feet =2.89221
log feet to meters =9.48402
colog r =3.19579
log C =8.58253
C =0.0382 meter, always negative
(9) Corrections for erroneous tension are seldom needed. Variations in tension change the effective length of the tape in two ways: First, by changing the shape of the catenary (correction for sag), and second, by changing the length of the tape due to stretching, both changes tending to increase the effective length when the tension is increased. Since it is easy to keep the error in the applied tension within a 100-gram limit, the errors in length attributable to incorrect tension are negligible on third- or second-order base measurement. In order that a true tension of 15 kilograms may be applied, the dial pointing on the spring balance should be adjusted to the proper reading whenever the tests show it to be appreciably in error. If it cannot be adjusted, the proper allowance should be made in the dial reading when applying tension to the tape and a remark giving the dial reading used should be inserted in the record book immediately following the statement giving the results of the testing of the balances.
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CORPS OF ENGINEERS
(10) The alinement correction should more properly be called the alinement error, for although the same correction formula and tables apply to differences in alinement of the tape as to differences of grade the alinement can usually be made sufficiently exact to require no correction. It should be borne in mind, however, that alinement errors are always of the same algebraic sign, tending to make the measured length greater than the actual length, and for that reason they should be kept much smaller in magnitude than the inaccuracies in the grade corrections. The section describing the staking of the base gives details of the precautions to be taken in alining the stakes. In addition, some member of the taping party, usually the rear contact man or the front stretcher man, should check each tape length as the measurement progresses to see that the tape does not change its horizontal direction at the middle support, and also that the forward stake has not been disturbed in alinement.
(11) Finally the algebraic sum of the uncorrected length and all corrections gives the reduced length for the section, and the mean of the reduced lengths from the forward and backward measurements gives the adopted length. The columns headed “r” and “r2” are used in computing the probable error of the measurement of the base.
(12) (a) The probable error is usually computed by the method described below. This method is based on the theory that the errors of standardization and of the determination of the coefficients of expansion are either largely included in or are masked by the discrepancies in the measured lengths of the sections. The probable error of each section is computed by the formula
p. i.—0,6745-./-^ -r
\ n(n— 1)
where v is a residual (the result of subtracting the mean from a single value) and n the number of measures of the section. Where a section is measured only twice the probable error will be 0.6745 times one-half the difference between the two measured lengths. The probable error of the entire base is the square root of the sums of the squares of the probable errors of the component sections.
(6) The “probable error” of the measurement of a physical quantity is obtained by mathematical formulas applied to the differences between the two or more measured values of a quantity and their mean value. The probable error is a measure of the accidental errors only—that is, of those small errors which have no marked tendency to be predominantly either plus or minus. The probable error is simply a measure of the closeness of agreement among the several
202
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SURVEYING 105
values of a quantity obtained by successive measurements. It will give no indication of the presence of systematic errors—for example, if a steel tape graduated at 30° C. is used at 0° C. and no temperature correction is applied, the measurements may agree within a very small limit and give a very small probable error, yet the result would be in error about 0.4 inch in every 100 feet or about 1 part in 3,000. Neither will the probable error give any indication of blunders, for a tape length dropped from each measure will not affect adversely the probable error of the measurement of a base.
(13) (a) The “actual error” is the difference between the true value and the measured value of a physical quantity. It is the sum of all the systematic and accidental errors which have not been eliminated from the final adopted measured value. As the absolute value cannot ever be known, the actual error cannot be exactly determined, but its maximum value can always be estimated. The accuracy of the estimation depends directly and entirely upon knowledge of the maximum uncorrected effect of each source of error. After the error to be expected from each source is evaluated an estimate can be made of the “total actual error”, which is one of the criteria for base measures.
(6) To illustrate again by the measurement of a base: suppose that the error in marking and the error in correcting for temperature of the tape are the only ones affecting the measurement. The error in marking the ends of a tape is partly systematic and partly accidental; the systematic error will be eliminated by taking the mean of an equal number of forward or backward measures if the person marking remains always on the same side of the base line, and experiments show that with proper methods the accidental error in marking a single tape end is about 0.1 millimeters, or 1 part in 500,000. For a kilometer section of 20 tape lengths, the probable error from marking errors alone would be 1 part in -/20X500,000 or 1 part in 2,235,000. In correcting for temperature there are three principal component sources of error— namely, the error in the calibration of the thermometer, error in reading the thermometer, and the undetermined difference between the true thermometric reading and the mean temperature of the tape. Suppose standardizations and tests show that the probable error of calibration is half a degree centigrade and that the probable error of reading is of the same magnitude. Also, that the average difference between the true thermometric readings and the mean temperature of the tape under the conditions of measurements would not exceed 2° C., but that this difference is always of one sign. The probable divergence in temperature between the tape and the thermometer readings would certainly not exceed 3°. If the tape to be used were made of invar,
203
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105-106
CORPS OF ENGINEERS
with a coefficient of expansion of 1 part in 1,000,000 per degree centigrade, the maximum error to be expected would be 3 parts in 1,000,000, or 1 part in 333,000.
106. Base lines with steel tapes.—a. General.—If possible, the measurement of base lines for grid triangulation should be avoided by some of the expedients of paragraph 103. However, the methods described below are intended to yield an accuracy of 1:10,000, which is consistent with grid triangulation, without the procurement of special equipment, and at the minimum expenditure of time and men. This method of base measurement should be considered as a refinement of the 1:5,000 taping described in paragraph 47c by utilizing standardized tapes, thermometer, accurate spring balance, Abney level, and perhaps stakes or tripods over rough ground and on heavy slopes; by measuring the base once in each direction; and by applying corrections consistent with the required accuracy. An emergency might justify the short base method described in paragraph 132, at the expense of accuracy.
b. Apparatus.—(1) Standardization of tape.—Each organization should reserve at least one standardized tape of each length with standardization certificate, to be utilized solely for calibrating purposes. To insure proper calibration the reference tape should be made from the same metal as the field tape being calibrated. If possible the calibrating course should be selected on smooth ground, either level or uniformly sloping, and sheltered from sun and wind, so that a true comparison can be made in whatever position of the tape is desired, and without reduction for difference in temperature. Expose both tapes for about one-quarter of an hour. Then lay off the length of the standardized reference tape with the tension and supports specified in the certificate accompanying this tape. (The end marks may be recorded by fine pencil lines on patches of adhesive tape stuck to some smooth, fixed surface.) Immediately afterward, the field tape is stretched over the course with the tension and method of support which will be employed in measuring the base, and the length is recorded. These marks should be carefully checked by several trials. The marked length of the reference tape is then corrected for any deviation from true length as shown by the certificate, to establish marks for the true length. If the field tape is longer than the true established length, the excess is the error and the correction is plus and must be added to all measurements. If the field tape is shorter, the correction is minus and must be subtracted from the recorded measurements during the computation of the base line. As it is assumed that both reference and field tapes are at the same
204
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106
SURVEYING
temperature, no account is taken of temperature during the calibration but the field tape measurements have to be corrected for the average difference in temperature from the original standardization temperature shown in the certificate. On smooth, even ground, the most rapid progress can be made with a 300-foot tape, supported throughout. Over rough, broken ground, a 100-foot tape supported at both ends is more satisfactory. One of each should be compared with reference tapes before and after the base measurement if both are used.
(2) Tape-stretching apparatus.—Heavy rawhide thongs, long enough to wrap around the hand, make the most satisfactory tape handles. The spring balance, which is kept attached to the front end of the tape, should be of ample capacity and frequently compared with one reserved as a standard. As substitutes for tape stretchers, a stout staff may be inserted through a turn of the rawhide at either end of the tape, but utmost precautions must be taken that the tension is applied slowly and steadily while observing the spring balance. A steel tape may be ruined by stretching it beyond its yielding point.
(3) Accessories include flagged range poles which should be lined up with a transit, hand and Abney levels, a backed thermometer which should be attached to the rear end of the tape with adhesive tape in such a way that the bulb is in contact with the steel and the whole protected from breakage, a few 2- by 4-inch stakes, and chaining bucks or light tripods which may be employed to support the ends of the tape over rough, broken ground. For the last, instrument tripods with a 4- by 6-inch block of wood rigidly secured to the top will be adequate. A pin or pencil mark may be used to show the end of the tape, and “breaking the tape” may be thus avoided.
c. Preparation of base.—This is limited to selecting the most suitable site and cutting the brush. If the measurement is along a steel rail or hard-surfaced road, the measurement should not be made during a sunny day, as the temperature readings will not be reliable.
d. Procedure for measuring—(1) Organization of party.—While shortness of personnel might limit the party to two men, the increase in accuracy and speed would justify the following:
Front contact man (in charge).
Head tape man.
Rear tape man.
Recorder.
Stakeman or tripod carrier.
(2) The method of measuring is in general similar to the 1:5,000 taping described in paragraph 47c. Measuring the line both ways
205
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106
CORPS OF ENGINEERS
and taking the other precautions mentioned here and making the corrections as outlined in e below should give results of 1:10,000 accuracy, provided both tapemen are skilled and in practice. However the division of dut'es in the larger party is at least an insurance against mistakes. The front contact man levels the tape or reads the slope with an Abney level, besides marking the length, which leaves the front tapeman free for alinement and tension. The recorder keeps all the notes, reads the thermometer for every whole tape length, and assists the rear tapeman set on the mark when necessary. If the stretcher staffs are utilized the rear tapeman quickly sets the end to the. mark and holds fast while the head tapeman applies the tension. If the tripods are used much, time will be saved by using three with a man to carry each. On remeasurement, a short length should be measured at the beginning, if necessary, in order to avoid confusion which might be caused by having the old and new marks together.
(3) Record data.—Figure 68 shows notes of the field work and the results of the computation for one measurement of the two that are required. If they do not agree within 1:10,000, the measurement will be repeated until there are two, in opposite directions, which are within the allowance. In the heading the data for the two tapes used are the results from the comparison with the reference tapes with the field tension and the method of support immediately before measuring the base.
e. Computations.— These may include corrections for tape length, temperature, sag, slope, and mean sea level. The corrections are shown at the bottom of the field notes (fig. 68).
(I) The correction for tape length is positive if the field tape is longer than the true distance, and negative, if shorter.
(2) The correction for temperature is made at the average of the temperatures recorded for each tape length. The coefficient of expansion of steel tapes averages 0.0000065 for each degree Fahrenheit. The correction equals 0.0000065 times (the standardization temperature minus the mean temperature of the field measurements with that tape). This correction is negative if the recorded temperatures average over 68° and positive if less.
(3) The correction for sag is always negative, but is unnecessary if the tapes have been calibrated under field conditions.
Let
n=number of sections into which each tape length is divided by its equidistant supports.
I—length of each section in feet. w— weight of tape in pounds per foot. t— tension in pounds.
206
Figure 68.—Notes and computation for base line with steel tape.
Then the correction is
BASE LINE /AE BELV. TO /AW BELV.
390 ft tape no. 1608 corr - 0.19 ft. (a) 68°F lOOft tape no 1617 corr + 0.07ft. (a) 68*F
300 ft. tape on ground 30lb. pull
. . . d2
(4) The correction for slope is always negative, and equals 7^-> where Z=the inclined length, and d=the difference of elevation of the two ends. The correct horizontal distance equals the length of tape times
TM 5-235
106
1 Front contact; T Sgt J. Doe ~~
, Head Tape. Sgt R. Ross Jan.21,1940
I Rear Tope- CpI T. Cane gentle breezed /$
। Recorder : St Sgt L. Vane very cloudy \> | !OO ft tope supported at both ends. 20 !b pull________
the cosine of the angle of slope, which may be obtained from Abney level or transit readings.
(5) The reduction to sea level is always negative.
Let
L=length of line in feet.
H= average height above sea level in feet.
#=mean radius of curvature of the earth in feet.
(colog #=2.67981 —10)
Sta. 300'tape temp ° F V. A. slope corr IOO'tape | temp ° F V.A slope corr Support Sun Remarks
EsE.Betv. 300.00 80 gravel cloudy 8:20a.m.
100.00 79 ends
100.00 78 3° 40' -0.20 . do
100.00 78 3°OO‘ — 0.14 do
300.00 77 1° 20' —0.08 ■ 1 ' concrete
300. 00 77 l°OO' -0.05 ’ 1 .. do
300. 00 76 2°!0‘ -0.21 1 do -
300 00 76 2°OO‘ -0.18 do
300. 00 76 !°40' -0.13 1 do
100.00 1 76 4‘! O' -0.26 ends
56.76 ' 3°OO' -0.08 do
300. 00 78 O°2O' -O.O! 1 concrete
300.00 79 0°20‘ -O.OI 1 do
100.00 I 78 5°OO' -0.38 ends
A » Belv. 76.56 , 2°2O' -0.06 do 9 30a.m.
Total 2400.00 619 -0.67 633.32 389 -1.12
Mean 77 78
Tape corr. -1.52 + 0.44 ' 300 ft. Tape 2397.67
Temp. corr. -0.14 —O.O4 [ !ogL = 3.48148 100ft. Tape 63260
Slope corr. -0.67 — 1.12 togH- 3.00000 Total 3030.27
2397. 67 632.60 colog R- 2.67969 M S.L. -0.14
1 9.16! 17 one way 3030.13
1
1 Computed ]/cu+njer
1 1 Checked S' 0a J
R
207
SURVEYING
Then the correction for each tape length is p =_2L/W/3 s 24\ Z /
TM 5-235
106-107
CORPS OF ENGINEERS
f. Exercise XVI.—Measuring a base line with steel tape.—By the methods of this paragraph, calibrate the field tapes, measure an assigned base line, keeping the notes as in figure 68, and obtain the final length as the mean of two measurements in opposite directions which agree within 1:10,000.
Section XVIII
MEASURING ANGLES—TRIANGULATION
Paragraph
Measuring horizontal angles_______________________________________________ 107
Description of station____________________________________________________ 108
Eccentric stations___________________________________________________.__ 109
Vertical angles___________________________________________________________ 110
Special instructions____________________________________________________ 111
Equipment________________________________________________________________ 112
Method of observing--------------------_-------------------------------- 113
Disposition of records_______________________________________.__________ 114
107. Measuring horizontal angles.—a. General.—(1) Only specially trained men using suitable equipment can observe angles with the accuracy specified for triangulation without wasting time. The observing party proper consists of two men, both of whom should be skilled in every phase of their work, as an uncertain recorder can seriously hamper an expert observer. Light tenders should be reliable men imbued with the importance of properly displaying their lamps. Transportation and other assistants are detailed as required.
(2) Even the best 20-second transits would cause marked decreases in accuracy anil speed. On the other hand, the excess bulk and the delicate refinements of the large, heavy instruments made for firstand second-order work interfere with the more rapid manipulation fitting for third-order and grid triangulation, for which any of the theodolites described in section X are suitable. Particular instructions in the proper handling, care, and adjustment of these instruments should be imparted to the men using them.
(3) In measuring angles with either the direction or the repeating instrument, certain errors are reduced or eliminated by—
(a) Taking a number of readings to diminish the error in pointing.
(6) Taking half of the readings with the telescope direct and half reversed. This eliminates errors due to lack of adjustment of the line of collimation and of the horizontal axis.
(c) Taking initial readings at different points on the graduated circle to reduce errors due to faults in its graduation.
(4) The program of observation must be arranged to secure triangle closures within the limits required with the instruments issued for the work. The number of observations usually required for each order of
208
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SURVEYING 107
accuracy as given in paragraph 92a is based upon the experience of the United States Coast and Geodetic Survey, whose observers are experienced and equipped with instruments designed for the different orders. Partially trained army observers may require 50 percent more observations to obtain the specified triangle closures.
b. The direction method of measuring angles consists of measuring the direction to each station from some one station taken as an initial. The directions are the angles measured clockwise from the initial station to each of the other stations. The angle at a station between any two observed stations is the difference of their directions. A direction theodolite does not usually have a slow motion screw for the lower motion, though the direction method of observing may be used with a theodolite arranged for repetitions by keeping the lower motion clamped. A direction theodolite is almost invariably read by means of micrometer microscopes. In observing, a pointing is made on the initial station and then upon each station around the horizon in a clockwise direction, closing on the initial station; the telescope is then reversed and readings made counterclockwise, the double set of readings constituting one position.
(1) Circle settings.—When two or more sets of observations with either a direction or a repeating theodolite are made on the same angle, the initial setting for each set should differ by an amount depending upon the number of positions to be observed and the number of verniers or micrometers on the theodolite. The interval in degrees between successive settings with a 2-micrometer or a 2-venier 360°
theodolite is given by the formula where /is the interval in
degrees, m the number of verniers or micrometers, and n the number of positions or sets. In addition, an increment represented by the value of one division of the circle divided by the number of sets to be observed should be added to the difference in degrees between settings in order to eliminate the error of graduation of the verniers or the run of the micrometers. For instance, with a circle graduated to 10 minutes and with two sets observed on an angle, the settings would be approximately 0°00'00" and 90°05'00".
(2) The notes in figure 69 show the results for two positions, with the readings for each station grouped for ready comparison. The degrees and minutes for the counterclockwise readings are recorded as a check only in case of observing a single position. On the righthand page each direction is entered separately and then meaned for the final values. The angles may be entered in the “Remarks” column.
262341°—40----14 209
TM 5-235
107
CORPS OF ENGINEERS
(3) With any direction instrument when a broken series is observed the missing signals are to be observed later in connection with the chosen initial, or with some other one, and only one, of the signals already observed in that series. With this system of observing, no local adjustment is necessary. Little time should be spent in waiting for a doubtful signal to show. If it is not showing within, say, 1 minute when wanted, pass to the next. A saving of time results from observing many or all of the signals in each series, provided
I Obs:T Sgt J Doe April 17,1940
HORIZONTAL DIRECTIONS ] Rec: Opt T. Cane Clear and warm (IE
At A Gunter Clarke Co., Ohio । Inst, t"Berger 8796! Moderate wind
Objects obs DorR Reading A Backwardg Mean "I ° ' •• Direction Remarks
A Bane D O°OO' 22 22 22 1 O ! u 4:0!pm.
24 28 26 1 24
R 26 28 27 1 4 13
2/ 25 23 1 25
R 270 05 39 42 40.5 { 4:21
33 37 35 37.8
D 31 33 32 J" 4:30
29 32 30.5 ! 31.2
1 1 2=45 4000!
A White D 45 40 23 29 26 । 45 40 02
R 20 22 21 39 56
R 3/5 45 35 38 36.5 45 39 58.7
D 33 '37 35 । 40 03.8 45 40 00. I
1 2 = 30 55 03.3
A Staunton D 76 35 28 30 29 । .76 35 05
R 24 26 25 | 00
R 346 40 38 4! 39.5 | 76 35 01.7
D 36 40 38 06.8 76 35 03.4
1 2=10 2938.2
A Glen D 87 05 04 08 06 | 87 04 42 Signa! in shade
R 0! 06 03.5 1 38.5
R 357 10 17 20 18.5 1 87 04 40.7
D 15 18 16.5 I 45.3 87 04 41.6
1 2=272 55 18.4
I Checked j-.J3o6. y
Figure 69.—Notes of horizontal directions.
there are no long waits for signals to show, but not otherwise. When the elevations of the stations differ greatly it is necessary to keep the horizontal axis of the instrument level in order to avoid large and troublesome errors. Any releveling should be done between positions.
(4) With an instrument of the Wild type, reading directly to 1 second, the two micrometers are meaned by the process of reading and the tenths of seconds should be recorded leaving the fifth and sixth columns blank. Another advantage of the Wild type is that all readings are made without moving from the eye end of the telescope.
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SURVEYING
c. The repetition method.—(1) The 10-second vernier theodolite is a repeating instrument on which successive observations of a horizontal angle are added by repetition and finally meaned to secure an accurate measure of the angle. A set of observations consists of six repetitions of the angle with the telescope in the direct (or reversed) position, followed immediately by six repetitions of the explement of the angle with the telescope in the reversed (or direct) position. (“6 D)R’' is the abbreviation for such set.) Set the A vernier at or near zero,
Horizon! 5 fate ■ Of, At a! Angle, to County •oil • Clarke Jr HS. /< 16 8 14 9 m Z ft. Z 4.6 ft Obs. T5i Rec-.Cp/ Inst-./O'l it. J. Doe rCane '&£ 606. >6 Hpn7 78, / "Joudy at 15 tn He 740 d cool find
Objects observed Tel Rep. Readings A B Mean Mean o> ' 6 5et Mean Hor Adj. Rerr arKs
A 5hom der D O 0° 00' OO to 05 70-35 AM.
Knob t 30 15 30
6 181 32 40 50 45 30° 15' 26.7"
R 6 359 59 50 OO 5S 55 28.3 27.5 26.6 30° 75' 26.6'
ItsKnob R 0 00 00 20 30 25 70:55 AM.
2 .Top / 82 41 OO
6 136 06 30 40 35 82 4! Ot.7
D 6 0 OO 40 40 40 40 592 *00.4 40595 82° 40 59.5"
DsTop 0 O O OO 25 30 275 7/70 AM.
AZ boulder / 247 03 40
6 42 2! 50 60 55 \247 03 34.6
R 6 0 OO 20 30 NA 35.0 34.8 33.9 247° 03 33.9"
...
Ve -tical 4ng> 'es
+ Readings C o Mean Angles
Shou/ate. O 5° 22' OO OO OO 7:00 RM
R 5 21 30 60 z' 45 \+5 2! 52.5 1
Knob D + 2 41 OO 30 d5 —4
R 2 4/ OO OO OO +2 4/ 07.5 A
top D - 3 16 OO OO OO MRFD
R 3 76 30 30 X -3 76 75.0 — TJO PM.
. .. Checker
Figure 70— Notes of horizontal and vertical angles.
read and record both verniers and their mean as in figure 70. Set on left-hand station, unclamp above, set on right-hand station, read and record A vernier only. From this the recorder subtracts the initial reading, multiplies the result by 6, and notes the product on scratch paper so that he can give the degrees and approximate minutes of the sixth repetition at the request of the observer. Make 5 more repetitions, setting on the left-hand station with the lower motion and tangent screw, and with the upper motion for the right-hand station. Read and record both verniers and their mean. From this subtract the initial mean, divide by 6, and record as the “Mean of 6.” With-
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TM 5-235 107
out disturbing the verniers, reverse the telescope, and take 6 repetitions of the explement, measuring the angle from the former righthand station to the other, recording the final readings of both verniers and their mean, which should be nearly the same as the initial mean. Subtract the final mean from the sixth repetition mean, divide by 6, and record as a second value of the mean of 6. The mean of the set is recorded in the next column. Before beginning another set, the circle reading should be changed in order that an error in reading may not affect 2 angles.
(2) With any repeating theodolite, measure only the single angles between adjacent lines of the main scheme and the angle necessary to close the horizon. Releveling may be done between sets or between the separate angle measures of a set; that is, when the lower clamp is loose. After observing a set for each of the angles, the horizon is adjusted to make the sum of the adjusted angles equal 360°. Record under “Hor. adj.” A second set of the same angles may be recorded on another page and the mean of the two horizon adjustments recorded in full, bold figures in the “Remarks” column. If it is certain that several sets will be required, a page of the notebook may be allotted for all the sets of each angle. The initial circle settings should be as described in 6(1) above.
d. Observations on intersection stations.—(1) An intersection station is one which is not occupied, the position of which is determined by observations upon it from stations of the main scheme or from supplementary stations. It may be a signal over a marked point or it may be a well defined natural or artificial object, such as a tank, church spire, or sharp mountain peak. Here the term “intersection station” is used in a restricted sense to mean a station located by intersections with fewer observations than are specified for the main scheme. A line to such a station must not be used as a base for new triangulation.
(2) In selecting intersection stations it should be kept in mind that the geographic value of triangulation depends upon the number of points determined, the size of the area over which they are distributed, and the permanence with which they are marked. The geographic value of a triangulation is lost for a given area when stations cannot be recovered within that area. The chance of permanency is made greater by increasing the number of stations as well as by thorough marking. For the reasons stated there should be determined as intersection stations many artificial objects of a permanent character, such as lighthouses, church spires, cupolas, towers, chimneys, and standpipes. Make the description definite whenever practicable. It is advisable to observe upon each intersection station from at least
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SURVEYING
three stations in order to obtain a check upon the position, and the directions from at least two of the stations should, if practicable, form a good angle of intersection at the object to be located. A possible intersection station should not be disregarded if only two directions to it can be secured.
(3) The direction method of observation should be used in observations upon intersection stations even if the theodolite is a repeater. Each series of observations on intersection stations should contain some one line, and only one, of the main scheme (or a line used in fixing the position of a supplementary station, which may be established for the purpose of making more intersection readings possible). This main scheme line is always made the initial. The notes for the repeating instrument are similar to figure 69, except that the page is headed “Intersection Stations.” Two positions should be observed with a 10-second instrument, one with a 1- or 2-second direction instrument. When only one position is observed, the degrees and minutes of the counterclockwise readings are recorded to provide a check on the clockwise readings. The vertical angles are recorded as in figures 70 and 72, and may be recorded on the same page as the above directions.
108. Description of station.—After checking the data received from the reconnaissance and station construction parties (see par. 98?i for other details), the original description should be written in the angle or direction record book or in a separate notebook carried by the recorder for that purpose. Taking one of the main scheme stations as an initial, the directions to the nearby azimuth and reference marks are observed to the nearest 10 seconds. These marks are observed separately so as to avoid changing the focus during other observations. As soon as possible after leaving the station, while the topography of the vicinity is fresh in mind, the written notes should be transferred to Form 4, “Description of station” (fig. 60). A single copy only need be sent to headquarters, but it is a good plan always to make one carbon copy to be retained in the field for reference until the end of the season, when the duplicates can be transmitted to the office if no longer needed. The form, after being completely filled out, should be read over carefully to see that there are no reversed directions and that no part of the description is vague, ambiguous, or erroneous. The name of the station given in the description should correspond to that given in the triangulation records and computations. On account of inadequate descriptions, there has been considerable confusion in identifying such objects as flagpoles, which are sometimes replaced by another pole in the immediate vicinity. The description
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of such objects should state the particular part of the grounds, building, or other structure where located. While the written description must be complete without a sketch, one may be added if desired.
109. Eccentric stations.—a. General.—(1) When such an object as a church spire or flagpole is used as a triangulation point, the instrument is set up over a point called the eccentric station, which should be as close to the true station as possible. Occasionally a target or signal pole may be out of plumb, due to heavy wind or other disturbance, thus becoming an eccentric object. Any eccentricity of the instrument or object should be avoided when possible because of the added computing necessary to reduce the observations to center and because of the greater danger of angular errors. Eccentricities of more than a meter or two are especially apt to cause poor triangle closures because of the difficulty of securing a true value of the horizontal distance to the eccentric point.
(2) The importance of the proper recording of the eccentricity of signals or lights and theodolites must be emphasized for the reason that many serious mistakes and ambiguities in triangulation records are traceable to that source. The computation necessary to correct the directions and angles to make them refer to the true station is called the reduction to center.
b. Eccentric station.—The horizontal distance between the eccentric station and the center of the station must be carefully measured. The notebook should contain a sketch which shows the relation between the two stations, and the line extending to that station of the main scheme which was used as the initial station in making the horizontal angle observations. Form 6, “Transcript of results” (figs. 82 and 83), as observed at the eccentric station, should contain the direction to the nearest minute only from a main scheme station as an initial to the center of the station, and the distance should be shown in a sketch at the bottom of the sheet.
c. Eccentric object.—The notebook and transcript of results should show definitely the amount of eccentricity of the pole or target, and the direction in which the signal is eccentric. Frequently the eccentric pole is in the line from the center of the station to one of the other stations. In such case the fact should be noted, with the eccentric distance, and a statement as to which side of the center of the station the center pole lies. From the eccentric distance and direction, corrections are computed for any observations made upon the eccentric pole from other stations.
d. Reduction to center.—With approximate distances to the objects observed as scaled from the map or plat of the triangulation system,
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the observing party makes a preliminary computation of the reduction to center, so that the observer may have a record of all the triangle closures. Form 5, “Reduction to center,” bears full directions and the copy in figure 71 shows examples worked out. As this reduction to center is based upon approximate distances, the resulting corrections are not made on form 6, but the completed form 5 should be attached for the further guidance of the computing section. The instructions which should appear on the form are printed in full below.
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CORPS OF ENGINEERS
216
(ft. to yds.) log -9.5226ft) cross out one a Diagram
Eccentric! &ChaS(? (ft. to m. ) log = 9.48402] or both
Station j.................. log d = !,55703. OccemCcLFf
colog sin l" = 5.31443 station
d= 36,0.6.... (I) sum -Q.35548 4/1^^
___________________ _______________________________________________________ (2) STATIONS_______Center LTraU BBossing 4 Little A Lyon s
________________________________________________________________River______________________________________
(3) s (if log unknown)........tt-.........J....'..............__._TT_______.7TZ...........................
(4)A (direction).............0°. 00‘. 124....27_. I79...../8:... 242....47.. 249.02........................
(5) log sin A.................. ........9,9/62.5...8..08690. 9.949.04 9,97025. ............................
(6) log s (meters or yards) 4.40254. 4.49198 4,5I928„ .4,306/6...........................................)
(7) log (sin A/s) ............ (5)H6) 55)371/.... 3,59498. 5.42976..5,66.409...............................
(8) log C (correction)........(7) + .(J.j ..1,86919.9,95046..1,785.24. .2,0/9.57 .............-..... ......
(9) C in seconds........._..4-.pr_—. ...t.7.4.,Q....?!:.^.._...l..Ti 9 74 3886
5 27 \ 40 | 03/ - 0.9 02.2 -a/ 023 9\666 8322 ' T 1
6 27 i !3 \ 08.0 - 0.9 073 54 i 53 \ 09.3 -03 07.0 :izr: 9 [660 \2836
7 94 \ 45 \ 41.8 - 1.0 40.8 -0.5 40.3 9\998.4987 1 i .. .1
8 3o \ 2! i II.9 - 0.9 H.q 125 \ 06 \ 5/8 -0.4 !0.6 9\1O3\57/O
360 ..PO ...PZ4 6)07.4 _0,9_ 00.0 + 0,2. 4)0.3 0.0+0 3 4) 1.9 0.4 +0.3 POO 39,./PQ 6573 3 ?, /PP_ 6753. 6573
1 = + l = - /80 i
(10) (II) (12) (13) (14) (15) (16) (17) (18) (19)
No. d Sums Corr. Log sines Log sines
of for d2 d-U Corr. of opp Adjusted odd numbered even numbered
Angle 1 sec. Ed2 angle pairs angle angles angles angles
1 524 3528,4 r /.2 . 57J. :Q:L /9 J7.0 si/5-2.3 —1 -< 7J.5.2 1 T —
2 297 8823 -0.6 32,6 097 -0.2 22 32.4 1 1 9\ 762 "*“f 6297
3 14,9 222.0 +0.3 223 — ...54.. 40. 225 5'P/./. 8!.7.9 1 ]
4 7.5 56.2 -0.2 28.3 51.0 -0 2 7O_ .26. .28.3 1 1- - — — 9\9 74 1883
5 .40,2 J6/6.0 + 0.8 02.9 7.OZ 27 40 03.1 9\666 8363 ...l
6 .40.9 1672.8 -0.8 . 06,2 093 to,!... ...27... 06.3 --J 9[660 2808
7 ~/.7 2.9 — 40,3 +02 9.4 .45... 405 .91? 98 2987 I .....1 —
8 36.0 1296.0 -0.7 099 50.2 +0.2 _30_ 10.1 1 9\703 5692
Sum 9276.4 op.o 360 QO 00 668/ 68 80.
'PP. = O.Oc 9276.4 1 = 6 6 8P. t / l=“ —
59.4
29.7
X O.O2 = /.a
X 0.02 =0.6
Etc.
Add Sum angles Log sines
A 1 88 49 5/ \473 9\88 3 38/0
8 283 90 02\54.9 9\9 9 9 9999
C 485 98 ' 06 3/.2 9\9 95\6362
D 687 121 58 46.8 9\928 .5/67
Date March 25, !?40 Computed byr.JU
Checked
by: J J J . FORM 7
Figure 74.—Quadrilateral adjustment (approximate).
236
R
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QUADRILATERAL ADJUSTMENT (APPROXIMATE)
instructions
(1) and (10) The angles are numbered as in diagram.
(2) Filled from form 6 or from notebooks.
(3) and (6) Apply the extra tenths to the larger angles.
(4) Spherical excess of less than 1 second per triangle may be disregarded at this point.
(8) and (9) Log sines of corrected angles shown in (7). Z is algebraic sum of log sines in (8) and (9), regarding even numbers as negative.
(11) Tabular difference (log sin) for 1 second, negative if angle is over 90°.
(13) ^Xdn=correction applied to each angle, remembering that even numbers are considered negative.
(15) The sums of pairs unbalanced during the side adjustment are corrected in (16), keeping sum 360° and all triangles 180°.
(18) and (19) To detect residual errors.
Last block, sum angles and log sines are placed here for convenience in solving triangles.
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d. Solution of triangles.—(1) Form 8 (fig. 75) is arranged for the computation of log sides by the well-known law of sines. The clockwise manner of listing the angles and triangles should be habitually followed as outlined at the top of the form. Misunderstandings are thus avoided, and at the same time the form is adapted to other purposes as described in paragraph 1196 and c. The instructions which should appear on the form are given below.
SOLUTION OF TRIANGLES
INSTRUCTIONS
(1) Entered from the diagram in clockwise order, naming first the ends of the known side. The triangles are listed in clockwise succession, beginning with the one containing the known side.
(3) and (4) The extra tenths to larger angles. The seconds of (2) may now be marked out to avoid confusion.
(5) and (6) Subtracting log (sine of opposite angle) from log (known side) yields log (known side divided by sine of opposite angle) which is written in fourth line of (5). By adding the latter in turn to each of the other log sines, the log (side opposite each) is obtained and written in (6).
(7) Using same notation as in (1).
(8) For convenience in checking identical values.
(9) If spherical angles are required, the spherical excess is computed and entered in fourth line of (1). One-third of spherical excess is added to each of the adjusted plane angles of (4).
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Corr.
(1) (2) '*(3) (4)^ (5) (6) (7) (8) (9)
Station Observed Sph. Exc. See Sph.
and letters Ms AhqIq Log sine Log side Side No. Angle
French C A- D Lee BC
1 AC
Herkness B A Proc tor 1 ... J AB
No. 1 Sph. Exc.
E Proctor (0 A BC= 3 AB=4. 828/ 2785 79° 30 37.0 9\523 7/52 3\828 0596 BC 3 37/
A Herkness B 8 = O. OOOO 90 02 54.9 9\999 9999 304 3443 AC 4 55.0
A French (4) C wn= /. 4046 70 26 28t 9\9 74 1883 278 5327 AB 5 28.2
No. 2 Sph. Exc. = 03 tog 6.32 = 9 5112 180 ' 00 000 4\3D4 3444
A Herkness 13) B BC = 3.823! CD =4.0794 54 40 22.5 9\9! / \6/79 4 0 793967 CD 4 22.6
E French C C = 9:9956 98 06 372 1 • 9\9956362 = 163 4/50 BD 5 3/. 3
A Lee (6) D m'- Z 4046 27 !3 063 9\66O 2808 J 828 0596 BC 2 06.3
No. 3 Sph. Exc =0.2 fog 0.20= 9/3077 /8o 00 00.0 4\t6 7 7788
E French (5) AD= 4:0427 00=4.0794 27 40 03/ 9\66 6 8363 4\042 6638 AD 5 03.2
E Lee D D = 9.9285 121 58 46.8 9\9 28 5167 4 304- 3443 AC 2 46.9
A Proctor (8) A rm- 1.4046 30 2! 10.1 ■■"I 9l 703 5692 4^079 3967 CD 3 !0.2
No. 4 Sph. Exc. = 0.3 tog 6:29= 9/4552 780 OO 00.0 T\375 8275 (Because of 7- / on t ->rm 7
4 Lee 77) D AB=4.2785 AD= 4 0427 94 45 405 9\99B 4987 4\278 532% AB 2 40.7
E Proctor A ,A~ 9.8834 49 5/ 47J 9\883 3810 1 #j7<55 4/50 BD 3 47.2
A Herkness (2) B 7m= /. 4046 35 22 32.4 9\762 6297 4\O42 6638 AD 4 32.5
No. 5 Sph. Exc =0.4 tog 0.41 = 9.6092 780 00 00.0 4\28O 034!
38 36 12 A ABC S/ofl. £xc. 0\32
38 42 Ot A CDA 0\29 J
38 42 08 Sum OF/.
No. 6 Sph. Exc 3 )//6 00 2/ A BCD A
38 40 07 A DAB 0\4t Check
log /m =1.40465-10 o\6t : 1
1 : i • 1 : ""1
No. 7 Sph. Exc. 1 : • 1
1 i
! 1
No. 8 Sph. Exc. 1 1 1
Dote: March 25,7940 Computed by Checked bv:.^.^+„FORM 8
Figure 75.—Solution of triangles.
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CORPS OF ENGINEERS
(2) In figure 75, the figure diagram has been copied from Form 7, “Quadrilateral adjustment,” as were the corrected angles and log sines. The headings of columns (2), (3), and (4) have been changed to leave space in column (2) for the computation of the spherical excess. The sum of the spherical excess for two triangles with one diagonal of the quadrilateral common to both shoidd exactly equal the sum for the two triangles on the other diagonal, as shown in the lower part of the form. Solution of only two of the triangles would enable the computation to have been carried forward. Nevertheless, all of the triangles shoidd invariably be solved, in order that the agreement of the values of common sides, derived by different routes, may independently check the accuracy of the competition.
e. Computation of position.—Form 9 (fig. 76) is in two separate halves, the new position being computed from station 2 in the left half, and from station 3 in the other. In this form the angles are still numbered clockwise but start with the unknown angle. The instructions which should appear on the form are given below.
COMPUTATION OF POSITION
• INSTRUCTIONS
Latitudes and longitudes of stations 2 and 3, and the azimuth and back azimuth between them must be known or computed.
The logs s (side in meters) and the spherical angles are obtained from form 8, angles 1 and 2, being positive, and 3 negative.
The logarithmic factors A', B, C, and D are found in Special Publication No. 8, United States Coast and Geodetic Survey or Bulletin 650, United States Geological Survey, A' for latitude of new station, the others for old station.
The first term is negative if new station is north, positive if south of the old station. Second and third terms are always positive.
A X is negative if new station is east of old.
After transcribing all above (except A') to the form, find a(2—1) in third line, solve for Arf> in lower left quarter, deduce ' in the ninth line and solve for AX and Aa in the lower right quarter of each half of the form and deduce X' and a' in the upper portion.
If latitudes or longitudes fail to check by one unit in the last place of decimals, change one of the values by one unit in such manner as to make both this position and the next one check.
ff azimuth (1—2) plus angle (1) fails to check azimuth (1—3) by one unit in the last decimal place, a correction must be applied to make the result consistent before proceeding with the next position.
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I Lee
__Herkness.2 Proctor.......................... * 2 ...-............ t0 3 ....... .124° 38 '\„595 a. f3 ................ »° 2 ........ .304°: 32fi /p"?
& i _ ________________ a ................\*49 i 5/ j 47.2 & \ ....... ... a .............. ~ 35 \ 22 j 32.5
a 2________ ________ to I _ __ 30 \ 467 a I 3 ________________ , _ __ tot ____ ; 269J 09 \43.2
Aa±| i.-.|.00 i.,273 Aa±| j.06 \ /6.9 _
±i iab i do 00.0 i ± iso 00 000
«• : 1 Z\ Lee _ t° 2 Proctor i 354 \ 30 \ 19.4 a' | 1 A Lee to 3 Z\ Herkness 69 - 16 \0O.J _
Angle 1 + 54 i #5 40.7 ________——" " '
, L, 8F\.dF...viPq.i ---—-—” ec , o, ■
* [3/- 36 / l'.707 T _______________I x \.76\.58\,,.34,834 9 [ .38°\.42.\.. ..P/".368 3 ______| * I. 77 J 09 J 2/, ",326,
A 9 ±k ' 05 56 /40 AX ± + \ OQ \ 43.656 6+ 9') 38° 39' 09*777 s I 4\/63\4/5O ■ 4(9+9') 38° 42' 04*608
Cosai 9 98\ 0054 ■ 1 Logarithms | Value in Cos a | 8\/65\/059 i j Logarithms i Value in
B | 8 i 5/0 I 95 74 ’ + s I 4\o42\6638 ; seconds B ! 8\5 70,950/ I + si 4\7 63.4150 i seconds
h \_2\55l\6266 'tst term -356'./45 Sin a \ 8',98O\55O4\, h j o[839\47/0 1st. term -_6*9IO Sin a \ _9\999 9535 \
s2 I. 8\O85.33-1 A' \_.8\5O9'15/ 7 \ s2 i.513 26\83 —j A1 j 5 509) 15/1 i
Sin2*:.7] 96/ /O — \ Sec 9' : C>\/07'579/ i Sin2 a.1 S']95919/.-i Sec 9' j o\/07]679/ i
C < /\3O6 87--j AX ± /\640::0444 \+43.656 C ; /\308\37--; AX ±1 2780'1987 !- 602.835
•-1---------: I t ■.. I .!...•;...... j” ”■ •----;---- I ?..I...f...— ■.......
\.....7 553 30— 2d ,erm L..PPO2 Sin ) 9\795\6OQ8 : [....?! 035\// — 2.d term \ 0.432, Sin ^() i 9\796,06Q7 i
h2 L.4'Z?.4J3—— i “Aa A . . hZ । -Aoc ii....2\5 76]2594 376,9
D : 2\38/\4---; D i 2\38/\7——j
I f\4847---:3d term + 0.003 I 4\060 .6--3d term + o OOO
i.I...i.....; ------- ’................................r....J....:■ ------
III I ~A» -356./4O\__________________________________ i||____________; ~A - 6.478__________________________
March 26j!940 Computed by: .................... Checked by: .. FORM 9
Figure 76.—Computation of position.
262341°—40----16 241
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J. Geographic to grid coordinates.—(1) If the control points are furnished on Form 13, “Geographic positions,” the need for this conversion before grid computation is obvious. United States Coast and Geodetic Survey Special Publication No. 59 shows a method of converting by interpolation, and a more precise method of computing by formula. Form 10 (fig. 77®) follows the latter with some modifications. Form 10 also differs from the coast artillery form in that the meridional distance on the central meridian is interpolated from the coordinate tables instead of from Special Publication No. 8. The results check within a few tenths of those obtained by the usual “computation of artillery grid coordinates from geographic coordinates.” Computers accustomed to using seven-place tables will find form 10 less laborious.
(2) The logarithm of K is obtained in the first third of the form, * followed by Xf, log Y'. The last quarter of the form is devoted to obtaining the Y value on the central meridian for the latitude of the station, and the Y coordinate results. The formulas for each are
a cot cf>
f 1 — e2 sin2
X'=K sin (3 k sin )
Y' = 2K sin2 (3 k sin h-2)
X' is the distance of the station grid-east or grid-west of the central meridian in yards; Y' is the distance in yards of the station grid-north of the intersection of the central meridian of the zone and the parallel of latitude passing through the station. The instructions which should appear on the form are given below.
GEOGRAPHIC TO GRID COORDINATES
INSTRUCTIONS
X and Ycoordinates are on (25) and (44) respectively.
(7Af=central meridian, e=eccentricity, a=-equatorial radius in yards.
(21) and (29) From table XII, TM 5-236.
(24) Be careful to get all significant figures correct. X' is positive east, negative west of CM.
(34) Y' is due to curvature of parallels.
(35) Y5 is CM value at first 5-minute intersection above or below station latitude.
(39) i is difference in seconds between of station and first 5-minute grid line to south.
Use seven-place tables with careful interpolation.
242
1 Station BHerkness A Proctor
2 Zone Letter B B
3 Latitude 0 38.42,0l\368 38'367/\707 ■ !• '
4 Longitude X 77\092l'\326 76 5834\834 i : ] .. • i i
5 6X( sec to CM) !3838\674 74485\766 I i
6 log sin 0 (see 16) 9796,0522 9'795/3/7 i • 1 :
7 log sin2 0(X 2) 9592/044 9590,2634 1 1 .. • i i
8 log e2 71830 5026 718305026 7]8 30 5026 7j8 30 5026
9 log e2 sin2 0(sum) 7'422.6070 1 ■ 1
IO e2 sin2 0 0'002,646/ 0'\002.6349 1 !
1 1 l-e2 sin2 0 0\997\3539 O\997 365! 1 •
12 log (l-e2sin20) 99988493 9\998 854/ 1 •’
13 •jlog (l-e2sin20) 9 999 4246 9\999 4270 1 : I ; t -r - 1 j
14 colog (l-e2sin20)| 0\000\5754 0\O00 5730
15 log a 6] 8435615 6'8435615 6^84 35615 6|843156I5
16 log cot 0 0\096\2797 0\097\7890 i ■ i ;
17 log K (sum) 6\940 4/66 6\941,9235
18 log 6 X(see 5) 4\/4/ 0945 4\/60 9235 1 ■
19 log sin 0 (from 6) 51796,0522 9\795,/3/7 1 : 1 :
20 log (6Xsin 0) (sum) 3'937,1467 3\956\0552 1 : 1 ' ' 1 1
21 S for log (6Xsin 0) 4685 4475 4\685\4359 '“"I I"-
22 log K (from 17) 6\940,4/66 6\941.9235 1 • i : r ■;
23 log X1 (sum) 5^63,0/08 5\583,4/46 i : I : •
24 X' \365\6O 3'\9 \383\t90\4 : ■ 1 i ; 1
25 X = 1,000,000 ± X' /\365\603\9 7 383 190 \4 • • : !
26 log (6Xsin0) (from 20) 3\937\7467 3\956\0552 1 I 1 ! i :
27 colog 2 9,69819700 9'698'9700 9^698 9700 9'698 9700
28 log (6Xsin0r2)(sum) 3\636,776 7 3655,0252 1 j i : 1 :
29 S for log (6Xsin 0r2) 46855430 4^685540/ ’ "1 * ! ■ i 1 i
30 log sin(6Xsin0-?2)(sum) 8'32/,6597 8'340,5653 1 j l :
31 log sin2(6Xsin 0-2) (X2) 6'643.3/94 6\68t .1306 1 : 1 • 1 i 1 :
32 log 2 0,301 0300 0,301 0300 0j30l0300 0|30l 0300
33 log K (from 17) 6^404/66 6'941,9235 1 ; i J i :
34 log Y1 (sum) 3\8847660 3\924 0847
35 Y5 N of Sta. (see 42) 7\787 5/8 \5 7777'407'5 : ‘ I I । : ■ : - 1
36 diff. Y5s (35-42) ; /O\//6\6 i /6j/6\5 ! • i : : 1 : • I : i 1
37 log (diff. Y5s) 4'605 0345 4\005.0302 1 I : 1 J.. «
38 colog 300 7522 8787 71522 8787 7,522'8787 715228787
39 log 60 (sec. over 5 S.) 2'084,7042 /\d55'56/6 r 1 ; 1 :
40 log 8Y(0-5) 3'612,0/74 3\383,4705 1 ' 1 • 1 : 1 ■■
41 6Y(0-5) + ; 4.0928 : 2\4/8\/ ; i -i ; i j..„ : ; 1
42 Y5 S. of Sta. 7'777.40/\9 r-767'28 5\4 : ■ 1 ’.......J J : I- 1 ...J j 1
43 Y' (antilog 34) + ■ 7,669\5 i 8 3962 : 1 _i ; l__
44 Y (sum) 1789.164'2 1,7 78,099'7 , ; i • i I
SURVEYING
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117
Date: March 3/^7940 Computed by: Checked by: FORM IO
® Geographic to grid coordinates.
Figure 77.—Interpolations and conversions.
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CORPS OF ENGINEERS
INTERPOLATION OF GRID COORDINATES FROM GEOGRAPHIC COORDINATES
INSTRUCTIONS
X is on line 19 Y is on line 32
(2) and (5): Seconds of 0 and X above next lower 5-minute line for 5-minute intersections, above next lower minute line for |-minute intersections.
(3) and (6): Divide by 3OO(seconds) for the 5-minute intersections, and by 6O(seconds) for the l-minute intersections, 4 ond 3 decimal places respectively.
Date: March.23,1940 Computed by : />U Checked by: X fl FORM IOA
No. Symbol Operation Herkness B Herkness B
O : t • z z
1 0 38 ,42 07 \368 38 42 10/ \368
2 Sec. 0 over 5 or 1 min : \j27\368 ■\ : 7 \368
3 C0 (2)/3OOor6O 4046 .023
4 •x 77 09'2! >326 77\09\2i '\326
5 Sec X over 5 or 1 min 26/\326 • ,2/ \326
6 ex 15)-300 or 60 .<57// .355
7 XI SW 7364,75 3\7 7364■5 8 4 |<5 I 1 ; 1
8 (13)X (3) ± - J7/\3 - ' W : 1 : 1
9 X2 NW 7364 3 3O\2 7364,4 9 98 : . 1 i L
IO X3 NE 7372 245 ,5 I366\O83 l<5 L 4 _...X
II X4 SE /372\678\4 7366 ,76 8 8 ! 1
12 (I4)X(3)± - \775\2 - flp
13 X2-XI (9)-(7)± - ,423'5 - ; 84,8 : 1
14 X3-X4 (10)—(II) i - ;432\9 ~ \ S5^ i 1 j
15 XA (7)+ (8) 1364 \582\4 I364\582fl T“" L j..... : “1
16 xe (II)+(I2) 1372 503 \2 7366 ,766 8 "■? T"-! 1
17 (I8)X(6) ± - 6 899'\8 -■ ,562 4 j 1 "" : * "I
18 XA-XB (I5)-(I6)± - 7,92O\8 - 7.5842 ■. ~'r‘ .. J--
19 X (I6)+(I7) 1365,603 4 7 3 65,604 '4 1
20 Yl SW 7785\O25f 1789,0 74 [4 . ; 1
21 (26)X(3) 4,O95\2 • 46 l<5 i 1 ■■■; ; i"
22 Y2 NW 7 795,74 7 \3 779/ 098 6 ■ : 1 ...... ... 1
23 Y3 NE 7795 482 \6 779/,765 1/ 4. 1... .
24 Y4 SE 7 785.36 O18 I789\I4O [d |.._..
25 (27)X(3) 4 095^3 : 46 [<5 i : i ।
26 Y2-YI (22)—(20) IO ,7 2 7 \6 2,O24\2 \ ■ ■■■■■1■'■■■ i i
27 Y3-Y4 (23)—(24) 70,72 / \8 2.024 \5 : 1
28 YA (20)+(2l) / 789,720 \9 1789, 7 2 / [O ; 1
29 YB (24)+(25) 7789\456\7 / 789, 7872 1 "T —1 : 1
30 (3I)X(6)± - \2 92\o - i 23^ 1 „...• !.. j... 1
31 YA-YB (281-129) ± - \335\2 - :■ 66\2
32 Y (29)+(30) 1789.164 1/ 7789\!63\7 _ ; i : 1 • 1
® Interpolation of grid coordinates from geographic coordinates.
Figure 77.—Interpolations and conversions—Continued.
X is on line 19; Y is on line 32.
(2) and (5) Seconds of and X above next lower 5-minute line for 5-minute intersections, above next lower minute line for l-minute intersections.
(3) and (6) Divide by 300 (seconds) for the 5-minute intersections, and by 60 (seconds) for the l-minute intersections, 4 and 3 decimal places, respectively.
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CORRECTIONS TO CONVERT GEOGRAPHIC AZIMUTHS TO GRID AZIMUTHS
CSW, CNW, CNE ond CSE » Azimuth corrections at the degree intersection SW, NW, NE and SE of point, from Special Publication No. 59.
60 and 6X-minutes and seconds of latitude and longitude expressed as 3-place decimal. (I5)=difference between geographic and grid azimuths,(~) in east half, (t) in west half of zone._________________
Stotion Zone 0 X Herkness B Herkness A See page 79 Sp Bab No 59
38 .42 07 38 42 ! 07 42 \5O \OO • [
77 09 27 77 09 i 27 70 \ 78 \00
1 2 3 CNW CSW (l)-(2) I \53 15 3 3 08.39 04 54 7 i / 2! i 50 !
7 ,50 47 20 i !7 ; r i
: 2 28 4 ,06 i ! 33
4 5 60 (4)X(3) °-700 i / 44 ■Oi 700 2,52 j 0.833 i ! \77 V-4--- -i— ......
6 (2)+(5) / 52 37 3 07 25 7 ! 34
7 8 CNE CSE i Aj M : M 58 4/ 2 2 30 27 58 47 no N; eg; 44 25 -4- •- - ....... — ;
9 (71-(8) 3 i 77 3 i 77 • 2 79 I ■
10 (4)X(9) 2 : 18 2 ' 18 : / 56
II (8)+(IO) 2 29.59 2 29\5O 2 i 02 2!
12 13 (6)-(ll) ± 6> - 37 28 Di,756 37 26 0i,/56 - \40\47 ' I 07,300 X 7 - : — i—
14 (I3)X(I2) ± - 5 : 57 t 5 ,50 - ; 72 !4
15 (II)+
14 (I3)X(I2) ±
15 (II)+(I4) ± • !
Vla\a-...Mqrch.23,l94O Computed by: ... Checked by: ____ FORM IOP
@ Corrections to convert geographic azimuths to grid azimuths.
Figure 77.—Interpolations and conversions—Continued.
CSW, CNW, CNE, and CSE=azimuth corrections at the degree intersection SB', iVW, NE, and SEof point, from Special Publication No. 59.
8 and «X — minutes and seconds of latitude and longitude expressed as 3-place decimal.
(15) Difference between geographic and grid azimuths, (—) in east half, (+) in west half.
245
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117 CORPS OF ENGINEERS
(3) While five-place logarithms are generally employed in grid computations, they are not useful, on Form 10, as X', for example, often has seven significant figures, which require complete interpolation.
(4) Form 10A (fig. 77®) is a rearrangement of the “Computation of artillery grid coordinates from geographic coordinates,” shown in Special Publication No. 59. Either 5-minute or 1-minute intersections may be used, and logarithms are not needed. The coordinates should not differ more than a yard from those computed on Form 10. The instructions which should appear on the form are given below.
(5) Form 10B, “Corrections to convert geographic azimuths to grid azimuths” (fig. 77®), is an application of the “Transformation of geographic azimuths to grid azimuths” in United States Coast and Geodetic Survey Special Publication No. 59, a method of interpolating in the table of “Corrections for the reduction of geographic azimuths to grid azimuths” in the same publication.
g. Azimuth and distance from grid coordinates.—(1) In Form 11 (fig. 78), before the X and Y coordinate differences are obtained, the magnification of scale (see par. 118c) is deducted from the Y component, and the grid-azimuth is found through the tangent of its bearing. The direction diagram should always be plotted, as the quadrant of the azimuth is thus indicated with certainty. The form is partly self-checking as the log distance is found by both sine and cosine of the bearing. The two values should check closely, and the mean is taken as the log distance.
(2) In figure 78, one of the lines of the figure computed on the third-order forms is used as an example. This is an extreme case, since grid computation is not intended for such large figures. While the distance always checks within a yard or so, the geodetic line being the shorter, the azimuth may differ 10 seconds or more. This variation may be partly due to the use of five-place tables and the coarseness of the interpolation of the scale magnification. However, the differences between grid and geographic azimuths should be remembered because geographic coordinates derived from grid triangulation cannot be used to carry third-order work forward. In using the grid azimuth correc-
246
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117
Figure 78.—Azimuth and distance from grid coordinates.
247
SURVEYING
AZIMUTH AND DISTANCE FROM GRID COORDINATES
The diagram shows the quadrant of the azimuth.
_________As the magnification of scale will not be carried further, it is deducted from 6Y.
Sta. I AHerkness X / 365 603\9 Y j\ 789\ / 64\2 Magnification of scale
Sta 2 A Proctor X /'383\/9OL Y / 778 0 99 7 at A Proctor
6X j / 7 686 5 6Y ! H''O64\5 1000 yds. (lOths.)//./
Grid |North |Og 6X 4\245/8 J MnS : /6 yds, per 1000 1.5
____________ -tog6(Y-M) 4, 043 28 6(Y-M) i ! 104 7*9 MNS /6.6 log tan a. O\ 2OI 90 , Bearingi S7 5/ 47
log 6X 4\245./8 log6(Y-M) 4\ 043 28 Az. 1-2 .302 08 .93
Mean -log sin a 9^,927-77 ; -log cos a 725 86
logs 4.3/ 742 log S g.\3/74l log S 4\377 42 Yards 20769.0
Sta. I X : i । Y । Magnification of scale
Sta. 2.............. X T..............]....j Y T" j"” I
6X i i I 6Y T r~ 1000 yds. (lOths.)
GridiNorth |Og 6X “■ j MnS _ ........i.....yds. per 1000
-log6(Y-M) । i i 6(Y-M) ~1 I T~ MNS
------------ 1 - - .. < ... ---X--- I . , ----- log tan a i s---i Bearing i i
log 6X ""J ' +log6(Y-M) i Az. 1-2
Mean -log sin a j ' ; -log cos a . ________
logs log S ) i i log S i Yards
-■ ■— —..... —u.. = =?= ■ ■ ■ ? J1 r - ■ ’
Sta. I X ; i Y •! j i Magnification of scale
Sta. 2 X \ j Y Ji l at
6X ■ j 6Y i j । 1000 yds. (lOths.)
Grid|North |Og 6X j j i MnS """ |..........................' yds per 1000
____________-log6(Y-M) [...............1 6(Y-M) , 7~ MNS log tana I i ;................Bearing i
log 6X + ; logb(Y-M) [ i Az. 1-2
j....•;....J ..’ - * ——------------------— •—
Mean -log sina , : ; -logcosa । ;_______
logs ° log S , log S { ! Yards _______________________
Sta. I X j i । Y : j j Magnification of scale
Sta. 2 ......... X ..............}....j.. Y I ........... : j at
............... 6X i j ~T~ 6Y : i j 1000 yds. (lOths.)
GridiNorth !og6x MnS L;.......J 1"~ yds. per |QQQ
____________-log6(Y-M) ..........j P 6(Y-M) i ; j MNS log tan a I j ; Bearing
log6X | : log6(Y-M) j.... L_______Az. 1-2......... ’ ...
Mean -log sin a { j i -log cos a [ ________
logs log S j ’ j log S j , Yards
Sta. I X • , I Y i I । Magnification of scale
Sta. 2 X ' : ; Y i I at .......................................
6x j ; ~f~ 6Y ’ i 1 1000 yds (lOths )
GridiNorth |og $x ~( MnS ...........[.....j'" yds, per 1000
____________-log6(Y-M ~i............. 7 6(Y-M) : i ] MNS log tan a ‘ i ' Bearing ............................!....j____
log6X j । j log6(Y-M)J...................I ......Az. 1-2:____[....{ ...
Mean -bgsin a j j j -logcos a { ;_______
togs log S { ■ ■ log S { ;_______Yards__________________
Date: April 3, /94O Computed by: _____Checked by:M.J-.X. ....... FORM II
TM 5-235
117 CORPS OP ENGINEERS
tion table in Special Publication No. 59 (duplicated in table L, TM 5-236), the interpolation must be as close as possible (fig. 77®). In using some of the tables in the front of Special Publication No. 59, close attention must be given the grid zone letters before entering the longitude columns. In the tables of grid coordinates for 5-minute intersections, the values for the east half of each zone are given on the left hand pages.
h. Trigonometric elevations.—The determination of elevations from vertical angles to the ocean horizon, the effect of curvature, the opposite but varying effect of refraction, and the use of the correction angle K (table XVI; TM 5-236) have been explained in paragraph 110a to d, inclusive. Examples of the computations on Form 12, “Trigonometric Elevations,” are shown in figures 79 and 86. The instructions which should appear on the form are given below.
TRIGONOMETRIC ELEVATIONS
INSTRUCTIONS
(1) and (5) Station 2, elevation unknown, station 1, elevation known.
(7) and (10) Cross out inapplicable unit.
(8) and (9) Cross out one or both conversion logs.
If reciprocal angles have been observed— Use block II, and omit block III.
Block I and line (22) The correction for heights of signals and instruments is J4 (Sl-f-Zl—S2—Z2).
(11), (12), and (14) Signs must be shown; (11) same sign as Form 6; (12) sign opposite to Form 6; (14) same sign as the greater of (11) and (12).
If the vertical angle has been observed at only one station— Use block III, and omit block II.
Block I and line (22) The correction for heights of signal and instrument is—
+U— 82 if the observation was made at station 1 (known elevation).
+71 if the station mark at station 2 has been observed.
—Z2+81 if the observation was made at station 2 (unknown elevation).
(16) K is interpolated from tabic XVI, TM 5-236. Note that tabular distances are in feet.
(17) Algebraic sum of (15) and (16).
If observations have been made only at station 2 (unknown elevation).—(21) A h has sign opposite that of V, line (17).
(In all other cases A h has same sign as V.)
Use five-place logarithms, except that log tan V should be taken from single-second table in Vega (rounded off to five places). Angles to nearest second only.
248
249
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SURVEYING
m (I) station 2 A Lee A Lee A French A French________A French____________________________
■^(2) ...... Heights S2 '8.6 Heights S2 IdP. Heights S2 Heights S2 777 Heights Sa XL Heights S2 . Heights S2 -
0 (3) 12 4.9 12 4.9 12 24.3 12 243 12 24.3 I.2___ 12----------
* (4) ..... 2) 23.5 2) 23.5 2) 59.9 2) 59.9 2) 59.9 2)____________ 2)________________
e (5)Elevation of 1 357.3 ft. - H.8 2946 ft]....-.... HL 3573 u -. 39.6 294.6 til. 300 a .30.0.n... ft.L..
£ (6)station 1 A Tierhness__A Proctor AHer/iness A Proctor A Lee _____________________________________
E (7)!og (l-2)ydtm 4I6342^>\ 15.2 4.04-266\9>\ !5.0 382806\..>...- -.T.4—...+.. ......>.T........—...- .I.r-i-...L..|..— I.).-
18 .........:■■■■-...i..:......i..r-— ...-.....;.t ......- -........!..... .-i.—-■— 19............'......:......: i I :.!.......>.......i..............•.|....• I
.....-.........-...■..■- - ..I..4—.I— ! .....—i. .........-.........I- - -i I...i..J 20......-.......I....j...-.I...i...i...1-..-.i..u..................L....I...1...1..1-21..............i....i.................4-4...4..4...-.........4....L......1.....i..I......
22 -........ -....i.!......4..1..-.i.-i..-.. . J.i__....-...-..!...1....I..L._.I..;.....
2Z_________________1_i____1_4__U_____1_i zrz_ j________i______1_J___i___L_1_I I i ! -I
__________________________________________________________Computed by^/S. Checked by.^^.P-.... FORM 13
Figure 80.—Geographic positions.
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TM 5-235
SURVEYING 117-118
i. Geographic positions.—Form 13 (fig. 80), copied from a similar United States Coast and Geodetic Survey form of the same title, has been filled out so far as the computations have been carried in this paragraph. The data are obtained from Forms 13, 8, 9, and 12. The azimuth and back azimuth of a line are given only once. The compiler and checker initial only the office copy.
j. Disposition of completed computations.—On completion of a project in time of peace, all notebooks, with general index, all computations, and a set of the aerial photographs used are sent to the headquarters of the corps area or department in which the work was done. In time of war, the above records are retained in the organization as long as they may be of further use, and are then disposed of as directed by higher authority.
118. Solution of grid triangulation.—a. General.—The chief purposes of the military grid are to—
(1) Aid in the designation of map positions.
(2) Provide a reference for azimuths on parallel lines, independent of the convergency of the meridians.
(3) Facilitate the accurate calculation of the azimuth and distance between points in the field.
All map and control data furnished the combat troops are referred to standard military grid coordinates, which are also adapted for the determination of such control data. All basic geographic data have to be converted before being used. Grid azimuths are clockwise from grid or Y north.
b. Computing on military grid coordinates.—As grid triangulation is intended for the most rapid determination of control data, the computations have been simplified. Since the figures are generally simple triangles, adjustment is reduced to correcting the sum of the angles to 180°, though a method of obtaining consistent results through more complicated figures by small adjustments during solution of the component triangles is explained in paragraph 1196 and c. Lengthy position computations are avoided on the rectangular grid where small discrepancies of coordinates and azimuths may be adjusted by adopting the means of discordant results, provided no errors have been made in the calculations. As the notebooks may never be accessible during computation, Form 6, “Transcript of results,” from which the computing section works, must be most thoroughly checked in the field to insure freedom from mistakes, omissions, and ambiguities. Five-place logarithms are used throughout, except that it is convenient to get the log tangents of the vertical angles needed for Form 12, “Trigonometric elevations,” from the single-second tables in the
251
TM 5-235
118 CORPS OF ENGINEERS
seven-place Vega, rounding them off to five places for the computation.
c. Magnification of scale.—The polyconic projection enlarges north and south distances,' the amount of enlargement varying from zero on the central meridian of the grid zone to 2 yards per thousand yards at 4° east or west of the central meridian. The rectangular grid of course remains constant in scale and the error appears in the coordinates as magnification of scale. A table of “Corrections to y coordinates for magnification of scale” is given in United States Coast and Geodetic Survey Special Publication No. 59, and is reprinted as table XLIX, TM 5-236. In the computations of grid triangulation, one of the known stations is designated as the base station for the computation. The one farthest north or south is preferred, in order to avoid confusing positive and negative corrections. The differences in the y coordinates between the chosen base station and each of the other known stations has to be corrected before computation by applying the correction for that vicinity to the grid y differences. After the computing is otherwise completed, the magnification of scale in the correct amount for the y differences between the base station and each of the others is so applied to the y coordinate of the latter as to increase the distances, thus restoring all the stations to the correct military or map grid coordinates.
d. Map and true grid azimuths.—Because of the magnification of scale, no map grid azimuth (except one exactly grid north-south or east-west) computed from map grid coordinates is the true grid azimuth. The table “Corrections for the Reduction of Map Grid Azimuths to True Grid Azimuths,” Special Publication No. 59, shows these errors, which may amount to several minutes, for various azimuths and parts of the grid zone. By the procedure described in c above, the magnification of scale is eliminated and all azimuths obtained during the computation must be the desired true grid azimuths. The latter should agree closely with any obtained by applying the “Corrections for the reduction of geographic azimuths to grid azimuths” (see table in Special Publication No. 59; also table L, TM 5236), to the geographic azimuths, allowing 180° for the change of reference from south to north (par. 117/(5)). .
e. Procedure of computation.—(1) The computation of a grid triangulation should be commenced as soon as sufficient data are received from the field, as this may be the slowest part of the work unless several computers are available and the work is well organized. By careful consideration in the assignment of tasks, time can be saved in two ways:
(a) If the work can be so organized that errors are detected at once, less time will be spent in searching for mistakes.
252
SURVEYING
forward
764D!2
64E!
[6482 £
Figure 81.—Diagram of grid triangulation.
TM 5-235
118
(6) The work to be done by each computer should be reduced to & minimum and kept to computations of the same nature, so far as possible.
(2) Detection of errors is best insured by carrying out all computations in the same form, and by having each computation done by twc men working concurrently, but separately and independently. Tc do this throughout the work would mean that each portion of it is done twice, but it should be generally sufficient to duplicate the work in this way only so far as the computation of the base and the log sides. Coordinates of each point must be computed from two known points. If these two computations are done by separate computers, the fact that the coordinates agree is a check on both computations,
Intersected points must be fixed by at least two triangles; thus they have their own internal check.
(3) The order in which the main scheme triangles are to be solved must first be decided, it being remembered that a triangle cannot be solved until one side is known. Coordinates of the point forming the apex of a triangle should be computed as soon as the triangle is solved, a check thus being secured on the log sides. If this were not done, an undetected error in a log side might be carried through the entire computation, and much time wasted.
f. Organization of computing section.—(1) The diagram of a small grid triangulation, traced from the reconnaissance plot (par. 98o), is shown in figure 81. A rough copy should be given each computer.
253
118 CORPS OF ENGINEERS
An inspection of the diagram shows the order in which the computations should be accomplished, as follows:
(A) Staff noncommissioned officer in charge of section.
(B) Noncommissioned officer, assistant.
Triangle Base Log sides Coordinates
ABC AB AC, BC J [C from A |C from B
CBE CB CE, BE J \E from C \E from B
ACD AC AD, (CD) D from A
CED CE {CD), ED D from E
{CD) is check side for an intersected point. All of these computa-
tions are shown in figures 82 to 87, inclusive.
(2) In a computing section of five experienced men the work
might be distributed as follows:
(D) ^Compute log sides and coordinates.
(D) Computes elevations and acts as draftsman.
(a) Assembling data.—Assume that the grid coordinates, log distance, azimuth, and elevations of line AB have been furnished or computed from the geographic coordinates as described in paragraph 117/ and g, and that the other data have been received on Form 6, Transcript of Results.
(6) Eccentric corrections.—(A), assisted and checked by (B), computes any required Form 5, Reduction to Center, and makes the necessary corrections on Form 6. No Form 5 received from the field will be adopted. Any preliminary log computations needed in connection with the eccentric corrections are made by (C) and (D) as outlined in (t/) below.
(c) Calculation of azimuths.—Assisted and checked by (B), (A) completes the upper part of Form 6 and works out the azimuths from each point to all points observed. This must be done in order for all occupied stations, beginning with A and ending with E. As deduced on Form 6, the azimuths are entered on Form 15, Control Data. Slight differences between azimuths and back azimuths will not be ineaned, but will be entered as found.
(d) Solution of triangles.—(A), assisted by (B), prepares two copies of Form 8, Solution of Triangles, for the triangle ABC, filling in the observed angles at A, B, and C, and log base AB. These forms are then handed to (C) and (D), who correct the observed angles and compute logs AC and BC.
254
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118
SURVEYING
(e) Computation of coordinates.—Assisted by (B), (A) prepares two copies of Form 14, Coordinates From Azimuth and Distance, filling in the following data:
(1) Station C From station A X for A Y for A Azimuth AC log AC
(2) Station C From station B X for B Y for B Azimuth BC log BC
Form (1) above is handed to (<7) and form (2) to (D) who compute the coordinates of C from A and B, respectively. Stages (/ (8) Mean correction ±______________ _____________
(9) Stations Observed \ A For ward | 77 64E3 | '7645/ ] |
Horizontal Angles 1 ' i | ' I This
(10) Observed Calculated ] 40 29 54 \26l. /2 !5 I '58 !7 5/ ' I | angle
(I I) Eccentricity corrected I I j l ] lot left
(!2)Adjusted angle .......|,„ ....j.............;........... J.... J....................; side.
Directions
(l3)Observed Calculated 00° 00'00"261° 12' !5" 3/9° 30'06" _ ° " ° ' "
(14) Eccentric reduction — — ----
(15)Eccentricity corrected — — —
tie) Azimuth ________ ' Z98 06 /218327 737 36 78..............................jAAAAAAAA.
(l7)Adjusted azimuth
(18) Sketch of signal , / J T-*
—o—T—7^—„..........— \/ /nsrrumenf L J
Note Book 12 Pages 22,23 X.
(19) Copied by 73. A ' '
(20) Checked by f
(21) Vertical angle ±| .....yOl !8 I5\l-O2 46 /7\ _______________________
FORM 6
Figure 82.—Transcript of results at A Forward.
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SURVEYING
TRANSCRIPT OF RESULTS
INSTRUCTIONS
Every figure of the notebook must be checked by the observer before this form is made out. The observing party fills in only the date, the station occupied, a diagram of its signal heights, and the H.I.; the stations observed and the observed angles or directions; the last four lines showing the vertical angles, and the parts of the signals to which vertical angles were read; the notebook references, etc. Every figure of the transcript must be checked by the observer to insure freedom from mistakes, omissions, and ambisuities, since computations will usually be started, and often completed, before the notebook reaches the computing section.
No corrections for eccentricity will be made on Form 6 in the field.but a copy of computed Form 5 should be attached for the guidance of the computing section.
262341°—40---17
257
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CORPS OF ENGINEERS
(f)Transcript of results at V 64E/
Date: „ HI.fee*
Signal heights (2) With V64D/2 qy (3)Azimuth from ditto 25 With A Forward 7° 36' 78" ditto 761° 27' 38"
Computed by J—7.0 (4) ± 180 00 00 ±180 00 00 (5)Azimuth to ditto 77 36 78 ditto 347 2/ 38 (6)Angle from initial sta - 96 74 3/ - 00 00 00 — (7)Correction 4347 27 47 434/ 27 38 ■iff.. Checked by: 2 5.2/ (8) Mean correction ± 34! 2! 42 ■—
(9) Stations Observed A For ward V 64 D 72 V64E3 ' [64E2
Horizontal Angles (10)Observed- Calculated 'j04 00 30 (II)Eccentricity corrected ! 96 74 31'64 29 48\95 7 5 ll\ I-TU- i This | angle lat left
(!2)Adjusted angle — 1 i side.
Directions (l3)0bserved Ctrteulafed. 00 ° 00' 00" 96° 74'3!" 760° 44' 79" 255° 59' 30" 0 1 II
(14) Eccentric reduction — —
(15) Eccentricity corrected — — —
(l6)Azimuth 34! 2! 42 77 - 16 73 742 06 0/ 237 2/ 72
(l7)Adjusted azimuth
(18) Sketch of signal H tr*— Sta mark Grey tank (7op)
Note Book 10 Pages II,72 (19) Copied by £ 92 b \
(20) Checked (21) Vertical by or 2-angle ± -07 75 06 -02 42 57 -07 22 77 -02 09 05
11) Transcript of results at V 64 E 3 Date: April 2,794-0 H.l. 5.2 feet
(2) With V64D72 WhV64FJ (3)Azimuth from ditto 799° 76' 27" ditto
(4) .....±180 00 00
Signal heights
9.5
9.0
-7.0
□
742° 06' 07"
±180 00 00
(5)Azimuth to ditto /_9 18 27 ditto 322 06 0/
(6)Angle from initial sta.-OO 00 00 -302 47 79
(7)Correction + 79 78 27 + 79 76 42
Checked by.
(8) Mean correction +79 78 35
Computed by: /V
(9) Stations Observed V 647972 164E2 77646!
Horizontal Angles ; : (lO)Observed Cuteuta+ed- \57 72 47,263 56 06\38 5/ 73 (II) Eccentricity corrected | (l2)Adjusted angle i This I 1 । j i angle at left — i - 1 ' side.
Directions (l3)Dbserved- Calculated (14) Eccentric reduction 00° 00' OO" 263° 56' 06" 302° 47' 79" o 1 II o I II
(15) Eccentricity corrected-(!6)Azimuth (17)Adjusted azimuth 283 74 4/ 322 05 54 —
(18) Sketch of signal
Top of grey tank Instrument
Note Book 12 Pages 24,25 (19)Copied by 73.6.
(20) Checked by Of (21)Vertical angle £ -07 76 47 -OO 24 24 tO! 79 06
FORM 6
Figure S3.—Transcript of results at V64E1.
258
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TRANSCRIPT OF RESULTS
INSTRUCTIONS
Every figure of the notebook must, be cheeked by the observer before this form is made out. The observing party fills in only the date, the station occupied, a diagram of its signal heights, and the H. 7./the stations observed and the observed angles or directions; the last four lines showing the vertical angles, and the parts of the signals to which vertical angles were read; the notebook references, etc. Every figure of the transcript must be checked by the observer to insure freedom from mistakes, omissions, and ambiguities, since computations will usually be started, and often completed, before the notebook reaches the computing section.
No corrections for eccentricity will be made on Form 6 in the field, but a copy of computed Form 5 should be attached for the guidance of the computing section.
259
TM 5-235
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CORPS OF ENGINEERS
(1) Station and letters (2) Observed angles (3) Corr. ± (4) Corr. Plane Angle (5) Log sine (6) Log side (7) Side (8) See No. (9) Sph. Angle
Forward A D/2 B fl C No 1 Sph Exc. 43 i /5 4029 96 /4 179 59 26 54. 34 5! / 3 + 3 t... A 29 57 34 1 9\835 9'812 ' 1 ' 9\997 3\709 87 53. 4/ 66 3 \545 .53 3\522\l9 3'707.07 i BC AC A B 2 3 -
_E! C .............D/2 B El E No 2 Sph Exc. 64 58 57 180 29 . !7 . /2 OO «i* .7... -...7... - 6 4! .44 35 1 : ?)?55tf7_. 9D29 8/ "'I ”i 9'924 62 3\620 9/ A576\38.. 3-35072 3\545-.53 1 i - 6E 08 . BC .4... /
Forward A E/L......... c ... . IE2 _.D No. 3 Sph Exc. 36. ./PF. 39 !8O 26 oo 32 OO X $ $ s - / - 2. - / 52 28. 40 ?\77.18A... 9\986 -89 fi803\92 . 3 7/ 8 \27 1 ,o 3\492 3'705 76 .3522 (3/054 yd. ?/ 09. AD 4C 95./yc 4 ../ . ' Erro " 3ya
El C E3 E IE2 D. No 4 Sph. Exc. 95 38 45 179 75 .51..... 53 59 29 53 + 3 t...?.. t....2 14 .15... .7.1... 9^998.17 7797 50 9,856/4... 3\694 58 3'692.75 7<9 3f 92 08' 3'55072 ’1 1 1 i - DE c.P Of 3 2...
No.5 Sph. Exc. - - - - 4— . . . - 1 1 I I —1 1 "T 1 1 i ~t - i । ••••I- 1 — -- . _ —
No.6 Sph. Exc. ■ — “1 ■ ' 1 ' - T“ I 1 i ‘ T : 1 ; l I I -{ 1 —4. 1 - - - — . ..
No 7 Sph. Exc. - -■ - - 1 i "T i - I i —t 1 i : i ? — 1 1 I 1- - ...4L........ — - —- —
No.8 Sph. Exc. _. .. . ....... .. . .. 1 ....1— 1 —1- 1 l..._ 1 . ....... ” T 1 -■•t- 1 — - ... . ..... — —
Oa\^'.....Apri,i,2^/940 Computed by.ji.yz’.. Checked by..^^ 3/ ... FORM 8
Figure 84.—Solution of triangles.
260
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SURVEYING
h. Eccentric corrections.—The use of Form 5, “Reduction to center” (fig. 71), has been explained in paragraph 109.
i. Calculation of azimuths is accomplished on Form 6 as shown in figures 82 and 83.
j. Exercise XVIII. Calculation of azimuths.—Commencing the office computation of the data resulting from exercise XVII, and pertinent basic data furnished by the instructor, the student will now complete Form 6, incidentally making any required reductions to center on Form 5, as outlined in /(2)(6) and (c) above.
k. Solution of triangles.—Form 8 has been explained in paragraph 117(/. Figure 84 shows the usual employment of this form with the triangles listed clockwise, giving first the ends of the known side. In those with one station unoccupied, the third angle has been deduced from the azimuths of the sides, which gives a more probable value than would be obtained by subtracting the sum of the other two angles from 180°. Neatly lining out discarded values, as the seconds in column (2), is permissible in any Form where it is believed necessary to prevent abstracting an uncorrected value, provided the crossed figures are left quite legible. In this example, the antilogs for the side CD have been set down in order to show that their difference is negligible. .
I. Exercise XIX. Solution of triangles.—Utilizing the completed Form 6 and the given data, the student will fill out Form 8 and compute all logs sides from the corrected angles. This exercise and the next should be worked concurrently, thus securing an independent check on the log sides before continuing with the solution of the next triangle.
261
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118
CORPS OF ENGINEERS
Sto. 2 £/ Sta. 1 Forward 1 : i !og(l-2) 3\d22\!9 J log sin a 9\504'63 i log(l-2) 3,522/9 log cos a f 97660 i Magnification of scale From forward
(l"2) log(l-2) 3'676'38 ! Magnification of scale
S’a 1 £>/2 log sin a 9\5/935 i “T f • log cos a 9'974 86 = From Forward
(l-2) 897 /2 i From
(l-2)oc /42 <9 Graph 6 O/ 1 i ; log AX _3\339\09H AX ± j\ 2/83'2 log ... ^447.84 \ Ay ± -: 2 8044 Thousand yds. (to tenths) Yds. per thous.(to tenths)
— r— + X| /.379'893\8 ! ■ '1 yi l'823.038\2 Magnification ±
No. 4 X2 /382O77\O I2- /.82O 233\8 Map y2
Adopted coordinates '' X2 = ; _i_ 1 y2= ; — Map y2= See No. 3
Sta. 2 j££ log (1-2) 3'705/6 1 T 1 — log since 9\435 49 log AX 3\/9O65 i 1 : •' log (1*2) 3706/6 : Magnification of scale
Sta. I A Forward (1-2)a /97 48 3/ ' " I : ~'T log cos a ^157^6(9 ; log Ay 3\683 d4- i From For war a[ Thousand yds.(to tenths) 4 3
Graph AX± -i 1,65^1 I r “T Ay ± -• 4.\8Z8\8 Yds. per thous.fto tenths) 1.5
1-+ X| 1378 8301 yi /'■826\l9l\7 Magnification! -7.2
No. 5 . /. ■ ! 1 X2 1377 2790 y2 1821 362'9 Map y2
Adopted coordinates X2= / 377 279\/ y2 = /'-.SB/-363\0 Map y2 = /,.82/,.335.8
Sta. 2 I££ log(l-2) ! log (1'2) 3\692 75 : Magnification of scale
Sta. 1 £"3 (l-2)a 2Q3 14 4/ log sin a g\ 988 ,29 | log AX ^68/ 04 ; log cos a 9^36005 i log Ay 3'052 80 i From Thousand yds.(to tenths)
Graph AX ± -i 4:7371^- : ! f Ay ± i-\ //29\3 Yds. per thous.fto tenths)
— + 1 : 1 xl 13820770 y\ i\82O\233\8 Magnification ±
No. 6 X2 /\377-.279\2 y2 i82/ 363\/ Map y2
Adopted coordinates X2 i -j— 77. ' 4- Mcp y2 5ee No. 5
___Computed by: Checked by:£ J. 37...FORM 14
Figure 85.—Coordinates from azimuth and distance.
262
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COORDINATES FROM AZIMUTHS AND DISTANCE
INSTRUCTIONS
In a system of grid triangulation, this form should be computed after the solution of each triangle, thus securing an independent check on the log sides.
Every point is computed independently from two points of known coordinates; station 1, known; station 2, unknown.
The azimuth (a) is obtained from Form 6; the graph indicates the correct signs for AX and AF.
The log sides are obtained from Form 8.
For the magnification of scale, the thousands of yards are obtained by subtracting Y of the base station selected for the computation from Vof the new station. The yards per thousand are interpolated from the table, “Corrections to y coordinates for magnification of scale” in Special Publication No. 59 or the identical table XLIX, TM 5-236. The sign of the product must be such as to increase the true grid distance to the map grid distance.
The adopted coordinates are the means of the independently determined coordinates. Adopted Ya may be crossed out after map grid Ka is obtained.
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|(I)station 2 77 645! 7764E/ 7764E 3 7764E 3 I 64E2 I 64 Efl I 64E2
(2)..... Heights S2__9.8 Heights S2 .9.8 Heights S2 5.2 Heights S2 0.0 HeightsS2 Heights S2 Heights S2
® (3)............ 12 5./ 12 5! 12 5.2 12 52 12 [2 12
§(4).............. 2) 14.9 2) !4.9 2) 10.4 2', 52 2', 2\___ 2)
(5) Elevation of i... 3856 ft[-.7.4 103.5 ft - 7.4 103.5 ft." 5.2 611.0 ft.- 2.6 885.6 ft 6/1.0 ft ‘ 363.3 ft
e (6)Station I__ E Forward_7764D/2____77 64D/27J64EI......... N Forward' \764E! ..7764E 3
£ (7) log (1-2) yds. S. 352219fl\ 14.3 354553 si 15.0 357638 \ 51. 370516 [si 3.49210 fly 8.69275fly
E (8) log yds.-ft. 0.47712 II 47 0.47712 II 5.0 0.4 7 71211I 5.0 0.47712 II 5! 0.47712 li 4 7 0 47712 II 5./ 047712 II 5.2
£ (9) log m. to ft.. 51598 2 190 0.5 1598 2) 0 51598 2’ 20.0 0 02Hi 21 .'0.2. 1075-1-5-9-8 2 -0-5T5VB 2)_ 0 5.598 2
(I0)iog (1-2) ft. 39993/] + 9.5 4 02265, + 10.0 4053502 /P.O 4.02784 + 53 4.18228 + 4.7 3.96922\ + 5! 416987. + F'.
GD+VAl ± + 0/ /8 36 + 02 46 F7 +0! !8 15 -01 22 17
(i2)-VA2.... ,± + 01 15 06 + 02 42 57 tQ! "!5 47-0/.!9..0'6~'~...... .............................
(13)Divide sum by Z\02 33 42, z05 29 74 Z\02 35 02 Z\02 4/ 23 Z) 2) z}
(14)...V.. ± + 0/ !6 5/ + 02 44 37 + 0! !7 3! - 0/ 20 42_____________________________
(15)VAl.... ± ...... ..........__...................... ^7.00 28 46 -02 09 05 -00 24 ~24~
(I6)K.........+.......... t............+___________+............+....... 6/ 04.+..00 39 +......0/ " 02
(I7)V......±____________________________________________________- 00 27 42 - 02 08 26 -OO 23"""22
(18) log tan V 8.34944 8.68053.8.353/9 ..8.37068 790622 8.5726/ 783 23 3
(19)..........log (1-2). .3. 9993/_4.02265__4 05350_____4.02784_____4 18228_____ 3 96922 4 16987
(20)log Ah (sum). 2.34875__________2. 703/8_2.40669,____2.39852_____2.08850 ___ 2 54183 2.00220
(2D Ah.... ± . +. 223.2 ft + 504.9 ft___ + 255.J ft. ..-250. 3 p ............7..I22 6'. ft -348.2 ft - /00.5. ft
(22)his a hss. ± * 2 1 + 2 6 ... + 48 + 25 _+ 4 7 + 5 / +52
(23) Elevation of i _385.6_103.5_103.5_____6! 10' .....3856 6iio 363.3
(24)Elevation of 2 .._6!0. 9_____________611.0_363.4_____363.2________267 7 2679 2680
(25)Adopted EI.of 2. 6!1.0 363.3 \ ~_______267.9
Da,e; April. 2,194:0 _ Computed by:.l^(^’_. Checked by _ FORM 12
Figure 86.—Trigonometric elevations.
H H ft
264
CONTROL DATA Organization;.^th._Engr.Q>._(Jo/pg}. No. /_Date:..April.2J.94O....
.... _ . Basic datum: North American 1927
Map Index ___________ _________Zone Letter 5 ................. ....
____________ Vicinity :...6flrr/(o<7 .....Car/fpn County Mgryjand, .State Line Station and_Grid Coordinates (Yards) Elevation True Grid_Log (Yds.) Distance Line
To Station Diagrams No. Description X----Y--------Feet Azimuth Distance Yards No.
1 ZA Forward i\378\83O\l l\826\l 9 l'\7 :385l6 7/8 \ 06 \ 72 ^64012_3 707'07 I.O94\/ I |~-£0 "\.// T
2____________________Concrete\.mpn,_ ..J_[_L_|.j_j........ I. .£7.1.2/J. . Y. __\363\3_ _/9 (78'y35_ 764D(2 .^576)38 _ 3(77ofi. » rFl~*° hf trd 11
15 .2(Pipe___:__j_.J...[.j..J............................{.|__ 283\/4_), 4/ 164E2 3(692(75 _. 4\928\9.15 LJ—70 96 ftNcTfi
16 ..........[__J__।..I__i__4_____________1_\-... 332\_O3\ 54 V764EI_3'55O)(72._..................................3\5_54fi__ 16 J_ of rum G
17 i I I i i J | j : ’I i I 17
IB I64E2...._iA77(379'l....f82/\355'^_ .\26 7\9 ..........J__......i__|.... IB ■*_: Top of grey
19 Grey TanH . I ( J tfop)}...... 4 ............. I ■ ■ 19 tank.
20 _ .. . ' 1 I.... ......I.. ! ...i. . I 20
21 _ i ....[......J.I.I........L.J i ] I ' | _ 21
22 _ ........ J j. .. L. J J..............I i. ...... I.... .J. j.. 22
23............i..i..I..J..I. I ...i..J.. ...J.I......................J... .i 23
1241_________I ■ : ill i I 1 ; l| i I ...........I _________|l I I I 12^1__________________ _______
___________________________________________.________ Computed by Checked by d/O form 15
Figure 87.—Control data.
SURVEYING
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118
265
TM 5-235
118-119 CORPS OF ENGINEERS
m. Exercise XX. Coordinates from azimuth and distance.—In conjunction with exercise XIX the coordinates of the unknown point in each triangle should be computed on Form 14 (fig. 85) as soon as each triangle is solved. The instructions which should appear on the form are given on page 263.
n. Trigonometric elevations.—Form 12 (fig. 86) has been explained in paragraph 117A, where the instructions have also been reprinted. General information on curvature, refraction, and the K correction angles is given in paragraph 110a to d, inclusive.
o. Exercise XXI. Trigonometric elevations.—From the data furnished and derived on Forms 6 and 8 compute on Form 12 the elevations of all stations of the grid triangulation scheme, showing the adopted elevation for each of them.
p. Control data.—All data in military grid coordinates should be published on Form 15 (fig. 87). Only the office copy is signed by the compiler and checker. The given data in this sample have been underlined.
q. Exercise XXII. Control data.—Fill out Form 15 for the triangulation and computations which have been performed in exercises XVII to XXI, inclusive.
119. Miscellaneous computations.—a. General.—Several examples of computations which are less frequently needed have been collected in this paragraph. The list is not exhaustive, but familiarity with all of the procedures in this section should enable a computer to undertake any problem that may arise short of least-square adjustments and such specialities as the adjustment of large level nets and the final adjustment of positions in extensive triangulation systems.
b. Adjustment of central point figure.—(1) This figure may occasionally come up in grid triangulation as the result of the single point circuit described in paragraph 128. A diagram is shown in figure 88, where Form 8, “Solution of triangles,” is utilized to make the adjustment during the solution of the triangles. The column headings have been changed to suit the case. Having AB as the known side, listing the triangles in the usual clockwise order and naming first the ends of the known side in each triangle, the solution is carried out until it is discovered that the log side AC in block No. 5, disagrees with the common side in triangle ABC by +8 in the last decimal place. In order to leave space on the form for the adjustment, the sums of each triangle have been brought to 180° before listing. Anticipating the need of adjustment the tabular differences in each log sine for a 10-second change, in the peripheral angles only, have been entered in (4) as the sines were looked up, with the negative sign for angles exceed-
266
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119
Tab. Diff.
_______________________ IQ sec.
(I) (2) Corrl (3) 1/(4) (5) (6) Corrl (7) (8) (9)
i Corp i See corn X £
Station Observed CoT 1 Tab Diff > 3ee 3Ph
(Aclosed) angle IO \ Adj.log side
and letters angles Y. Angle Log sine J. Log side Side -No— Angle
— , , -
E Pool A 54 . 4! : 52 4 7 I 9\9H\75 3(736 49 BC 3.73 649
\ ~ +'5 ] : "+/ i ■ //
.....APehcan_______ B 54 , 27 37...............42.............2 _ 9510 48_3(73522,.kZ 3.73 523 ..........................................................................___.„7/,Cow..C ,7O_j 50 ] . 9\975 .26_3800 00 AB 3.8GOOO No. I Sph. Exc. i i.3\b24 '!74
* I : I :
C 54 : /6 \ 32 32 9'909,47 3\654 72 BD 3.65 472
.......................I......V"-5..................... ..!..................................r" -/ ’ i.T.- / ..
B 47 ; // : 20 15 2 9\865.46 3'6/0 7/ CD 3.6/070
r f-5 .; ' r 'o -[ ■ ■ ■ ■
.....V Wo/f .......D 78 (32 08...13................0 _ 9 9 91 24..............................3(736 49. BC 3.73,649
No.2 Sph Exc. । i 3'[74-525 i ;
-----------------------------------------------;------------------------------------------I-----------------------------------------------------------------
C 8/ ■ 28 .28 28 9\995\/7 3\742 88 DE 3 74 286
.........;.....T -5 40 ............................ I.:"--7...............................J..->.
D 5/ \ 4/ ■ 03 58 2 9\894-65 3\64236 CE 3.64 233
...:.......................\""35. ................................1...l"77.1...Oj................................................
77Bramble E 46 50 \ 29 34 2 9'86 3 00 3'6/0 7/ CD 3.6/070
...-.............................. : ■ ............■...................................... 1.■...-2.T..i..................................................... No.3 Sph. Exc..............................................................................i 1.3(74-7(7/.1 I
. , _
C 93 ■■ 40 ■ 4! 4! 9'999/0 3\758 83 EF 3.75 879
.................... ..........................r...i.-5.. । • -2 । ■ ' '-6 ...........................................
2 36 i 34.37 32 3 9\775 F7 3 834 90 CF 3.53 4-84
...............................................I.:'("+5...................................i..'('/■/.1..U -j .............................................
77Seacow F 49 i 44 I 42 47 2 9'882 63 3\64236 CE 3.64 233
.............................................■."1.......।...................................-4 ......■......
No. 4 Sph. Exc.________________________________i ■________________________________________3(75973 । :____________________________________________________
C 59 .43 '48 48 9'936 34 3(576 23 8 AF 3.67 6/5
.......................:...i.-5 ..................................j..:.6 " "I..-X ...............................................
F 8/ \ 40 ■ 46 41 0 9\995.4/ 3'73530-7 AC 3.73 5 23
.......................•...F 'Fs..................................I..TTz.t-.;....................................................
A 38 • 35 i 26 31 3 9\795 0/ 3534 90 CF 3.53 484
..................................... .............;............r- .■ ■■■:■£ r •.-....................................................................... ... No. 5 Sph. Exc.............................................................................i •.3'73 9 89 !.!
✓/T>SC S । : I
/7 777/0=3 5 /oj AC error .......................y\................................\e\a................................""'1. '...T" e/ ; c..............................................................'was\-8
....................... \ 7\j.....7...................‘...............................................1..............................................!... \ i +./ ................................................................................;.1...................................
No. 6 Sph. Exc. 1 i
_____ n n ...............................................T.i....... ................................r."'i.1.1... ..........................................................................................t.f.t".;.—'.?•“.....—.
• > _ _ 1 i 1 :
No. 7 Sph. Exc. i i 1 I ’
------------------------------------------------------------------------------------------
........................~.......................“1.r.......................................r-T.■.... ......................................................................................... -i ...1 1.।.i .—
: ; I I ■
...............................................J...i-.. ...4.--------------------------------i......4..I................................................-.-.
No. 8 Sph. Exc. 1 i I j______j 1
Date:.Oanuarj /7,/94O Computed by:/.-^^ Checked FORM 8
Figure 88.—Adjustment of central point figure.
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CORPS OF ENGINEERS
ing 90°. The spaces in (4) opposite the central angles are left blank as no change in these is contemplated. The sum of the tabular differences is shown at the foot of (4).
(2) The change in each angle is seen to be 8 (the difference between logs A(7)X10 seconds, divided by 17 (the sum of the tabular differences). At the foot of (5) this works out as ±5, the sign for the successive angles alternating. To shortenAC the opposite angle must be diminished and so the correction for the upper angle of each pair is negative as the signs are shown on the form. The corresponding changes in the log sines are computed, +5X2-p10= + 1 for log sin B,
Figure 89.—Triangle computation by coordinates method.
for example, and written above the log sines. The changes are then marked in for each of the other quantities as they would change if the computation were repeated with the altered log sines. The desired change of —8 is obtained for log AC in block 5, but it is made —7 to take care of dne unit increase which has occurred in the first log AC.
(S') The object of the adjustment was to obtain this agreement so that subsequent work would be free from discrepancies which would nullify any internal checks in the computations. It should not be supposed that the adjustment increases the accuracy of the positions.
c. Adjustment of quadrilateral.—In the rare case where a quadrilateral might occur in grid triangulation, consistency in the log sides may be obtained by the same method as explained in b above. In
268
Given : A, b and c.
Find ; B, C and a.
- X Axis
c
B
\a
Xb
\c
Y Axis
TM 5-235
119
SURVEYING
the quadrilateral no changes should be expected in the sum angles at the lettered corners of the figure, so the positive and negative corrections are applied to the odd- and even-numbered angles of the diagram, similar to that at the head of Form 7 (fig. 74) in such sense as to obtain the desired agreement of the log sides.
d. Triangle computation using two sides and included angles.— (1) Any organization employing the angle method of adjusting large systems of triangulation will meet this problem frequently. They will doubtless secure a supply of the United States Coast and Geodetic Survey Form 665 for this purpose, which contains its own check computations.
(2) The solution is easiest on coordinates. If the coordinates of the apex of the known angle are known, the solution is obvious. If not, suppose A is at the origin and AB coincides with either axis of a system of local coordinates (fig. 89). The coordinates of B are determined by the length of the side AB, those of C arc computed, and the azimuth and length of BC can then be found. The calculations may be checked by solution on Form 8.
e. Inverse solution.—It sometimes becomes necessary in tin1, adjustment of triangulation to compute the azimuths and Length of a line joining two stations which are fixed in position, but which have not been directly connected by the observations. In order to compute this line an inverse or back computation must be made. This computation can be made on Form 9, “Computation of Position” (fig. 76), but it can be made more easily and simply on Form 16. In figure 90, triangulation stations Herkness and Proctor are fixed in position (latitude and longitude) and it is desired to determine the azimuth, back azimuth, and length of the line Herkness to Proctor. The instructions which should appear on the form are given below.
269
TM 5-235
119
CORPS OF ENGINEERS
NAME OF STATION
1. 0 O 38 • 42 i " O/\363 A Her Press X 77 ’ 09 2/\326
2. O' A 0 (= 0-0) 38 36 //i 707 A Proctor X* 76 58 ; 34\834-
— C ■>5 4966/ AX(=X‘ -X ) - !O '.46\492
3 "IS 38 02 39 54^830 06\538 AX 2 05 \23\246
A0(secs.) — 349.66/ AX(secs.) 646.492
log A0 cor. orc-sin log A0i 2\ 543 647,2/n 1 • j log AX cor. arc -sin X- log AX, * 2 3/O 563 ,/m . 2
2\8/O 562\9m
log cos y * colog Bm log {si cos (a + A^)] log AX log sin 0 m log sec A^ log a Sj999 !\489 9995. 046 .2 (opposite in sign to A0) log cole log log cos 0m g Am 9.8 92 626 5 1 T-— T •••••. /\4 90 847 5
.Xp32\69 2.8/o'--56 9'l795 59 0000.00 2\9 _ s, sin (a + Ar) S| cos (a + Ap) 4 / 94- 036 9m 4\O32 692.9
o’./ 3 log AX log F log b log tan (a + -^) Bearing „ . Aa CL t log sin (a + Ay^) O\ /’ 6 / 34-4 0__ 5 55° 24' 22.4£ 304° 35 376 9\9/5 504 4
2 60 6 /5 5.5 m
0 b * —Aa. (secs.) A a. - ... 40. 40 89.... log cos (a + Ar) log s, cor arc-sin log s * Si 754 /60 4
II 3.9 42 78 532 5 __ + l 2
— 20/ ".9 4\2 78.53237
2 * o )3 2/\9
„+Aa a+ 2 a(l to 2) 304 35 37\6
304 32 /5'\7
As 76 1 44 --------------------------71---------------------
(Sum) log b Y :: | , "X I ; 'X 3 \459 54 ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZSIZZZZZZZZZZZ.-ILZZZZZZZZZZ
& y >:*....i...;.. ’• x* ..;....1.. ’ x* 7Z\88/ \Q zzzzzl:zzzzzzzzzzzzzzzzzzs>nzzzzzzzzzzzzzzzzz_Ezzzzzzzz
Station YR 4 94\99 / ;(9 ” X 565\O OOP ”X 56 7 88 i \6 ZZZZZZZZZZZZZZZZZZZZZZZZZZZ_^ZSi<X 3i 72 7 86 3' 36 7 60
t 6\457\4 /373. 570'0 - /3 2 3 6'7 7380 027'4 log 6Y - log tan PD PD * PB (3) competed Y(diff observed Y
0'360 26
1380,02 7\4 PX (sum 6Y ± ) 1366 79/ \3 66 735 : 25 55 50 4/
- 20,273 !802\ 50 / 2... ° t 13 6 72\2 1782\ 22 7\8
IY © PY (sum) 290 290 j 30 ) 30 09 2/
1782,227 8 1795. 9OO\O
Date: . April 2, 7940 Computed by : Checked by: A d f FORM 20
Figure 108.—Grid coordinate computation of three-point problem.
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GRID COORDINATE COMPUTATION OF THREE-POINT PROBLEM
INSTRUCTIONS
Fill out the data, carefully construct the diagram, correct the F’s for magnification of scale, and deduce the 6 angles before computing.
Letter the known points A, B, and C from left to right with A on the observer’s extreme left.
Mark angles APB as a; BPC, 0; and BPD, y.
When P is within triangle ABC, a'(ACI) = lW-a and 0'(CAI) = 180-0.
When P is outside triangle ABC, a'(ACI)=a and 0'(CAI) =0.
In either ease, I (AIC) = 180— (a'A0').
* Obtain quadrant or sign by inspection of diagram.
Apply MnS to the Y of P to obtain map grid coordinates.
303
TM 5-235
127-128 CORPS OF ENGINEERS
Section XXII
SPECIAL TRIANGULATION METHODS
Paragraph
General__________________________________•________________ 127
Single point circuit and single point net______________________________________ 128
Rapid triangulation______________________________________________________________ 129
Inaccessible base________________________________________________________________ 130
127. General.—In this section several methods adapted for obtain-ig quick results in grid triangulation are briefly considered. These ’e suggested as problems to work out in peacetime and on maneuvers, ith a view of preparing to meet any emergency which might arise in ar. The chief difficulties which justify such expedients are shortness ’ time and uncertainty as to when and in what direction the next iove will be made. The field work in any grid triangulation demands le use of small and readily portable instruments, preferably of the fild micrometer direction type since they yield excellent results so •omptly. Any reconnaissance must be made in minimum time, ex->pt when the advance may be retarded. The methods of this section Le further liberties in that any bases necessary would have to be easured rapidly and practically at a moment’s notice; that only two ations are occupied in most of the triangles; and that natural marks *e selected to serve as signals for stations owing to the frequent im-issibility of making a previous reconnaissance and erecting artificial rgets. On occasion some rather sharp angles will occur in the trian-es, perhaps as small as 15° or even 10°. It is said that distant lints can often be fixed within 100 yards by triangles of which the )exes do not exceed 4° or 5°. This weakness of figures and the fail-'o to occupy all stations make it desirable to determine each point om more than one triangle. In most of this rapid work, observa-jns should always be made to or from the highest point of a hill, • at least the highest ground in the neighborhood.
128. Single point circuit and single point net. These methods ay prove useful when a number of points are to be fixed in low-lying inntry from all of which some prominent feature is visible. The ro most usual types are shown in figure* 109® and ®, in both of hich A and B are two known points or the distance between them measured. Z is some point visible from A to which the azimuth is lown or can be calculated. C is some prominent object visible from and B and from points D, E, F, and G which are to be fixed. The igles at the bases of the triangles ABC, CAD, CDE, etc., are observed id the apex angles are deduced. The triangles are solved in order mmencing with ABC to find the log sides BD, DE, etc. The ad-
304
SURVEYING
® Circuit
the line AZ.
from
305
justment and solution of the triangles of a similar figure were described in paragraph 1196 (fig. 88). After the solution of the triangles the coordinates are computed as for a traverse, deducing the azimuths
Figure 110.—Rapid triangulation.
TM 5-235 128-129
129. Rapid triangulation.—Cases may arise where it is necessary to carry forward a triangulation with an advance. It may also happen that it is inconvenient to send men to the flanks, even to erect signals. In such case much greater use may be made of natural
In the single point net (fig. 109@) the base of the last triangle should close on known points or the distance should be measured as a check.
® Net.
Figure 109.—Single point circuit and net.
262341°—40---20
2<
^3
>4
>8
A
.B
xE
F
~G
C*
AZ
E
F
ab
\C/
Zz
TM 5-235
129
CORPS OF ENGINEERS
features and checks must be introduced by seeing that bases can be calculated from two or three triangles (fig. 110). It is here assumed that observations can be made only from the points A, B, C, D, and E. The distance AB must be measured unless they are points previously fixed. If it is possible to find natural features (7, 4, 7) to either flank which are visible from the stations to be occupied, the angles at the bases are observed and the others deduced. The triangles can be solved and the bases calculated. If the natural features can be found in pairs, values for the bases can each be calculated from two separate triangles. If the points can be found in groups of three, as in figure 110, a further check is available if the values from two
Figure 111.—Diagram of inaccessible base.
triangles disagree. A check base should be measured, if necessary. The computation for this example may be summarized as follows:
Triangle Base Log sides Coordinates
AB1 AB Bl
AB2 AB B2
AB3* AB B3
BC1 Bl BC C from B
BC2 B2 BC
BC3* 133 BC
BC4* BC C4
BC5 BC C5
BC6 BC C6
and so on.
’These triangles would be computed when two values of the same line disagree. The number of observations may be considerably reduced if the same natural features are visible to more than three of the observing stations
306
TM 5-235
130
SURVEYING
130. Inaccessible base.—a. General.—This is a method of fixing one or two points by observations taken from them when only two known stations are visible from them. Graphic solutions of this problem are explained in paragraph 124e (fig. 103). Another method would be to observe for an astronomic azimuth (see Secs. XXIX and XXX) at one of the points thus obtaining at once the azimuth to both of the fixed stations. At any rate, an observed astronomic azimuth will greatly strengthen any resection computation besides simplifying the work.
A and B (fig. Ill) are the inaccessible fixed points, C and D are two intervisible points from both of which A and B can be observed. The point D is required to be determined. The angles 4, 5, 6, and 7 are observed; 3 and 8 can be deduced. If x and y can be found, all the angles in triangles ABC and ABD will be known, and these triangles can be solved, the azimuths of AC, AD, BC, and BD can be deduced, and the coordinates of D, and C if desired, can be computed from A and B. Either of these methods might prove invaluable if one of three signals erected for resection from the advanced positions should prove invisible. See paragraph 98o(7).
b. Computations.—The computations can be made on form 21 (fig. 112). The instructions which should appear on the form are given below.
307
TM 5-235
130
CORPS OF ENGINEERS
Computed Checked by:
Dote: May 4, i 940
FORM 21
Azimuth AB = 302 08 /3 Angle log sines Angle log sines
Log AB= 4.3/742 Mop Y 4 6 8 5| 9 74 \/9 3 5 7 9 9 / / 6/
AX BX 1383 /9O\4 1365 6O3\9 Y Y /7 78 099\7 1789 !47\6 764/2 9'660 27 5| 70 3 57 666 9 98 83 50
Bose Stotion Proctor MnS Z 5 yds per 1000 Sum tan 0 7\338 03 Sum 9'5 76 -91338 94 03
(4) (5) C = (4) + (5) (6) (7) 0 = (6)+(7) (5) (6) x+ y = (5)+(6) ■xj_y 2 (8) =180 — (5 + D) (3) = l 80-(6 + C ) 70° 26 28 27 40 03 i
0\238 9/
98 06 3/ 27 ■ /3 06 94 45 4/ 121 58 47 0 60° 0/ '/4 0-45°= !5° 0/' !4
log tan (0-45°) xt y log tan —j— 9\428 68 9\775.42
27 ,40 03 27 \ 73 \ 06 \(4 +6 +8)greoter// , \ y, log Yon —g— (sum) (3 + 5+7)greater y-x log tan ~2“(sum) 9\/44 /O
54 53 I 09 27 26 34 30 2/ , /0 54 40 23 V/ /z \ X (sum) / y(dift ) y-x 2 2 X(diff.) y (sum) 7° 27 . A9 1 35 55 59 26 34 30 35 22 33
Letter Diagram Angles log sines log sides Side
A 8 C y +(3) (4) /9 ° 30 35 90 \ 02 \ 57 70 > 26 ; 28 9\523 70 i- -i <91 OOO 00 9\974 /9 4\343'23 3\8 66 4\343 4\3/ 7 93 23 42 BC AC AB
B C D (3) C (6) 54 40 23 98 06 i 3/ 27 /3 ; 06 9 9//. 6/ 9\9 95.64 9\66O 27 4\2O6 66 4' / / 8 4\202 3\866 r • 27 30 93 CD BD BC
C 0 A (5) D (8) 27 40 03 121 58 \47 30 \ 2/ /0 S’66683 9 . 928 52 9\703,57 4\4 /4\70 4\0 8 / 4\343 4\/ / 8 1 53 22 27 AD AC CD
D A B (7) x+(8) y 94 46 42 49 5/ 45 35 ,22 33 9\ 99 8 9\883 9\762 4-'\3 / 8 50 38 63 90 4^'3/7 4\2O2 4\08 / 40 28 53 AB BD AD
Azimuth AB Azimuth AC (8) Azimuth AD 302, 08 /3" + 79 30 \ 35 Azimuth BA y Azimuth BD (3) Azimuth BC 122° 08 ~ 35 \ 22 73" 33
32/ 38 48 + 30 2/ : 70 86 i 45 - 54 ,40 \ 40 23
357 59 58 32 i 05 !7
Figure 112.—Computation of inaccessible base.
308
. c d Lee _...................
4\5 6x^7
Pierkness B Fx_______'*>'■8 A Proctor
SURVEYING
TM 5—335
130
COMPUTATION OF INACCESSIBLE BASE FORMULAS
z+i/=(5)4-(6)
sin x sin (4) sin (6) sin (8)
• • Zr»\ • / r\ • „. fm. tcltl (p
sin y sin (3) sin (5) sin (7)
If above numerator is greater than the denominator
tan +4= tan tan (—45°)
If the denominator is greater
tan 4“ =tan tan (0 — 45°)
Make MnS correction to Y’s after abstracting data.
309
TM 5-235
130-132
CORPS OF ENGINEERS
c. Checks.—The computation provides oidy internal checks, and the agreement of the coordinates of C and D, as computed from A and B, only proves the correctness of the computation, and is no check on the accuracy of the observed angles. Observations might also have been made at a second point C' near C, and this point included in the observations taken at D. Two computations could then be made, one with C and D observations, the other with C and D. Agreement of the coordinates of D in both computations is an external check.
d. Exercise XXV. The inaccessible base.—The student will observe the angles from two assigned stations to an inaccessible base and perform all the computations on Form 21 and others necessary to check the coordinates of both the assigned points.
Section XXIII
MISCELLANEOUS ORIENTATION METHODS
. Paragraph
General____________________________________________________________________ 131
Short base_________________________________________________________________ 132
Subtense methods_________________________________________________________ 133
Subtense variations_______________________________________________________ 134
Coincidence method of obtaining distances__________________________________ 135
Interruption of triangulation______________________________________________ 136
Assumption of coordinates and azimuth______________________________________ 137
131. General.—With the exception of the subtense bar, everything in this section may be regarded as of fairly low accuracy, until proved otherwise by trials. Most of the methods described here are something to be tested now and then and reserved for some unusual emergency. The short base methods may be better than rated and the special problem described in paragraph 1326 is likely to occur.
132. Short base.—a. General.—(1) These methods assume that it is possible to extend one triangle to 5 or 6 times its base (fig. 113). Starting with a 250-foot base, the long side of the first triangle may be about 1,200 feet; of the second, about 7,000 feet. This involves apex angles around 10°, but the expansion is very rapid. (For the best methods, see (5) and b below.) Some armies have actually worked out detailed plans for such problems, showing just what each of the four observers does at each stage, and where the computing section is stationed.
(2) The position and elevation of the apex of first triangle are assumed.
(3) When coordinates have to be assumed by the artillery, the special short base method described below may be useful in aiding
310
SURVEYING
X (Assumed Co-ordinates)
(High Ground)
Short distance measured
Figure 113.—Diagrams of short base methods.
TM 5-235
132
of other men required to work there and its probable proximity to the enemy. The topographical unit’s most forward station C will be selected, normally near A’ and visible from a short base AB, the distance CX being measured. C will often be on the reverse slope of a
hill to assure liaison with the artillery, with reasonable immunity from fire. AB should be close to a road, when practicable, for easy access by the computation truck. The coordinates of X and the azimuth from X to A or B having been assumed, coordinates of A and B are deduced in the same terms and the base AB is extended in the usual manner, permitting the intersection of points in the battle area in
311
them to utilize the temporary grid until the triangulation catches up. This method requires very close liaison. Suppose (fig. 114) that the Field Artillery have assumed an origin (X), which may be too far forward to be occupied by the topographical unit, owing to the number
xShort base in valley.
Figure 114.—Extension from origin or assumed coordinates,
(High Ground)
Assumed Azimuth
I
E
B
A
^0
^0
A''
^0
A
G1
D
E
TM 5-235
132
CORPS OF ENGINEERS
the same terms (assumed coordinates) as the artillery, and extension forward if necessary. If the triangle ACX can he made well conditioned, it can be computed, checking by measurement of the distance CX. Other field artillery points may be included in the triangulation if required.
(4) A modification of the short base method is readily available with the use of the subtense bar (fig. 115). Obviously the smallest triangle or triangles of the usual short base method may be eliminated, and at the same time the extremely small angles become unnecessary.
Subtense bars at 8
Observers at 0
Figure 115.—Short base measured by subtense method.
(5) Short base extension net.—The ideal for this purpose is a series of similar isosceles triangles with apex angles as large as conveniently possible. •
b. Observations oj small angles.—Observing small angles suitable for short base extension and similar purposes with repetition instruments requires modification of the usual program, as follows:
(1) Set the circle at the required initial zero for the set, but do not record.
(2) Center on left hand target (2I) with the lower motion. Unclamp the upper motion, and rotate the instrument clockwise several times to take up backlash, and again center on (zl) with the upper motion, read, and record.
312
1000-2000 ft. \ 2000-4000 ft. \
f B I B 1 B 1 B
0 0 0 0
TM 5—235
132-133
SURVEYING
(3) With the upper motion, point at target (B), read, record, and secure the value for the first angle as a check against gross errors. It is not necessary to record again until the required number of repetitions have been completed, but a reading should be made after the sixth repetition and the mean compared with the first angle of a check to discover any false start.
(4) With lower upper motion.
(5) Repeat (4) about 180° from
initial reading and divide the result by the number of measures made.
(6) A similar set should be taken on the explement, with telescope reversed.
(7) If another set seems advisable, the telescope should be reversed for the angle and direct for the explement. In all of above the instrument should be turned only clockwise.
motion turn clockwise to (A), then to (B) with
until, pointing on (B), the reading of the limb is the initial zero; read and record. Subtract the
Figure 116.—Diagram of subtense measurement.
Note.—A theodolite of the Wild type cannot be used for the repetition method. For such small angles observe the number of positions required to cover about half the circle, making the interval between position initials about equal to twice the small angle being measured. Moreover, it must be remembered that all this extra trouble will be of no avail if the signals are not accurately centered over the station marks.
133. Subtense methods.—a. General (fig. 115).—From the angle subtended at the instrument by two targets (T and I") at known equal distances from the station observed (A), and on a line perpendicular to the ray OA from instrument to the observed station, the distance can be calculated. The accuracy of the distance depends upon the exactness of the measurements of the subtended angle and of the distance between the targets, and partly upon the relative magnitude of the subtended angle, since the distance is calculated from the formula
d a
D=^ cot w
TM 5-235
133
CORPS OF ENGINEERS
where d is the distance between the targets and a is the subtended angle. No correction for slope is necessary. Table V, TM 5-236 is convenient for the calculation though the instrument makers usually furnish tables with each bar (d(l) below).
b. Differences from the stadia method.—Stadia distances are read as the intercept between two fixed stadia hairs on a specially marked stadia rod as viewed at the distant station through the transit or alidade telescope. In ordinary circumstances the length of a stadia sight is limited to 1,000 feet or less by the visibility of the divisions on the rod which are usually 0.05 or 0.10 foot each. The size and separation of the subtense targets may be varied to suit the conditions so that sights of several miles may be taken. The stadia rod is hand held in a vertical position supported on the ground with some unsteadiness and deviation from the plumb position and variable errors due to differential refraction, which may be considerable close to the ground, while the subtense targets are rigidly supported approximately at the same height above the ground as the H. I. Subtense angles are almost always read horizontally. Finally, the subtense targets may be altered in size and made up to suit the conditions of observation. The comparative accuracy of the tivo methods may be estimated from error ratios given in e below.
c. Subtense angles.-—These may be read by direction or repetition. The Wild type of direction theodolite is particularly fitted for this class of work as the observations may be made in a fraction of the time required with other types of instrument. With a repeating theodolite at least four sets of six repetitions should be made at short distances and as many as ten such sets at the longer distances. The alternate sets should be made direct and reversed and a progressive change of zeros should be employed to overcome uneven division of the circle. If the angle is small enough to permit, say between 10 and 15 minutes, some observers prefer to leave both clamps set, turning back and forth with the upper and lower tangent screws.
d. Target types.—These include the subtense bar and two extra signals set up on either side of the station.
(1) As an accessory (fig. 117®), many of the European theodolites are equipped with invar steel bars about 5 feet long, with targets, universal levels, small sighting telescopes for insuring normality of the bar to the line, plumb bobs, and fittings for attachment to an extra tripod. Some of these bars have lights for night use. A subtense bar can be improvised from a level rod by putting on an extra target, securing to each target a 4-inch white disk with a solid black 1-inch disk at its center, setting the rod to exactly 10 feet, and securing the
314
SURVEYING
El-
® Wild type bar.
@ African type targets.
® Tripod targets.
315
Figure 117.—Subtense targets.
TM 5-235
133
TM 5-235
133-134 CORPS OF ENGINEERS
rod to the top of a level plane table board so that the line of the front of the disks will plumb to the station mark when the rod is set normal to the line of sight by sighting back to the instrument through a sighting alidade placed perpendicular to the face of the rod. If these preparations are made with care, so that disks are centered exactly 10 feet apart, distances up to 1,000 feet may be read in the daytime about as closely as on the invar bar, and from there up, they may be a little closer because of the better visibility of the targets and the increase in the subtended angle. Twenty-foot subtense bars have been used but are awkward to handle and require several supports, tripods or trestles.
(2) In Africa and Asia, exploratory and other traverses have been run with the separate targets made of guyed poles set in the ground by native employees. The poles have to be flagged for ready recognition, but the angle is measured on the poles as near the ground as possible with a background of white cloth to make the poles visible. A better arrangement would utilize two black centered white disks mounted on tripods light enough for a pair to be carried by one man, and there would have to be several pairs in use as the subtense angles are taken in both directions to get a mean value. The distance between targets should be such that the subtended angle will fall between 10 and 15 minutes. At 2 miles the white disks should be about a foot in diameter with round black centers 3 or 4 inches across.
e. Utility.—The usefulness of this method for short bases was mentioned in paragraph 132a(3). Check bases for grid triangulation could be similarly measured. Observing 2 D and 2 R, or 4 D and 4 R angles with a different zero for each angle, the Wild type bar and direction theodolite reading to 1 second yield an error ratio of 1:5,000 or less for distances around 500 feet in daylight, and at night, 1: 5,000 for distances around 1,000 feet. If two or more bars were available, they would aid in expediting traverses over rough ground.
134. Subtense variations.—a. With lateral station.—(1) This method may be employed for distance measurement in special circumstances by parties not equipped with theodolites suitable for the precision needed in the observation of the smaller angles described in paragraph 133e. It might be particularly useful where the ground is too rough for accurate taping or when some obstruction like woods or a body of water has to be passed. In figure 118 ® the distance OA is to be measured. A sub-base AB at right angles to the line OA is marked with range poles or other means, and the distance AB and the subtended angle at 0 are carefully measured. The distance OA is then calculated by the formula D = d cot a, where d is the
316
SURVEYING
A
0
® Distance by lateral station method.
® Distance by lateral bases.
Figure 118.—Subtense variations.
TM 5-235
134
distance AB and a is the subtended angle. No correction for slope is needed.
(2) The following precautions should be taken:
(a) The sub-base must be of suitable length and accurately taped.
(6) The subtended angle must be very exactly observed, as the cotangents of small angles change rapidly.
(c) The distance must be checked, either by a second sub-base of a different length or by some other method.
(3) The sub-base may be varied in length to fit the ground, though excessively small angles are to be avoided. The base might be roughly or the distance OA, which would make the subtended
angle about 3° to 5°. The right angle should be laid off with the transit, but a steel tape and 3-4-5 proportions may be used if necessary. The subtended angle should be measured by repetition as described in paragraph 107c. At least two sets should be taken, more with a 1-minute transit.
b. With lateral bases.— This method may be used to obtain the distance from one point to another which is undesirable or impracticable to visit. Two angles at the base of the triangle are observed instead of one subtended angle. In figure 118 ®, BD is the distance required. Two short bases AB and BC are marked on one or both sides of B, and about at right angles, or a little less, from BD. AB and BC are accurately taped; the two interior angles at B, one each at A and C are observed in enough positions or sets to secure the necessary accuracy, and the two apex angles at D are deduced. The distance is computed by the law of sines from each base separately. Observa-
317
B
A
B
C
0
TM 5-235
134-136 CORPS OF ENGINEERS
tions are repeated, if necessary, until the discrepancy between the two results is so small as to indicate that the desired accuracy has been attained. A sharp distinct point should be selected for the point D, the station marks should be small nails set vertically in the top of the stakes, and the instrument must be exactly centered over each of the marks.
135. Coincidence method of obtaining distances.—Some of the European instruments are equipped with a special sleeve containing two prisms which can be attached at the objective end of the telescope, and a specially marked bar or rod which is fitted to be supported horizontally on an extra tripod. One of the prisms may be rotated, and a scale indicates its position relative to the other, which is fixed. By rotating the prism while observing the horizontal rod, the images of certain portions of the scale may be brought into coincidence. The distance is obtained from tables furnished by the maker based upon the position of the prism and the readings of the bar which are brought to coincidence. This is more rapid than the subtense method but requires more equipment, is less adaptable, is limited to comparatively short distances, and on the average is probably half as accurate as the subtense bar for a corresponding distance.
136. Interruption of triangulation.—a. General.—It is desirable and expected that the topographical units should in any situation be prepared to furnish the true grid azimuth and standard grid coordinates of some point or points in or near the artillery areas. If the triangulation has fallen behind a rapid advance, the assumption of grid coordinates (par. 137) might become necessary. If that expedient cannot be avoided, the resultant harm should be minimized, if at all possible, by approximating the true grid azimuth and coordinates so closely that later corrections are unnecessary. Methods which might be employed either individually or in combination to meet such requirements include—
(1) Approximations from the best available map.
(2) Astronomic azimuth observations, which need not take long, weather permitting.
(3) Resection on three or more points previously fixed or approximately fixed.
(4) Resection on two points previously fixed.
(5) If only one known point is visible, the occupation of two others in the advanced position at which the two angles of the triangle and an azimuth at one or both the new stations are observed, and the distance between measured, directly or indirectly.
(6) An azimuth traverse (see b below).
318
TM 5-235
136-137
SURVEYING
(7) A determination of position from azimuth and latitude (c below).
b. The azimuth traverse is one run primarily to carry forward the true grid azimuth in case the weather prevents observations. If suitable landmarks are available, this may be accomplished by long shots ahead on distinctly marked details of the terrain which may then be occupied, leaving cloth marks for the backsight if the object to which the foresight was made will not serve. The landmarks might be supplemented by range poles sent ahead. If the stations have to be close together, two instruments might be used, one to be set up and the angle observed while the other is being advanced the length of two sights. Extra rodmen should be provided. The distances should at least be estimated, better approximated by range pole intercepts, rope traverse, or other means. Three or four men alternating in marking the rear end of a 100-yard rope can advance very rapidly if they can keep on line, as the rope is being moved almost constantly.
c. Determination of position by azimuth and latitude is feasible only when astronomic observations can be made for azimuth and latitude, and if a previously fixed landscape feature is visible within 45° of north or south. The computation is simple on geographic coordinates (fig. 119 ®).
The distance OA equals OB divided by cos a, OB being calculated from table XI, TM 5-236. Similarly the difference in longitude may be roughly calculated from the relation AB—OB tan a and the seconds of longitude calculated from the longitude column of above table. On the grid (fig. 119 ®) the coordinates of C could be converted to geographic (par. 119^), the distance OC calculated as above for OA, and the coordinates of 0 computed from the azimuth and distance OC on form 14. Ultra refinement in these calculations is not warranted, as the error of the observed latitude may be ±50 yards.
137. Assumption of coordinates and azimuth.—This step is always initiated by the Field Artillery as a means of coordinating the fire of various units, whenever standard grid azimuth and coordinates are not available in their areas of operations. The establishment of such temporary data is tactically undesirable since it diminishes the fire effect of any batteries operating with the data, delays units coming into action, and interferes with continuous operation during the conversion from temporary to standard data. The topographical units are interested in all of this as some of their forward elements in cooperation with the artillery may have started grid triangulation on the temporary grid for the purpose of aiding them in keeping their several units on the same relative control datum, temporary though it may be.
319
TM 5-235
137 CORPS OF ENGINEERS
As the topographical units will have to make further use of these points when the grid triangulation comes forward, the conversion from temporary to standard grid data should be accomplished on Form 17 (par. 119/0, as soon as a common point and the azimuth difference have been established. This not only causes extra work and duplication of effort, but tends to confuse the grid triangulation and the control data. Some of the methods of avoiding these conversions have been outlined
® ®
Figure 119.—Determination of position from latit ude and azimuth.
in paragraph 136. At all times such close liaison should be maintained with the artillery units concerned that their intentions may be known in advance and provision made for their needs, thus avoiding the necessity for assuming temporary data. Before assuming temporary data the artillery are expected to consult with the topographical units, with a view of securing the best possible assumption so as to minimize the later conversion of temporary data wherever practicable.
320
Meridian of 0 \
+d q
_ PQLaUel of _
Latitude of A
0/
------------ j- y —
-Para//
TM 5-235
SURVEYING 138
Section XXIV
PLANE TABLE AND TELESCOPIC ALIDADE ADJUSTMENTS
Paragraph General description_______________________________________ 138
Adjustment of plane table_________________________________ 139
Use of plane table________________________________________ 140
138. General description.—a. Board.—The plane table now used in the Army consists of a board 24 by 31 inches, built up of %-inch white pine strips glued and cleated at the ends with 2-inch maple strips. At the center of the under side of the board is attached a circular brass plate, which has at its center a circular hole, threaded to take the upper end of the clamping bolt of the tripod movement. Eight clamp screws and sockets are attached to the board to hold the paper in place on the upper face of the board. The board is provided with a flexible case of waterproof canvas.
b. Tripod.—The tripod consists of full-length split legs of hardwood, or collapsible legs, with pointed steel shoes, hinged to the Johnson movement ball-and-socket head. (See fig. 120.) This head provides for the motions of leveling and horizontal turning. The upper clamp (A) controls the leveling of the table while the lower clamp (B) controls the azimuth. When the instrument is to be set up both clamps are loosened. The table is leveled and clamp A tightened, which forces the level cup c against the tripod head d, friction holding it in this position. In practice, the upper clamp is seldom loosened, as the table is more quickly leveled by moving the feet of the tripod. The table is then turned to the required azimuth and the azimuth clamp B tightened, which forces the azimuth cup e against the tripod head d, thus preventing the table from turning in azimuth. The nut B acts as a check or lock nut on A. The tripod with head weighs 9 pounds complete.
c. Plumbing arm.-—The plumbing arm is a device for plumbing a point on the plane table over the station point. The arm is made of oak, shaped so that while the upper member rests on top of the board, the lower member extends at an acute angle below the board. The lower end of the lower member has a brass hook for the suspension of a plumb bob directly under the brass index on the free end of the upper arm.
d. Alidade.—The telescopic alidade (fig. 121) with all accessories should be neatly fitted and secured to fixtures on the inside of a hardwood case which has a hinged cover, two brass hooks, and a heavy leather strap with roller buckle. The plumbing arm and plumb bob
262341°—40-21 321
CORPS OF ENGINEERS
@ Section.
Figure 120.—Johnson piano table head.
TM 5-235
138
e. Use.—The same care and precautions should be taken in the use of the plane table alidade as for the transit and levels. Protection should be provided for the alidade and map in case of sudden showers or windstorms. All parts should be well cleaned at the end of each day’s work by being wiped with a soft, dry cloth.
322
are packed in the case or in the plane table case, depending upon the manufacturer. The accessories usually furnished arc—
1 extra tangent screw for the stadia arc.
1 extra tangent screw complete with socket for the telescopic axis.
1 extra striding level vial.
1 pocket magnifying glass.
1 suitable screw driver.
1 sunshade.
2 steel adjusting pins.
® View.
TM 5-235
138
SURVEYING
f. Beaman stadia arc, {fig. 122® and @).—(1) This provides a rapid and exact solution of the stadia problem and facilitates use of the plane table. With it, differences in elevation and reduced horizontal distances can be determined with great rapidity and without intricate calculation. The arc is attached to the vertical limb of the alidade and carries two scales having zero points marked 0 and 50, respectively, either scale being read by an index. The scale graduations of the Beaman arc are so spaced and numbered as to give simple multiples of the rod interval.
(2) To obtain differences in elevation between instrument and rod, the scale marked Vis used. The index point of this scale is marked 50, so a scale reading of less than 50 indicates that the telescope is depressed, while a reading greater than 50 shows that the telescope is
Figure 121.—Plane table alidade.
elevated. Only such inclinations of the telescope need be used as will give a whole number reading on the V scale, the fractional part of the elevation being shown by the rod reading.
(3) To obtain the desired multiple, sight anywhere on the rod (it does not matter where) so that a whole number reading is obtained on the V scale.
(4) For example, suppose the observed subtended stadia reading on the rod to be 6.40 (640 feet), to obtain a whole number for the V scale reading, the telescope is inclined so that the V scale reads 33, at which setting the middle wire reads 7.30 on the rod. Then the desired multiple equals
33 — 50= —17 and
— 17X6.40= —108.8
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Difference in elevation between instrument and base of rod is then
— 7.30—108.8= —116.1 feet
This subtracted from the II. I. of the instrument will be the elevation of the new point. For accurate work it is necessary to correct the distance for K, and (c+/) if any, before calculating the difference of elevation.
(5) The horizontal distance is found by means of the scale marked H, which gives at the same pointing which sets the F scale a direct
Figure 122.—Beaman arcs.
reading of the percentage of correction (always negative) necessary to reduce the observed stadia reading to the true horizontal distance.
(6) For example, at the setting for the above F scale reading the scale (H) would read 3, or 3 percent.
3 percent of 640 feet=19.2 feet
640—19.2 = 621 feet — horizontal distance
When the instrument has a stadia constant affecting the accuracy of the work the rod interval must be corrected for same before recording distance.
(7) The angular values of the divisions of the Beaman arc are as follows:
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® Old style.
® New style.
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TA. . . Angular value TA. . . ~ Angular value
Division: ° > Division—Continued. ° >
1______________________ 0 34. 4 15____________________ 8 43. 7
2______________________ 1 8. 8 20___________________ 11 47. 3
5______________________ 2 52.2 25_ 15 00.0
10___________________ 5 46. 1 30___________________ 18 26. 1
(8) Test the accuracy of the graduations of the Beaman arc by comparison with the regular degree arc as follows:
(a) Set the degree arc at 30° with main clamp and tangent screw.
(6) Set the Beaman arc index at 50 by means of the attached index spring screw.
(c) Set the Beaman arc on any graduation it is desired to test, using the main clamp and tangent screw only.
(d) Take the reading on the main arc, using 30° as the reference point. The angle, if for an even five division, should correspond with one of the readings given above, which are derived from the stadia formula H=D (constant) % sin 2 A, H being the difference in elevation, D the observed distance, and A the vertical angle.
139. Adjustment of plane table.—a. Board.—Test the surface of the board with a straightedge. If it is not perfectly flat, obtain a new board.
b. Straightedge.—(1) Test the beveled edge of the alidade by drawing a fine pencil line the full length of the edge.
(2) Rotate the alidade end for end and place the edge again on the line.
(3) If the lines do not coincide, the alidade should be replaced.
c. Blade level.—A) Test the spherical level attached to the base by leveling up the alidade on the plane table.
(2) Draw a line along the ruling edge of the alidade.
(3) Rotate the alidade by turning it end for end and placing it on the same line.
(4) If the level is out of adjustment, correct by bringing the bubble halfway back to its center position by means of the screws at the base of the housing.
d. Striding level.— (1) Place the striding level on the rings of the telescope and bring the bubble to the middle of the tube by means of the vertical tangent screw.
(2) Reverse the level end for end and place it again on the rings.
(3) If the bubble moves from the center position, bring it halfway back by means of the adjusting screw under one end.
(4) Repeat until the bubble remains in the center of the tube. (Check striding level adjustment before start of each day’s work.)
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139-140
CORPS OF ENGINEERS
e. Arc index level.—(1) Place alidade on a horizontal surface (the plane table board may be used) and level alidade by the striding level
(2) Set Beaman arc index at 50.
(3) If the bubble of the arc index level is not in the center, move it there by means of the adjusting screw at one end.
(4) Reverse the instrument (180°) and retest the adjustment, repeating same until the bubble remains in center.
f. Vertical wire.—To make the vertical wire vertical when the base is leveled—
(1) Level the plane table carefully by means of the striding level.
(2) Sight on a plumb line or rock the telescope on its horizontal axis while sighting on a well defined point.
(3) Loosen the reticle screws and rotate the reticle to correct error.
(4) Tighten the reticle screws and retest.
g. Line of sight.—To make the line of sight parallel to the axis of the rings—
(1) Loosen the knurled collar in front of the longitudinal telescope bearing.
(2) Focus the telescope on a distant point and revolve the telescope 180° in its collar.
(3) If the cross wires do not remain on the point, correct by moving the reticle one-half of the distance back to the point.
(4) Retest the vertical wire.
h. Beaman arc.-—Proceed as described in paragraph 138/ (8).
i. Determination of stadia constant (K) and (cfi-f).—The stadia constant and (c-f-/), if any, for the telescopic alidade of a plane table is determined as described for the transit in paragraph 70.
j. Exercise XXVI.—Make the adjustments to a plane table as described in this paragraph.
140. Use of plane table.—The plane table is used mainly in triangulation reconnaissance and certain mapping operations. The map or drawing paper is fastened to the top of the table, which is set horizontally. The telescopic alidade, resting on the table can be moved thereon from point to point. When the telescope is pointed at an object, a pencil line along the ruling edge of the alidade gives the direction to the object; the distance is then measured by tape or stadia. Since the plotting and the field work are carried on simultaneously, the instrument man can sketch in the ground forms as he goes. Rarely, if ever, will a topographer or surveyor be required to make a complete topographic survey with the plane table to a scale smaller than 1:10,000. Only when aerial photographs are unavailable
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or when parts of photographs are so indistinct as to be useless for interpretation will the topographic detail to a smaller scale be plotted in the field. Plane table surveys are normally limited to large scale maps, or plats required for construction work.
Section XXV
GENERAL INSTRUCTIONS—PLANE TABLE METHODS
Paragraph 141 142 143 144 145 146 147 148 149 150 151 152
General_________________________
Equipment for field work________
Field sheets____________________
Setting up and orientation______
Beaman (stadia) arc record______
Typical procedure of locating points. Application of plane table______
Supplementary (plane table) control Radiation_______________________
Traversing______________________
Intersection and resection______
Magnetic orientation____________
141. General.—Plane table surveys provide the advantages of—
a. Dispensing with the usual field notes and hence avoiding mistakes in recording measurements.
b. Visualizing the progress of the map in the field, thus easily preventing the omission of necessary data.
c. Easy location of inaccessible points without trigonometric calculation.
d. Quick determination of the position of any occupied point with respect to three known visible points.
e. Fewer men required.
142. Equipment for field work (fig. 123).—Besides the equipment described in section XXIV, the plane table man needs dividers, scale, No. 10 needles, pencils, eraser, Beaman arc record book, and waterproof cover for board and instrument. The equipment for each rodman should include stadia rod; hatchet, machete, or brush hook, if necessary; colored crayon; and strips of red and white signal cloth.
143. Field sheets.—Field sheets (or plane table sheets) which indicate the data required for control are usually prepared in the office and given to the topographer. A plane table sheet to be used in the field must show at least two stations, intervisible from each other, which have been accurately plotted with at least one elevation. The ideal situation would be to have sufficient control shown on the plane table sheet to enable the topographer merely to occupy one station after another and sketch in the surrounding detail. This, however,
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I
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CORPS OF ENGINEERS
cannot be expected under normal conditions. A cover sheet with an opening large enough to expose the area being worked should be fastened over the field sheet to protect it from hands and alidade.
144. Setting up and orientation.—a. Setting up plane table.— Set up the tripod with the board approximately level, two legs being placed downhill if the set-up is made on a slope. Some plane tables are equipped with three leveling screws. This is an advantage in leveling the board but involves additional weight. If the table is so equipped, place the alidade in the center of the table and by means
Figure 123.—Plane table accessories.
of two of the leveling screws, bring the bubble of the circular level to a line through the center of the level and perpendicular to the line of the two screws. Then, with the third screw, bring the bubble to the center of the level. When the table is equipped with a ball-and-socket joint or Johnson head, the board is moved by hand until the bubble is approximately in the center and the final adjustment made by tapping with the finger; the wing nut is then tightened. Experienced planetable men usually level the board by adjusting the tripod legs, as the board seldom needs to be precisely level.
328
Plumbing bar
Compass box
TM 5-235
SURVEYING 144-148
b. Orienting plane table.—To orient the table, place the edge of the alidade along the magnetic arrow or meridian, and then turn the table until the north end of the compass needle is at N, checking that the magnetism in the needle has not been reversed. If the station occupied and some distant and conspicuous point have been plotted on the map, a more accurate orientation is obtained by placing the alidade edge on these two plotted points, turning the table until the vertical wire of the telescope falls on the distant point, and clamping. This may be called the “backsight” method. Other plotted stations which are in view from the station occupied afford a check upon the position of the instrument. When working on a field scale of 1:20,000 or smaller, the point on the table need not be set exactly over the corresponding point on the ground, as under these circumstances the area of the whole table may be considered as a point without introducing serious error. When working on scales 1:10,000 and larger, the point on the table should be brought closely over its corresponding ground point by dropping small stones from the under side of the board or by use of the plumbing arm and bob; the accuracy of centering required is directly proportional to the scale.
145. Beaman (stadia) arc record.—To minimize any extensive repetition of field work in case of an occasional error in plotting distances or calculating elevations, the topographer should keep a record of such observations that may serve as a check and assist in a ready discovery of accidental errors. The Beaman (stadia arc) record in figure 124 shows notes on a standard page of Form 9-913A, United States Geological Survey. The headings of the various columns make the notes self-explanatory. Paragraph 1466 explains the method of recording.
146. Typical procedure of locating points.—a. General.-—The procedure outlined in this paragraph is typical of observations relating in general to radiation (par. 149) and traversing (par. 150), assuming that the plane table is to be oriented by the “backsight” method, the plotted station visible from the location of the plane table being utilized. In regions where local magnetic attraction is not too prevalent, magnetic orientation is employed in all plane table traversing at scales of 1:10,000 and smaller, thereby eliminating half the set-ups and giving the topographer the choice in locating the board on the spot best fitted for sketching the terrain. (See par. 152.)
6. Method.—To obtain the location of new points and their elevations from a known point—
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Date: 2/IO I946> Traverse from QA2 to ©Z77
Beaman
Distance Arc of Product . 0 . ' ' Hi. Elevation
Correction Elev.
I (O 137.4 133.6
F2 640 33 103.8 7.3 - 116.1 21.3
3 2/0 54 + 8.4 6.3 + 2.1 / 139.5
4 /90 58 + 15.2 4.8 + 10.4 / 147.3
5 230 40 C- 330 5i6 - 23.6 / 108.8
6 270 - 8.2 / 129.2
7 /85 — 0.9 / 136.5
8 205 35 30.8 7.1 - 37.9 / 99.5
9 (36) 24.9 21.3
C 10 640 68 ^+ //52 6.4 + 108.8 133.7
^11 490 60 Ll+ 49.0 4.3 + 44.7 69.6
12 160 60 /6.0 3.2 + 12.8 / 37.7
13 80 - 3.2 / 21.7
14 HO - 6.3 / /8.6
15 220 57 + 15.4 6.2 + 9.2 / 34.1
16 (82^ 72.8 69.6
C 17 490 40 CL- 49.0 2.4 - 5/.4 2/.4
/MS 520 53 + 15.6 3.2 + 12.4 85.2
19 /30 46 - 5.2 7.1 - !3.3 60.5
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Figure 124.—Beaman (stadia arc) record.
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SURVEYING
(1) Set up on station, level board so that spherical level bubble is approximately in center, get HI, and compute elevation of instrument. Send rodman to rear station.
(2) Reverse alidade on orientation ticks for line “new station to previous station.” Signal rodman.
(3) Sight on rod and clamp table. Send rodman to new station and signal.
(4) Pivot alidade and sight on rod. Signal rodman. Read distance, correct for stadia constant (K), if any, and record as “Distance.” (See sample notes, fig. 124.) Draw line to new station and a short “tick” at each end of alidade.
(5) Level telescope.
(6) If middle wire cuts rod, use telescope as a level. (Record rod reading as “Diff. elev.” and subtract from HI to obtain elevation of new point.)
(7) If middle wire does not cut rod, depress or elevate telescope until middle wire cuts rod, and clamp.
(8) Center arc index level, look at V scale, and with vertical slow motion further depress or elevate telescope until it reads exactly one of the full divisions.
(9) Read V scale and record as “arc.” If V scale reads 40 or less, or 60 or more, read H scale and record. This H scale reading is the percentage to be subtracted from the stadia distance (4) to obtain horizontal distance.
(10) Read rod at center hair middle wire and record as “rod correction.” Signal rodman “down.”
(11) The difference between 50 and the F scale reading (9), multiplied by 0.01 of the stadia distance (4) gives the difference of elevation between the instrument and the point on the rod cut by the center hair (10). This difference is recorded (with proper sign) as “product.”
(12) If the V scale reading (9) is less than 50, the sign of the product is minus, if greater than 50, it is plus. Add, algebraically, product and rod correction and record as “diff. elev.” Apply the latter to “HI” to obtain elevation of new point, recording each step in proper column.
(13) Plot shot and enter elevation beside it to read from bottom of sheet.
Note.—On stations which are part of a plane table traverse read distance and V scale both fore and back and take mean of results, as at C in figure 124.
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147. Application of plane table.—The plane table lends itself readily to the determination of the location of points by the following methods:
a. Radiation (par. 149).
b. Traversing (par. 150).
c. Traversing and radiation.
d. Intersection (par. 151).
e. Resection (par. 151).
Similarly, several methods of plane table leveling may be used for determination of elevations. The choice of methods depends upon the particular problem in hand.
148. Supplementary (plane table) control.—Frequently it is necessary for the topographer to supplement the initial control, plotted on the plane table sheet, with additional points. The amount of such control will depend on the required density of control station, the character of the area to be mapped, and the scale of the plot. All such supplementary control is plotted graphically and may be established by traversing (par. 150) or by graphic triangulation (par. 151). Elevations for supplementary control stations are obtained from stadia distances and Beaman arc readings (sometimes vertical angles) in the case of traversing, and scaled distances plus Beaman arc readings in the case of graphic triangulation. Supplementary control points for filling in topography are occasionally marked by plain stakes without witness or reference marks.
149. Radiation.—To plot points by radiation is identical with what is known as plotting “side shots.” This method (fig. 125) is as follows: Set up at 0, orient, and clamp the board. 0 is usually the adjusted position of some control traverse station or similar control point. Measure the height of the telescope above the ground for the H.I. Pivot the alidade with its edge at the point occupied and sight on a rod held at some salient point, as A. Read the Beaman arc; then read the distance by the stadia method and lay off to proper scale the distance Oa, marking the elevation near the point. Continue this method until all desired points have been located on the sheet. Ground features can be sketched in as the work progresses.
150. Traversing.—It is seldom possible to plot all the desired points within an area from one point; hence the plane table must be moved from one station to another This method is called traversing. Assuming that it is desired to plot the tract of land ABCD (fig. 126) with a ridge along the line AC, making D invisible from B, it is first necessary to set up over the point A, which has been assumed on the drawing paper. Draw radial lines from A toward B and D and make
332
TM 5-235
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SURVEYING
“ticks” at the ends of the alidade for better reorientation. Then measure the distances to these points. Lay off these distances from A, to scale, on their respective lines, thus locating points b and d. Next, move the table and set it over B. Place the alidade along the plotted line (ticks) bA and sight on A by rotating the table. When the rod, held on A, is bisected, clamp the board. The plane table is now oriented. Draw a radial line from B toward C, measure the distance from B to C, and lay off this distance to scale from b. This gives the position of C. Now move to C and orient the table by placing the alidade along the line (ticks) cB. sighting on B. Draw
Figure 125.—Radiation.
a radial line from C toward D and measure the distance. When this distance has been plotted to scale on the line cd, the point d thus located should fall on the point d previously located from station A. If it does not check on returning to the original point, the traverse must be adjusted as explained in paragraph 62.
151. Intersection and resection.—a. Intersection.—The process of locating a point by radial lines from two or more known stations at which the table has been set up is called intersection. After the point has been located on paper to the satisfaction of the topographer, distances from it to the original points are scaled. These distances, together with their corresponding vertical angles or Beaman arc
333
readings, are used for determining the elevation of the new point. (Seo also par. 121.)
b. Resection.—When a point is located by setting up on it and sighting at visible stations which have been plotted on the field sheet, the process is known as resection. Usually not less than three radial lines from well distributed stations around the occupied point to be located are used. (See also par. 124.)
152. Magnetic orientation.—While this method is sufficiently accurate for traversing, it cannot be employed with the longer sights
Figure 126.—Traversing.
required for plane table triangulation, except as a means of securing preliminary orientation in resection. In traversing, the H. I. is obtained by backsight, which requires the signs of the product and rod correction to be reversed from those used for foresights and side shots as described in paragraph 146. To avoid confusion the line for each backsight should be marked B in the Beaman arc record. The signs to bo affixed to “product” and “rod correction” are determined according to whether the observation is a B. S. or F. 8., by following the rule ol universal application, namely—
334
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TM 5-235
152-153
SURVEYING
Observation.
Product
Rod correction
B. S.
F. S.
Opposite sign to that indicated by arc reading. Same sign as that indicated by arc reading_____
For example, arc reading 54 indicates + ; therefore the sign of product is — for B. S. and + for F. S. Note that the sign of “rod correction” is the same as in leveling. When line of sight is level, arc reading is 50, and therefore only entry is rod reading, entered as “rod correction,” whose sign follows above rule.
Section XXVI
TOPOGRAPHY WITH PLANE TABLE
Paragraph
_ 153
154
155
159
._ 157
_ 158
_ 156
General______________________
Plotting detail______________
Habitual program at each set-up Inking field sheets__________
Checking completed field sheet-_ Sketching on aerial photographs_ Completing skeleton sheets___
153. General.—a. Requirements.—Before attempting to plot topography with the plane table the operator must be thoroughly familiar with the methods of sketching discussed in FM 21-35, must know the conventional signs and symbols shown in FM 21-30, and should have performed the basic drafting exercises enumerated in paragraph 2 and described in TM 5-230.
b. Plane table sheets.—(1) Topography is plotted to the scale of the projection or grid shown on the plane table sheet furnished the topographer. From the standpoint of efficiency the plane table sheet is the least satisfactory portion of the plane table equipment. Owing to its hygrometric nature it is very susceptible to atmospheric changes, expanding and contracting unceasingly. This would be but an insignificant source of error or annoyance if it were equal in all directions. The map or plan would then simply change its scale, for which an allowance could readily be made. But the objectionable feature is the unequal expansion and contraction which changes the relative distance and directions of the points. It has been determined by experiment that strips cut longitudinally from drawing paper vary from 10 to 25 percent more than strips cut transversely from the same
(2) Various other materials are used for plane table sheets, such as paper mounted on aluminum and “Pyralin” (white opaque). They
335
paper.
TM 5-235
153-154 CORPS OF ENGINEERS
are quite satisfactory and the latter can be used in rainy weather if necessary.
(3) Most plane table sheets, however, are made of two sheets of drawing paper, mounted with the grain at right angles, and with cloth between them. To reduce the distortion to a minimum, a sheet of this type should be thoroughly seasoned before it is taken to the field or a projection laid down on it. This is effected by exposing it alternately to a very damp and a very dry atmosphere. On testing a sheet after a week of such exposure it will be found to have much less tendency to expand or contract unequally. Paper stored away, piled in stacks, does not properly season.
c. Organization of party— In organizing a party for field work it is well to have the recorder carry the table. A part of his duty is to remain constantly wit h the instrument and never to leave it unguarded. He should be taught at the beginning of the work the correct method of setting the table over a point and taking it up. In the first instance he grasps firmly two legs of the tripod and “flips” the third one until it reaches the ground at the proper distance from the point; he then places the other two in position. The distances from the point will vary according to the slope of the ground. In taking up the table, two legs should be grasped firmly and raised, pivoting upon the other leg; the two held legs are closed and the table is raised in place upon the shoulder. At least one rodman is needed and if the topographer is experienced he should be able to keep two rodmen busy. Rapidity of execution is largely dependent upon their efficiency. When well trained they should be able to recognize the salient points of the features to be mapped, so that the topographer can draw in details correctly from the least number of readings. The amount of assistance an aide can give to his chief is limited only by his skill and experience, the logical inference being that he is in training to become a topographer himself, and can take charge of an increasing share of the work as he becomes more and more familiar with the methods employed.
154. Plotting detail.—a. Method.—Detail is located by the method described in paragraph 1466. At the larger scales, several side shots may be needed at each set-up for plotting the works of man and terrain features. As each point and its elevation are marked on the sheet, an effort should be made to add part of the contour above and below the point, as the topographer can estimate their positions best while the point is still marked by the rod. On succeeding shots the contours should be completed as the rod is moved, if practicable. In this manner the contours are finished as the salient features are located and additional shots are seldom necessary for contouring. At 1:48,000
336
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SURVEYING
and smaller scales, side shots, except a few local intersections, are scarcely ever required.
b. Use of conventional signs.—All topographic and military features will be shown by conventional signs and symbols conforming to those in FM 21-30. Features for which no sign or symbol is prescribed may be shown by special symbols provided they are explained in a legend on the sheet.
c. Contouring.—(1) No rule can be laid down as to the number of elevations that should be determined from each plane table station or for a given area. It will depend on the skill of the topographer and the configuration on the ground. It would indicate careless and slovenly work if contours were found to deviate frequently from their true position on the sheet by more than half an interval for a slope of less than 5° in open country. When the slope is steeper, and in wooded regions, a greater latitude is permissible, but even here, in representing the crests of ridges, prominent hilltops, and valley floors, this limit of half an interval should not be departed from.
(2) The topographer will be assisted in sketching contours, where the modeling is intricate, by lightly drawing a skeleton composed of ridge and valley lines in their proper positions around the station. On the ridge lines will be found the extreme outward or convex bends of the contours and on the stream lines the extreme inward or concave bends.
(3) Contours (fig. 128).—(a) A contour never splits (5), nor do two contours run into one (6), nor will they cross each other except in the rare instance of an overhanging cliff (8). When an auxiliary contour is introduced, no more of it is drawn than is sufficient to delineate the special feature which makes it necessary. A principal contour, on the other hand, should not have an end within the map; if it commences at one edge it must terminate at another.
(6) A closed contour encircled by one or more closed contours is either a hill, as shown in (1), or a depression, as shown in (2), the arrows showing the direction in which water would run. The summits of all the hills of importance should have their elevations determined and marked on the map.
(c) A series of contours, as shown in (3), is either a croupe (the end of a ridge or promontory) or a valley. If a croupe, the contours will have their concave sides toward the higher ground; if a valley, the contours will have their concave sides toward the lower ground.
(° 5®0 0 1000
Figure 127.—Plane table sheet.
338
SURVEYING
339
Figure 128.—Correct and incorrect contour groups.
TM 5-235
154
5
3
1
2
4
6
8
7
TM 5-235
154-158
CORPS OF ENGINEERS
(4) The progress of topographic work should be such that it affords the most favorable direction for drawing the curves of equal elevation, and it is usual that all work at a station be completed during occupancy to avoid the necessity of returning to it. The heights of a sufficient number of points must be determined to avoid any wide range of visual estimates.
(5) Having completed the contours and all other details at a given station, the topographer proceeds with his party and instruments to the next station from which he can gather the details of an area bordering upon the one last surveyed. The map is filled in by successively occupying stations over the whole expanse of the sheet.
155. Habitual program at each set-up.—The topographer, having oriented his board and determined the HI, proceeds to map the natural and artificial details of the area surrounding the station. For this purpose the direction of each detail is obtained by pointing the telescope upon it, the edge of the rule cutting the station point; its distance is determined by reading the stadia rod held there for the purpose. This distance is then taken off the scale with a pair of dividers and plotted along the edge of the rule. While this is in progress, the alidade is used both as a level for the observation of objects of the same height as the instrument and for measuring angles of elevation and depression.
156. Inking field sheets.—Accuracy, neatness, and clearness are necessary. The map or sketch should be inked up to date at the end of each day’s work. The location of the names upon the sheet should be such as not to cover or obliterate any detail or feature of the survey. The title should follow, with such notes as may be necessary to explain any peculiarity of the sheet or survey. The title and lettering should be placed for easy reading when the map is held normally with north at the top. All names well established and recognized in a neighborhood, both general and local, should be collected during the survey, and their correct spelling ascertained. The topography as drawn in the field is supposed to be correct when the sheet is finished, and no office amendments or changes are admissible.
157. Checking completed field sheet.—The completed field sheet must be checked for omissions, and its border strip areas traced if subsequent work of the same party is to be in areas adjacent to it.
158. Sketching on aerial photographs.—a. Prerequisites.—In order to satisfy an immediate demand for some kind of a map in unknown territory which has been photographed, the topographer may be required to furnish certain detail, especially relief and names by direct plotting on the photographs. If the scale of a photograph is
340
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unknown, the topographer may have to determine it by comparative measurements between objects on the ground and their images on the photograph. Such comparative determination should be made from at least two diagonally opposed lines or distances. If more than one photograph is to be used and the photographs have been made successively during the same flight, one determination of the scale (from two lines) will usually be accurate enough for all practical purposes. For other methods of determining the scale of aerial photographs, see section V, TM 5-230. At least one elevation, preferably of the starting point, should be known unless an elevation can be assumed.
b. Orientation.—Regardless of the purpose for which the sketch is made, or the data to be plotted thereon, the board is set over a point identified in the photograph and oriented by one of the following methods:
(1) Magnetic orientation is identical with the method described in paragraph 1446, regarding the photograph as a map.
(2) Orientation by true meridian is accomplished by placing the edge of the alidade ruler on a line between the occupied station and the distant (visible) object and rotating the table until the vertical wire of the alidade bisects the object. The table is clamped and sights in any direction may now be taken by sighting with the alidade at any desired point. This method is similar to the one described in the second half of paragraph 1446. •
(3) Orientation of the photograph can also be accomplished by graphic resection if two or preferably three distinct objects can be seen from the occupied station which at the same time can be recognized on the photographs. •
c. Plotting, detail, contours, names, etc.—The horizontal detail (planimetry) as a rule being complete on the average photograph, only such detail need be plotted as is indistinct or cannot be obtained photographically. In general, then, only contours, names, and occasionally some indistinct feature will have to be added by the topographer. This is done as explained for plane table sheets in paragraphs 154 and 155. All detail, after being completed, is inked in appropriate colors to contrast with the tone of the photograph. If the photograph is not too dark, black ink may be used exclusively, permitting quick, direct reproduction, if desired.
d. Checking completed photographs.—Completed photographs must be checked the same as completed field sheets. (See fig. 129.)
e. Exercise XXVII. On the photograph furnished, plot all contours, names, and indistinct detail; also correct any discrepancies
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Figure 129.—Completed (inked) photograph.
found in the horizontal detail that may be due to construction or developments subsequent to the date the photograph was taken. Ink and check the completed photograph.
159. Completing skeleton sheets.— a. Skeleton plane table sheets are prepared from aerial photographs and control data. They show the military grid, triangulation and traverse stations, bench marks, elevations of control points, and all planimetric detail obtainable by
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tracing or transferring from photographs. Orientation of a skeleton sheet over the occupied station is described in paragraph 1446. The plotting of detail, including contours, is identical with the methods described in paragraph 1466. The topographer, after completing the sheet, will check every detail as explained in paragraphs 156 and 157 before turning them over to the office for compilation.
b. Exercise XXVIII.—On the skeleton sheet furnished, plot all details, contours, and names as required and complete and check the sheet as explained in this paragraph. Figure 130 shows a part of a completed skeleton sheet.
SKELETON PLANE TAELE SHEET FROM AER/AL PHOTOGRAPHS 1365 7366 »
343
Figure 130.—Part of completed skeleton sheet.
TM 5-235
160 CORPS OF ENGINEERS
Section XXVII
PLOTTING CONTROL POINTS ON PHOTOGRAPHS IN
FIELD
Paragraph
Importance and necessity_________________________________ 160
Plotting by direct orientation (spotting)________________ 161
Plotting by instrumental methods_________________________ 162
160. Importance and necessity.—Methods used in the construction of maps from aerial photographs make it mandatory, if precise
Figure 131.—Form of paneling control point.
results are desired, that ground control points (see sec. XV, TM 5-230) located by instrumental methods—either triangulation or traverse— be plotted on the photographs. These ground control points are the principal or key points governing the degree of accuracy of the final map. When identified on photographs, control points should be spotted with a fine needle prick dot surrounded with a triangle
344
Cloth
Cloth
- 6' to 8’-
Cloth
Open
Cloth
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SURVEYING
and labeled. The triangles should be comparatively large (sides about 0.3 inch long) in order not to obscure the detail immediately around the point. If circles are used instead of triangles, they, too, should be large (diameter about 0.2 inch). When the ground control is established, special effort should be made to ascertain that all points selected can be readily identified on the photographs. In this case, the plotting of all ground control points is done in the drafting room; additional field work is eliminated. In selecting natural objects for points of control, preference should be given to those of fixed and permanent nature. If traverses are run to provide control, a wealth of natural objects will be found along roads, railroads, or other courses taken for the traverses. If the control be established by triangulation, there will not be readily available so many natural objects suitable for photographic targets, but usually some prominent object near a station can be tied to it. When unidentifiable control points must be used, their positions can be plotted only by instrumental location from the nearest identifiable point or they must be suitably marked on the ground before the photographs are taken. Marking should be limited to the minimum required, for it takes time and is rather expensive. Whenever artificial targets are required they can be most readily constructed of strips of white cloth in the form of a hollow cross, tacked to short pegs driven in the ground or weighted at the corners with heavy stones. Crosses made of panels 6 feet square will be large enough to show plainly if the scale of the photographs is not smaller than 1:20,000. For smaller scale photographs the panels should be 8 feet square. Figure 131 illustrates the form of cross which has been found most satisfactory.
161. Plotting by direct orientation (spotting).—To plot a point by direct orientation (spotting), the photograph is mounted on a sketching board or plane table and oriented upon a known object (par. 1586).
162. Plotting by instrumental methods.—a. When the point to be plotted on the photograph is too far away from the nearest plotted control point or nearest identifiable feature for spotting, one of the plane table methods may be utilized. The plane table, with the photograph fastened to it, is set up and oriented over the nearest picture point that can with certainty be identified, and a plane table traverse (par. 150) is run to the point to be plotted; or if the necessary number of picture points are available the location of the control point may be determined graphically by intersection or resection, as described in
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CORPS OF ENGINEERS
paragraph 151. Another method of marking a control point on a photograph is by determining its position from a stadia traverse (par. 80) and plotting the point by polar coordinates, or computing its coordinates and plotting the point as described in section XIII, TM 5-230. The plotting, in either case, will have to be done to the scale of the photograph.
b. Exercise XXIX.—The description and elevations of certain ground control points being given, locate and plot them on the photographs furnished, using either plane table methods or the stadiatraverse method as outlined above.
Section XXVIII
ELEMENTS OF FIELD ASTRONOMY
Paragraph
General_________________________________________________________________ 163
Definitions___________________________________________________________ 164
Time-------------------------------------------------------------------- 165
Determination of hour angle and declination_____________________________ 166
Astronomic triangle..__________________________________________________ 167
Comparison and choice of methods_____________________________________ 168
Observations on sun____________________________________________________ 169
Observations on stars_________________________________________________ 170
163. General.—a. Scope.—This section is intended to provide certain elementary instruction in field astronomy and should be read carefully as a guide to the methods best adapted to various circumstances. The determination of time and longitude, and the more precise latitudes and azimuths are treated in Special Publications of the United States Coast and Geodetic Survey (No. 14, Determination of Time, Longitude, Latitude, and Azimuth; and No. 109, Wireless Longitude).
b. Ephemeris.—The American Ephemeris and Nautical Almanac, issued by the United States Naval Observatory, will be needed for some of the methods of section XXX. The American Nautical Almanac, of the same issue and of one-third the bulk and one-fifth the cost, could be adapted for most purposes by changing the forms; but its ephemeris of the stars omits certain data, and the special tables on Polaris are missing. “ The Ephemeris of the Sun and Polaris and Tables of Azimuths and Altitudes of Polaris,” published by the General Land Office, gives condensed tables satisfactory for the sun and Polaris, but contains nothing of the other stars. The small pocket books issued by some instrument makers have practically the same contents as the Land Office Ephemeris.
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c. Meridians.—(1) The azimuth of a line is its angle, measured clockwise, from a base direction line, which may be the true meridian, the magnetic meridian, or a north and south grid line. In third-order triangulation, azimuths are measured from true south; in grid triangulations, from grid north. Astronomic azimuths will be considered as clockwise from the true north. Due to inequalities in the density of the earth’s crust, the plumb line does not point to the center of the earth at all points on its surface. Geodetic azimuth is azimuth corrected for error due to local deflection of the plumb line from the true vertical. It varies slightly from the uncorrected value known as astronomic azimuth. The azimuth of a celestial body is the spherical angle at the zenith between the meridian and the vertical circle of the celestial body, or the angle in the plane of the horizon between the plane of the meridian and the plane of the vertical circle through the celestial body. The azimuth of the celestial body S' (fig. 132) is the spherical angle PZS, which is the same as the plane angle NOJ.
(2) The basis of azimuth determination is the location of the true meridian of the observer. True north for any observer is represented on the earth by the arc of a great circle between the observer and the North Pole, created by the cutting of the surface of the earth by a plane through the observer and the North and South Poles. This great circle is known as the observer’s true meridian. The meridians defined in this paragraph are the meridians of the earth’s surface, that is, terrestrial longitude lines.
(3) Azimuth determination by observation of a celestial body may be divided into two main operations:
(a) Measurement of the angle between the position of the sun or star and a datum point, and recording that angle together with the exact time of day.
(6) By referring to tables for the observed body in the ephemeris, its actual azimuth can be computed for the exact time and date of the observations. Having found this true azimuth of the sun or star and the measured angle between it and the datum point, the azimuth of the datum point is established.
d. Terrestrial coordinates.—(1) The longitude of a place is the arc of the Equator intercepted between the meridian of that place and the meridian of Greenwich, England, adopted as the zero meridian, from which all longitudes are measured east or west up to 180° of arc. The difference in longitude between two places may also be defined as the angle between the planes of their respective meridians. Since the earth rotates through 360° in 24 hours, this difference can also be
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expressed in time instead of arc, 1 hour being equal to 15° of arc. As 1 second of time is therefore equivalent to 15 seconds of arc (over 1,100 feet at 40° of latitude), the astronomic determination of longitude with fair accuracy requires knowledge of the exact time and means of timing observations at fractions of seconds.
(2) The latitude of a place is described in several ways. The geodetic latitude of a place is the inclination of the line, normal to the spheroid, to the plane of the Equator, measured in the plane of the meridian. Since the earth is a spheroid, the normal line, except at the poles and on the Equator, does not pass through its center. The astronomical latitude is the inclination of the plumb line to the plane of the Equator. Because of the deflection of the plumb line, geodetic and astronomical latitudes are seldom in agreement, and may differ by several seconds. This is not enough to cause any material error through taking the latitude of a place from a good map for use in azimuth determination. On the other hand, the simple methods of latitude determination mentioned in paragraph 168c may be expected to average several seconds in error from the geodetic latitude, and so do not afford a good check on position.
e. Motions of earth and solar system.—(1) The earth has two motions, both clockwise when looking toward the north; it rotates about its own axis, and it revolves around the sun. The earth moves around the sun once a year in an orbit which lies practically in one plane, and whose form is that of an ellipse, the sun being at one of the foci. Since the earth is held in its position by the force of the sun’s gravity, its speed along its orbit depends on its distance from the sun. The orbit being an ellipse, this distance is constantly changing. It can therefore be said that the motion of the earth in its orbit around the sun is not uniform. This fact is of importance in its effect on solar time. The axis of rotation of the earth is inclined to the plane of the orbit at an angle of about 66%°; that is, the plane of the earth’s Equator is inclined at about 23%° to the plane of the orbit. This latter angle is known as the obliquity of the ecliptic. The direction of the earth’s axis is practically constant and it therefore points at nearly the same place in the sky throughout the year and from year to year.
(2) The sun appears to be farthest north about June 22, at which time the days are longest and the sun’s rays most direct in the Northern Hemisphere. In winter, due to the inclination of the earth’s axis, the sun is actually below the plane of the earth’s Equator; in summer it is above this plane. It must therefore cross the plane of the Equator in going from below to above (winter to summer), and again
348
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going from above to below (summer to winter). These two crossings occur about March 21 and September 22. On these dates the sun is in both the plane of the earth’s Equator and the plane of the earth’s orbit, and the days and nights are of equal length. These two points are called the equinoxes. The apparent motion of the sun is therefore a helical motion about the earth’s axis; that is, the sun, instead of following the path which would be followed by a fixed star, gradually increases or decreases its angular distance from the celestial equator (the celestial equator is the projection of the plane of the earth’s Equator on the sky) at the same time that it apparently revolves once a day around the earth. The movement of the earth in its orbit around the sun has a material bearing on solar time and should be thoroughly understood before undertaking the study of time.
(3) The solar system consists of the sun and the planets with their satellites. The planets have motions of rotation on their own axes and of revolution around the sun similar to those of the earth. The satellites revolve around the planets. The whole solar system, taken as a unit, is moving through space.
/. Motions of the stars.—Although the earth is constantly moving in its orbit around the sun and the whole solar system is moving through space, these combined movements are practically imperceptible when considered in relation to the great distance to the stars. For this reason the relative positions of the stars are said to be “fixed.” The principal motion of the stars discernible from the earth is one of apparent rotation about the earth’s axis caused by the earth’s own rotation. This movement is practically uniform, since the earth’s speed of rotation is the most constant of any known motion.
g. Celestial sphere.—The celestial sphere, used in all astronomic calculation, is an imaginary sphere of infinite radius with its center at the center of the earth. All celestial bodies appear as though projected on this sphere by straight lines radiating from the center of the earth. The radius of the earth is so small in comparison with the distances to the fixed stars that the position of an observer on the surface of the earth does not affect the projection of a star on the celestial sphere. However, the accuracy of the projection of the sun, as well as that of the planets, is affected by the fact that the observer is not at the center of the earth but on its surface. Therefore, the position of the observer is considered the center of the celestial sphere and the apparent positions of the sun, planets, and satellites are corrected for parallax due to the distance from the surface to the
349
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CORPS OF ENGINEERS
center of the earth. Figure 132 represents the celestial sphere. The radius of the earth is so small compared with the infinite radius of the celestial sphere that 0 may be regarded as any point on the surface of the earth.
ZENITH
n +< 2d
// i+d V <
X \ '7# V F ,/ \
/\ V r-K :'X\ " \
\ A J - 7 -> - xWtz \
TM T^Tx \
.. "SOUTH xK T _____NORTH\|.,
U KPOINT b\V mjo POINT J N
\ 1+Tj:£J
\ // p\£\ \ ■. \ \ ^ /
\ + . / \\- „ X
X'?' \ V' V\ 7/ /
Vd 'X. s
X CD1 R
^++al0 MER'Ol^ R
NADIR
Astronomic lines and points are named in capitals, angles in lower case letters, except for the following observer, O; a star, >S; portions of vertical circles, NZU, ZE, ZSJ; azimuth of star, spherical angle PZS. or plane angle NOJ.
Figure 132.—The celestial sphere.
h. Apparent motions of all celestial bodies.—All celestial bodies appear to revolve about the earth, but their motion (except a part of the motion of the sun, moon, and planets) is only apparent and is the direct result of the rotation of the earth itself. However, for convenience the earth is considered to remain stationary at the center of the celestial sphere and the latter is assumed to rotate about an axis which is the infinite prolongation of the earth’s polar axis. The stars
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SURVEYING 163-164
are fixed on this celestial sphere except for motions not capable of measurement during a short period. The sun and planets are displaced on this sphere according to their motions as viewed from the earth. Each fixed star will describe an apparent daily path from east to west around the earth, its apparent orbit being a plane perpendicular to the axis of the earth. The sun, in addition to its apparent motion due to the rotation of the earth on its axis, moves slowly each day along the ecliptic. This motion is the cause for the continual change in declination of the sun. The apparent daily path of the sun varies slightly, therefore, from a circle in a plane perpendicular to the earth’s axis.
164. Definitions.—A general comprehension of the fundamentals of practical astronomy is necessary before the solution of azimuth problems can be thoroughly understood. Nearly all of the astronomic points, lines, and angles defined below are named in figure 132, which should be studied with this paragraph. The common abbreviations for some of these terms are shown in parentheses after the names in the definitions. Other abbreviations are given in paragraph 167, or the colatitude
Side SZ>=90o — h, or the zenith distance (z)
PS-=90° — 8, or the polar distance (p)
A«=the azimuth of the celestial body
Spherical angle • i*=the hour angle of the celestial body y*=the parallactic angle
< R
^^^ICelestiol
Z
-—fa———.
A _
fs z
0/
yb~
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be taken with sufficient precision from any good map. The declinations of all of the principal celestial bodies are given in the ephemeris. Consequently, two of the required elements are always known. The parallactic angle (q) cannot be measured from the earth; consequently, the azimuth problem resolves itself into measuring either the hour angle or the zenith distance. These two methods of azimuth determination are called the hour-angle method and the altitude method.
d. Astronomic notation.—With few exceptions the notation given below is that generally employed in astronomic work and is used in this text and in the ephemeris:
GHA=Greenwich hour angle.
LHA=Local hour angle.
EST= Eastern standard time.
GCT— Greenwich civil (or mean) time.
GA T— Greenwich apparent time.
LCT— Local civil (or mean) time.
LAT= Local apparent time.
EQT= Equation of time.
Sid. T— Sidereal time.
G Sid. T— Greenwich sidereal time.
VE= Vernal equinox.
RA=Right ascension.
0h-=Midnight beginning date.
Latitude of place of observation.
X = Longitude of place, measured from meridian of Greenwich.
3=Declination of celestial body.
h—Altitude of celestial body.
7=Hour angle of celestial body.
A=Azimuth of celestial body (east or west of north). s=Zenith distance of celestial body (or 90° —h). p—Polar distance of celestial body (or 90° —6). q=Parallactic angle.
s~2 • ■
°=Degrees.
' = Minutes of arc.
"=Seconds of arc.
h=Hours.
m—Minutes of time. s=Seconds of time.
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e. Astronomic formulas— (1) The following formulas are used in connection with azimuth determinations. The choice of a formula should depend on the precision with which the angle is defined by the trigonometric function. If the angle is very small, it is more accurately found through its sine than through its cosine. If the angle is near 90°, the reverse is true. On account of the rapid variation of the tangent, an angle is always more accurately determined by use of this function than by use of either the sine or cosine. The formulas employed in the forms of sections XXIX and XXX have been chosen as those best fitted to the general case.
(a) To find azimuth, given latitude, declination, and local hour angle.
j sin (—5) j
tan y (A—q) =---y------cot t
cos 2 (0+0 ~ . (1)
1 cos 2 (0—0 J
tan (A+5) =-----y------cot -1
sin y (0+0
The algebraic sum of the values 5 (A—q) and 5 (A+5) equals J Ji
azimuth from the north.
tan A
a sin t
1 — 6 cos t
(2)
where a=sec 0 cot 8, 6=tan cot 8, and A=azimuth east or west of north.
(6) To find azimuth, given latitude, declination, and altitude.
cos x A= J
VCOS 8 COS (s—p) cos cos h
tan A=
J
/sin (s—h) sin (8—0) V COS 8 cos (s—p)
(3)
(4)
where s — (A+0 + p) and A=azimuth east or west of north.
(c) To find azimuth, given local hour angle, altitude, and declination. sin A=sin t sec h cos 6 (5)
where A=azimuth east or west of north.
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SURVEYING
(d) To find azimuth of a star at elongation.
sin A=cos 3 see
(6)
(*)
sin A=sin sin 5 +cos cos 5 cos t
(7)
sin A=sin esc 8
(8)
To find local hour angle, given latitude, declination and altitude.
(Z
(9)
To find local hour angle of a star at elongation.
cos /=tan cos 3
(10)
To find local hour angle and azimuth of a star on the horizon.
cos t— — tan tan 3
(U)
cos A=~sec sin 5
(12)
where A= azimuth east or west of north.
(7) To find local hour angle and altitude of a star at tran sit over prime vertical.
(13)
(14)
TM 5-235
167
cos /=tan 8 cot sin A=sin 6 esc
(2) Formula (1) is used in the hour angle method for sun and stars; (2) is used frequently for hour angle observations on circumpolar stars; (3) is preferred for the altitude method, as results are identical with those from (4) and the computation is somewhat simpler; (6) and (8) may be useful in preparing to observe circumpolar stars. The others may be of use in special cases occurring too infrequently to warrant detailed discussion. Some formulas, better adapted to machine computation, have been omitted. In all of the forms, five-place logarithms are used, as complete interpolation will give results correct to the second, except when all the data and computations are in tenths of minutes.
where A= azimuth east or west of north.
To find altitude, given latitude, declination and local hour angle.
± sin A —sin sin 5 cos t~----------------
cos cos 8
373
(f) To find altitude of a star at elongation.
TM 5-235
168 CORPS OF ENGINEERS
168. Comparison and choice of methods.—a. General information on astronomic observations.—(1) Before undertaking any survey operations, the observer and his recorder must have enough practice to gain some skill in their work, to form certain habits of procedure which will insure accuracy in the results, and to learn to choose the method most suitable to the work at hand. Signals, targets, and rods are immovable while being observed, but celestial bodies appear to move, often quite rapidly. This makes the pointing more difficult, and in some programs the exact time of centering has to be read and recorded. The use of the prismatic eyepiece and working at night seem strange at first. The computations are perhaps nore varied than in triangulation, and often seem rather abstract to the beginner. However, all of these difficulties are completely overcome through knowledge and experience.
(2) Before taking the field, the following have to be prepared or arranged in advance:
Adjusted instrument.
Known error of watch.
Flashlights, if at night.
Ephemeris and TM 5-236 (tables).
Notebook and blank forms.
Descriptions of stations to be occupied and observed. Signals or signal lamps to be posted.
(3) The instrument should be in good adjustment. The plate bubbles should have special attention as the only error not overcome by the combination of direct and reversed readings is the deviation of the vertical axis from the plumb line. Some observers prefer to rely upon the striding level or telescope level for the final leveling of the instrument. In most of the programs the instrument cannot be releveled during a set of observations (3 DIR). To allow it to become acclimatized, the instrument should be set up, centered, and leveled at least 20 minutes before observations are to begin. The tripod feet should be located so as to be least in the way during the observations. For best results, a surveyor’s umbrella should protect the instrument from the hot sun. As most of the instruments not of the Wild type have no interior illumination for the cross hairs at night, this is accomplished by having an assistant direct a flashlight, held at such distance as to secure the desired intensity, at a piece of white paper inside of and extending beyond the sunshade. This flashlight must be shielded from the observer’s eyes.
(4) The watch should be preferably a large-sized, 21-jewel railroad watch, with a large second hand. The error to the nearest second is
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easily obtained from radio time signals. The minute hand should be set to the nearest minute, and in exact correspondence with the second hand, reading the even minute wflien the second hand is at 60. No attempt should be made to set the second hand. The recorder does not attempt any computations during observation. He is responsible that the observer follows the prescribed program, for immediately requesting a check on any readings which seem discordant, and for reading the second of each observation where a space is provided. When the observer calls, “Ready,” the recorder starts counting the seconds on the watch to himself. When the observer calls, “Tip,” at the instant of centering, the recorder immediately records the time and is then ready to repeat and record the circle readings reported by the observer.
(5) A notebook should be carried at all times, in case the desired blank forms are not at hand. The forms, of which filled out samples are shown in the next two sections, have spaces for recording the observations. It wall be noticed that most of the azimuth observations are to be made in three separately computed sets, each of 3 DjR. If these do not provide at least two sets giving a close check, the observations should be repeated. With the Wild type of theodolite, each of the three sets may be reduced to only 1 DIR, as this will provide more accurate readings than 3 DIR on most of the instruments. In either case, the sets should be begun on different zeros about 60° apart. The recorder is responsible for advising the observer when to reverse, etc. It will be noticed that space is left for recording only one vernier reading. This is sufficient for the intended purpose, and time is saved.
(6) In all astronomic observations, the telescope must be focused for infinity so as to give the sharpest possible image of the celestial body. As the focus should not be changed during the observations, the signal or mark light should not be less than 2 miles distant from the observer, but may be brought to a half-mile distance if more is impracticable, as accurate centering is possible, even on a slightly blurred image. For accuracy in pointing, the terrestrial object should subtend between 2 and 4 seconds at the instrument. A signal box containing a flashlight or bulb and dry cells should be prepared, having an adjustable vertical slit or series of slits of varying width, one of which can be accurately plumbed over the mark while the light is directed exactly toward the instrument. If such a box is not at hand, a bare flashlight bulb may be made to serve. If the light seems too bright, the intensity may be reduced at the instrument by placing a piece of thin transparent paper in front of the objective.
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CORPS OF ENGINEERS
b. Choice oj method.—(1) While the sun is up, it is the only practicable celestial body available. For several reasons pointed out in paragraph 169, the sun is more difficult to observe than are the stars. However, if all of the precautions given in that paragraph can be taken, results from the sun can be surprisingly good, and well within military requirements. With the sun below the horizon, Polaris can be observed. The infinity focus must be exact, and a black cylinder of paper half a foot long secured around the sunshade with a rubber band helps in picking up the star. The approximate azimuth and altitude must be known and computed and set on the circles. Once the star is in the field, the direction may be marked by noting a landscape feature on line, and only the altitude need be set for further pointings.
(2) Polaris is the most useful celestial body for many purposes. Its position and appearance are known to nearly every one. Through the telescope, no other star of comparable magnitude is in the field.
(3) Other stars can be used for obtaining astronomic data when Polaris is obscured. In fact, by means of some programs or combinations, more accurate data may be obtained from them than from Polaris. A careful study of the heavens should be made in conjunction with the star charts (figs. 138, 139, and 140), so that at least a few of the more useful stars may be indentified on sight, no matter how small the area of the sky actually visible may be.
(4) The purpose of military astronomic observations must have full consideration in the choice of method. They are as follows:
(a) Latitude and longitude to establish an initial point for starting a survey in unmapped territory.
(6) Determination of time.
(c) Azimuths for checking computed azimuths in extensive systems of triangulation and adjusting traverse of third-order or greater accuracy.
(d) Azimuths for checking grid triangulation.
(e) Azimuths as a basis for assuming grid coordinates and azimuth.
(/) Azimuths for subsidiary purposes, such as checking traverses and aiding resection.
(g) Latitude for use in astronomic computations.
(Ji) Latitude to aid assumption of coordinates.
(i) Latitude for subsidiary purposes, such as the determination of position from latitude and azimuth and the interpolation of grid azimuth corrections.
(j) Longitude for (g), (ti), and (i).
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Method (a) requires special equipment and training not likely to be found in a topographic unit. Method (6) is no longer needed, since radio time signals are so accurate and frequent. While azimuths of (c) order are easily obtained with the 1-second theodolites of the Wild type and the method of sections XXIX and XXX, ordinary instruments require additional refinements in both observation and computation to yield such results. Methods ( Local c'v’' *'me (+ l2h ,or RM>----------19 30
from the intersection Of his hour circle ond his lot- CxN• 2 _____________________________---% ' 9....... «IBRa......*• *■-* 'vZiw Approximate local sidereal time........0 59
itude (or declination). The hour circles are shown os d kJ SBV _______________________________<—— -------------------—-—__ Then his 2enilh is °boul °" ,he 40” declination ond
dotted lines from the circumference to the center, Nr~~~ /CORPUS : • 'w lhe lh do,,3d line> ond Andromeda P is about over-
ond numbered from I to 24 in hours of Right As- •.....A ' X \. head’ Coss'°Peic ond Poioris (the loiter approaching
cension . 7 ” sr a i r . lower cu,miootion) ore due north, Cygnus ond
For example suppose the observer is in ' ______________—»?---------------- •’ ^... & 'V TV Pegasus ore to the westward, while Aldebor-
lotitude 40” N at 7:30 PM , Dec. 13th; S'-#'-.. ■ '■ ~—S_ ond Orion ore ,he easl
■ sd / crater -, . $------Some allowance has to be made for
s' . U 7 a \ distortion due to the projection of
\ X—- - —Z4"*?----------------________ \ •** , the celestial sphere which is on
f / ©v .......—L ^\?l UBRA\ \ X ,^Vo^k.4he plane of the equator.
/ 2 S'■ VIRGO,” v ■ / \ ; ' ffi
MAGinTVDES:
First
Third •
Fourth Q
Fifth *
stx-a- ♦
SYMBOLS.
O SUN.
C MOON.
V MERCURY.
2 VENUS.
8 MARS.
2T JUPITER.
»t SATURN. t> URANUS.
V NEPTUNE.
^—'L**”’****4Ell"Ltd, S*F-1J2I KbtM^ffeott.aC.putUdtadqeeJXlSak OkdrngrapKieOmar. EDITION: Sth, Aug- 1»1* 10/12100
. the eastward and westward of it. Plot the position of F/ y the Zenith by its Declination which is equal to the u Latitude of the observer. Since the Horizon is
v 90* from the Zenith, the approximate altitude of any on the Mer‘d'an may readily V. he seen. Th8 position of the well-known
bodies, the Sun and Moon will assist greatly in identifying unfamiliar Stars,and the Planets, not easily followed in their ever-changing positions, can readily be recognized by their l0cat'0n in regard to well-known Tk constellations, the Sun and Moon,
or with reference to the Meridian at anytime. The chart, being #. '-X a projection of the fixed
• ‘ stars on the plane of the
o nL 'Xk Equator, is eccentric to
' \ Tx 'X the Zenith of the ob. . • \ 'X server in every case
\ \ X, when not located
\ \ 'X at the Pole. Re-
• \ \ 'X member that
• 2k\ \ X 'X eastward is al-
HYDRAx^ \ ways in the
X. \ • ’ ’ \ direction of
........................... \ X 'X theincreas-\ \.......................X X ing Right
\ \ . \ • X *X Ascen’
\ \ . ■ ’ ‘ \ X \\ sion.
* I
! AQUILA
n/SeR’ENTIS /
/ OPHIUCHUS/
LIBR/
HYDRA-
SAGITTARIUS
CAPRICORNUsK
SYMBOLS.
0 SUN.
C MOON, v MERCURY. ? VENUS.
J MARS.
2 JUPITER, h SATURN.
S URANUS. V NEPTUNE.
MAGNITUDES :
First £
Second *
Third &
Fourth Q
FUth W
Sixth •
to-aU M|Frinted.J>w.-331 1i
|X S3 I EDITION, 30. 191,
No. 2101
onooNNo . Figure 139.—Star chart, Southern Hemisphere.
262341°—40 (Face n. 383) No. 2
CENTAURUS
■ _
No. 2100
WORLD STAR CHART NORTH RIGHT ASCENSION OR SIDEREAL TIME
. EXPLANATION
‘ Eastword is in the direction of increasing Right Ascension on this chart, which shows the ~ equatorial stars os viewed by on observer facing due south
' To identify stars near the observers meridian, or visible to the eastward or westward of ’ it: from the Ephemeris of the Sun, obtom the sidereal time (RA mean sun + 12h) for the near
• est midnight, ond odd the Standard Time (local civil time would be more accurate), plus I2h if
• PM For example, in latitude 40* N at 9 PM , Feb 1st
— Sidereal time at Oh Greenwich, Feb. 2 8 h 47 m
’ Standard time (plus IZh for PM ) 21 00
Approximate local sidereal time 6 00
A glance along the 6h RA line of the chart shows that the constellation of Orion is - near the meridian, thot Capello is almost directly overhead, and thot the first magnitude — stars, Sirius, Pollux, Procyon, and Regolus, should be visible to the eastward.
■ A bright celestial body which is not shown on this chart is probably one of the planets, - which con be plotted on this chart for any day from the right ascension and declinot-- ion as given in the Ephemeris for thot dote.
Scale of magnitudes ■■ M * 2nd ® 3rd » 4th '5tfr 6„ rorTON
H.KU.WW R>. tutbornr of th. SECRETARY OF THE NAVY tonwN Nov
Light travels at the rate of 186,000 miles per second and a light year is approximately six Wo. 21UU
trillion miles-, the mean distance of-first magnitude stars is 3645 light years; second magnitude stars 58 light years and third magnitude stars 92 light years.
Figube 140.—World star chart.
262341°—40 (Face p. 383) No. 3
GREEK ALPHABET
A,a, Alpho I, t, IOTA P, p, Rho
B,Z3, Beto K,A, Koppa Sigma
T, y, Gamma A, X, Lambda T, rt Tou
A,6, Delta M,/z, Mu T,v, Upsilon
E,€, Epsilon N, F, Nu 4>, ♦, Phi
Z,. Omega
CEPHEUS
DRACO
I Aid iramn
Kochab
URSA MINOR
CANES VENATICI
URSA
MAJOR
SOUTH DECLINATION NORTH 8
CASSIOPEIA
AN D ROME DA
: LYNCIS
dr' J /
Equinoctial (Equator)/
' Autumnal Equinox / hydra/
A/pharcf I
ARGO
ERIDANUS
CENTAU RUS
SOUTH
HYDRUS
« Doradus
AQ U I LA
CYGNUS
BOOTES
Efamtn
Alkai d
HYDRA^
LI BRA
SAGITTA RI US Kaus-Australis
SCORPIO
Hercules'
TM 5-235
170
SURVEYING
locating the observer’s meridian and zenith on the charts is explained in figures 138 and 140.
c. The first efforts should be concentrated on learning a half dozen stars in each 6 hours of RA, which would be useful for observing on or near the prime vertical or as east and west stars. For instance, there are several such just west of Orion forming a large pentagon with a Canis Minoris (Procyon) near the center. The Greek letters were originally assigned in each constellation to the stars in order of the relative magnitude. These were only relative but the a stars are nearly always bright, and many of them have special names. The stars are rated in order of brightness from first magnitude to fifth or sixth, which are the dimmest ordinarily visible without a telescope. On the star charts, the magnitude is indicated by conventional signs, and it also is shown at the head of the column for each star in the ephemeris. Having learned Castor, Pollux, Regulus, Alphard, Sirius, and other stars in this part of the heavens, it is easy to add others coming up from the east, as the night or the season advances. As soon as a few have been learned, some observations should be taken on them when they are near the prime vertical. The rapidity, ease, and accuracy of work on the stars will surprise any one unfamiliar with it. In using the ephemeris, it will be noticed that the stars are arranged in order of right ascension and that several important ones are given both the special name and the constellation name with Greek letter.
d. Observation methods for these stars include both the altitude and hour angle methods, and the same facts apply in regard to favorable and unfavorable positions as were described for the sun (par.
• 1696). However, in clear weather there never should be any temptation to observe on a star over 20° from the prime vertical. There never need be any delay waiting for a star to move into a favorable position, as some other star already in position can doubtless be identified. On or near the prime vertical, the stars seem to be moving so slowly in azimuth that there is no trouble in setting the vertical hair on the star. Usually the movement in azimuth will be so rapid that it is better to keep the vertical hair on the star and wait a few moments until the star moves to the intersection of the two hairs. This is similar to the method described for the sun (par. 169(7), but is much easier, for there is only one point of light requiring attention instead of two different limbs of the sun.
383
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171 CORPS OF ENGINEERS.
Section XXIX
AZIMUTHS FROM OBSERVATIONS ON SUN
Paragraph
Altitude method_______________________________________________ 171
Ageton method as applied to azimuth problem___________________ 172
Hour angle method_____________________________________________ 173
Equal altitude method____________________________:____________ 174
171. Altitude method.—a. General.—(1) In the altitude method of determining azimuths, the observation consists of measuring the horizontal angle between the mark whose azimuth is desired and the celestial body whose azimuth can be computed. The known elements of the astronomic triangle are—
(a) The side from the zenith to the pole, which is the complement of the latitude of the place of observation.
(6) The side from the pole to the celestial body (polar distance), which is the complement of the declination of the body.
The element obtained from observation is the side from the zenith to the celestial body (zenith distance), which is the complement of the observed altitude. As in the hour angle method, the desired element in the triangle is the angle at the zenith which is the azimuth of the celestial body.
(2) Following are two formulas suitable for the logarithmic computation of the angle at the zenith, either one of which may be used, although the first is simpler:
1 A /cos 8 COS (s —-»)
cos ~A=-*/-------l L (1)
2 V cos 0 cos h v ’
1 A- /sin (s—h) sin (s-0)
tan 2A-y cQs 8 cos (s_p) (2)
where
A=observed altitude, after all corrections have been applied.
=latitude of the station.
2>=polar distance of the celestial body (90° — declination).
s==2
A = azimuth of the celestial body (less than 180°) from the north.
(3) Particular attention should be paid to securing the best available data. Roughly, an error of 1 minute in either latitude, declination, or altitude may cause a corresponding error of over half a minute in the azimuth. Time is less important here, because a difference of 5 minutes cannot change the azimuth over %0 minute. A set of 3D/R
384
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can be made in less than 10 minutes without hurrying, and the elapsed time should not be much more. All field notes and computations may be completed on form 22 (fig. 141).
b. Procedure in observing.—(1) Set up the transit over the station and level carefully. It is common practice to use the striding or the telescope level for greater accuracy.
(2) Attach the prismatic eyepiece and check the parallax adjustment. Lightly clamp the horizontal axis and leave it so until set is completed. Slip the dark glass over the prismatic eyepiece, and point the telescope at the sun. This can be done quickly by holding the hand behind the eyepiece and moving the telescope horizontally and vertically while watching the shadow on the hand. Focus until the sun’s image is sharply defined. Watch the sun for a moment and decide in which quadrants, as seen by the observer through the eyepiece, and which tangent screws should be used for the direct and reversed pointings (par. 169d). Have the recorder mark the quadrants as they are to be observed.
(3) Set the A vernier at 00, turn the dark glass away from aperture, and sight on the mark indicating the far end of the direction line with the lower motion. The lower motion is not touched again and the instrument cannot be releveled until the set is completed.
(4) Slide the colored glass over the prismatic eyepiece, unclamp the upper motion, and point the telescope (direct) at the sun.
(5) With the sun in the field of the telescope, clamp the upper motion. With both hands operating upper horizontal and vertical tangent screws simultaneously, set image of the sun into the selected quadrant and tangent to the vertical cross hair, and in position to make contact with the center hair by its own movement. Call, “Ready.” Using only the horizontal motion, hold the vertical hair tangent to the sun while it moves toward the horizontal hair. (See fig. 137.) Just as the edge arrives at tangency the observer calls, “Tip,” at which the recorder takes and records the time. The observer then reads to the recorder the A vernier and the vertical vernier, which are recorded.
(6) The operations of (5) are now repeated twice, except that the time is not taken on these readings.
(7) The telescope is reversed and a set of three readings on the B vernier taken as in (6) except that the sun’s image is placed in the quadrant of the cross hairs diagonally opposite the quadrant used in (5) and (6). On the third reversed pointing at the sun the time is taken and recorded as in (5).
262341°—40----25
385
386
TM 5-235
171 CORPS OF ENGINEERS
(8) The telescope is now plunged and sighted back to the mark direct. The vernier should again read 00.
(9) Read and record magnetic bearing to the mark. This completes one set of observations, which should be followed by two more sets immediately.
(10) The results may be roughly checked by testing the proportions of changes in horizontal and vertical angles between the first and second, second and third, fourth and fifth, and fifth and sixth pointings at the sun. If the observations are made rapidly and evenly, there will not be much variation in this relationship. Perhaps the simplest way is to record the four differences of horizontal and vertical angles in columns on scratch paper, ascertain the fractional change to bring each of the horizontal differences to 20, and apply these fractional changes to the respective vertical angles. This can be done mentally, and quickly gives a rough indication of any gross error which would require a repetition of the observations.
c. Computation.—The three sets are computed separately in order to secure an independent check on the work.
(1) Compute the mean values of the time of the first and last solar pointings, of the horizontal angles recorded, and of the vertical angles recorded.
(2) The mean of the vertical angles is corrected for refraction of light due to the earth’s atmosphere and for parallax by values obtained from tables XXI and XXII, TM 5-236.
. (3) The mean ST of the set is converted to GCT by adding 12 hours
to p. m. observations, and the difference in time between Greenwich and the ST used.
(4) Obtain the sun’s declination from the ephemeris for 0" GCT. Correct the declination for the GCT of the observation.
(5) If 3 is (+), the polar distance (P) equals 90° —3; if 3 is (—), P=90° + 3.
(6) is taken from the best available map, if not otherwise known.
(7) s—p is the arithmetical difference between s and p, and is always positive.
(8) The azimuth of the sun from the north is then derived by substituting in the formula
, A I cos s cos (s— p) cos I ------------------
V cos cos A
The true azimuth of the sun is deduced from A.
(9) The mean horizontal angle between the mark and the sun must be subtracted from the azimuth of the sun to give the true azimuth of the line to the mark.
TM 5-235
171
SURVEYING
(10) The azimuth of the mark is then converted to true grid azimuth by applying the “Correction for the reduction of geographic azimuth to grid azimuth” interpolated in the table in United States Coast and Geodetic Survey Special Publication No. 59. The magnetic declination from grid north may be obtained by deducting the grid azimuth from the magnetic azimuth.
(11) The instructions which should appear on the form are given below.
387
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171 CORPS OF ENGINEERS
AZIMUTH DETERMINATION—ALTITUDE METHOD
INSTRUCTIONS
Observation.—Before set, adjust parallax, focus sun sharply, choose quadrants for D and R. Do not touch lower motion, leveling screws, or horizontal axis clamp during set.
Computation.- Three sets are computed separately for cheek. Refraction and parallax from tables XXI and XXII, TM 5-236.
p. m.=add 12 hours for p. m. observations.
TZC=time zone correction to Greenwich time.
5 correction gCTX^tlon per day)~
24
If 6 is (+), p=90°-5; if a is (-), p=90°+«.
(s—p)= arithmetical difference, always positive.
Formula is cos --1 = /cos s cos (s-p).
2 V cos cos h
A =astronomic azimuth east or west of north. Cross inapplicable letter and deduce true azimuth.
For stars, no time need be recorded.
388
SURVEYING
389
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171
Station '°46 Latitude (0): 38°42'36"TrueiNorth
S : Sun Longitude (X): 77°08 '46 "W t
Mark :OX Watch Rref-(-) Slow(+) 50s
............................. .......................... Obs.
Date .April 23,/94! /°.M. When tested: April 23, noon M, JEff
Locality '.Fort Be/voir,Fairfax Co., Va. ST Zone: 6
............................................................ Sun
Weather .C/ear, warm. Observer: S. Sgt Scar/ett xx
Instrument: White /234-/‘ Recorder: T. Sgt. Woo/ Diagram
Reliability of observation: Fair_____________________ Notes checked: <£..
_ . . [~ Hor. Angle 7T Hor. Angle VA I Hoc Angle VA
Tel. to h rn o i o \ h rn o i o i hm o i o . i
0 Mark^fa^ 0 OO 0 oo 0 00
D ± " 3 20.0 105.20 40 22 —(y 3 26.7 /O6 O/ 39 06 ±- 3 348 /OS 06 3 7 4 7
105 28 140 : /5 ± t°6 ' 09 138 '■ 59 ± \ 708 20 f37 ■ 35
105 36 140 07 /<26 • Z7 IJS '. 52 ± f°8 26 137 i 29
R /O5_. 12. 39 22 A '°7 2 2 37.57 /O8 . // 36 33
106 21 39 13 dr 107 3/ 37 50 ± 708 /8 36 27
R ~b £ 3 24.4 105 34 39 02 ±- 3 3/3 /07 37 37 44 ± 3 38.9 /O8 i 27 36 i /8
D Mark 0 OOP ° '■ OO O OO
Mean 3 22.2 /05 25.2 39 43.6 3 29.0 /O6 .49.5 38 24.7 3 36.8 108 /8.0 37:0/5
W 8 PM 12 008 Parallax + > ./ /2 00.8 Parallax + ; ./ !2 00.8 Parallax + : ./
TZC 5 Refract - ; 1.2 5 Refract. - 1.2 5 j Refract. - /.3
GCT 20 23.0 Barom. ± x— 20 29.8 Barom. + —t— 20 37.6 Barom. t —)—
Therm. ± — Therm. ± —t- Therm. ± —j—
_________________h(sum) 39 42.4__________________h(sum) 38 23.6________________h(sum) 37'00.3 6 at OhGCT_______±.t/2\ !9.5 6 at c/’GCT_________± t/2 . /95 S at OhGCT_____± t/2 ; 19.5
GCT x 6 vac per hour ± + . 17.0 GCT x 6var. per hour ±+ 17.1 GCT x &vor per hour ± + \ 17.2
& _________±t/2 36.5 6 _________± t/2 36 6 6 ±+!2 ,36.7
P 77 23.5 ~| i P 77 23.4 j . P 77 \23.3
0 38 42-6 colog cos 0\/0773 'N-HOI Mark J JR AN( ta 02 sle teg 'tnst:K& \Warm,pe HL Chap Mower f 60606 rt/y clouc tau 70") May 8. /9 Watch 2 Comparer Eastern to t-5 stow ' Jp.m Me 5t (if) y 8^'
Locality Fort B Hvoir, Fa rfax Co , Va \Lat 38°‘ '2‘ 36"N Long 7 r08 46" Vf
\RetiabHi ty of obs ervation Good
Objects 7 me p.m Verniers, Remarks
Observed West limb Cast limb Mean Reading A 5 Mea>
h m s h m s h m s o t * »
Mark D 00 OO 00 00 00
Sun D 4 37 49 4 4t 37 4 39 43 123 49 50 50 50 123 49 50
5un R 4 43 07 4 46 54 4 45 00 304 38 40 40 40 \!24 38 40
Mark R 180 00 00 00 00
Z1 ver age 4 42 22 124 14 15
Mark R 60 00 20 20 20
Sun R 4 47 30 4 5t 18 4 49 24 185 19 50 50 50\/25 19 30
Sun D 4 5t 50 4 55 38 4 53 44 5 59 20 20 20\!25 59 00
Mark D 240 00 20 20 20
Average 4 5t 34 125 39 75
Mark D 120 OO to to to
Sun D 4 57 04 5 00 5t 4 58 58 246 47 00 00 00 '.126 46 50
Sun R 5 0/ 34 5 05 2t 5 03 28 67 27 40 40 40 727 27 30
Mark R 300 00 to to to
A verage 5 0/ 13 '127 07 !0
Mag. A. Z. of Ma rk 754' —(Frism atic Con pass)
Checked: »JtC.
■ J
Figure 142.—Hour angle method of determining azimuth.
392
TM 5-235
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SURVEYING
AZIMUTH COMPUTATION-HOUR ANGLE METHOD
(See par. 173c for sun, 178c (3) for star)
Latitude (0): 38° 42'36"N
Longitude (X): 77° 08'46"w Watch ~Fost Slow 24 ® When tested: May 8 S T Zone I E
....................................... Observer: Sgt. Chapeau Instrument : A & E 60606-/0" Recorder. Opt. Mower Reliability of observation: Good
Station . O 54
S : Sun
Mark : OZ
Date ■.May 8,1941 P.w.
Locality '.Fort Belvoir, Fairfax Co.,Va.
Weather : Warm, partly cloudy
True North
HOUR ANGLES
Time of observation
Watch, Tost-Ud Slow( + )
E ST (odd 12 hours if PM)
GOT of obs. (± diff. in time) 0^ Greenwich EQT tot—St4T(Sunl
GCT x var. per hour ~or Tabfe-4S-(Eph.)
(5 + 6) Correct EQT -or-GSidT C4-+5 + 6).
GHA(time)(-l2n) -or (7-8) GHA(orc)(Table 20, TM5-236) Longitude, W(~) E(+) LHA____________________________
Diagram
Notes checked: + <■
SET I SET n SET HI
h 4 m s 22 h 4 m 5/ i s i ^4 h • m 5 i 0/ s !3
+ 24 /■ i 24 + i 24
!6 42 46 !6 5! 58 !7 i 0/ 37
2! 42 46 2/ 5! 58 22 Oi 37
+ 3 33 3 33 f 3.33
3.3 3.3 t i 3.4
+ 3 36.3 3 36.3 + : 3 36.4
21 46 22.3 2/ 55 34.3 22 \ 05 \ !3.4
9 46 22.3 9 55 34.3 /O \ 05 \ /3.4
/46 35 34 /48 53 34 151 . 18 '■ 2/
- 77 08 46 - 77 08 46 - 77 08 .46
69 26 48 7/ 44 48 74 09 \ 35
To find LHA, add GHA and the longitude algebraically, subtracting 360° if necessary.
If LHA is greater than 180’ subtract from 360’ making the difference negative.
If (0-6) is (+), A= g(A+q) + ;(A-q); if (0-6) is (~), A= difference of some.______________
AZIMUTHS (A)
tan|(A+q)= 'g®® x^tyCOt \
tonl(A_o)= jin 2(0-8) . 1
,an2lA q’ cosl(0 + 6)co' 2
LHA 0 6 0-6 0+8 69 26 '-48 4 LHA |(0-6) 34 : 43 24 cot cos log - sin tan Oy59 2445 919 92 2778 cot sin log -cos tan ...o 9 !.F9\2445 27 / .6432
38 n 42 36 09 53 !O \ 46 \ 22
Numerator O\/5 / 5223 9\6 70.7/32 9\4 3 O 88 77 9\946 \/876
2/ 55 32 52 43 29 2 (0+6) 27 i 56 /4
0.480 809! 9\4 84 700/
A| = i(A+q) +|( A-q ) = 88 \ 4/ \ /3 4(A+q) 7/ ' 42 i 38 H A“ q) /6 \ 58 \ 55
LHA 0 S 0-6 0+6 7/ 44 I 48 4 LHA 4(0-6) 35.52 \,24 10 \ 46 \ /8 cot cos log -sin tan O\ / 40 7595 51 9 9 2,2794 cot sin log -cos tan d'/4O .7595 9\2 7/ 5990
18 17 42 i 36 09 \ 59
Numerator dy 3 3 0389 9\6 7O\729! 9>4 / 2 3585 9\946 ,/83 /
2/ 55 32 : 37 52 \ 35 4(0+6) 27 \56 \ /8
o'\4 62'.3098 9\466 \/754
A2= a(A+q) + 2r(A—q) = 87 16 36 447 04 //
/44 40 - 2 24 32
94 J44 39 39
FORM 23
Date of computation: .May 9^ /94/__________Computed bv:
® Azimuth computation.
Figure 142.—Hour angle method of determining azimuth—Continued.
393
TM 5-235
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CORPS OF ENGINEERS
the sun’s image, and call, “Ready.” At the instant the image touches the vertical hair, call, “Tip.” The exact time is recorded, and the A and B plate verniers are read and recorded. Keeping the image roughly bisected as before, allow the sun to move across the field of the telescope until the vertical cross hair falls on the east limb of the sun’s image; record the exact time of the contact. Between 2 and 3 minutes will be required for the sun to move across the vertical cross hair. During this time the transit must not be moved in azimuth.
(5) Unclamp the upper horizontal plate, reverse the telescope, and again point on the sun, recording the readings as in (4) above.
(6) Unclamp the upper horizontal plate and sight the aximuth mark with the transit reversed.
(7) This completes one set of readings. Two additional sets should be taken with the relative positions of the horizontal plates shifted so as to have the readings on different parts of the horizontal circle. The mean of the times of pointing on the two limbs of the sun will correspond to the readings on the horizontal circle for the center of the image of the sun. The average time and angle for each set are recorded opposite the word “average.”
c. Computation is accomplished on form 23, “Azimuth computation, hour angle method” (fig. 142 ®). The data are transcribed from the notebook to the spaces at the top of the form, the average times of each set to line (1) of the “hour angle” block, and average angles for each set to the third line of the “grid azimuth” block. As this form is also used for the computation of similar observations on stars, the abbreviations referring to the star computation on lines (5) to (9) are crossed out. The solution then proceeds as follows:
(1) Correct the time of observation for watch error and record true standard time of observation.
(2) Convert the standard time of observations into Greenwich apparent time (see par. 165?*).
(3) Determine the hour angle of sun by the equation: Hour angle—apparent time minus 12 hours.
(4) Determine the declination of the sun for the time of observation by referring to part I of ephemeris for date of observation, and applying correction for hourly variation since 0* Greenwich civil time in the same manner as the declination was determined in paragraph 1668.
(5) Solve for the azimuth of the sun by substituting latitude, declination, and hour angle in the formula given above.
(6) The formula (1) is printed on the form, also the following rules: To find LUA, add GLIA and longitude algebraically, subtracting 360° if necessary.
394
TM 5-235
SURVEYING 173-175
If LHA is greater than 180°, subtract from 360°, making the difference negative.
If —<5 is (+), A=%(A-f q) + %(A—q); if tj>— b is (—), A=difference of same.
d. Exercise XXXI.—Azimuth determination from hour angles of the sun.—Using a watch of known error, occupy the station and observe the sun while near the prime vertical for the angle mark-sun, recording the time to the nearest second, as shown in figure 142 ®. Compute the true grid azimuth on form 23.
174. Equal altitude method.—a. This method is not a desirable one for military surveys, as the same station has to be occupied in both morning and afternoon. Even then the above method is not so accurate as others, as it is not well adapted to the refinement of results by repetition or by taking the mean of a series of observations.
h. If a station can be reoccupied, and it is desirable to check some hour angle observations made in the morning, for instance, a better check could be obtained from three additional sets by either the altitude or hour angle method.
c. If conditions require the use of an equal altitude method, observations should be on a star as described in paragraph 178e.
Section XXX
AZIMUTHS FROM OBSERVATIONS ON STARS
Paragraph
Polaris________________________________________________________________ 175
Azimuth from observations on Polaris at elongation_____________________ 176
Azimuth from observation on Polaris at any hour angle__________________ 177
Azimuth from other stars_______________________________________________ 178
175. Polaris.—a. Identification.—Polaris, listed in the ephemeris as a Ursae Minoris, is a star of the second magnitude which rotates about the north celestial pole at a radius of about 1°. No other close circumpolar star is of comparable magnitude. Figure 143 shows Polaris and also another constellation, about 30° from the pole, called the Great Dipper (Latin name Ursa Major) because of the outline formed by its seven bright stars. A pair of these on the side of the bowl opposite the handle are called the “pointers” because a line through them points at Polaris, which is sometimes called the North or Pole Star. Polaris is almost on line between f Ursae Majoris (special name, Mizar) and 3 Cassiopeiae, the latter in a group of five stars forming a large W. All of these stars are shown in the figure and are easily recognized during any clear night by an observer north
395
175 CORPS OP ENGINEERS
of the Tropics. Like all stars they seem to rotate about the celestial axis in a westward direction. The same effect may be had by rotating (fig. 143) counterclockwise about the pole as a center.
b. Location.—When the star crosses the meridian above the pole it is said to be at upper culmination; when it crosses the meridian below the pole it is said to be at lower culmination. When the star
n
*
URSA MAJOR ''
URSA
MINOR
Pole—_s
Polaris +
® r CASSIOPEIA jfr-- * 's
a
Figure 143.—Location of Polaris near lower culmination.
reaches the point in its apparent path where its azimuth east of geographic north is the greatest it is said to be at eastern elongation, when it reaches the point where its azimuth west of geographic north is greatest it is said to be at western elongation. The star appears to make one complete revolution every sidereal day (23/,56m04.1s of mean solar time). Consequently, it crosses the meridian approxi-^mately 3"'56s earlier each successive day. The apparent motion of
396
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175
SURVEYING
the star being uniform, one-quarter of its apparent path will be described in 5*59w01s, one-half in llh58m02s, three-quarters in 17*57w03s of mean solar time. However, only to an observer on the Equator does this star reach western or eastern elongation at one-quarter or three-quarters of its apparent path. At other points the mean time interval between upper culmination and west or east elongation is less than 5*59"'01s by an amount depending upon the latitude. Observations on Polaris for azimuth may be made at either elongation, or at any time between. Referring again to figure 143, Polaris is on the opposite side of the celestial pole from Mizar, in the Dipper handle. By remembering this relationship, it is easy to estimate how soon the star may be at elongation, or even to estimate the hour angle, within an hour or less. In the figure the hour angle is about 11* 30™, according to the ephemeris, table VI. •
c. Advantages.—Polaris is the most useful star in military surveying because of its proximity to the pole. There is no comparable star within 10° of the south celestial pole. The small radius of rotation so reduces the apparent speed of motion that accurate pointings can easily be made in any aspect, and errors due to mistakes in watch time have much less effect on results. There is a smaller star quite close to Polaris, invisible to the eye but easily seen through the telescope. If the observer will note the position of the small star as he makes the first deliberate pointing, it will serve as an identification for succeeding pointings which may be more hastily made.
d. Special tables.—(1) Precise determinations of azimuth by observations on Polaris are made and computed in exactly the same manner as observations on any other star.
Forms 22 and 23 may be used for Polaris and other stars (see par. 178), as for the sun, with some slight changes.
(2) For ordinary military purposes computations of azimuths are shortened and simplified by the use of tables. Polaris is not included in the Ephemeris general tables of “apparent places of stars,” but an enlarged table, adjacent to the other special tables for Polaris, gives the right ascension and declination for every day of the year. The special tables in the Ephemeris include the following:
Table I.—For Finding the Latitude by an Observed Altitude of Polaris.
Table II.—For Converting Sidereal into Mean Solar Time. Table HI.—For Converting Mean Solar into Sidereal Time. Table IV.—For Finding the Azimuth of Polaris at All Hour Angles.
397
TM 5-235
175-176 CORPS OF ENGINEERS
Table V.—For Finding the Azimuth of Polaris at Elongation.
Table VI.—For Finding, by Observation, when Polaris passes the Meridian.
Table VII.—For Finding the Apparent Place, Time of Upper Culmination, and Time Interval between Upper Culmination and Elongation, of Polaris.
176. Azimuth from observations on Polaris at elongation.—
a. General.—(1) Figure 144 shows in proper relation the various
Figure 144.—The aspects of Polaris, including hour angles.
a=Hour angle of Polaris at western elongation.
6=Hour angle of Polaris at lower culmination.
c=Hour angle of Polaris at eastern elongation.
^C' \ ■
West elongation fo- East elongation
A fk
I % 4^ I
I ~p6th o'
~~~~A'~.+°rthern Horizon H/ —----------------------—— E
N
TM 5-235
SURVEYING 176
In the figure the vertical line represents a portion of the meridian passing through the zenith and intersecting the northern horizon at the point N (north point) from which, for all practical purposes, the azimuths of Polaris may be reckoned east or west. At the instant Polaris crosses the meridian it is at either upper or lower culmination, depending upon whether its position is above or below the North Pole. In the figure Polaris is supposed to be on the meridian. At the instant Polaris is farthest east or west of the North Pole it is said to be at either eastern or western elongation. The corresponding hour angles are also indicated.
(2) Observations for determining azimuths may be made at any time, the exact time being carefully noted. Whenever possible observations should be made when Polaris is either at its eastern or western elongation, as this method gives somewhat more accurate results and involves very little computation besides calculating the time of the star’s elongation. During certain times of the year Polaris is not easily visible (on account of daylight) at elongation; therefore, the method of determining azimuths from observations from Polaris at any hour angle, described in paragraph 177, is used to a large extent.
(3) Azimuth observations made on Polaris at elongation offer to the inexperienced observer less chance of error either in observing or in computation than any other method. When near either elongation, the star is changing very little in azimuth. With only approximate time the star may be tracked until no change in azimuth is apparent. During 10 minutes before or after either elongation, the star varies not more than Xo minute in azimuth. (See ephemeris, table Va.)
(4) Though it is a convenience, the time of elongation need not be known in advance of observation. When Polaris is at culmination it is nearly on the same vertical line (meridian) as the stars Mizar and 3 Cassiopeiae. About 6 (and 18) hours later Polaris may be observed for elongation.
b. Procedure in observing.—The observations are recorded and all computations are made on Form 24 (fig. 145).
(1) Before the night of observation compute the standard time of elongation within 1 or 2 minutes.
(2) Set up the instrument one-half hour before elongation and keep the vertical crosshair exactly on Polaris until about 10 minutes before elongation, when the star no longer appears to move laterally.
(3) Measure the angle mark-star, 3 DfR, reading the A vernier of the first angle to secure a check on the sixth repetition. The vertical hair should not be set upon Polaris at its intersection with the center
399
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176
CORPS OF ENGINEERS
Figure 145.—Azimuth by Polaris at elongation.
400
_________________AZIMUTH BY POLARIS AT ELONGATION_________________________________________________________
Station : ZA Lewis Latitude ().'44 ° LO 49 N True iNorth
POLARIS E "W-elongation Longitude ( X): 76° /8'32"W. \
Mark > Z\ Pine Watch Fast Slow + % m * \ J N\p"™
Date Oct 2, 794/ B «• When tested. Oct. 2,/94! 5 PM. A)ls'
Place ! Lewis, tfmg Co., N.Y. ST Zone: E \ -vos.
.....................■...... .................—■
Weather 'Coo/, hazy, no wind. Observer. T Sgt. Burr ____________________*
Instrument: Berger /28O3 -20" Recorder 5 Sgt A/den Mizar Qjagram p°laris
Reliability of observation: Fair (very hazy) Notes checked
I Oct 3 Date of observation
2 Sept 2 7 Next preceding dote in Ephemeris Tgble 3E
3 6 Days intervening (no fractions)
4 — • 23 : 36 (3) X 3m 56s = Correction to GCT, Upper Culmination
5 / 23 22 GCT UC for date (2) Table ZU
6 \ 59 46 (5) — (4) GCT UC for date obs.
7 — ; 5/ ± Correction for X (Degrees of XXIo+l5) E (+) W(-)
8 \ 58 \ 55 (Sum) LCT UC
9 - 5 i 55 \ 04 ± Meon time interval between UC and elongation at (j) of Station Table ZE
10 19 \ 03 \ 5/ LCT El. at Sta. W EI.(8)+(9) E El. (8)-(9)
II : i 76 : /8 \ 32 Longitude of Station
12 ; ; - 75 i 00 ; 00 Meridian of standard time
13 : i 1/8 .32 (II)-(12) Difference in longitude
14 y- ,5 /4 + (ISj/Zig Difference between LCT ond standard time
15 PM.7 \ 09 j 05 (IO)±(I4) Standard time of elongation (14) is (+) Wof ST meridian (—) if E
Time ID 6 \ 57\45 7 \ 06 '40 7 \ /4 ,OO
Time 6R 7 \O5\2O 7 /2 \3O 7 \22 \/O
Set No. I u in nr z zi
Mark OO \OO\ OO 60 \O5\2O /20 \/O ,20
0 I 299 i 54 ; OO 359 59 ,40 6O \O4 \ 20
R 6 359 25 ,00 59 30,20 H9 34 OO
Sum 1799 25 j OO 1799 25 j OO 7799 23 40 i ; i [
X 299 54 i /O 299 54 /O 299,53 57
Table Vai ------:----i— --------t---;— ----i----i--
Cor. Angle -----i----i— --------;—- -----------j----i---
17. Mean of good sets 299 54 06
18. With declination for nearest Oh Eph.Table Z Declination
from E ph.“Apparent place of Polaris” Latitude 88.59.00 88 .59 06 88,59 /0
and the latitude of the Sta.,from Eph. 4-4-./O .00 / .26 03 ; ; / . 24 49
Table Z “Azimuth of Polaris at elonga- 44; /0 49 / .2.5.04 / 24 56 / 24 50
tion’,’interpolate the azimuth of Polaris. 44.20 OO / 25/7 / .25.03
19 Azimuth of Polaris E (+)-or-W-f-T of North + y / 24 56
20 True azimuth to Polaris, 360° ± (19) / 24 56
21 Magnetic azimuth to Mark 5/ 3/ Mean azimuth to Mark (20) —(17) 6/ ■ 3O\5O
22 Grid azimuth to Mark — 63 i 49 Grid correction (S.P 59) + y 2 \ /8 ; /9
23 Magnetic Decl. from grid N E(-)'WHd-/2 ; /8 Grid Azimuth to Mark 6 3 ,49 09
Date of computation. Oc/.4,194/ Computed by. f ,N/J. Checked if .2-t j FORM 24
TM 5-235
176-177
SURVEYING
Calculate the mean of the
sets until 10 minutes after
entirely of calculating the
hair, but a little above (or below). When the telescope is reversed, use the same part of the hair, which is then a little below (or above) the center hair. Record the A vernier on the 1 D and 6 R settings, reading the B vernier only as a check.
six repetitions.
(4) Continue taking observations in elongation time.
c. The computation consists almost time of elongation, as explained on the form.
d. Exercise XXXII.—Azimuth by observation on Polaris at elongation.—Compute the time of elongation, observe Polaris during the 20-minute bracket of the calculated time, and find the true grid azimuth and magnetic declination, making all necessary notes and computations on form 24.
177. Azimuth from observations on Polaris at any hour angle.—a. Procedure in observing.—Both field notes and computation are recorded on Form 25 (fig. 146). The watch error should be known within 10 seconds.
(1) Center and level the instrument carefully over the mark. Do not change the leveling or the lightly clamped, horizontal axis clamp until the set is finished.
(2) Set the A vernier at zero, sight the mark with the telescope in the direct position using only the lower motion, and read and record the magnetic azimuth.
(3) Measure by 6 repetitions (3 DfR) the angle mark-star, recording exact time of each setting on the star, read and record the A vernier for the 1 D and 6 R settings on the star. Subtract the initial reading from the sixth repetition and divide by 6 to get the mean value of the angle for the set after restoring the multiples of 60° which may have been dropped by passing the 360° of the circle.
(4) This set should be immediately followed by two more.
b. The computation is accomplished in the following steps:
(1) Correct the time of observation for watch error, thus obtaining the accurate standard time of observation.
(2) Convert the standard time of observation to local sidereal time.
(3) Compute the hour angle of Polaris by the equation, hour angle equals local sidereal time minus right ascension. The right ascension is found in Apparent Place of Polaris (ephemeris table).
(4) Determine the azimuth of Polaris by referring to table IV of the ephemeris using the latitude of the point of observation and the hour angle computed in (3) above as arguments.
262341°— 40--26
401
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CORPS OF ENGINEERS
Figure 146.—Azimuth by Polaris at any hour angle.
402
AZIMUTH BY POLARIS AT ANY HOUR ANGLE____________________________________________________
Station : Pier I Latitude: ° 42' 55"N True North
Polaris Longitude: 77° OB'BO'W 1
Mark .063 _ _ Watch Fast 'Stow....tO^' /\\
Date -.Mar. 6,1941 P.M. When tested Mar. 6,1941 5 PM ( ftOb*/
Place .Fort Belvoir, Fairfax. Co, Va. ST Zone: £ FMgr>»
Weather :Coo! and windy. Observer: Cpi Mower MizaF*
Instrument: Berger 12803-20" Recorder: 5t.Sgt Scarleft Diagram .
Reliability of observation: Good_______________ Notes checked: £ J. 77}.
___"A" Vernier Set I Time . 'A1'Vernier Set H_____Time ‘A11 Vernier Set m Time
2 DI 196 09 ; OO\ 7 ,30 46 196 07,20 \ 7 ,39 03 196 07 j OO I 7 \48 \ II
3 D2 7 32 29
4 D3 7 J Tf''\5o'\ 34
5 R4 7 -34r257'4246
6 R5 7 36 ..?.. 4^- 3g
7 R6 96 48 20 7 36 58 96 \ 4l \ 20 7 45 !8 96 \37\z6 ""'7 "\54\48
8 Sum 1176,48'20 203.591176 41,20 252 32 H76\ 37 i 20 \3O8\29
9 i 196 08 03 7 ,34 , OO 196 06 53 7 42 05 196 ! 06 i TT 7 ,5/ ,25
Set I__________SetH___________Set HI
10 Mean time of observation from (9) 7 i 34 i 00 7 : 42I 05 ~7 j 5/ i 25
II Watch Fast (-) ~Staw4+>- ± r ( ; /6 - 1 ■/O - \ \'/O
12 £ ST (add 12 hours if P.M.) ________(10)4-(II) /9 \33\ 50 !9 ,4! \55 19 .5! \I5
13 Longitude of station 77 i 08 i 50 i ; . ! ; '
14 Meridian of Standard Time — 75 : OO : OO i • • i ! ; ■ :
15 Difference in longitude (13-14) 2 \O8 ■ 50 : i I ' ' ' i 1'
16 Difference between ST and LOT (I5)/I5 ± - \ 8 \ 35 - 8 \ 35 - 1■
17 LOT (16) is(+)E,(-)W of ST Meridian (I2)±(I6) 19 ,25 \l5 !9 .33 \ 20 19 ■ 42'\ 40
18 Eph. Table JU, mean solar into SidT ' \ 3 \ H , ] 3 : /3 ' '1'3 : 14'
19 Sidereal interval since 0h (I7)+(I8) 19 .28 \26 ~19 i 36 \ 33 19 ,45 1 54
20 SidT OhGCT (Eph. of Sun) I/O i 55 i .................~T....I! ! ~.....' t
21 Corr, for"X (DegreesXxJOs/i5)W(+) E(-) f i \ 51 T i...................■........ I........f....
22 SidT Local Oh (20)±(2l) IO ' \54 \ 1/ 70 \54 f/l ''/d'p4 \ // '
23 Sid T of observation (19)+ (22) 6 \22\37 6 , 30 ,44 6 ,40 ,05
24 RA of Polaris nearest 0n (Approximate place of Polaris)- / i 42,54 l~]42'54i\42\64
25 HA of Polaris at time of observation (23)—(24) ~4 ,39 \43 ~4 ! 47 ; 50-~4 j 57 j //
26 Toble 12 Latitude__________Tablelwith the HA and (J> of the Sto. from Eph. Tab H,
27 HA 38 ; ' 38,42 ; 55 40, ; Igg Azimuth of Polaris at all HA*, interpolate the azi-
2® ....i...i...../ 1__j... muth of Polaris. With declination for nearest 0h
29 J j___F.../45. '-.._______________ ^rom Eph.‘Apparent place of Polaris',and the <(> of
:.I9. A9.... ....I. S4A • _ ! ',150', the Sta. from Eph. Tab. Ha interpolate the corr*
51 P.;A.7\.Ll.....i.... 1 .. ! i i ection for each of the azimuths found above.
32 A ] 6o[oo 17 jAisf 7 ;zii6i ' i jefi .............
33 Azimuth of Polaris E(+) or W(-) of north ' ±| ~ / \ !3 \ 36 ~ | 14 \24 -/ \. !5 \ !8
34 True azimuth of Polaris, 360 ± (33) 358 \ 46 \24 358 .45.36 358 ',.44 ; 42
35 Mean Angle to Mark from (9) - 196 \ 08,03 196 i 06 i 53 /96 \ 06 : 13
36 True azimuth to Mark___________________________ /62,38 \ 21 162 . 38 43 162 ■ 38 ,29
37 Magnetic azimuth to Mark 166 I 55 Meon azimuth to Mark,from (36) 162 38 \3!
38 Grid azimuth to Mark — 160 ; 14 Grid correction (S.P. 59) ± -27 24 \3i
39 Magnetic Decl. from Grid N, ~EMW(+) + 6 \ 4I Grid azimuth to Mark (37)±(38) /60 ■ <4 \OO
Date of computationi ....... Computed by: Checked by:^.z^ FORM 25
TM 5-235
177-178
SURVEYING
(5) Correct this azimuth for variation in declination by referring to table IVa and using the declination and azimuth determined in (4) above as arguments. The declination of Polaris for any day in the year is found in Apparent Place oj Polaris. The result is the azimuth of Polaris east or west of north. Convert to true azimuth.
(6) Determine the true azimuth of mark by deducting the angle mark-star from the true azimuth of Polaris.
(7) Determine the correction for grid divergence from Specification Publication No. 59, and obtain the grid azimuth.
c. Exercise XXXIII.—Azimuth by observations on Polaris at any hour angle.—Recording all notes and computations on Form 25, obtain the azimuth of a line assigned by the instructor by observations on Polaris at any hour.
178. Azimuth from other stars.—a. General.—(1) In making azimuth observations on a star the procedure is practically the same as for the sun, except that pointings are made on the center of the star and not on the limb. The procedure in observing and the forms of field notes are similar to those for the corresponding methods on the sun. Forms 22 and 23 may be used for the computation with but slight modification, as explained below in b and c.
(2) The above applies equally well to the computation of Polaris observations, when a more precise solution is desired than can be obtained with the special tables previously described (par. 175g? (2) ). A still more precise computation of Polaris observations may be secured by using formula (2) (par. 167e), which is especially adapted for close circumpolar stars.
(3) More nearly correct azimuths may be obtained from the computations of observations taken on stars which are in favorable positions. Rather than wait until some particular star is in a position favorable for observation, it is generally better to select from the Ephemeris some other star which will answer the requirements at the desired time of observation.
b. Altitude method.—(1) Favorable positions .—The accuracy of the solution is maximum where A is 90° or, in other words, when the celestial body is to the east or west of the observer. However, other factors must also be considered. When the altitude is less than 20° the corrections for refraction are uncertain. When the altitude is greater than 45° the inaccuracies of the oridnary instrument will introduce serious errors when the telescope is depressed to sight the azimuth mark. The instrument should be carefully leveled before each set of readings. Observations by the altitude method should not be taken when the celestial body is near the meridian, as the altitude is changing
403
TM 5-235
178 CORPS OF ENGINEERS
very slowly and the solution will give poor results. Time is needed only in order to interpolate for declination at the time of observation. In observations on stars the exact time need not be known.
(2) Figure 147 ® shows the field notes and computation of observations made with a direction theodolite of the Wild type, reading directly to one second. Three sets of 1 DIB each were taken, setting random new initials for each set. When computed with the 1939 ephemeris, the azimuth was correct within 3 seconds.
(3) The computation differs from that of a solar observation (par. 171c) only in that the altitude needs no correction for parallax and the declination needs only correction to the date of the observation, the hourly change being disregarded.
c. Hour angle method.—(1) Favorable positions.—Examination of the formula (1) (par. 167e) will show that the most favorable time for observations by the hour angle method is when the hour angle is near 6 or 18 hours, and the least favorable is when the hour angle is near 0. The error introduced by observations on celestial bodies near the meridian depends on the latitude of the place and the declination of the body. Consequently, no definite limits can be given. In latitude 45° N, when the sun is on the meridian and its declination is zero, an error of 1 second in time, will give an error of 21 seconds in azimuth. Under the same conditions with an hour angle of 6 hours, an error of 1 second in time will give an error of 11 seconds in azimuth. In observations on Polaris, in latitude 45° N, when the star is on the meridian an error of 2 seconds in time will give an error less than 1 second in azimuth. In the same latitude, when the star is at elongation an error of 30 seconds in time will give an error of less than 1 second in azimuth. In general, hour angle observations should not be made on a celestial body less than 2 hours from the meridian. In the case of close circumpolar stars, the most favorable time for observation is when the star is near elongation. In the case of other stars the most favorable time is when the star is to the east or west of the observer and less than 45° in altitude.
(2) The notes are recorded in a manner similar to that shown in figure 142®, but three individual pointings direct and three reversed, reading only the vernier next the eyepiece, with the exact time for each, are recorded for each set, and three sets are taken. The initials are changed to 60° and 120° and the second set may be begun in the reversed position. This method is similar to that shown on Form 22 (fig. 141), except that times are required for each horizontal angle, and vertical angles are not read. The star may be allowed to make its own contacts if it does not move too slowly. The star should not
404
TM 5-235
SURVEYING 178
be set on the intersection of the cross hairs, but on the same point each time, a little above the intersection direct, and the same amount below for the reversed position. An unsuspected watch error is just as harmful as with the sun (par. 173a (5)).
(3) The computation is made on Form 23 (fig. 147®). In lines (5) to (9) of the “hour angles” block, the abbreviations for EQT and GAT and other references to the sun are crossed out, as sidereal time is used with stars. The LHA is found as demonstrated in paragraph 1666 (3); the time of the observation is converted to G Sid. T, from which the RA is subtracted to get GHA, which in turn is corrected to LHA. If LHA is less than 12*, the star is to the west; if more than 12*, it is to the east of the meridian. If LHA is greater than 12*, subtract its value from 24* for use in the formulas. The right ascensions and declinations of the principal stars are given in the ephemeris for the upper transit at Greenwich in 10-day intervals. The variation is so small that interpolation to the date of observation is all that is required, interpolation for longitude from the meridian of Greenwich being unnecessary.
d. Observations on east and west stars.—(1) Excellent results will be obtained by observations made on two stars, one to the east and one to the west of the meridian. These stars should be selected near the prime vertical and between limits of 20° and 45° of altitude. The average azimuth of the mark determined from the two observations should be adopted. This procedure will eliminate gross errors both in observation and computation. If the results are computed immediately at the station, two sets to each star may be sufficient. If the computations are to be made later or at another location, 3 sets should be observed on each star, in case one (or more) of the sets should prove defective.
(2) With the altitude method, this procedure should minimize errors in the assumed latitude or in the adopted refraction. If east and west stars of roughly the same altitude can be observed, the error in refraction may be balanced out.
(3) In the hour angle method, any error in latitude or an incorrect value of the watch error should be diminished by observing east and west stars.
(4) This method is not well adapted for sun observations as the east and west observations will be separated by several hours, during which the declination will change materially.
(5) Observations on east and west stars should yield more consistent accuracy than any other method, except precise computation of Polaris observations, which include correction for curvature of the star’s path during each set of observations.
405
TM 5-235
178
CORPS OF ENGINEERS
Station S 0 38 Latitude (0): 38° 4/' 20 "N. Longitude(X)77°08 ' /3"W True^ 4-oQ North y
Reg ulus
Mark Date Locality Weather Instrument O 40 Jan 24, /94! P .M. Fort Be/voir, Fairfax Co, Ya. Clearyco/d Wi/d 6388-72 Watch Fast(-) §low(+) - S Barpm: 29.<5 Therm; 4B',F Observer: St. Sgt. Kosten Recorder: St. Sgt. Alden J8 ( Dio Begulus gram
Reliability of observation: Very good. Notes checked IM.
Tel. to D -Merk JTT Hor. Angle/ 00.6' V.A. cr r D * m 6°><8 Hor. Angle/ er 38.3 V. A. zr T D •h- er 'f°>32 Hor. Angle, * 40.8 \ M.A.
uns j +l o t/9 /4 21.1 ) 62° 04 i 07.0 P+ 179 20 13.3, 67° 4/ \ 07.9 240. Ot 26.9 6 ° !O 12.7
H.3 298 04 57.0 *4 25.8,298 29 i 26.5 50^/6 22.2.299 00 2/.0
*4< Ang/es + A ng/es 4 A ng/es
X X + 4 orent po 08^9 2t.i\ 27' H.3 ; 28 55 53.0 O4\ 57.0 + + 3 5.0 28 47.5\ 28 !8 i 52/ 29 ,26.5 4 4- 119^37 46./ 41.4 28 29 49 OO 47.3 2/0
R + S 4- 4
0 Mark
Mean iaj Ci pee H8 45 76"\ 28 o6\ 25 /79°\ 06 II" : 28° 24 i 09 H9 • 33 14 28° 55 04
Parallax + 4— Parallax. + 4— ♦ Parallax + -i
: TZG- Refract Barom. ± Therm. ± h(sum) -07, 49 ! Refract Barom. ± -O/\47 Refract Borom. ± -or, 45 - i 04 t i 04 28 53/9
- 04 - '■ 04
■GCT
t i 04 27 '5836 Therm. ± h(sum) + : 04 28 22 22 Therm. ± h (sum)
6 at OhGCT ± GCT x S van per hour ± & ± 6 at OhGCT ± GCT x 6var.pe>r hour ± 6 ± 6 at OhGCT ± GCT x Svor. per hour ± 6 ± - 1-
t!2° \i5 10
P 0 h 2) S P S-P 77°',44 50 colog cos colog cos log cos log cos 0\!07\6O P 0 h 2) S P S-P 7744 56 colog cos colog cos log cos log cos i I i. ? 0\/07\6O P 0 h 2> S P S-P 77\44 50 colog cos colog cos log cos log cos ■■ 1 — i j O^O7\6O 0857''7/ . — .-.4- - 1 • 1 | 9\!74?2
38 4! 20 38 '41 20 28 \2Z 22 38 '41 20
27 58 36 o\o53\97 0'055\58 28 \53 !9
144 24 46 9\485,/4 144 .48 32 1 9\48O\43 145 \/9 29
72 72 23 72 '24 16 72 \3944
77 .4450 999797 77 44 50 "T 9[\998,// 77 4450 1 ; 1 i 9\998\29
05 322/ 05 \20 34 05 05 06
(sum) 2) log cos jA 9'644 68 (sum) 2) log cos-gA 964/72 (sum) 2) log co?.|a 9637.82
9\82234 982086 9\8/8\9!
2 A A E orAW Azimuth of S Angle, Mark-S -True. Az. to Mark 48° 22 26 Ta A Ew-W- Azimuth of S Angle, Mark-S -True Az. to Mark 48 \32 $/" J-A A Eor-W-Azimuth of S Angle, Mark -S -True Az. to Mark 43 '46 24
96 44 52 97 05 42 97 32 48
96 44 52 97 \05 42 //9 06 // 97 \32 48
H8 45 J6 H9\33 !4
337,59 36 337,59 3! 337,59 3 V
Magnetic Azimuth to Mark Grid Azimuth to Mark
Mean Azimuth to Mark
Grid Correction (S.P. No 59)
Grid Azimuth to Mark
337 59 34
-.2)2443
33534 45
Magnetic Decl. from Grid N. E(-)W(+)
Date of compution; Jan. 25, 1941
Computed by:0l.+j^ Checked by: J.
FORM 22
® Altitude method.
Figure 147.—Azimuth computation—Continued.
406
TM 5-235
178
SURVEYING
AZIMUTH COMPUTATION-HOUR ANGLE METHOD (See par. 173c for sun, I78c(3) for star) Latitude (0): 38°4/' 36"-N Longitude(X): 77°08' /3"W Watch: Fast -Stew. /2 s
Dec. 13,1941 PH. When tested: Dec. !3
'.Fort Belvoir,Fairfax Co.,7a S T Zone : £
:Cool, dear, windy Observer: Sgt. Chapeau
Recorder: Cpl. Mower
:O39
: Betelgeu*
True North
Bete/geux
Station S
Mark Date
Locality Weather
Instrument: Berger I /8 !3 - 2O ‘‘ Reliability of observation: Fair
__________Diagram______
Notes checked :
HOUR ANGLES SET I SETH SET HI
h m s h m s h m : s
i Time of observation 8 Z<5 45 8 25 24 8 33 ! 58
2 Watch, Fast (—) 'Stnw-Ltl f - 72 - • 12 - ■ Z2
3 £ ST (add 12 hours if PM) 20 Z6 33 20 25 i 12 20 33 46
4 GCT of obs. (± diff. in time) / Z<5 33 Z 25 i 12 Z 33 ■ 46
5 0h Greenwich TZZT—ar SidT(Sun) ± * 5 . 29 51 t- 5 . 29 , 5.1 t 5 29 ; 5.1
6 GCT x -van. per-houn or Toble HI (Eph.) ± 72.6 + .14.0 15.4
7 (5 + 6) Correef-EQT or- GSidT (4+5+6) i. + 6 45 50.1 t 6 54 .31.1 t 7 03 ‘ 06.5
8 <4 1 7) GAT on- -RA(Star) - 5 52 02.8 - 5 52 .02.8 - 5 52 : 02.8
9 GHAltimeXXjfaoc (7-8) i S3 47.9 Z 02 28.3 / II .03.7
10 GHA(arc)(Table 20, TM 5-236) 13 26 58 75 37 [ 04 77 45 i 56
II Longitude, W(-) E(+) ± - 77 08 13 - 77 08 \ 73 -77 08 \ !3
12 LHA ± -63 4/ 15 -6t 3! '■ 09 - 59 22 i Z7
To find LHA, odd GHA and the longitude algebraically, subtracting 360° if necessary If LHA is greater than 180’ subtract from 360° making the difference negative If (0- 6) is (+), A=I(A + q ) ti(A-q)i if (0- 6) Is (~), A = difference of same
AZIMUTHS (A)
tan 1 (A- a )= Ainj^~&)cot 1
tan 2 (A q) cosx(0+£)) 2
tan l(A+a)= c°s ?(0-6)cot t
Tan2lAt<’' sin4(0+6) 5
LHA 0 6 0-6 0+6 63 38 4/ 4! ts 36 j LHA 1(0-6) /Z 15 50 38 38 56 cot cos log - sin tan 9\9 83 84 74 5 960 cot sin log -cos tan 0\2O6 9\4 30 8474 9479
7 23 44 Ni ■2(0+6) merator O !9O 4434 9\63 7 7953
3/ _ 46 J.7. 05 52 20 23 02 i 40 9 592 6708 9\96 3 8829
597 7726 9\6 73 9124
A| = -£(A+q)+|(A-q) = IO/ 05 45 ■j(A+q) 75 j 49 i 48. I(A-q) 25 /5 : 57
LHA 0 6 0-6 0 + 6 6/ 3/ 09 fLHA |(0-6) Ni |(0+6) 30 : 45 merator L - 35 cot cos log -sin tan O\22 5\36O9 cot sin log -cos tan 225 3609
— 9\983\596O O\ 208.9569 9\592\6708 9\43O 9\656 9\963 9479 3088 8829
O\6 7 6 .286 Z ' 9\692 4259
Az= -£(A+q) + |(A-q) = 102 i 37 73 2 (A+q) 76 \ 23 \ 56 2(A-q) 26 73 i Z7
LHA 0 6 0-6 0 + 6 59 22 i Z7 5 1 .291.^/. 08 cot cos log -sin tan 0\244 9\9 83 0826 5960 cot sin log -cos tan 0^244 9\43O 0826 9479
il — Numerator 0\22 7 '9\'592 O\635 6786 6 708 0078 9\6 75 9\963 9\7 ! ! 0305 8829 14 76
A3 = ^(A +q) + |(A-q)= 704 \O9\ 57 £(A+q) 76 \ 57 \ tO ■£(A-q) 27 12 i 47
azimuth: A is west if LHA is (+)t east if (—)
Azimuth (A) East or West True azimuth to S Average angle, Mark-S True azimuth to Mark Magnetic azimuth to Mark Grid azimuth to Mark
Mag. decl. for Grid North,~EF4 W(+) Date of computation:.Dec. 74, 7947
tot 05 45 102 I 37 : !3 /04 09 57
IOI 05 45 102 i 37 i 13 704 09 57
-122 06 53 ~/23 • 38 ■ 05 -125 n 27
338 58 52 338 i 59 ; 08 338 58 30
345 336 55 34 Mean true Az. to Mark Grid correction (SP 59) ± 338 _ 'ft' 58 '24 50 50
9 2! Grit azimuth to Mark 336 34 00
Compute'4 by:..fj,.l3.....Checked by: .A
FORM 23
® Hour angle method.
Figure 147.—Azimuth computation—Continued.
407
CORPS OF ENGINEERS
TM 5-235
178
e. (1) Equal altitudes of star.—The meridian (true north or south) may be determined in a very simple manner if observations are made on a star when it is at the same altitude on both sides of the meridian.
The meridian is then midway between the two positions of the stars. The method has the advantage that time, use of tables, and computations are not required, but a decided disadvantage in that two observations several hours apart are necessary. The best results will be obtained by selecting a star of polar distance a few degrees less than the latitude, observing it in the lower part of its apparent path at a suitable altitude, first east of the meridian and later to the west.
(2) Procedure in observing.—(a) Center the instrument over the station and level plate bubbles carefully. Do not change the leveling during a single set of readings.
(&) With telescope direct, sight the star, clamp the horizontal and vertical circles, and record the readings of both verniers.
(c) Unclamp the upper horizontal plate and sight the azimuth mark. Record the readings on horizontal verniers.
(d) About 10 minutes later repeat the operations with telescope reversed.
(e) When the star is approaching the same altitude on the opposite side of the meridian, set the telescope in reversed position at exactly the same altitude as found in the second set. Keep the image of the star covered by the vertical wire and, at the instant it is bisected by the horizontal wire, clamp the horizontal plate and measure the angle to the mark.
(/) Repeat the operation with telescope direct and at exactly the same altitude as in the first set.
(f) Bisect the horizontal angles between corresponding equal altitude positions of the star and adopt the mean as the true meridian.
f. Exercise XXAIV.—Azimuth determination from the altitude of a star. By this method find the azimuth of a direction assigned by the instructor, making all notes and computations on form 22, figure 147®.
Section XXXI
PRELIMINARY AND LOCATION SURVEYS
Paragraph
General_______________________________________________________ _ - 17g
Study of existing maps___________________________________________________ X80
Reconnaissance___________________________________________________________ 181
Preliminary survey_______________________________________________________ 182
Topography--------------------------------------------------------------- 183
Location survey_______________________________________________ _ _______ 184
Running center line_____________________________________________________ 185
Curves------------------------------------------------------------------- 186
Plotting profiles, etc___________________________________________________ 187
Setting slope stakes_____________________________________________________ 188
408
SURVFA'ING
409
TM 5-235
179-184
179. General.—The survey operations for a road, railroad, or other route may be classified as—reconnaissance, preliminary survey, and location survey.
180. Study of existing maps.—A study of the latest available maps will generally furnish a dependable guide as to routes or section of country to be examined. Maps of the United States Geological Survey, with contours and topography shown, and maps and aerial photographs of other agencies are very helpful in planning a reconnaissance.
181. Reconnaissance.—The final location of a military road or railroad may be governed more by tactical and strategical considerations than by terrain. After studying the map (or photographs) to determine best possible lines, the engineer should go with the surveyor and observe actual field conditions, recording such information as will assist in deciding the final location.
182. Preliminary survey.—The preliminary survey is based upon results of the reconnaissance and is made with the ordinary surveying instruments. In military practice, the preliminary survey is often conducted as a part of the location survey, and in general for the following purposes:
a. To determine the shortest practicable route.
b. To fix the maximum grade for use in locating the line.
c. To provide a map upon which the “location” can properly be made.
183. Topography.—The result of the preliminary survey is a topographical map, preferably to a scale of not less than 1: 20,000, and data for a profile (par. 55), showing the best practical line, with alternate lines or sections if required. Special attention should be given to difficult places such as river crossings, tunnels, and steep grades.
184. Location survey.—a. Definition.—The location survey is the final fitting of the line to the ground, with curves laid out to connect straight lines or “tangents,” ready for construction.
b. Party.-—The party consists of—
1 chief of party, who makes final selection of line.
1 transit man.
1 recorder.
1 stakeman. >Transit party.
2 chainmen.
2 flagmen.
1 levelman.] T ,
. Level party.
1 rodman. J
TM 5-235
184-186
CORPS OF ENGINEERS
c. Methods.—There are two distinct methods of location. The first is to use the preliminary survey and preliminary profile to locate the line upon the ground. Experience will enable the surveyor to get excellent results in this way. As a rule it is best to lay the tangents first and then the curves. The other method is to use the preliminary line, preliminary profile, and contour lines on the preliminary map, make a paper location, and run this in on the ground.
185. Running center line.—The final line or “location” is staked out by center stakes which mark a succession of straight lines connected by curves to which the straight lines are tangent. The center line is staked, numbered, and measured as explained for profile leveling (par. 55).
186. Curves.—a. General.—(1) Circular curves are classed as simple, compound, reverse, and spiral. Only simple circular curves will be considered here. It is a well accepted fact that no reverse curve should be used; a tangent of at least 200 feet should be between curves, and no curve should be less than 300 feet in length.
(2) A simple curve is a circular arc, extending from one tangent to the next (fig. 148).
(3) The measurements of a curve are made—
(a) From PC by a subchord (sometimes a full chord) to the next full (100-foot) station, then
(6) By full chords of 100 feet each between full stations, and finally
(c) By a subchord (sometimes a full chord) to PT.
(4) The total distance form PC to PT measured in this way is the length oj curve L.
(5) The degree oj curve is the angle subtended by a chord of 100 feet.
(6) The radius of a 1° curve=% chord X cot 30 minutes=50 XI 14.589 = 5,729.45 or 5,730 feet. (This should be memorized.)
(7) When a chord of 100 feet subtends an angle of 1° at the center, the curve is said to be a 1° curve. . Within the range of curvature used in railroad construction the elements of the curve are approximately inversely proportional to the degree of curve, D, and having the elements for the curvature of 1°, those for any other curvature may be obtained by dividing the quantity for 1° by the desired value of D. A table in TM 5-236 gives the elements for a curvature of 1°. To obtain the elements for any other curvature, take out the quantities from this table for some central angle and divide them by D.
(8) It is desirable to have the number of the station at any point indicate the total length of the line to that point, and hence in pass-
410
SURVEYING
CHORDS
SUB-CHORD
CENTER
first station on the tangent will be at a distance from PT equal to 100 feet less the length of the subchord. Only in rare cases will the PC fall on a station of the tangent, hence we usually find a subchord at each end of a curve.
(9) The angle between a chord (or subchord) and a tangent to the circle at one of its ends is measured by one-half of the arc corresponding
ing from curve to tangent, or from tangent to curve, there should be 100 feet between the last station on the one and the first station on the other. If the point of curve, PC, is at a fractional station on a tangent (called a “plus”) the curve should begin with a subchord equal to the difference between 100 feet and the plus. If the point of tangent, PT, is at a plus, or the curve ends with a subchord, the
TM 5-235
186
PC— Point of curvature, where curve leaves first tangent.
PT= Point of tangency, where curve joins next tangent.
V= Vertex, point of intersection if tangents were produced.
7'= Tangent distance, PC to I’and PT to V.
E= External distance, Uto C.
M= Middle ordinate, distance Cto A.
R=Radius. .
2>=Degree of curve.
Z= Intersection angle.
Figure 148.—Elements of simple curve.
411
TM 5-235
186
CORPS OF ENGINEERS
to the chord or subchord. The angle between a chord or subchord and a secant, or the angle between two secants intersecting on an arc, is measured by one-half the difference of the arcs subtended by the chords or secants.
(10) With equal chords of 100 feet, as in railroad practice, the arc corresponding to a chord is D, the degree of curvature; and the difference of the arcs corresponding to a chord or subchord and the secant to the first station beyond it, or between the secants to adjacent stations, is also D. Hence the angle between tangent and chord, or between choid and the secant to the next station beyond it, or between secants to adjacent stations, is %D. This is called the deflection angle and is very important in curve location.
(11) For simple curves the angle at any station between any other two in the same direction is %Z>X(n' —n); in which n' is the serial number of the farther and n of the nearer station. For example, the angle at station 12 between station 17 and 22 = %Z>X (22—17)=2%ZZ
(12) The deflection angle for any subchord is proportional to the length of the subchord, or is in which I is the length of the
subchord in feet, and generally the angle at any point of the curve between the two points. The deflection angle of the long chord is y2 A, which relation is valuable as a check and should always be so used.
b. Laying out curves.—If at the PC an angle of }'2D is measured from the tangent in the direction of curvature, the line of sight passes through the first station beyond the PC and if the length I is measured on this line from PC, the station is determined. If, now, another or an additional angle of is measured, the line of sight passes through the next station, and if a 100-foot tape is stretched from the previous station and its forward end swung until it is on this line, the point so determined is the next station. Similarly, any station may be located. The above-described method of determining the chords and subchords of a simple curve is called “location by deflections.” It is the usual method and is employed for curves of two or more stations whenever possible.
c. Practical lay-out of a curve— (1) The general case will be that in which two tangents already located are to be connected by a curve. The steps in running in the curve follow:
(2) Run the tangents out to their intersection, if it has not already been done, and measure the external angle or difference of azimuth, which is A.
412
TM 5-235
SURVEYING 186
(3) Chain or pace over the ground on which it is desired to locate the curve, determine its approximate length in feet, and point off two places from the right, which gives the length in stations. If a map is available, this distance may be scaled. Divide A by this number and the quotient will be D. If this is not a convenient degree of curve to use, take the nearest one above or below it and divide it into A for the corrected length in stations.
(4) Take from the table (TM 5-236) the tangent distance T corresponding to A; divide it by D, which gives the tangent distance of the curve, or the distance of PC and PT from V. Locate PC and PT on their respective tangents by measuring back from PI. Measure from PC back to the next preceding station to determine the plus. Begin the curve with a subchord equal to the difference between 100 feet and the plus.
(5) Compute and tabulate all the deflections from the PC thus: The deflection for the—
first subchord =
first chord = kDv4s + %D
second chord = y>D-~^-\-D
third chord = %Z>|-T1 kZ)
fourth chord = %Zp£~ + 2D
In /1
last subchord = ^D^rr + ^Z> — ViD-^ = kA
In the above tabulation I and ll represent the lengths of the first and last subchords in feet, and n the number of 100-foot chords in the curve.
(6) Set up the transit at PC, put the 0-180 line on the tangent, and turn off in the proper direction the first tabulated angle. Measure on this line the length of the first subchord and locate the first station of the curve. Turn off, from the tangent also, the second tabulated angle and locate the second station by swinging a 100-foot tape from the first station. Continue as long as the stations can be seen clearly from PC. If all cannot be seen, shift the transit forward and set on a station which has been determined, and orient by the following rule:
(7) Set the vernier at the reading in the tabulated deflections corresponding to any convenient preceding station, point to that station, and clamp the limb. Plunge the telescope and locate forward sta-
413
TM 5-235
186
CORPS OF ENGINEERS
tions by using the tabulated deflections originally computed for those stations, precisely as if still working from PC. In using this rule remember that the deflection corresponding to PC is the azimuth of the back tangent from which the deflections were started.
(8) Usually the forward tangent will not have been run out much beyond PT. Measure off on it from PT a distance equal to 100 feet minus the last subchord of the curve, and locate the station next to the curve on the tangent. From this run out the tangent, setting stations 100 feet apart until another curve is reached.
(9) When the PI is inaccessible, it may be necessary to make several changes of direction, as in figure 150. The point V would be
the PI, but it is inaccessible. The line is run along APQB, QB being the desired direction of the new tangent. The external angle is then equal to the sum of the deflection angles at P and at Q. In the triangle QPS all the angles and the side PQ are known. Solve the triangle lor QV and PV. Find the tangent distance VB and VA, and lay off from Q, QB equal to VB minus VQ; and from P, a distance equal to VA minus VP. The points B and A thus located are the PT and PC, respectively. The curve is then laid out as heretofore described.
(10) As errors will creep into the location of a curve if very long lines of sight are used in laying it out, it is customary not to lay out more than four to six stations from one point; therefore, on curves longer than this, two or more settings of the instrument will be necessary.
Figure 149.—Laying out of simple curve by deflection angles.
414
SURVEYING
415
Figure 150.—Point of intersection inaccessible.
Figure 151.—Vertical curve, case I,
d. Vertical curves.—At each change of grade a different vertical angle is formed. To avoid sudden bumps it is customary to introduce a vertical curve at such points. The curve commonly used is a para-
Let AVB be the known points, and AHB the parabola. Join AB and produce AV to Y. Draw vertical lines AX, LV (through H) and MY (through B). Let AV and VB be equal, also their horizontal
bola, as it effects the transition better than a circle. This curve is generally laid to extend an equal number of stations on each side of the vertex. Two cases are shown in figures 151 and 152, respectively.
TM 5-235
186
X S T L U W M
0
A
P
Q
A
IK
E
H.
0
■I
B
Y
D
J
V
F
N
TM 5-235
186 CORPS OF ENGINEERS
projection AL=ML. Then AG=GB and AV=VY. VG is a diameter of the parabola, also AX is a diameter. Now
VG HV=~, and
J
... TT 1/Elcv. A+Elev. B . ™ __\
Elev. «=2< -----2-----+Elev. Vy
Let LU= UW= WM; then
4 Elev. C= Elev. D+^HV
Elev. Z=Elev.
Let AS=ST= TL - then
Elov. K=Elev. N~l~
4 Elev. £=Elev. F+^ HV.
r:
1 1
ir' h——;b
e H
' I '
0^+^ I
; ! । ; !
i ! i i
D" E" L f E M
Figure 152.—-Vertical curve, case II.
Given the rates of grade ( Jake. Pettry i’w'q 5. E corner
36 + 60 G 22° 301 1980° 30 E :Opp pt 9 hill 5 1 below falls at Peltry’s rord
30 + 00 ROT 85. 1
1 Date: Ju ly 15, 19. 39
/feather C/oudy
1 Temp. '■
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
i
1 J
Figure J56.—Transit notes, preliminary survey.
(8) Levels.—The level party establishes bench marks and levels along the traverse, taking a reading and recording the elevation at each 100-foot station. The elevation of the starting point, if not definitely known, is assumed at some round figure. Two or more bench marks should be established in every mile. The method of recording level notes is illustrated in figure 157. These notes are used to assist in preparing a contoured map, and the bench marks are used as checks in making the field location.
422
TM 5-235
191
SURVEYING
(9) Topography.—The topographic party records data from each side of the center line by stadia readings, obtaining that necessary for contours and locating features of the landscape over a strip extending at least 500 feet on each side of the center line.
c. Paper location.—Upon the map and profile prepared from the notes taken in the preliminary survey, a “paper location” of
proposed railway line is projected (figs. 158 and 159). The line of the preliminary survey is shown in figure 158 as a broken line, while the located line is made solid. The grade elevation for each station
the
Pret/mt a PRELIM lary 5c. a/ River NARY rvey fZei ■ £x tens SURV ■et notes, on EY ) '/nstrarr \fiodman 1 ent 5gt. Cp/. <. R. Roe '.Doe B&B Du r>py *12^ 20 (IO)
Sfa Pod Rd g. HI. Elev. 1 Ren ’arks
B M. 5.50 130.50 125.00 ' Nail in yamore. root 5tc 29 + 90 6N. ’eech
3O+OO 4.3 126.2 /o'e.
/ 6.4 124 1 I
2 69 123.6 1 Date: Ju N 16,193 9
3 7.5 /23.0 1 Weather Cloudy
4 5.7 124 8 | Temp 7. 6°
TP -F.5. = 2.20 |
+B.5. = 8.60 136.90 i
33+00 U.8 125.1 . i
6 10.9 126 0 i
7 1.7 135.2
TP -/75.= 2.10 1
+B5. = 14.60 149.40 i
38+00 U.4 138.0 1
9 9.9 139.5
40+ OO H4 138.0 ■ 1
/ 8.9 740.5 1
BM 6.62 142.78 \5pike // i river boulder.
1
1
1
1
1 1
1 1
1 J
Figure 157.—Level notes, preliminary survey.
on the line being located is taken from the profile (fig. 159) or is obtained by interpolating between the contours in figure 158; points having the required elevation are located opposite the corresponding stations of the preliminary survey. These points are’inclosed in a circle and marked with the number of the station of the preliminary survey to which they correspond. A line joining the points thus marked is called the grade contour. The paper location is made by selecting a line that will nearly conform to the configuration of the ground, in order to avoid heavy cuts and fills. An approximate
423
TM 5-235
191
CORPS OF ENGINEERS
Figure 158.—Map from preliminary survey showing paper location.
424
TM 5-235
SURVEYING 191
profile of the ground along the paper location is then made and approximate grades established, with particular attention to balancing the cuts and fills. This paper location is taken into the field and used by the final locating parties.
d. Field location.—One or more field parties may he organized in accordance with the urgency of the situation. If only one party is organized, it establishes the first tangent in the field by scaling (from the paper location) distances from the original traverse and establishing base points. It then establishes the second tangent in the same manner, produces these two tangents to a common point of intersection, and measures the central angle. With this point of intersection and the degree of curvature shown on the paper location, the party then establishes the tangent distance, which is measured back from the point of intersection to the point of curve and ahead from the point of intersection to the point of tangent. The stationing is established on the tangent up to this curve, and the
Figure 159.—Preliminary profile and paper location.
correct station of the point of curve is then determined; the instrument is set up on this point of curve and the curve laid out as described in paragraph 186. The party next proceeds with the stationing on the second tangent until it reaches approximately the point of curve of the next curve. The third tangent, is then established in the. same manner as described above, the point of intersection fixed, the degree of central angle measured, and the curve laid out. again in the same manner as described for the first curve. The notes kept by this party are illustrated in figure 160. If two or more parties are sent to the field to establish the line, the line is divided into several sections according to the number of parties and each party begins with the establishing of the first tangent within its section and proceeds as described above, with this difference, that it docs not establish the stationing on the line but merely determines by stakes the points of curve and points of tangent, so that the party following can proceed without interruption. In other words, the second, third, or fourth parties will only lay out
425
150
145
140
135
130
125
EL-150
145
140
135
130
EL-125
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
TM 5-235
191
CORPS OF ENGINEERS
the line, chopping down trees and clearing brush where necessary so as to have a clear sight for establishing the tangents and points of curve. The chaining is carried on by party No. 1, which will then upon arriving at the section of party No. 2 or 3 lay out the curves as found necessary. Where two parties join and where revisions have been necessary in the paper location, a modification will have to be made in the curve joining the tangents of the two adjacent sections, but the degree of curvature on the paper location should be adhered to if possible. After the location has been definitely established in the field and stakes
/ Co 'mat Lot at txTve LOC at/onfTr • Extern ATLON insit nc ion Les) \/nst: Sgt \Recorde+ front Ro \Rear Roc R Roe ■:Cpt J. Do d:Pvt H. t Pvt. T e tone's >mi th Berger *H6H @1
Station Def Chk. Def Course Remark ?
45+00< 1P.O. T. N2f /O'E (d=/o° Date du ly 30,19 39
PT 40+5 o=40+7t ahead 27° 00 54° 00 1 l.A-54° 90' Weather . C/ear
40 26° 24 | T = 29t. 94' Temp: 5 ■>"
39 2t° 24 ’ L = 540'
38 /6° 24 . 1
37 H‘ 24 1
36 6° 24' 1
35 t° 24 i
PC. 34 + 72otO'i 1
B5. PO T 30 t 00 /V47f /O'E
1
1
1
1
1
1
—r’
।
।
i
■ i ■ y
Figure 160.—Transit notes, final location.
placed every 100 feet on the line, a leveling party is organized to take levels at every one of these stakes, establishing bench marks as it goes along. This leveling party should follow immediately after party No. 1 so as not to delay the work. The level notes kept by this party are similar to those in figure 157.
e. Construction stakes.—In order to proceed with the grading, slope stakes are set out, being placed at the top of a slope when in a cut, and at the foot of a slope when on a fill. (See par. 188.) The construction party grades up to or down from these stakes. No further
426
TM 5-235
SURVEYING 191-192
instrumental work is necessary except for the definite location of culverts, abutments, or similar structures. It is advisable to place stakes at 50-foot intervals on sharp curves. For curves up to 6 it is not necessary to place stakes closer than 100 feet apart for military railroads.
f. Exercise XXXV.—With a party properly organized and equipped, lay out as instructed the “location” for a railroad bed, including necessary curves and set all grade and slope stakes as described in section XXXI and in this paragraph.
192. Water reservoirs.—a. Areas a,nd volumes.—(1) For a preliminary determination of the capacity of a reservoir a study of a contoured map will ordinarily he sufficient. The position of the flow line, marking the outline of the submerged area of a proposed reservoir can be plotted, and the area of the drainage basin can readily be found with the planimeter. Two general methods used in determining the capacity of reservoirs are by contours and cross sections.
(2) The contour method gives more accurate results. After the flow line has been determined and plotted on the contoured map, the area enclosed by the flow line and by each contour is determined separately with the planimeter. The average of areas enclosed by two consecutive contours, multiplied by the vertical interval between them, gives the volume of water lying between these two contours. Hence, the sum of the volumes between all the contours within the submerged area, phis the volume between the bottom contour and the deepest part, phis the volume between the How line area and highest contour, gives the capacity of the reservoir. The volume between the bottom contour and the deepest part is generally small and is estimated or neglected. The total volume is usually expressed in acre-feet, one acre-foot being 43,560 cubic feet, equal to 325,851 gallons.
(3) The cross section method may be used when only a fair degree of accuracy is required. After the How line has been plotted the area is divided into sections of convenient lengths, usually 100 feet. The sections are plotted on cross section paper and the end areas determined with the planimeter. The approximate volume can then be calculated from the average end areas as described in section X, TM 5-230.
b. Flooded, area and drainage basin.— The source of the water supply stored or distributed from a reservoir is the drainage basin. This must be large enough, considering all factors such as the annual yield of water from a stream, precipitation, evaporation, leakage, etc., to meet the maximum consumption at all times, especially during dry seasons of the year when water is most needed. It is best when the drainage
427
TM 5-235
192 CORPS OF ENGINEERS
basin, especially near populated centers, can be made inaccessible to the general public. The Hooded area should be fenced if the drainage basin cannot be completely secured against possible intrusion. Very often the drainage basin, and in all cases the flooded area, will be on property owned, leased, or otherwise controlled by the military authorities. Before acquiring control of land for the flooded area of a reservoir a careful survey of the flow line must be made to make sure
abcdefghijk
11 i i-।।--1-1-1-1-
Figure 163.—Coordinate-point method.
that enough land is acquired so that the area after being flooded will not encroach on the property of others. This calls for precise work with the tape, transit, and level. Here the level is used first to locate the contour line representing the maximum stage of impounded water plus (the flow line). Then, with a transit and tape enough points are located (with a traverse) for boundary monuments or marks so that the area within them will embrace every part of the flooded area.
428
TM 5-235
SURVEYING 193
193. Miscellaneous construction.—a. General.—Surveys for miscellaneous construction include those for the location of structures and those for the determination of earthwork. The accuracy required in large-scale surveys is attained by either the trace-point or the coordinate-point methods. The coordinate-point method, being used more than any other, is described in b below. Details for large-scale maps may be located by a variety of methods and instruments.
b. Coordinate-point method.— (1) This method may be applied in the field in many ways, the principle being to establish control and to subdivide the area in question into squares with sides equal to multiples of 50 feet.
(2) The first step is to run a rectangular traverse as in figure 161 near the perimeter of the tract, setting stakes at every 100 feet (or as required) as the traverse proceeds. Next, parallel lines are laid off from each 100-foot point of the traverse. One set of parallel lines is lettered A, B, C, etc; the other set perpendicular thereto is numbered 1,2,3, etc; so that each point actually is known as Al, A2, Bl, B2, etc.
(3) Or coordinate axes may be established to cross near the center of the tract, and coordinate lines may be run parallel to these axes to the corners of the tract.
(4) Often, after the traverse has been run around the tract or the coordinate axes have been established, interior points are laid out with tapes only. Three chainmen and two 100-foot tapes are needed. They work as follows: With one chainman at F7 (fig. 161) and a second at E6, the third chainman locates E7 with the two 100-foot tapes stretched and meeting, and sets a stake. Proceeding, the chainman at F7 goes to F8 and the chainman at E6 to E7, while the third chainman locates E8. The remaining interior points are located in a similar manner.
(5) Distances are usually not recorded. Elevations of each point are observed and recorded as for profile leveling, or are noted on the plot.
(6) The plane table is a great aid to mapping by the coordinate method if many irregular features are found. The methods of establishing the points are the same as described above. The details, however, are drawn on a plane table sheet instead of from notes or sketches in the office as is usually the case when a transit and tape are used.
c. Batter boards.-—When excavation is required for structures, the first step is to set stakes that will serve as a guide in digging. Before the excavation reaches its full depth, the surveyor usually sets batter boards which are horizontal boards nailed to posts or other supports.
429
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CORPS OF ENGINEERS
The upper edges of these boards are usually set at some certain elevation, as the top of a foundation wall. They are also in such position (fig. 162) that by stretching strings from one to another the contractor can get the most important lines (neat lines) of the structure. The exact points where the strings should be fastened to the boards are marked by nails or notches cut in the board.
Detail of batter-boards
Plan
Figure 162.—Batter boards.
Batter boards are set a few feet out from the building line so they cannot be knocked out during the excavation. The contractor usually furnishes the surveyor with the necessary data so that the building lines he is to establish will be properly located with respect to street line, adjacent buildings, etc. No notes are kept.
194. Utilities maps.—a. General.—Utilities maps are made to large scales and show specified areas such as towns, military posts, cantonments, and similar places of permanent or semipermanent character. Their principal purpose is to serve as a guide for eventual extension of construction and as a permanent record of utilities installations.
b. Detail.—They show in detail all buildings, roads, sidewalks, sewer lines, water lines, gas lines, manholes, main valves, fire hydrants, electric power lines, street lights, telephone lines, and any other items
430
Batter-boards 3 to 6 ft from building line
Outside line of foundation
Strings
Nail
l"x 6"-
2"x4" or
f'-2" x6" posts
Nail
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SURVEYING
that may he useful to the construction or maintenance section serving the particular locality. Frequently they have contours, especially if additional construction is anticipated. Utilities maps may be advantageously used for planning landscape lay-outs and similar projects. Trees, bushes, hedges, etc., are usually omitted to avoid the observing of more important detail.
c. Scale and contour interval.—The scale of utilities maps is usually from 1 inch = 50 feet to 1 inch = 200 feet, and the normal interval of contours (when shown) is 1 or 2 feet.
d. Field work.—The field work consists of—
(1) Horizontal control, established by transit and tape, with perhaps some triangulation for larger areas.
(2) Vertical control, by differential leveling.
(3) Plotting detail, best done by the coordinate-point method (par. 1936) combined with use of the plane table. Coordinate points are established as described, to be occupied in turn by the plane table for plotting detail.
e. Symbols.—Symbols for representing detail on utilities maps are the same as prescribed in FM 21-30. Special symbols to represent objects not covered in FM 21-30 are shown in figure 163.
j. Office work.—The final map is compiled by the draftsman by methods described in TM 5-230. A careful record of all items that cannot be shown properly on the map is compiled from data gathered by the survey party and kept in a special file properly indexed. Figure 164 is part of a completed utilities map.
431
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194 CORPS OF engineers;
Buildings____________ Frame Brick Lateral-Screwed________________ Tunnel.. . . _ ... ..
Steam Piping......... Gate Valve-Screwed. _____________________ City Fire Alarm Station . .. Qk]
Cold Water Piping..... Iron Sewer Pipe . . _~' 1 Local Fire Alarm Station ...
/ Run concealed \
Hot Water Piping ._... " * ' Sanitary Iron Sewer Pipe । S I +r- Branch Circuit (under floor above/---
Gas Piping............ Tile Sewer ___________________ ..... _ 4 Branch Circuit (Run exposed) ---------------
|___ -i- -r--/Run concealed) . T" Sanitary Tile Sewer_______~S—|—S—|---S- Branch Circuit ( under floor )------
_________________________ _______ I Concealed) Oil Piping...—------- Drainage Tile................_......F> D Signal Wires in Conduit (under floor/--------
r /Concealed)
WA C>D underfloor
Soil Pipe________________O r. Signal Wires in Conduit( above /---------
_ 4- /Concealed linden
Elbow 45 -Screwed___________I Waste Pipe ............... <7 Vv.r Feeder Run \ floor above / --------
Elbow,Long Radius-Screwed ..... T Floor Drain_______________Feeder Run (Exposed) .-----------------------
-+y+-Double Branch Elbow-Screwed__T Hydrant .............______ Feeder Run (Concealed under floor) ~—
Tee-Screwed________________' ' ' Elevated Tank ________________ Pole Line
: a
Cross-Screwed .... ...... 1 Septic Tank or Cesspool . ... Well ... _________________ ........ ®
Figure 163. Special symbols for utilities maps.
432
Figure 164.—Part of completed utilities map.
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SURVEYING
N C 0 AREA
N C 0. AREA
IO io r o IO
TM 5-235
195-196
CORPS OF ENGINEERS
Section XXXIII
HYDROGRAPHIC SURVEYS
Paragraph
General_______________________________________________________________ 195
Instruments and equipment_____________________________________________ 196
Soundings_____________________________________________________________ I97
Determination of tidal conditions______________________________________ 198
Tide peculiarities_____________________________________________________ 199
Tide observations______________________________________________________ 200
Location of gages______________________________________________________ 201
Datum planes___________________________________________________________ 202
Types of gages--------------------------------------------------------- 203
Establishing and checking gage-height readings________________________ 204
Records of automatic gage______________________________________________ 205
Staff gage records____________________________________________________ 206
Tabulation of high and low waters______________________________________ 207
Reduction of tide records_____________________________________________ 208
Computations of lunitidal intervals____________________________________ 209
Corrections for lunitidal intervals___________________________________ 210
Computation of mean high water (HW), mean low water (LW), mean range (Mn)y and mean tide level (MTL)_________________________________ 211
Computation of mean higher high water (HHW), mean lower low water
(LLW), and diurnal inequalities (DHQ and DLQ)______________________ 212
Correction for longitude of moon’s node________________________________ 213
Stream discharge_______________________________________________________ 214
Determination of velocity______________________________________________ 215
Value of results_______________________________________________________ 216
195. General.—The main purposes and phases of hydrographic surveying are soundings made to determine submerged relief near shores where landing places may be needed (par. 197); observations of tidal conditions for establishment of a standard datum (par 198); and stream discharge measurements to indicate preferred locations for certain engineering projects, such as for water supply.
196. Instruments and equipment.—a. Sounding poles.—These are best employed at depths less than 15 feet. They are readily made from iron pipe or from wood of sufficient cross section to withstand bending effects of the current. Poles should be graduated to read feet and tenths, according to the accuracy required.
b. Sounding line.—The lead (or weight) carried by such a line varies from 5 pounds for shallow, still water, to 20 pounds for deep, running water, and is usually long and slender to diminish the water resistance. The line should preferably be made of Italian hemp of a size suitable to the weight of the lead. It is prepared for use by stretching to prevent subsequent elongation and distortion of scale. This is done by winding it tightly around a smooth tree and securely
434
SURVEYING
Figure 165.—Price current meter,
TM 5-235
196
nite available depth, as pinnacle obstructions may exist. In order to be sure that a certain depth is available at all points in a given water area, usually at all points within the limits of a marked channel, “sweeping” is undertaken. A sweep consists of a horizontal member suspended at the desired depth and towed over the area. It is usually a wire cable suspended by wire lines from buoys. Sometimes heavy bars or railroad rails suspended from scows are used. The length of the drag may be varied through a wide range to suit the requirements of the survey.
fastening both ends. The line is then wet thoroughly and allowed to dry. The operation is repeated until the rope, on drying, leaves no slack. It is then graduated and marked with tags.
c. Making soundings.—The leadsman stands in the bow of the boat and, at the desired location, casts the lead far enough forward to enable it to reach bottom by the time the line becomes vertical. The speed of the boat is not checked, as a rule. When depth and current make this method impossible, the boat is allowed to drift down with the current, and soundings are taken at intervals without drawing-up the lead. The boat is then pulled back upstream and soundings are taken on another range.
d. Sweeping.—The use of the sounding line does not assure a defi-
435
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196 CORPS OF ENGINEERS
e. Current meters.—(1) A current meter consists of a propeller and a mechanism to indicate or record its revolutions. The recording mechanism of practically all meters is based upon the make and break of an electric circuit at each revolution. Current meters are mounted on poles or suspended from ropes or cables with heavy weights so that velocities may be determined at any desired depth.
(2) There are two general classes of these instruments—
(a) Those in which the revolving part turns about a vertical axis, as in the Price meter (fig. 165).
(6) Those in which it turns about a horizontal axis, as in the Haskell and Fteley meters.
Locatio Make T.,Pa)p.Rj Price yer Str Wind. 5.6 Length c earn dis 1 Light f Cours :harge durrent Date\.Npv. 11,1 e: 700ft\ ■neter rc 939 'ting Current Meter A b A-3/2 (CF)
Rec, •tster Revo- | Velocity
Run Time Start End futions Bps. \(fps) Remarks
/ _ 180 1,892 1,927 35 0/94 | 0.555 Chief of party gt. Blank
2 ........ ns t,927 1,963 36 202 .562 Rec order C, ■>! Burr
3 60 1,987 2,023 36 .600' 7.666 Ass/ ifonfs p 0
b
D-
F-
&
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196
CORPS OF ENGINEERS
with the telescope and move the index arm IV until the reflected image of Cis in apparent coincidence with D. The required angle is read directly on the arc by reason of the graduation ratio noted in (1) above and explained in (3) below.
(3) Draw perpendiculars FE and HE. Since angles of incidence and reflection are equal, CIF^FIH and IHE=EIIO: Also, VIZ=IEH, since the sides of one angle are perpendicular to the sides of the other, respectively. In triangle HIE
IEH-\-IEH=FIH—a
IEH=a-IHE=a-b = VIZ.
In triangle IHO,
I0H-\IH0=CIIl=2a
I OH = 2a - IH0=2a ~2b=COD.
Therefore, C0D=2VIZ.
(4) When altitudes (vertical angles) are to be measured on land, an artificial horizon must be used instead of the visible horizon.
Figure 170.—Artificial horizon.
While mercury is usually used lor this purpose, the surface of any heavy liquid, such as molasses or heavy oil, may be used. Such artificial horizon must be sheltered from wind. This is done by covering horizon and container with a glass roof, shaped like a roof of a house. Still another arrangement is to use a piece of plane black glass after having leveled it with a spirit level and leveling screws. The principle of the artificial horizon is shown in figure 170. The image of the sun as seen in the artificial horizon is as far below the true horizon as the actual sun is above it.
h. Rules for care and use of sextant.—(1) Keep your fingers off the graduated arc. It tarnishes readily.
(2) locus the telescope with great care so as to secure sharply defined images.
(3) Make the direct and reflected images equally bright by moving the telescope to or from the plane of the sextant with the adjusting screw provided for this purpose.
440
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SURVEYING
(4) Bring the images into contact midway between the guide threads.
(5) Do not try to hold the images still in the field of view. Give the reflected image a regular oscillating motion by twisting the wrist and note its relation to the direct image as it swings by.
(6) Determine the index correction as carefully as the angle which you wish to measure.
(7) Whenever possible use a shade glass over the eyepiece instead of those attached to the sextant frame.
(8) Work as rapidly as you can without hurrying.
i. Adjustments of the sextant.— (1) Check perpendicularity of the index glass to the frame as follows: Set the index near the middle of the arc; remove the telescope and place the eye near the index glass nearly in the plane of the frame. Look at the right hand edge of the index glass to determine whether the arc as seen directly and its reflected image form one continuous arc. If it does, the glass is perpendicular and no adjustment is necessary; otherwise the glass must be tipped slightly by use of the proper screws.
(2) The first adjustment having been perfected, perpendicularity of the horizon glass to the frame is tested by noting whether the two mirrors are parallel for some one position of the index glass. Point the telescope to a star or a distant terrestrial point, the plane of the frame being vertical. Move the index arm slowly back and forth over the zero. This will cause the reflected image to pass through the field. If it passes exactly over the direct image, the two mirrors must be perpendicular to the frame. If it passes to one side, tip the horizon glass by the proper screws until this is corrected.
(3) In the more recent types of sextant, two peep sights are furnished with the sextant for making the axis of the telescope parallel to the frame. To make the adjustment, place the instrument on a table resting on its three legs and place the peep sights on the graduated arc. Look through the peep sights and locate a point on a wall not less than 20 feet distant. Next sight through the telescope in the direction of the mark on the wall and note where its line of sight cuts the wall with reference to the mark. The peep sights are so constructed that the height of the peep line of sight above the plane of the graduated arc is the same as that of the center of the ring into which the telescope is screwed. Hence, the two lines of sight should strike the wall at the same elevation. If this is not the case, vary the position of the telescope by tilting its supporting ring with its adjusting screws.
(4) If the sextant is not equipped with peep sights, the adjustment may be made as follows: With the sextant mounted on a stand move
441
TM 5-235
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CORPS OF ENGINEERS
the index so as to separate the direct and reflected images of some distant object (such as a star) by a distance nearly equal to the length of the parallel wires of the telescope. Turn the eyepiece until the direct image of the object coincides with one extremity of the wire at the same time that the reflected image coincides with the other extremity. The wires will then be parallel to the plane of the sextant. Select two distinct distant objects and make a coincidence of the reflected and direct images on the middle of one wire, and then on the middle of the other. If the readings agree, the adjustment is correct; if not, the adjusting screws in the collar of the up and down piece must be moved until the coincidence is exact.
(5) To make the horizon glass parallel to the index glass when the vernier reads zero, set the index at zero and point to a distant object as explained for the second adjustment. If the two images
Figure 171.—Eccentricity error.
are exactly coincident, the adjustment is perfect. If not, turn the horizon glass about its axis perpendicular to the graduated arc, with the proper screws, until coincidence is secured. No matter how carefully this adjustment is made, it is necessary to check frequently. For this reason the adjustment is usually not made, but instead a correction is obtained by first establishing exact coincidence of images and then reading the vernier if it departs from zero; then apply this “index correction” with proper sign to all readings of the series.
(6) If the center of motion of the index arm is not coincident with the center of the graduated arc, another correction known as the “eccentricity correction” must be applied to all observations. In figure 171, B is the center of the index arm and A that of the graduated arc. When the arm is in position BE, in prolongation of the two centers, there is obviously no error in the reading due to noncoincidence of centers. But when the arm is at BC, 90° from BE, the error=
442
TM 5-235
196-197
SURVEYING
CD. Between these two points, the error is intermediate. Also beyond the point D the error again approaches zero. Corrections for a number of angles at suitable intervals may be obtained by measuring each angle with a good theodolite and with the inaccurate sextant. A curve may then be plotted between sextant angles (corrected for index error) and the eccentricity error; corrections for intermediate angles may be taken from this curve, which will be similar to a sine curve.
197. Soundings.—a. Control.—(1) Horizontal control for hydrographic surveys is effected by the establishment of known points by triangulation (fig. 172) or by the traverse methods outlined in section XII. These control points serve to locate each sounding position and are generally placed on shore.
(2) Vertical control is referred to an adopted datum plane which for navigable waters is mean low water or lower low water, as described in paragraphs 198 to 213. It is effected by the establishment of tide gages, the zero readings of which are related to the datum plane.
b. Ranges.—(1) Ranges are established by placing two or more signals on a line. These signals consist of stakes on shore or buoys anchored in the water. It is very desirable to have flags of white or colored cloth on the stakes and buoys, the selected color to contrast with the background. Whether on shore or in the water, range signals on alternate ranges should have different .colored flags to prevent error and confusion.
(2) The establishment of ranges on shore is effected in varying ways, depending upon the accuracy desired. Where repeated surveys with soundings at the same points are to be made, the signals should be set on range by transit and tape or by triangulation and made to last during the period of measurements. When the accuracy of the survey permits, the signals may be set by instruments of less precision, such as the prismatic compass, and by pacing. This method is applicable to relatively small areas and where the survey is in the nature of a reconnaissance. The establishment of signals on ranges in water should be carried out with the accuracy demanded for shore points.
(3) While range signals may be located either on shore or in the water, it is best to have all of them on one side of the work so that the sounding boat may be kept on a range by the person in it. If the boat operates between two signals on a range, it is necessary to have an extra man to “line in” the boat on its run.
c. Methods.—(1) Soundings are taken at such intervals as will give the desired information. These intervals are timed or measured with
443
CORPS OF ENGINEERS
TM 5-235
197
commensurate accuracy to avoid waste of time and labor in making the survey and to assure that the area is adequately and systematically covered. Without ranges a boat covers the area with unequal
Figure 172—Triangulation systems for horizontal control.
intervals; its runs are not parallel and often cross. Ranges are, therefore, placed as a guide for the boat’s run, as well as for use in making locations.
(2) The following methods for determining the locations of soundings are used under varying circumstances, depending on the purpose of the survey and the area to be covered:
444
A
B
C
TM 5-235
197
SURVEYING
(a)
(6) (c) (d) (e) a.) (. 75// me ‘hod CD
7i vo-irons t J
Range Na Time Angie 'o boat 5et up < n/\H r Ren. arks
8 hr 0° OO' bight o. 7 4Z | Date: 5 pt. 7J9. 9
m s 11447/-/77, calm
I I 45 73 3 15 |*m ATr tn sit- 5g t A.A Jon ?5
2 43 7 32 । tes- Cot o. J. Smit h
3 46 13 12 48 'Watch 7 70.1792. This is 47 seco: ids s/ov ver than
4 43 18 /7 \watch +1793 n boat
5 47 13 24 07
6 44 30 12
' 1
|
1
~i
J
Figure 174.—Transit notes for two-transit method.
making the first sounding, and at every fifth sounding, it is dropped to a horizontal position. If it is desired to have transit readings for each sounding, the white flag is used for each one, except that every fifth one is signaled by a red flag. When soundings are discontinued on one range the red flag is waved in a wide arc. Before commencing on another range the white flag is again waved in a wide arc.
(8) Forms for notes are shown in figures 174 (transit) and 175 (boat and gage).
(9) This method is quick and accurate for use in comparatively small areas. It requires two instrumentmen, however, and over
446
TM 5-235
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SURVEYING
areas of considerable size it may be necessary to shift the transits frequently to obtain good intersections. Soundings must be suspended during these shifts.
e. One angle from shore and one range line (one-transit method} (fig. 176).—(1) Ranges are placed at desired intervals and the boat is run on them, the soundings being taken as described in d above. At the signal for a sounding by flag from the boat, the instrumentman reads the angle to the range subtended by the sight on the boat, and a backsight on a known point, and calls it for his recorder. The notes are similar to those for the two-transit method.
A 5oundin 1 g notes-Two-tra 75// me, lhod (/#)
Two-tri •nsit Corr ।
/Range No Time 5ndg Tide Corr Sndg ' Ren larks
8 hr 'Date. - ept 7,19 39
m s \warmJ •?o wind Tide ebt fng
/ / 46 00 47 — .8 39 \Boat hi 'corder: 5gt. R. Ro e Fk igman F / J. Doe
2 30 8.6 7.8 । Lea. is man ■ Corp PAL •-own 5/$ na/monf- 4. PWhite
3 47 9.3 8.5 j Boc tman Corp H14 /son
4 30 9.5 8.7 1 Wat ch No 1793-8-3 9-/4
5 48 9.4 8.6 | ’ 1792-8'2 9-27
6 30 9.8 9.0 | ' '794-8-3 9-23
1
1
1
□
1
|
i
. 1
1
1
\ " ! J
Figure 175.—Sounding notes for two-transit method.
(2) This method requires one transitman only, and if the range signals are accurately set and immovable, and the boat is kept on the line, it is quite accurate.
f. Uniform speed and time interval on range.—In this method the boat is run on the ranges between two points, the establishment of which determines the total distance of run. Starting at the initial point, the time of starting and that of reaching the second point on range determine the rate of speed which permits the location of soundings on the lines. Notes for this method are shown in figure 177.
447
TM 5-235
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CORPS OF ENGINEERS
g. Intersection of two sets of ranges.—(1) A set of ranges is placed from shore to cover the area to be sounded. On one of the ranges of this set, usually the first or the last, positions for a set of cross ranges or courses are established by anchoring buoys at desired intervals on the line. Both sets are numbered.
(2) A boat is anchored, for example, on range No. 1, course No. 1. A signalman in this boat lines in, by means of a prismatic compass, the boat carrying the sounding party and keeps it on the line during its run across the ranges of the first set. Any angle with the first set greater than 45° is used in accord with the desired lay-out of the soundings. As the sounding boat proceeds on its course, a signalman
in it calls, “Sound,” upon picking up a range of the first set. The resulting sounding is recorded in the notes referring to the ranges used (fig. 178). Time is also noted in order to connect the work with tide gage readings. If the position of the sounding boat on the course run is between the signals of a range, an additional man is required on shore to signal the sounding at the moment the boat crosses the range. He must thus proceed from range No. 1 to No. 2 of the first set, and so on, in order to flag the sounding party.
h. Angle and stadia distance.— (1) In this method a sounding is located by angle and stadia distance from shore. The area, if small, may be covered by one set-up, resulting in polar coordinates referred
448
SURVEYING
TM 5-235
197
Figure 177.—Sounding notes, timing method.
ioundmg 1 1 I notes -1 Timing method
rim ELZ
Range No. Time 5ndg Tide Corr Corr 5 | Per narks
8 hr '•■Date: 3 ept /O,/. 939
m s. | Coo/ so ith we st winds.
1 / 34 00 6.2 t 0.4 6.6 \25O‘to shore........ Recorde r : 3g t. / A. done s
2 35 00 68 7.2 \Tide etu vng _ teadsmc n: Pvt. f- 7 White
3 36 00 7.4 78 I 5igna/rr. an: Pvt. <_ Doe
4 37 OO !0.6 no j Boaima p ' Corp. Wilson
5 38 00 /O.7 ///
I
|
l
1
1 1
1
■ 1
I - 1
1 1
1
\ 1 J
Soundm 1 1 1 ' notes -\Method if inters acting r inges
// ter sect 'ng rang ’S 1
Course Range Time Sndg. Tide Corr Corr S | Rer narks
2 \Date ■ 5ept. ti, 939
m. s. \Coots a ear
I / 45 00 4.2 7- 04 4 .6 Tide f/0 id Recorde - Pvt 77 White
47 10 40 44 \ Leadsma 1 Pvt. c/ Doe
49 30 4.0 4.4 । Boafmar > No i, t 7vt. R B/a ch
5t 45 3.4 38 | Boot mar No2, /= vt M dor les
54 00 3.2 36 1 5/gnaim<. ’n No /, pi TBrc >kVF?
5/gna/mi. 3 Sgt. \ A. Jones Recorde r. Pvt P. White
5 45 00 48 33 56 33 22. t 21. 9 । Reac 'ings Tr im Sign ai on B< ML W
I ; r------1-----— 1-----------1-----1------1---—-i--------
hour iiii । ।
-----------I-----I-----1 1-----------I----------1-----1------I_____1_________ Minute-----Date
0 ; ; i ; I I I | ! +2Z2
to ! _____; ; | I ; i I U
20 ; I ; ______________I ' —______i ; : r____________
30 T ! T r~ ! i r I do I j ; j d a r r~
i i i ; i i ; i i _______
__________________________Date_________|_____
o ; ; r I I I ; ’ r !
-----------1------------------1-----■-—I----------1------1-----1------1---■---—
M9_________;_____!______1_____L-_________ . ______1______I_____1______:________
2o ______; __________________i_ I ______________i _____l______!_____i_________
so ______। ____j r_____i i r_____! i r_________
—i!L-------;---------------------------1----------!- ----|-----I-----L---------
SO ______1_____L-____L______I________E__________1_____E______1______I________
Date
~d—--------1-----'------1 i ! i I !
_________________।_____i______।--------1----------1-------------------1--------
>0 ______1_____!______I_____I________I__________L_ __________;______1_______
2Q_______l_ j ________i_____i________;__________:______i_____।______:________
30 ______t-___________l_____l_ ____I______।_____I______;________
m__________i______i_____I______L ____i______।______I_____i________
5Q ______L_____L______L______I i _______________I T__________I T_____________
i ---------------------------------------! ---------------------------------------1-------------------------------------- ---------------------------------------I--------------------------------------
V I I I I 1____________________________I______________________________________2
Figure 188.—Tides—10-minute readings.
206. Staff gage records.—It is often necessary to determine mean
low and high waters when no automatic gages are available. To do this, establish a staff gage at the desired location. Beginning at about 30 minutes prior to predicted time of high and low water, take readings on the staff gage at 10-minute intervals over an hour period, or until the records show that the tide is changing direction. These records are reduced in the same manner as automatic-gage records. When time is available and more detailed information is desired, the records can be continued throughout the day at the desired interval. The form indicated in figure 188 may be used to record results.
466
TM 5-235
205-206 CORPS OF ENGINEERS
TM 5-235
SURVEYING 206
Station .. Station b Observat Fort Ham ions begi. T /ton Location. ?, March, des Hig. Govern rm 7 and tc ?nt'har Observat w water. f, Fort ft, ons end, 'cni/ton,^. Date May Series N Tide Gag. TypeGar ! Correction 1939 0.47 ’ Ato.J... Print in t .... feet (g?
Date MOON 3 TRANSITS Time of- Lun it ide t/ interval Heigh / of-
Year ('GREENWICH High Low High Low High Low Per narks
1939 MTAN CIVIL ) Water Water Water Water Water Water
14 77
Mo. d Hr dec Hr dec. Hr dec Hr dec Hr dec. feet feet
May / (3.22) /O.77 4 57 (7.55) (130) 6547 i.925
1567 22.77 16.40 7 tO 073 7.040 2.3/0
2 (4/2) 11,41 5.53 (7.29) (/4i) 6507 / 966/
1658 23.78 1753 7.20 0.95 6904/ 2.3/4
3 (503) — 5.9/ — (0.88) 2.0/6 /
1748 12.53 18.28 (7.50) 0.80 6.6// 2484
4 (5.93) 0.66 7.53 7/8 (/■ 60) 7.489/ 2.733 /
18.38 73.78 19.53 (7.85) 115 7.20/ 3.345
5 (6.83) /.78 8.78 7.40 (/95) 8/73 / 3.360
1928 /4.53 2/03- (7.70) 175 7.888 3.227/
6 (772) 2.78 9.53 7.50 (t.8!) 7.740 2 743 /
2037 /5.53 2228 (7.8/) 2.H 8.090 / 2.897
7 (8.6/) 366 10.66 7.49 (2.05) 7.860 2.440
2/05 16.41 234/ (780) 2.36 8 /00 / 2/36 /
8 (9.49) 466 H78 7.6/ (229) 7.442 L.580
2/94 16.53 — (7.04) — 8.003 / —
9 (10.39) 5 9/ 0.03 7.97 2.09 7523 t.5/0
22.85 18.50 12.50 (8.//) (2//) 8.396/ 1.420/
17 17 17 17
Sums, carried forward 128.10 27.34 127.514 40.406
.
®
Station Station Observe fort i T/des High and ami/ton Low wa. rent Wi 1939 'er 5 - continued on d,............ Date May Series He Tide Gage Type, Gar I Cor rec tion !73S No . J ^..Printing feet
ig.r.f>,F°r, Observe •Hami It ion s er
No- /9-A t/ons 4 Locator egin, M : Govern, arch 3L
Date MOON'S TRANSITS Time of — Lumtidal interval Heigt t of-
year ( GREENWICH High Low High Low High Low Remi irks
/939 MEAN water water water water water water
/4 77
Mo. d Hr. dec. Hr dec Hr dec Hr dec Hr dec. feet feet
Bro. fid 128.10 27.34 1275/4 40.406
May 10 (H30) 688 LOO 8.03 2/5 7.803 1.562/
23.77 19.50 13.25 (8.20) (L95) 8.875/ 1.688
H — 7.77 t.77 8.00 2.00 7.966 1.704/
( 12.23) 2002 74/5 (7 79) (L92)\ 8.96// 2.0/8
/2 0.69 840 2.52 7.7/ /83 8.062 2/00/
(13.16) 2/00 L4.75 (T84) (759) 8.924/ 2.495
/3 1.62 925 3.25 763 763 7.875 2/38/
(/407) 22.00 15.38 (7.93) (7.31) 8425/ 2.5/3
!4 2.52 to 00 4.25 748 173 7.6/0 2.250/
(14.97) 22.65 16.25 (7.68) (L28) 8.094/ 2699
15 3.40 /H5 4.90 7.75 L50 7.338 2.488/
(15.82) 2352 17.02 (770) (L20) 7794/ 3.120
16 4.23 — 5.52 — L29 — 2.663/
(16.63) /2.02 17.77 779 (1.14) 7/90 3.533
!7 5.03 0.02 6.27 (7.39) 124 7.650/ 3053/
(17.41) 12.52 18.77 749 (L36) 7.35/ 4.352
t6 77 16 17
Sums, carried Forward, 244.5! 52.46 247.432 80.782
1 1
■ I )
®
Figure 189.—Tides—high and low waters.
467
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206
CORPS’ OP ENGINEERS
Highest Lowest 1 I- ..Uh tide: Da de: Dai 0,)pMz c Tides: H 'e, May i. e}May ‘ r 2(DHQ oh and 7; heigh i height tDLQ)N low wal 9.030 i.420 f< 4n = 202 ers - continued 'eet et. 1 F(Mn))=0.97 102 T,=l to Date: Ma\ Semes Ho. Lot40 -36 Long. 74‘-i Time mer ',1939 48 ■30" N 12'-O7“W , di an, 75 w.
Date MOON'S TRANSITS Tim, of- Lun it ide, /interval Height of-
year {GREENWICH High Low High Low High Low Rerr. arks
1939 MOAN CIVIL ) water water water water water water
17.41 _
Mo. d. Hr dec. Hr. dec. Hr. dec. Hr. dec Hr. dec\ feet feet
Bro tf’w'd 244.5/ 52.46 \247.432 80.782
May !8 5.78 0.77 7.40 (7.36) 1.62 7990) 3.686)
(18/6) 14.02 20.52 8.24 (2.36) 7.64/ 4940
19 6.52 1.27 9.03 (7.H) 2.5/ 8075) 4453
(18.88) 14.41 2/ 03 7.89 (2/5) 7498 373/ 7
20 7.23 2.28 9.53 (7.40) 2.30 6897 3268)
(19.58) 15.28 21.91 8.05 (2.33) 7/79 |/ 3463
2/ 7.93 3.78 9.78 (8.20) /.85 6.8/3 28907
(20.29) 16.28 23.03 8.35 (274) 7/58 / 3.2/5
22 8.65 4.03 10.80 (7.74) 2/5 6.823 2.8927
(2/0/) 16.78 23.53 8/3 (2.52) 7372) 2962
23 9.38 5.03 H.30 (8.02) /.92 7.000 28837
(2/76) 17.55 8.17 7.650)
24 10.14 5.93 0.05 (8.17) (2.29) 6884 2.693
(22.53) 18.30 12.05 836 7.9/ 7.6307 25027
25 10.94. 6.55 7.05 (8.02) (252) 7.057 23987
(23.36) 18.75 12.68 7.8/ 174 7.9407 2.500
!7 /6 Z7 /6
Sums-, carried forwarc < 37/33 8*537 365.039 129.258
/
©
Highest Lowest /=...._.(K, tide: Dai ‘-ide: Daj +0,)-M£ Ti des H, es.Mqy.2. e^MayS or 2(Dt ah and 's.h.eig.ht. , height Q+DLQ) 'ow wate 9.030 t. '/42Q fe -Mn='2d2 's - confii .et ’/ ' 'f(Mn) tued 097 10.2F, = HO Date -.May Series No. Lat 4QT3< Long .74.°-( Time me. J939....... 43 , :-3o^..... 2-02 IN id/an..7.5'. @ w...
Date MOON‘5 TRANSITS Time of- Lun/hda/ interval Height of-
year (GREENWICH High Low High Low High Low Rem, irks
1939 MTAN CIVIL ) water water water water water water
17.41 27 days: May 2-2I (6/ve fir s/ and
Mo d Hr dec. Hr dec Hr dec Hr dec. Hr dec Feet Feet /ast <■ /ate)
Bro't f'w'd 37/33 85.37 365 039 129.258 HHA 25 LLW. 26
May 26 H78 7.50 i.63 (8.14) (227) 7040 2 OiO) 5ums !9. 9950 65 i- 78
19.63 13 50 7.85 172 8.068) 2.235 Means 7.998 2.5 06
27 (0.22) 7.88 2 25 (766) (203) 8354 2.324)
12.66 20.25 14.25 7.59 /.59 9.030) 3.793 D/HQ = .. ^58
28 (HD 9.00 3 25 (7.89) (2/4) 7.4/0 2490 DLQ= . 147
13.57 20.75 14.98 7./8 1.41 7 980\i 2.365) Correct ’d Mn-- 1.987 TO. 77=4.837
29 (2.03) 9.73 3.6/ (7 70) (!58)\ 7/05 1.917 Correcte / DHQ--. 358 X. L/C = .394
74.49 22 H 15.73 7.62 /.24 7836 2.165 Correcte / DLQ = . J47 X HO = .162
Sums, 29 days ■ Mr y /-29(Gn e first. 9 9 9 9
and /< 1st date) 432 96 9935 ^427.862 148.557 Datum / ; 5 feet tbe/ow Ad ’5L
Means.. 7.73/ 1774 I 7640 2.653
Correct/ in to inte rva/. - O./O8 - 0.108 1
7.623 / 666 j 4 987 Mn .
Duratioi 7 of rise 5.957 ! 5.146 MTL.
Mean rn •e mterv '/ 4.644 1 Tabu/ate d by C 5.
30 (2.96) 10.48 4.48 (7.52) (/5Z) 7234 2.039 Date 6- 23-39
1542 22.73 /6.23 7.3/ 0.8/ 1 7.972 2.594 Reducer by : C.S
3/ (388) H.48 5.36 (760) (/.48)\ 7.420 2.3/0 Date <5 23-39
16.33 23.6/ 17.36 728 /.03 1 7.758 2.700 Checker ' by: J./ 1B.
L__ 1 )
Figure 189.—Tides—high and low waters—Continued.
468
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207
SURVEYING
207. Tabulation of high and low waters.—a. The form shown in figure 189 is used for the tabulation of high and low waters, which may be either read from the tide curve made by an automatic gage, or taken from plain staff readings as recorded in a tide book, or from the printed record of a printing gage. The times are to be expressed in hours and decimals instead of hours and minutes; when great accuracy is desired, the times are carried to hundredths of an hour. One-tenth of an hour, or 6 minutes, is as close as an observed high or low water can usually be determined. The following table gives the equivalents of the minutes in tenths of an hour:
Minutes Tenths of hour Minutes Tenths of hour Minutes Tenths of hour Examples
0 to 3___ 0. 0 21 to 27. 0. 4 45 to 51 0. 8 h m hrs. 4 02 = 4.0
4 to 8 . 1 28 to 32 . 5 52 to 56 . 9 4 31 = 4. 5
9 to 15__ . 2 33 to 39 . 6 57 to 59 1. 0 4 50 = 4.8
16 to 20_ . 3 40 to 44 . 7 4 58 = 5.0
b. The heights are usually referred to the zero of the tide staff, and are given in feet and decimals of a foot. If the position of the tide staff is changed during the observations, the heights should all be referred to the zero of one staff, and a full explanation should be given in the column “Remarks.” Any point of an automatic tide gage curve is readily referred to the zero of staff by using the true or corrected scale setting as calculated from the comparative readings on the datum. (See par. 205.)
c. When the period of observations is less than 6 months, the high and low waters should be tabulated in groups of 29 days each, beginning each group on the first line of the front side of a sheet. Allow two lines for each day, which will enable 17 days of record to be tabulated on the front page. The remaining 12 days of the group will be tabulated on the back of the form. If any part of the record is lost, leave vacant line for missing tide. If the series is longer than 6 months, the high and low waters should be tabulated by calendar months. Begin each sheet with the first of the month, and after 29 days have been tabulated, place the remaining days of the month below the long black horizontal line near the bottom of the back of the form. For February of common years insert March 1 after February 28 in order to complete the 29-day group. The high and low waters for March 1 should be repeated at the beginning of the sheet for March.
d. The method of tabulating the year, month, and days is shown on the specimen in figure 189. Generally, the morning tides are entered
469
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207-209
CORPS OF ENGINEERS
on the first line and the afternoon tides on the second line for each day. A tide occurring at midnight (0*) is taken as belonging to the morning of the day just beginning. While tabulating the times and height of the high and low waters, the columns “Moon’s transits” and “Lunitidal interval” are left blank. These are to be filled in afterward in case the reductions described in paragraphs 208 to 213 are made.
e. After the times and heights have been tabulated, the highest and low’est tide occurring during the entire month, or during the period represented by the sheet should be noted and entered in the heading on the back of the sheet. If during this time the observer was unable to obtain a complete record because of some abnormal weather conditions, an estimation of the height of an extreme high water or extreme low water referred to the tide staff may be made from the evidence at hand and an explanation entered in the column “Remarks.”
208. Reduction of tide records.—To obtain tidal constants and tidal datum for any station, the tabulated tides together with intervals and ranges depending upon them must be reduced to their mean values. In order to secure uniformity, the spaces for the sums are indicated in the forms, and the number of items included in each sum should be written in small figures just above the sum, as indicated in the specimen, figure 189. In the tabulations the individual times are given to two decimal places. The mean values are carried to three decimal places, and heights to three decimal places. Where great accuracy is not essential the number of decimal places may be made one less. When this is done, the last decimal figure of the mean value should be taken to the nearest hundredth, but if the remainder should be exactly one-half of the divisor, the second decimal should be made even, if not already even, by adding one.
209. Computation of lunitidal intervals.—This computation is made directly on the form shown in figure 189.
a. The mean solar (civil) times of the moon’s transit for the meridian of Greenwich are obtained from ephemeris tables and centered in the proper column; minutes are converted into decimals of an hour. The times inclosed by parentheses are for the lower transits of the moon; the unmarked ones are for the upper transits.
b. Subtract from the time of each high and low water the time of the last preceding moon’s transit and write the difference in the appropriate column on the same line as the tide from which it was obtained. In case the time of high or low water runs nearly the same as that of the moon’s transit, take the transit which precedes the tide by about 12 hours; but in no case must the same transit be used for two consecutive high waters or for two consecutive low waters. When the time of the moon’s transit is on one day and the following high or low water is
470
TM 5-235
209-210
SURVEYING
on the next day, add 24 hours to the time of the tide, then subtract the time of the transit. The high water intervals will usually be approximately 6 hours greater or less than the low water intervals, but the intervals for each phase of tide will rarely vary among themselves more than a few hours. Intervals from the lower transit of the moon are indicated by parentheses.
c. Sum both columns of the intervals for 29 days, placing the results in the spaces provided on the back of the form.
d. Compute the means by dividing each sum by the number of intervals combined to obtain it, carrying the results to an additional decimal place, and enter the means on next line.
e. Apply the correction to intervals, as obtained from tables I and II, and enter the results in the spaces provided below the second horizontal black line near the bottom of the form. The corrected high water interval thus obtained is known as the corrected establishment of the port.
210. Corrections for lunitidal intervals.—a. The true lunitidal interval is the difference between the mean local time of the tide and the mean local time of the moon’s transit over the local meridian. But on account of the use of standard (instead of local) time and the inconvenience of changing the times Greenwich to the local meridian, it intervals between times of Greenwich tides, as shown in figure 189. From
computed, then corrected to local meridian and time.
Let Z=west longitude of station in degrees and decimals.
$=west longitude of time meridian used for tides.
iS" = west longitude of time meridian used for transits. X— correction to lunitidal intervals in hours.
Then, the correction for lag of the moon is
24.8412—24.0000 ^_£)=0.00233667 (JS'-L) oOU
The correction for reduction of standard time to local time is 24
X,=~(S-Z)=0.06666667 (S-L) oOv
Combining (1) and (2) gives:
X=0.06666667 (S-L)+0.00233667 (S'-L)
When Greenwich transits are used “ro L-4’,0* ., t | R 3’°
-1
£ t .. <60° \
_w i d \
7 _ <-4" -I 3°°Y
1 Type H \ ////////////////
-FT k tn o\z
-2 -p° \
I Type F \
M7/////7/M///77A7
I—43'0 L—
-J—~>fR s 30
■*“ m -X 60"
CM \
- -
f Type J \
WWW
H-» 3-0 •*—
----7TX R - 3‘°
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r Type K \
R=3‘38s^ zby , ।
7 \ / co
4?7 F>
^7Type L 10
V/77/77777 ----9'.92--»
8
7 7///////////////
«----- b -----•
-* at
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1 '7777777777777 ~ -----b------*
TM 5-235
SURVEYING 214
termined from experiments upon full-sized models at the Hydraulic
Laboratory of Cornell University. (See fig. 192.)
Table VII.—Discharge in cubic feet per second per foot of length over sharp-edged vertical weirs without end contractions
[Computed by Bazin’s formula]
Head (H) feet Height in feet of crest of weir above bottom of channel of approach
G = 2 G=3 G=4 G=5 G=6 G==7 G=8
0.2 0. 33 0. 33 0. 33 0. 33 0. 33 0. 33 0. 33
. 3 0. 58 0. 58 0. 58 0. 58 0. 58 0. 58 0. 58
.4 0. 88 0. 88 0. 88 0. 87 0. 87 0. 87 0. 87
. 5 1. 23 1. 21 1. 21 1. 21 1. 21 1. 21 1. 21
.6 1. 62 1. 59 1. 59 1. 58 1. 58 1. 58 1. 58
.7 2. 04 2. 01 1. 99 1. 98 1. 98 1. 98 1. 98
.8 2. 50 2. 45 2. 43 2. 42 2. 41 2.41 2. 41
. 9 3. 00 2. 93 2. 90 2. 88 2. 88 2. 87 2. 86
1.0 3. 53 3. 44 3.40 3. 38 3. 36 3. 36 3. 35
1. 2 4. 68 4. 55 4. 48 4. 47 4. 42 4. 41 4. 40
1.4 5. 99 5. 78 5. 68 5. 62 5. 58 5. 56 5. 54
1. 5 6. 68 6. 44 6. 30 6. 23 6. 20 6. 18 6. 16
1. 6 7. 40 7. 12 6. 97 6. 89 6. 84 6. 80 6. 78
1. 8 8. 93 8. 56 8. 37 8. 25 8. 18 8. 13 8. 09
2. 0 10. 58 10. 12 9. 87 9. 72 9. 62 9. 55 9. 51
2. 2 12. 34 11. 77 11. 46 11. 27 11. 14 11. 06 10. 99
2. 4 14. 20 13. 53 13. 15 12. 91 12. 75 12. 64 12. 56
2. 5 15. 17 14. 45 14. 03 13. 76 13. 59 13. 47 13. 38
2. 6 16. 16 15. 38 14. 92 14. 63 14. 44 14. 30 14. 20
2.8 18. 23 17. 23 16. 79 16. 44 16. 21 16. 04 15. 92
3.0 20. 39 19. 36 18. 74 18. 33 18. 06 17. 86 17. 71
3. 2 22. 64 21. 48 20. 77 20. 31 19. 98 19. 75 19. 58
3.4 24. 98 23. 70 22. 89 22. 36 21. 99 21. 72 21. 52
3. 5 26. 20 24. 83 24. 00 23. 43 23. 01 22. 73 22. 48
3.6 27. 41 25. 99 25. 09 24. 49 24. 06 23. 75 23. 52
3.8 29. 94 28. 38 27. 38 26. 70 26. 22 25. 87 25. 60
4. 0 32. 54 30. 84 29. 74 28. 99 28. 45 28. 05 27. 74
4. 2 35. 22 33. 39 32. 18 31. 35 30. 75 30. 30 29. 96
4. 4 37. 99 36. 01 34. 70 33. 78 33. 12 32. 62 32. 24
4. 6 40. 83 38. 71 37. 29 36. 29 35. 56 35. 01 34. 58
4.8 43. 75 41. 49 39. 96 38. 87 38. 07 37. 45 37. 00
5.0 46. 71 44. 31 42. 67 41. 49 40. 62 39. 96 39. 44
5.2 49. 81 47. 27 45. 50 44. 23 43. 29 42. 57 42. 01
5.4 52. 94 50. 23 48. 38 47. 02 46. 00 45. 22 44. 60
5. 6 56. 15 53. 33 51. 34 49. 88 48. 79 47. 94 47. 28
5. 8 59. 42 56. 45 54. 34 52. 79 51. 62 50. 71 49. 99
6. 0 62. 77 59. 65 57. 43 55. 78 54. 53 53. 55 52. 78
487
TM 5-235
214 CORPS OF ENGINEERS
Table VII.—Discharge in cubic feet per second per foot of length over sharp-edged vertical weirs without end contractions—Continued
Head (H) feet Height in feet of crest of weir above bottom of channel of approach
G = 9 G=10 G=12 G=16 G=20 G = 25 G=30
0. 2 0. 33 0. 33 0. 33 0. 33 0. 33 0. 33 0. 33
0. 3 0. 58 0. 58 0. 58 0. 58 0. 58 0. 58 0. 58
0. 4 0. 87 0. 87 0. 87 0. 87 0. 87 0. 87 0. 87
0. 5 1. 21 1. 21 1. 21 1. 21 1. 20 1. 20 1. 20
0. 6 1. 57 1. 57 1. 57 1. 57 1. 57 1. 57 1. 57
0. 7 1. 97 1. 97 1. 97 1. 97 1. 97 1. 97 1. 97
0. 8 2. 40 2. 40 2. 40 2. 40 2. 40 2. 40 2. 40
0. 9 2. 86 2. 86 2. 86 2. 86 2. 85 2. 85 2. 85
1. 0 3. 35 3. 34 3. 34 3. 33 3. 33 3. 33 3. 33
1. 2 4. 39 4. 38 4. 38 4. 37 4. 36 4. 36 4. 36
1.4 5. 53 5. 52 5. 51 5. 49 5. 49 5. 48 5. 48
1. 5 6. 14 6. 13 6. 12 6. 11 6. 10 6. 09 6. 09
1. 6 6. 76 6. 74 6. 73 6. 71 6. 69 6. 69 6. 69
1. 8 8. 07 8. 05 8. 02 7. 99 7. 98 7. 97 7. 96
2. 0 9. 47 9. 44 9. 40 9. 36 9. 34 9. 33 9. 32
2. 2 10. 95 10. 91 10. 86 10. 81 10. 78 10. 76 10. 75
2. 4 12. 50 12. 45 12. 39 12. 32 12. 28 12. 25 12. 24
2. 5 13. 31 13. 26 13. 18 13. 10 13. 06 13. 03 13. 01
2. 6 14. 13 14. 07 13. 99 13. 90 13. 85 13. 82 13. 80
2. 8 15. 83 15. 76 15. 66 15. 54 15. 48 15. 44 15. 42
3. 0 17. 60 17. 52 17. 39 17. 25 17. 18 17. 13 17. 10
3. 2 19. 45 19. 34 19. 19 19. 02 18. 93 18. 87 18. 83
3. 4 21. 36 21. 24 21. 06 20. 86 20. 75 20. 68 20. 63
3. 5 22. 38 22. 22 22. 00 21. 83 21. 69 21. 62 21. 60
3. 6 23. 34 23. 20 22. 99 22. 75 22. 62 22. 53 22. 48
3. 8 25. 39 25. 23 24. 99 24. 71 24. 56 24. 45 24. 39
4. 0 27. 51 27. 32 27. 05 26. 72 26. 55 26. 42 26. 35
4. 2 29. 69 29. 48 29. 17 28. 79 28. 59 28. 45 28. 36
4. 4 31. 94 31. 70 31. 34 30. 92 30. 66 30. 52 30. 42
4. 6 34. 25 33. 98 33. 58 33. 10 32. 84 32. 65 32. 53
4. 8 36. 62 36. 33 35. 88 35. 35 35. 05 34. 83 34. 70
5. 0 39. 03 38. 70 38. 21 37. 61 37. 28 37. 03 36. 88
5. 2 41. 56 41. 20 40. 65 39. 99 39. 61 39. 33 39. 17
5. 4 44. 11 43. 71 43. 12 42. 38 41. 96 41. 66 41. 47
5. 6 46. 74 46. 31 45. 65 44. 84 44. 38 44. 04 43. 83
5. 8 49. 41 48. 94 48. 22 47. 33 46. 83 46. 45 46. 22
6. 0 52. 15 51. 64 50. 86 49. 90 49. 34 48. 92 48. 67
488
TM 5-235
SURVEYING 214
Table VIII.—Values of n for various values of^j (fig- 191)
H'/H n H'/H n H'/H n H'/H n
0. 00 1. 000 0. 18 0. 989 0. 38 0. 935 0. 58 0. 856
. 01 1. 004 . 20 . 985 .40 . 929 . 60 . 846
.02 1. 006 . 22 . 980 .42 . 922 . 62 . 836
.04 1. 007 . 24 . 975 .44 . 915 .64 . 824
.06 1. 007 .26 . 970 .46 . 908 .66 . 813
. 08 1. 006 . 28 . 964 .48 . 900 . 70 . 787
. 10 1. 005 . 30 . 959 . 50 . 892 .75 . 750
. 12 1. 002 . 32 . 953 . 52 . 884 .80 . 703
. 14 . 998 . 34 . 947 . 54 . 875 . 90 . 574
. 16 . 994 . 36 . 941 .56 . 866 1. 00 . 000
Table IX.—Multipliers for flat-topped weirs (A, fig. 192)
Head (H) feet Width of flat crest in feet
6 = 0.48 6=0.93 6 = 1.65 6 = 3.17 6=5.89 6 = 8.98 6=12.24 6=16.30
0. 5 0. 902 0. 830 0. 819 0. 797 0. 785 0. 783 0. 783 0. 783
1. 0 . 972 . 904 . 879 . 812 . 800 . 798 . 795 . 792
1. 5 1. 000 . 957 . 910 . 821 . 807 . 803 . 802 . 797
2. 0 1. 000 . 989 . 925 . 821 . 805 . 800 . 798 . 795
2. 5 1. 000 1. 000 . 932 . 816 . 800 . 795 . 792 . 789
3. 0 1. 000 1. 000 . 938 . 813 . 796 . 791 . 787 . 784
3. 5 1. 000 1. 000 . 942 . 810 . 793 . 787 . 783 . 780
4. 0 1. 000 1. 000 . 947 . 808 . 790 . 783 . 780 . 777
Table X.—Multipliers for triangular weirs (B, fig. 192)
Head (H) feet 6=6.65 6=11.25
0. 5 1. 060 1. 060
1. 0 1. 079 1. 079
1. 5 1. 091 1. 092
2. 0 1. 086 1. 097
2. 5 1. 076 1. 096
3. 0 1. 067 1. 095
3. 5 1. 060 1. 094
4. 0 1. 054 1. 093
489
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214-215
CORPS OF ENGINEERS
Table XI.—Multipliers for compound weirs {fig. 192)
Head (H) feet Type F Type G Type H Type I Type J Type K Type L
0. 5 0. 964 0. 932 0. 934 0. 968 0. 971 0. 971 0. 971
1.0 1. 026 .982 1. 000 1. 008 1. 040 1. 040 . 983
1.5 1. 064 1. 015 1. 040 1. 032 1. 083 1. 092 1. 022
2.0 1. 066 1. 031 1. 061 1. 041 1. 105 1. 126 1. 040
2. 5 1. 025 1. 038 1. 073 1. 043 1. 118 1. 146 1. 057
3.0 . 992 1. 044 1. 082 1. 044 1. 128 1. 163 1. 072
3. 5 . 966 1. 049 1. 090 1. 045 1. 136 1. 177 1. 085
4.0 .944 1. 053 1. 097 1. 046 1. 144 1. 190 1. 097
f. Discharge by measuring velocity and cross-sectional area, their product being the discharge.—This method involves the accurate finding of the stream cross section and mean velocity.
(1) A study of many streams has developed the following facts:
(a) Velocities are least near the bottom and sides of the channel.
(6) The surface velocity is not the greatest velocity.
(c) The greatest velocity is near the center of the channel, at about 13 percent of the depth below the surface.
(d) The mean velocity in any vertical section is very nearly that found at 60 percent of the depth. It is given still more accurately by taking the average of the velocities at 20 percent and 80 percent of the depth.
(e) Velocity is affected by the presence of bridge piers, dams, etc.
(2) Determine the cross section by making soundings at measured intervals across the stream. Divide the cross section into a number of sections, the number depending upon the accuracy with which the measurement is to be made. Determine the mean velocity in each section. From the mean velocity and the area, determine the partial discharge through each section. The sum of all such partial discharges gives the discharge of the stream.
215. Determination of velocity.—a. Select a gaging site in a straight stretch—500 feet both above and below station is desirable— where the river bed is permanent but not stony, the banks are of sufficient height to contain floodwater, and no disturbing influences such as piers are present.
b. Velocities may be determined by use of floats or current meters. To determine velocity by floats, note the time required for floats of various kinds to traverse a given, distance. This given distance is
490
TM 5-235
215-216
SURVEYING
usually a carefully determined base line from 100 feet to 300 feet in length.
c. Floats are of three kinds—surface, submerged, and rod or tube floats.
(1) Surface floats are made of any buoyant material. They may be used in shallow streams. They are placed so as to travel over the various sections of the cross sections. The time of travel of each float divided by the length of the base line gives the surface velocity. The mean velocity in each section is taken as 0.8 of the surface velocity shown for that section. Results may be accurate within about 10 percent provided the stream is shallow and no wind is blowing.
(2) A submerged “float” is connected by a slender cord to a surface float having sufficient buoyancy to hold the submerged body suspended at any desired depth.
(3) Rod floats consist of hollow tin cylinders or wooden rods weighted to float vertically with a short section exposed. They should be long enough to pass as close to the bottom as possible without striking. Such floats integrate the velocities in a vertical filament and give reliable results. Place the floats so as to give determinations of the mean velocity in each section. The total discharge of the stream is the sum of the discharges of the several sections.
d. The velocity may also be determined by the use of a current meter. See paragraph 196e for description of meters and their rating.
(1) To find the mean velocity of the stream, divide the cross section into a number of narrow sections. Find the mean velocity in each section by one of the following three methods:
(a) Observe velocity at 0.2 and 0.8 depth below the surface and average the two observations.
(6) Observe velocity at 0.6 depth.
(c) Observe the velocity at several points in the vertical by placing the meter at these points successively to determine the vertical velocity curve. From a plot of these curves, determine the mean ordinate which is the desired mean velocity for the section.
(2) The discharge for each section is obtained by multiplying the mean velocity (obtained as a result of the observations from the rating table) by the section area. The sum of the discharges for all the sections is the total stream discharge.
(3) Figure 193 is an example of notes for the observation and reduction of current meter readings for velocities.
216. Value of results.—The value of the results depends largely on the accuracy of the methods pursued. If the discharge of the
491
TM 5-235
216-217 ' CORPS' OF ENGINEERS
stream over a long period is desired, measurements must be made at various seasons and a mean discharge found. If only one measurement is to be made, it should when possible be made under normal conditions. Trees, landmarks, etc., can be examined to determine high water marks, and reports examined to find low water records.
(' Current meter observations
Current Meter ,Vo. 32J/...... | xft)
Loe a hop Curren* Meter Section, Indi dp ....'River____________________________________________
Depth Time__________Rec ’ister Revo-__________\Vetocity_____________________________________
meterfft) (seconds) Start End tutions Rps ftps)________________________Remarks_________________
!9 /OO 1,328 1,382 54 0.54 | 136 Date May 3, i&39_________________________
/7 100 '182 (462 80_________80 | t.93 Wind NE Light __________^ZZZLZZZZ
/5 /OO 1,462 1,560 93 .93 I 2.30 Depth wafer 20 ft, /Q:3QAM~____________
!3 iOO (563 ',673 HO MO I 2.60 Chief of party 5gt R Rse_ _______________________
// 100 (673 (789 H6 /!6 I 2.75 Assistant. Cpt Buri _____________________________
9 100 (789 1,917 728 t.28 I 3.0/_________________________________________
7 /OO 1,9/7 2,054 137 L37 | 3/9___________________________________________
5 iOO 2,055 2,194 139 t.39 I 3.26 ________________________
3 iOO 2,/9 9 2,338 139 139 3 26_______________________________________________
/ /OO 2,338 2,473 135 i.35 3/5 __________________________________________
n I 268/
-----------------. ~ I.................................................
-------------------------------------------I -----------------------------------
_ :____________________________________ !______________-- ............................ .
-----------------------------------------------1......................।—-----------------------
L----------------------------------------------1-------:--------------------------------------J
k_____________________________________________J_______________________________J_______________7
Figure 193.—Notes for observation and reduction of current meter readings.
This information should be carefully analyzed and an attempt made to determine the average conditions.
Section XXXIV
OUTLINE OF INSTRUCTION COURSES
Paragraph
General________________________________________________________________________ 2J7
Basic instructions, surveyors__________________________________________________ 218
Advanced instructions, surveyors_______________________________________________ 219
Instructions, computers________________________________________________________ 220
217. General .—a. Special training courses for surveyors and computers, details of which are given in the preceding sections of this manual, include 36 exercises.
b. The basic instructions for surveyors, intended to cover the work usually performed in the average engineer organizations are included
492
TM 5-235
217-218
SURVEYING
in 16 exercises (see par. 218). These together with the eight exercises in paragraph 219 should be sufficient to train any suitable man for the higher branches of surveying, including geodetic work and astronomical observations.
c. The sixteen exorcises listed in paragraph 220 should be given to those men who are to perform the duties of computers. It is understood that all men detailed to take any part of the surveyors or computers course must be familiar with, or be instructed in, mathematics up to and including plane trigonometry.
d. The training courses here given are to be considered as guides only, to assist instructors in planning exercises for a course based upon local conditions and specific requirements, which will vary to some extent with the type of available instructional material.
e. The time allotted for each exercise, based on experience with Army student classes over a period of some 20 years, will be found necessary to give the student showing aptitude and willingness to learn just enough practice to be useful when detailed for work with a survey party after completing the course.
f. Exercises enumerated in paragraph 218 should be given first before any attempt is made to cover the more advanced subjects in paragraph 219. Instructions for computers may be given concurrently with the field work preceding it, or, if desired, as a separate course. Exercises may be rearranged within practical limits, if desired.
218. Basic instructions, surveyors.
Exercise Paragraph Figure number Hours, field Hours, classroom Total hours
1. Measuring distances 47i 7 12 6 18
2. Adjustment of dumpy level 53e 15, 15A 3 1 4
3. Differential leveling 54/ 15 3 18
4. Profile leveling 55/ 16 7 2 9
5. Cross section levels 56c 17, 18 7 5 12
6. Determination of stadia con-
stant 70e 35 3 1 4
7. Adjustment of transit 71 /z — 3 1 4
9. Conversion of azimuths and
bearings 76c — 2 2
10. Horizontal angles by repeti-
tion 79<7 40 12 1 13
11. Azimuth traverse with stadia. 80/ 42 18 3 21
12. Compass (needle) traverse 81/ — 6 1 7
26. Adjustment of plane table 139/ — 2 1 3
27. Plotting detail on photo- 158e
graph — 7 1 8
28. Completing skeleton plane 12
table sheet 1595 130 1 13
29. Locating control points on
photographs 1626 — 4 1 5
35. Location survey 191/ — 18 3 21
— 129 33 162
493
TM 5-235
219-220
CORPS OF ENGINEERS
219. Advanced instructions, surveyors.
Exercise Paragraph Figure number Hours, field Hours, classroom Total hours
8. 16. 17. 30. 31. 32. 33. 34. Adjustment of theodolite Measuring base line with steel tape Grid triangulation Azimuth observation—altitude method (sun) Azimuth observation—hour angles of sun Azimuth observation — Polaris at elongation Azimuth observation — Polaris at any hour angle Azimuth observation—altitude method (star) 74(7 106/ 114d 171d 173d 17 6d 177c 178/ 68 71, 82, 83 141 142a 145 146 147 3 18 13 4 2 3 3 6 1 3 4 2 2 4 1 2 4 21 17 6 4 7 4 8
— 52 19 71
220. Instructions, computers.
Exercise Paragraph Figure number Hours
13. Calculating and adjusting azimuths 84c 46 3
14. Computation and adjustment of rectangular coordinates 886 47 10
15. Area computation by DMD method 896 48 6
18. Calculation of azimuths 118/ 71, 82 5
19. Solution of triangles 118? 75, 82 3
20. Coordinates from azimuth and distance 118m 85 6
21. Trigonometric elevation 118o 79 6
22. Control data II87 87 2
23. Semigraphic intersection 122c 98 5
24. Semigraphic resection 1256 105 6
25. The inaccessible base 130d 112 3
30. Azimuth computation—altitude method (sun) 171d 141 3
31. Azimuth computation—hour angle of sun 173d 1426 4
32. Azimuth computation—Polaris at elongation 176d 145 2
33. Azimuth computation—Polaris at any hour angle. _ 177c 146 4
34. Azimuth computation—altitude method (star) 178/ 147 3
71
494
TM 5—235
(495)
6, 7, 160,
Pages
371
58
11
Aerial photographs_________
As guide maps__._________
As map substitute________
Contours from____________
For supplementary control
Importance of____________
Planimetric detail from--
Plotting control points on
Sketching on_____________
Use______________________
Alidade, plane table_______
Almanac, Nautical__________
Altitude___________________
Altitude method____________
American Ephemeris_________
Aneroid barometer__________
Angles, triangulation:
Direction________________
Explement________________
Horizontal_______________
Abbreviations, astronomic____________
Abney level__________________________
Accuracy of measurement______________
Adjustments:
Computations:
Angles, horizontal (triangulation)
Azimuths (control traverse)____
Central point figure____________
Horizon (triangulation)_________
Quadrilateral______
Graphic:
Intersection_______
Resection__________
Traverse___________
Instruments:
Barometer, aneroid Level, dumpy.
Plane table________
Sextant____________
Theodolite:
Direction_______
Repeating_______
Wild T2_________
Transit____________
Paragraphs
167d
52
Angles___________________________________________________ 101, 102 182
Azimuths__________________________________________________ 84 133
' 133
135
142
Computations______________________ 84, 86, 87, 99-103, 115<7, 118e (2) ISO-
183
231-
253
f 39
Distances_________________________________________________ 47, 80c j ^4
Field work________________________________________________ 100 182
Traverses_________________________________________________ 86 135
{180—
1 22 ioo
Chords______________________________________________________ 186c (5) 413
Circle settings_____________________________________________ 1076 (1) 209
262341°—40----32 497
TM 5-235
INDEX
Civil time.
Closures:
Paragraphs
... 165c
Pages
357
On bases
92a, 100
Horizon
102, 107c (2)
Triangle__________________________
Coefficient of expansion:
Invar tape________________________
Steel tape________________________
Computations:
Adjustment of central point figure
Angles, quadrilaterals___________
Area______________________________
92a, 101
146
182
182
212
146
182
Azimuths
Azimuth from star (Polaris)
Azimuth from other stars
Azimuth from sun
Base line
Compilation of data.
Control traverse.
Coordinates from azimuth and distance. _ Distances and azimuths from coordinates
Eccentric corrections
Elevations, trigonometric_________
Geographic from grid coordinates. Grid azimuths from geographic... Grid coordinates from geographic Grid triangulation________________
Inaccessible base_________________
Inverse solution__________________
Positions_________________________
Reduction to center
Semigraphic intersection
Semigraphic resection___
Spherical excess________
1046, 105d (3)
_____ 46a (3)
117c,
1196
119c
89a
____ 846, 118/ ... 176c, 1776 1786 (3), c (3)
171c, 173c
105d, 106e
117z, 118(7
82, 86a
---- 118m
____117(7
109d, 1176
117A, 118c
._ 119(7 117/(5) • 117/
118 1306
. 119e 117e
109d,
1176
122c
125e
1166,
117d
184
199
34
266 234 268 142
133 253 401 404 405 386 394
197 206 251
255 130
135 266 246 214 234 248 252
271 246 242 251
307 269 240 214 234 283
297 232 238
498
TM 5-235
INDEX
Computations—Continued.
Stadia traverse______________
Temporary to grid coordinates
Third-order triangulation____
Paragraphs
__ 88a
__ 1196 __ 117
Triangles
117d, 1186,
119d
Three-point problem, grid coordinates
Triangulation between points_______
Volumes____________________________
Computing:
Advice to beginners________________
Mechanical aids____________________
Construction surveys_________________
1265
119/
190e
115d 115/ 5d
Contours
296,
154c
Control, horizontal (see Computations, triangulation)-------45, 27, 58, 59
Control, vertical (see Elevations, trigonometric)__45, 27, 50, 54, 55, 56
Conventional signs______
Convergence of meridians Conversion of time______
Cooperative efforts_____
Coordinates:
1545 116c 165/
19
Assumed
1196, 137
Celestial
164/
Geographic
117/, 119|7
Grid
117/, 119gr
Coordinate point method
Corrections:
1935
Base lines
105d,
106c
Barometer___________
Declination (magnetic) Cross hairs, replacement. Cross sections_________
57
76
39
56
Culmination
176a,
164t»
Current meters
196e
Curvature and refraction
98d, 110
Curves:
Horizontal.
Vertical___
Cut__________
186 186d 1885
Pages
142
272
234
f 238
261
I 269
301
275
421
230
231
5
15
337
3, 14
73
3, 14
45, 59
65, 67
337
233
360
11
272
319
352
242
271
242
271
429
197
205
69
114
24
67
398
354
436
159
218
410
415
417
499
TM 5-235
INDEX
Data
Assembling_____
Basic for control
Collection of--
Compilation, etc.
Conversion of_________________
Field notes. (See Field notes.)
Marginal______________________
Datum plane.
Declination:
Astronomic.
Magnetic.
Declinator..
Description of stations_____
Difference in elevation_____
Differential leveling_______
Direction method____________
Discharge, volume___________
Distance:
Computed__________________
Horizontal________________
Slope_____________________
Stadia____________________
Tape______________________
Dropping extra decimal places
Dumpy level_________________
Adjustments_______________
Care of___________________
Earthwork, computations_____
Eccentric stations__________
Ecliptic_____
Elevations:
Barometric. Clinometer Level______
Trigonometric
Elongation______
Ephemeris_______
Equation of time
Equinoxes_______
16,
110,
Paragraphs Pages
117a, 118(7 [ 234 [ 255
.___ 13, 95 9, 152
___ 10 9
1171, 118p ' 10 251
11 [ 266 9
.___ 26 14
)b, 195, 202 46 434
. 164?, 166 . 460 [ 253 366
76 114
152 334
98?i, 108 54 [ 175 1 213 59
54 59
107b 209
214 479
49 45
.___ 8 8
47d, e 42
48 45
45-47 33-39
115c 229
51b 53
53 58
51b 53
56a 67
. 109, 117b [ 241 | 234
163e, 164j [ 348 I 352
___ 501,57 51, 69
50j 51
50, 54 45, 59
117b, U8n < [ 218 248
164w I 266 354
163b 346
165b 356
164 b 352
500
TM 5-235
INDEX
Equipment:
Astronomic observations________
Base line______________________
Level__________________________
Reconnaissance for triangulation
Tapes__________________________
Theodolites____________________
Transits_______________________
Triangulation------------------
Error:
Accidental_____________________
Actual_________________________
Allowable______________________
Compensating-------------------
Cumulative---------------------
Paragraphs __ 168a __ 105
__ 51
__ 976
_ 46
__ 636
_ _ 63a
__ 112
78 105d(13) 206 __ 78
__ 78
Instrumental
54d (2), 786
Prevention of
78, 99
Probable___________
Estimates, earthwork
Explement____________
Exercises, list of---
105d
(12) 1886 107c
218
Field artillery, cooperation with
56, 98o(l), (8), 1326, 136, 137
Field notes. (See Notes.)
Field work, general instructions---------------------
Fire control data____________________________________
Flags. (See Signals.)
Flooded area-----------------------------------------
Focus________________________________________________
Forms for computation-------------------------------
1. Calculation and ^adjustment of azimuth (fig. 46) 1A. Substitute (figs. 99, 106)--------------------
2. Traverse sheet (fig. 47)-----------------------
3. Area computation (D. M. D. method) (fig. 48) __ 4. Description of station (fig. 60)---------------
5. Reduction to center (fig. 71)------------------
Transcript of results (figs. 82, 83)---------
Quadrilateral adjustment (fig. 74)------------
Solution of triangles (figs. 75, 84, 88)------
Computation of position (fig. 76)-------------
Geographic to grid coordinates (fig. 77®)------
31-34
56
1926
40 1156
846 84c 86a 89a 98n
109d
6.
1146, 118gr
. 117c
_ 117d
. 117e 117/(1)
7.
8.
9.
10.
10A. Interpolation of grid coordinates from geographic coordinates (fig. 77®)---------------------------------------------117/(4)
10B. Corrections to convert geographic azimuths to grid azimuth (fig. 77@)------------------------------------------------ 117/ (5)
Pages
374
185
51
155
34
78
77
224
120
203
11
120
120
( 61
| 121
( 120
( 180
202
417
211
493
'4, 176
180
312
318
, 319
16-20
4
427
25 229 133 134 135 142 175 214 227 255 234 238 240 242
246
246
501
TM 5-235
INDEX
Forms for computation—Continued. Paragraphs Pages
11. Azimuth and distance from grid coordinates (fig. 78)____117(7 246
12. Trigonometric elevations (figs. 79, 86)________________ 1176. 248
13. Geographic positions (fig. 80)__________________________ 117i 251
14. Coordinates from azimuth and distance (fig. 85)_________ 118m 266
15. Control data (fig. 87)__________________________________ 118p 266
16. Inverse solution (fig. 90)______________________________ 119e 269
17. Temporary to standard grid coordinates (fig. 93)________ 1196 272
18. Semigraphic intersection (fig. 98)______________________ 122c 283
19. Semigraphic Resection (fig. 105)________________________ 125e 297
20. Grid coordinate computation of three-point problem (fig.
108) 1266 301
21. Computation of inaccessible base (fig. 112)_____________ 1306 307
22. Azimuth determination-—altitude method (figs. 141, 147) __ 171c 386
23. Azimuth computation-hour angle method (figs. 142®, 147®)_________________________________________________________ 173c 394
24. Azimuth by Polaris at elongation (fig. 145)_____________ 176c 401
25. Azimuth by Polaris at any hour angle (fig. 146)________ 177 401
Formulas. (See Computations.)
Fteley meter__________________________________________________ 196e 436
Gage, self-registering__________________________________________ 203c 461
Gages, types of___________________________________.'________ 203 460
Geodetic surveying, definition_______•______________________ 8 8
Geographic index____________________________________________ 24 13
Grades______________________________________________________ 55e, 56a 66, 67
Graduations:
Tapes_____________________________________________________ 46a 34
Verniers__________________________________________________ 40d 29
Graphic intersection___________________________________________ 121 278
Graphic resection______________________________________________ 124 288
Graphic triangulation_______________________________________ 12Id 280
Graphical adjustment methods__________________________________ 61 74
Grazing sight__________________________________________________ 98e 159
{362
Grid coordinates____________________________________________ 826 130
Grid, standard______________________________________________ 23 13
’ 146 148
Grid triangulation________________________91e, 92d, 98o, 103, 118, 128
1 oo 251 304
Hand level_________.’_______________________________________ 52/ 58
Height of instrument___________________________________________ 54c 60
Height of signals_______________________________________________ 98d 159
Heliotropes_____________________________________________________ 987i 167
Hemisphere, northern (fig. 138)________________________________ 170 382
Hemisphere, southern (fig. 139)________________________________ 170 382
Hook gage_______________________________________________________ 196/ 436
502
TM 5-235
INDEX
. Paragraphs Pages
Horizon________________________________________________________ 164/ 351
Horizontal angles_______________________________________________ 107 208
Distances______________________________________________________ 8 8
Traverse______________________________________________________ 77 118
Triangulation________________________________________________ 102 182
TT i iR/t 1 An / 353
Hour angle_______________________________________________ 164o, 166 • ^gg
Hour angle method_______________________________________________ 173 390
Hour circle____________________________________________________ 164n 353
f 434-
Hydrographic surveys________________________________________ 195-216 •,
Inclined sight----------------------------------------------- 70c (2) 100
Information on notes_________________________________________ 33 69
Instructions. (See Exercises.)
Instrumental errors__________________________________________ 54d 60
Instruments:
Packing and shipping__________________________________________ 35 21
(See under name of instrument, as level, etc.)
Use in field__________________________________________________ 43 30
Interpolation, contours________________________________________ 154c 337
' 212
277-
Intersections____________________________________ 107d, 120-122, 151 9e9
404
, 333
Intersection stations______________1_________________________ 107d 212
Intervisibility of stations__________________________________ 98c, e |
Invar tape___________________________________________________ 105a (2) 185
Inverse solution_______________________________________________ 119e 269
Isogonic chart (fig. 38)----------------------------------------- 76 114
(K) stadia constant______________________________________________ 70 98
Lamps, signal___________________________________________________ 98b 167
Lateral base method__________________________________________ 134b 317
Lateral station method_________________________________________ 134a 316
f 347
Latitude_________________________________________________ 163d, 164m ,
[ 353
Latitude determination_________________________________________ 168c 378
Leadline_______________________________________________________ 196b 434
Leadsman_______________________________________________________ 196c 435
Level: 52/
Abney_________________________________________________•___ 52