Field Manual 334.331 TOPOGRAPHIC SURVEYING 16 January 2001
TOC Chap1 2 3 4 5 6 7 8 9 10 11 AppA AppB AppC AppD Gl Bib
This appendix contains recommended procedures for performing basic survey computations. Until recently, three different forms were used to compute a twopoint intersection. Army units have developed a onesheet format (Figure C1) to use when computing a twopoint intersection. This onesheet format is broken down into three parts and combines portions of DA Forms 1920, 1938, and 1947. Part I is from DA Form 1920, Part II is from DA Form 1938, and Part III is from DA Form 1947.
C1. Tabulate data (known and field) for a twopoint intersection on DA Form 1962 (Figure C2) or on a blank piece of paper with an identifying heading. Include the following information:
NOTE: The grid azimuth (denoted by t) and the grid distance may be computed on DA Form 1934 by using UTM coordinates. If needed, conversions can be computed on DA Forms 1932 and 1933.
COMPLETE PART I OF THE ONESHEET FORMATC2. Perform the following steps to complete Part I (Figure C1):
Step 1. Abstract all pertinent information from DA Form 1962 onto Part I. Include the following information:C3. Perform the following steps to complete Part II (Figure C1):
Step 1. Abstract all necessary information from DA Forms 1962 and Part I onto Part II. Record theNOTE: Compare the two sets of N_{1} and E_{1}. They must agree to within 0.001. If they do not, then a math or abstraction error was made, and Part II must be recomputed.
COMPLETE PART III OF THE ONESHEET FORMATC4. Perform the following steps to complete Part III (Figure C1):
Step 1. Abstract all information from DA Forms 1962 and Part II onto Part III. Record theNOTE: The azimuth of a line is recorded to the nearest minute and is obtained from Part II. The mean latitude is obtained by converting the northings and eastings computed on Part II to geographic positions and then taking the mean of the latitudes.
where
R = radius of curvature in the plane of the meridian (obtained from NIMA's
table generating software)
N = radius of curvature in the plane of the prime vertical (obtained from
NIMA's table generating software)
k (in secs)
where
m = mean coefficient of refraction
h_{2}  h_{1} = s �tan(90�  _{1} + k)
NOTE: Compute the DE between the two computed elevations. Use the following formula to determine the AE:
Use the shortest of the two distances to the unknown point. If the DE is larger than the AE, check for math and abstraction errors. If none are found, the intersection does not meet specifications and needs to be reobserved.
C5. DA Form 1940 is used to compute a grid traverse. Tabulate known and field data for the traverse on a DA Form 1962 (Figure C3) or on a blank piece of notepaper with an identifying heading. Include the following:
C6. Figure C4 shows a completed DA Form 1940. This figure is further broken down into separate figures to demonstrate the computation process. Refer to Figures C5 and C6 when working step 1 and Figure C7 when working steps 2 through 7.
Step 1. Transfer the information from DA Form 1962 to DA Form 1940. Record the following information:
NOTE: The starting and ending T may be obtained from UTM coordinates by computing t and (t  T) on DA Form 1934.
Step 2. Compute the summation of angles (� �s) by adding all of the observed angles to the starting back azimuth. Leave the sum in decimal degrees. Record on DA Form 1940 to six decimal places (round the answer).Step 3. Compute the ending azimuth by subtracting 180� from the � �s until it is as close as possible to the known ending azimuth. Record on DA Form 1940 in degrees, minutes, and seconds. Record seconds to one decimal place (round the answers).
Step 4. Compute the AEC by subtracting the fixed (known) ending azimuth from the computed ending azimuth. Compute to one decimal place with the sign. Record in the "Total Angular Closure" block on DA Form 1940.
NOTE: The AEC is always equal to the computed values minus the fixed values as shown in the following formula:
Step 5. Compute the allowable AEC by using the formula from DMS Special Text (ST) 031. Since this is a thirdorder, Class I traverse, the formula used for computing the AE is �10" , where N is the number of segments or distances. This traverse has four distances; therefore AE = �10" = �20.0".NOTE: The AE is always truncated. Do not round up the AE, because rounding will allow more error. Record to one decimal place.
Step 6. Compute the correction per station by dividing the AEC by the number of observed angles, then change the sign of the answer. Record to two decimal places with the sign, and truncate the answer.NOTE: No one angle contains more of the error than another since the angular error is accidental. The error must be distributed evenly among the station angles.
Step 7. Compute the correction per observed angle and properly assign corrections to be applied to the observed angles. Record to one decimal place with the sign. After computing the correction per station, if the division does not result evenly to 0.1", produce a group of corrections that are within 0.1" of each other as in the following example.
+1.94" 

+2.0" 



+1.94" 

+2.0" 

2 @ 
+2.0" = +4.0" 
+1.94" 
or 
+1.9" 
or 


+1.94" 

+1.9" 



+1.94" 

+1.9" 

3 @ 
+1.9" = +5.7" 
+9.7" 

+9.7" 


9.7" total correction 
C7. After computing the correction per angle, assign the proper correction to each angle. For uniformity, apply the larger corrections to the larger angles. Record the correction per station in the "Angular Closure Per Station" block on DA Form 1940 (for example, 2 @ +2.0" and 3 @ +1.9"). Sum the corrections. Record in the appropriate block on DA Form 1940.
NOTE: The sum of the corrections must equal the AEC, with the opposite sign. For example, if the AEC is negative, the corrections will be positive. If the AEC is positive, the corrections will be negative.
C8. Refer to Figure C8 for working steps 1 through 4.
Step 1. Compute the adjusted angles by algebraically adding the correction per angle to the observed angle. Record to one decimal place.
Step 2. Compute the azimuth of each traverse section by adding the first adjusted angle to the starting back azimuth. If the azimuth is over 360�, subtract 360�. This is the azimuth to the forward station. The azimuth of all lines must always be stated in the direction that the traverse is being computed.
Starting back azimuth 
= 
63�54'20.3" 
Adjusted angle at TILDON 
= 
263�24'15.5" 
Forward azimuth: TILDON to AIR FORCE 
= 
327�18'35.8" 
Step 3. Convert the forward azimuth of the line to a back azimuth by either adding or subtracting 180� from the forward azimuth. The forward azimuth to the next station is then computed by adding the back azimuth from the previous line to the adjusted angle of the next station. If the new forward azimuth to the station is greater than 360�, subtract 360�.
Forward azimuth: TILDON to AIR FORCE 
= 
327�18'35.8" 


 180�00'00.0" 
Back azimuth: TILDON to AIR FORCE 
= 
147�18'35.8" 
Adjusted angle at AIR FORCE 
= 
+ 149�47'14.1" 
Forward azimuth: AIR FORCE to ARMY 
= 
297�05'49.9" 
Step 4. Repeat this procedure until the final station obtains a perfect check. The computed closing azimuth must agree exactly with the known closing azimuth. If not, a math error has been made and must be corrected.
NOTE: It is very important that particular attention be given to the direction of the azimuth. An error of 180� may go undetected, and two errors of 180� will cancel out (providing a final azimuth check). This will result in some sections being reversed in direction. Always refer to the sketch provided with the surveyor's field notes.
C9. Refer to Figure C9 when working steps 1 through 10.
Step 1. Compute the
SLC. Record to six decimal places.
where
h = the mean elevation
R = the mean radius of the earth (If h is in feet, use R = 20,906,000 feet.
If h is in meters, use R = 6,372,000 meters.)
Step 2. Compute the middle northing (denoted by MID N) and the middle easting (denoted by MID E). To compute the MID N, add the northing of the beginning traverse station to the northing of the ending traverse station. Then divide by two. Record to the nearest 1,000 meters. To compute the MID E, add the easting of the beginning traverse station to the easting of the ending traverse station. Then divide by two. Record to the nearest 1,000 meters.
Northing for Tildon 
= 
4,283,839.177 
m 
Easting for Tildon 
= 
314,225.115 
m 
Northing for Abbot 
= 
+ 4,287,595.893 
m 
Easting for Abbot 
= 
+ 310,461.502 
m 



m 



m 

= 
4,285,717.535 
m 

= 
312,343.3085 
m 
MID N 
= 
4,286,000 
m 
MID E 
= 
312,000 
m 
NOTE: A scale factor (denoted by K) is required to convert a measured distance to a grid distance. A mean K may be computed for the entire traverse or for each section in the traverse. For this example, a single K will be used since the traverse's total length is 8,000 meters or less. Traverses over 8,000 meters require a K to be computed for each section. Compute the northing and easting of the midpoint for the desired traverse or section to the nearest 1,000 meters. Record the formula in the appropriate block on DA Form 1940.
Step 3. Compute K.
Record to six decimal places (round the answer).
K = K_{o}[1 + (XVIII)q2 + 0.00003 q4]
where
K_{o} = the scale factor at the CM (0.9996)
XVIII = the Table 18 value
q = a factor used to convert E' to millionths
Step 4. Obtain the Table 18 (denoted by XVIII) value. The XVIII value is extracted from the tables in DMS ST 045, using the MID N as the argument. Interpolate to compute the XVIII value to six decimal places (round the answer). An example follows:
MID N 
XVIII Value 
1) 4,200,000 
1) 0.012321 
2) 4,286,000 
2) Unknown 
3) 4,300,000 
3) 0.012318 












� 0.012318 
Step 5. Compute E'
by subtracting 500,000 from the MID E. Record to 1,000 meters as an absolute
value.
E' = MID E  500,000 = 312,000  500,000 = 188,000 m
where
E' = absolute value of MID E
Step 6. Compute q
by multiplying E' by 0.000001. Record to six decimal places (round the answer).
q = E' � 0.000001 = 188,000 � 0.000001 = 0.188000
where
q = a factor used to convert E' millionths
Step 7. Compute q^{2}
and q^{4}. Record to six decimal places (round the answers).
q^{2} = 0.1880002 = 0.035344
q^{4} = 0.1880004 = 0.001249
Step 8. Compute K. Record to six decimal places (round the answer).
K = Ko[1 + (XVIII) q^{2}
+ 0.00003 q^{4}]
= 0.9996[1 + 0.012318 � 0.035344 + 0.00003 � 0.001249]
= 1.000035
where
Ko = the scale factor at the CM (0.9996)
q = a factor used to convert E' millionths
Step 9. Compute a scale factor used to reduce the grid distance (denoted by K�) by multiplying K by the SLC. Record to six decimal places (round the answer).
K� = K � SLC = 1.000035 � 0.999989 = 1.000024
NOTE: After computing K and K�, record the values in the "Scale Factor x SLC" blocks on DA Form 1940 beside the appropriate corrected field distance.
Step 10. Compute grid distances as follows.Taped distances (corrected
horizontal field distances) are reduced to grid distances by multiplying
the taped distance by K�.
G = H � K�
where
G = grid distance
H = taped distance
EDME distances (reduced
geodetic distances) are corrected by multiplying the geodetic distance by
K.
G = S � K
where
G = grid distance
S = geodetic distance
NOTE: Compute the total length of the traverse. Record to three decimal places in the "Length of Traverse" block on DA Form 1940 (Figure C10).
C10. Refer to Figure C11 when working steps 1 through 3:
Step 1. Compute the cosines and sines of the azimuths. Record to seven decimal places with the sign (round the answer).
Step 2. Compute the dNs and the dEs.
The dN is computed by multiplying the grid distance by the cosine of the azimuth. Record to three decimal places with the sign (round the answer).
dN = grid distance � cos (t)
The dE is computed by multiplying the grid distance by the sine of the azimuth. Record to three decimal places with the sign (round the answer).
dE = grid distance � sin (t)
Step 3. Compute errors in the dN and the dE (denoted by En and Ee).
Ee = computed dE  fixed dE = 3,763.327  (3,763.613) = +0.286
C11. Refer to Figure C12 when working steps 1 through 5.
Step 1. Compute the LEC. Record to four decimal places in the "Linear Closure Ratio" block on DA Form 1940. Compute the LEC by using the following formula:
Step 2. Compute the RC. Round down to the nearest 100. Record in the "Linear Closure Ratio" block on DA Form 1940. Compute the RC by dividing the length of traverse (in meters) by the LEC. Use the following formula:
Step 3. Compute the AE for position closure. Since this is a thirdorder, Class I traverse, the AE for position closure is equal to 0.4 times the square root of the distance of the traverse in kilometers. Compute the AE for position closure by using the following formula (found in DMS ST 031) (truncate and record the answer to four decimal places):
where
k = the distance of the traverse in kilometers
NOTE: The LEC must be compared to the AE. If the LEC is equal to or less than the AE, the traverse has met specifications. If the LEC is greater than the AE, no further computations are necessary.
Step 4. Compute the correction factors (correction to northing [denoted by KN] and correction to easting [denoted by KE]) to be used in adjusting the traverse.
NOTE: A correction factor will always have the opposite sign of the En and the Ee.
Step 5. Compute corrections to dNs and dEs.
dN

dE

Correction to dE 
New dE

+0.084 
0.074 

0.074 
+0.197 
0.173 
0.001 
0.174 
+0.038 
0.033 

0.033 
+0.006 
0.005 

0.005 
+0.325 
0.285 

0.286 
C12. Refer to Figure C13 when working steps 1 and 2.
Step 1. Compute the adjusted grid coordinates (northings and eastings).
dN 
= 
+1,357.957 
Correction to dN 
= 
+0.084 
Northing for Tildon 
= 
+4,283,839.177 
Northing for Air Force 
= 
+4,285,197.218 
dE 
= 
871.461 
Correction to dE 
= 
0.074 
Easting for Tildon 
= 
+314,225.115 
Easting for Air Force 
= 
+313,353.580 
NOTE: Continue in a like manner for each station. As a math check, apply the last dN and the last correction of dN to the northing of the preceding station. The answer must equal the fixed northing of the closing station. The same is true for the easting.
Step 2. Sign and date the form.
C13. Compute the Cfactor. Record on DMS Form 5820R. Refer to Figure C14 and Figure C15 when working steps 1 through 15. The step numbers correspond to the numbered blocks on Figure C14. Figure C15 shows a completed DMS Form 5820R.
Step 1. Complete the heading information (1).
Step 2. Record the stadia constant for the instrument (2).
Step 3. Record the backsightrod (nearrod) readings (in millimeters) (3a).
Step 4.Record the foresightrod (farrod) readings (in millimeters) (4a).
Step 5. Record the backsightrod (nearrod) readings (in millimeters) (5a).
Step 6. Record the foresightrod (farrod) readings (in millimeters) (6a).
Step 7. Compute and record the cumulative totals as follows:
3e + the sum of the second set of nearrod readings from 5a (7a)
3d + 5d (7b) (perform a page check
7a � 3)
3c + 5c (7c)
4e + the sum of the second set of
nearrod readings from 6a (7d)
4d + 6d (7e) (perform a page check
7d � 3)
4c + 6c (7f)
7f  7c (7g)
Step 8. Apply the correction for C&R. Due to the short distance from the instrument to the near rod, no corrections are required to the nearrod readings.
Distance (m) 
Correction to Rod (m) 
0 to 27.0 
 0.0 
27.1 to 46.8 
 0.1 
46.9 to 60.4 
 0.2 
60.5 to 71.4 
 0.3 
71.5 to 81.0 
 0.4 
81.1 to 89.5 
 0.5 
89.6 to 97.3 
 0.6 
97.4 to 104.5 
 0.7 
Step 9. Compute the Cvalue by dividing 8e by 7g. Truncate and record to four decimal places with the sign (9).
NOTE: If the sum of the farrod mean middlewire readings (8d) is larger than the sum of the nearrod mean middlewire readings (7b), the Cvalue is negative.
Step 10. Compare the Cvalue with that allowed for the instrument. The allowable Cvalue in most instruments is +0.004. If the Cvalue is within specifications, no further computations are required.
Step 11. Correct the Cvalue if it is not within the specifications.
Step 12. Initial the form (12).
Step 13. Perform field adjustments.
Step 14. Repeat steps 1 through 13 until the Cvalue is within specifications.
Step 15. Give the recording form to the instrument operator once it has been determined that the instrument is within specifications. The instrument operator will check the form for completeness and the computations for correctness and initial the form (15).
C14. Compute a level line on DA Form 1942. Refer to Figure C16 when working steps 1 through 20 (the step numbers correspond to the numbered blocks). Figure C17 shows a completed >DA Form 1942. Data will be required from the field notes (DA Form 5820R) shown in Figures C18 through C21.
Step 1. Complete the headings (1).
Step 2. Record the name of the
Step 3. Record the name of the
Step 4. Record the name of the beginning BM (4).
Step 5. Record the direction of the run (forward [F] or backward [B]) (5).
Step 6. Abstract the length of the forward and backward runs per section from the level field notes. Record to the nearest 0.001 kilometer, in their respective directions (6).
Step 7. Compute the length of the line by adding the shortest distance of each section of the level line (7a). Record the total length of the line (7b).
Step 8. Compute the observed DE of the forward and backward runs per section from the level field notes. Record to four decimal places with the sign (in their respective running directions) (8).
Step 9. Compute the DE between the forward and the backward runs per section. Record to four decimal places as an absolute value (no algebraic signs) (9).
Step 10. Determine the mean DE by computing the absolute mean of the forward and the backward DE. Give the mean DE the algebraic sign of the forward run. Record to four decimal places (round the answer) (10).
Step 11. Record the known elevation of the beginning BM (11).
Step 12. Record the known elevation of the ending BM (12).
Step 13. Compute the observed elevation by algebraically adding the mean difference (shown in 10) and the elevation of the beginning BM (shown in 11). Record to four decimal places (13a). Compute each successive observed elevation by algebraically adding it to the preceding elevation and the respective section's mean DE. Record to four decimal places (13b).
NOTE: The last entry will be the observed elevation of the ending BM. This entry must be compared to the fixed ending elevation.
Step 14. Record the known elevation of the ending BM (from step 12) (14).Step 15. Compute the closure by subtracting the known elevation of the ending BM (shown in 14) from the computed observed elevation of the ending BM (shown in 13b). Record to four decimal places with the sign (15).
Step 16. Compute the AE. Truncate and record to four decimal places (16). For thirdorder specifications, use the following formula:
where
Km = length of line in kilometers (from 7b)
Compare the AE (16) to the closure (shown in 15). If the numerical value of the closure is equal to or smaller than the AE, the level line meets thirdorder specifications. If it does not, there is no need to continue with the computations on DA Form 1942.
Step 17. Compute the correction per kilometer. Divide the closure (shown in 15) by the total length of the line (shown in 7b) and change the sign. Record to six decimal places with the sign (round the answer) (17).
Step 18. Compute the correction for each section. Multiply the length of the line (shown in 7a) of each section by the correction per kilometer (shown in 17). Record to four decimal places with the sign (round the answer) (18).
NOTE: The correction to the final section must be equal to the closure (15), with the opposite sign.
Step 19. Compute the adjusted elevation. Algebraically add the correction (shown in 18) to the observed elevation (shown in 13a) of each station. Record to four decimal places (round the answer) (19).
Step 20. Sign and date the form (20).