TOTAL STATION TRAVERSING ADJUSTMENT BY BOWDITCH METHOD
PROCEDURE FOR TRAVERSE CALCULATIONS
- Adjust angles or directions
- Determine bearings or azimuths
- Calculate and adjust latitudes and departures
- Calculate rectangular coordinates
DETERMINING BEARINGS OR AZIMUTHS
- Requires the direction of at least one line within the traverse to be known or assumed
- For many purposes, an assumed direction is sufficient
- A magnetic bearing of one of the lines may be measured and used as the reference for determining the other directions
- For boundary surveys, true directions are needed
LATITUDES AND DEPARTURES
|
Line
|
Dir
|
Deg
|
Min
|
Sec
|
Dir
|
Degrees
|
Length
|
Cumulative
Length |
Azimuthal
Angles |
Departure
|
Latitude
|
|
AB
|
N
|
26
|
10
|
0
|
E
|
N26.167E
|
285.1
|
285.1
|
26.167
|
+125.726
|
+255.881
|
|
BC
|
S
|
75
|
25
|
0
|
E
|
S75.417E
|
610.45
|
895.55
|
+104.583
|
+590.784
|
-153.700
|
|
CD
|
S
|
15
|
30
|
0
|
W
|
S15.5W
|
720.48
|
1616.03
|
+195.500
|
-192.540
|
-694.276
|
|
DE
|
N
|
1
|
42
|
0
|
W
|
N1.7W
|
203
|
1819.03
|
+358.300
|
-6.022
|
+202.911
|
|
EA
|
N
|
53
|
0
|
0
|
W
|
N53W
|
647.02
|
2466.05
|
+307.000
|
-516.733
|
+389.386
|
CLOSURE OF LATITUDES AND DEPARTURES
- The algebraic sum of all latitudes must equal zero or the difference in latitude between the initial and final control points
- The algebraic sum of all departures must equal zero or the difference in departure between the initial and final control points
ADJUSTMENT OF LATITUDES AND DEPARTURES
|
Line
|
Dir
|
Deg
|
Min
|
Sec
|
Dir
|
Length
|
Cumulative
Length |
Azimuthal
Angles |
Departure
|
Latitude
|
|
AB
|
N
|
26
|
10
|
0
|
E
|
285.1
|
285.1
|
26.167
|
+125.726
|
+255.881
|
|
BC
|
S
|
75
|
25
|
0
|
E
|
610.45
|
895.55
|
+104.583
|
+590.784
|
-153.700
|
|
CD
|
S
|
15
|
30
|
0
|
W
|
720.48
|
1616.03
|
+195.500
|
-192.540
|
-694.276
|
|
DE
|
N
|
1
|
42
|
0
|
W
|
203
|
1819.03
|
+358.300
|
-6.022
|
+202.911
|
|
EA
|
N
|
53
|
0
|
0
|
W
|
647.02
|
2466.05
|
+307.000
|
-516.733
|
+389.386
|
ADJUSTED LATITUDES AND DEPARTURES
|
Line
|
Dir
|
Deg
|
Min
|
Sec
|
Dir
|
Length
|
Cumulative
Length |
Azimuthal
Angles |
Departure
Misclosure |
Latitude
Misclosue |
Corrected
Departure |
Corrected
Latitude |
|
AB
|
N
|
26
|
10
|
0
|
E
|
285.1
|
285.1
|
26.167
|
+0.140
|
+0.023
|
+125.586
|
+255.858
|
|
BC
|
S
|
75
|
25
|
0
|
E
|
610.45
|
895.55
|
+104.583
|
+0.301
|
+0.050
|
+590.483
|
-153.750
|
|
CD
|
S
|
15
|
30
|
0
|
W
|
720.48
|
1616.03
|
+195.500
|
+0.355
|
+0.059
|
-192.895
|
-694.335
|
|
DE
|
N
|
1
|
42
|
0
|
W
|
203
|
1819.03
|
+358.300
|
+0.100
|
+0.017
|
-6.122
|
+202.894
|
|
EA
|
N
|
53
|
0
|
0
|
W
|
647.02
|
2466.05
|
+307.000
|
+0.319
|
+0.053
|
-517.052
|
+389.334
|
αCorr.Dep=0 αCorr.Lat=0
The Sum of total Corrected Departure and Sum of total Corrected latitude is 0.00, proves that the traverse is balanced
RECTANGULAR COORDINATES
- Rectangular X and Y coordinates of any point give its position with respect to a reference coordinate system
- Useful for determining length and direction of lines, calculating areas, and locating points
- You need one starting point on a traverse (which may be arbitrarily defined) to calculate the coordinates of all other points
- A large initial coordinate is often chosen to avoid negative values, making calculations easier.
CALCULATING X AND Y COORDINATES
Given the X and Y coordinates of any starting point A, the X and Y coordinates of the next point B are determined by:
|
Line
|
Dir
|
Deg
|
Min
|
Sec
|
Dir
|
Length
|
Azimuthal
Angles |
Calculated
Easting |
Calculated
Northing |
Adjusted
Easting |
Corrected
Northing |
|
AB
|
N
|
26
|
10
|
0
|
E
|
285.1
|
26.167
|
+5125.726
|
+10255.881
|
+5125.586
|
+10255.858
|
|
BC
|
S
|
75
|
25
|
0
|
E
|
610.45
|
+104.583
|
+5716.510
|
+10102.180
|
+5716.069
|
+10102.107
|
|
CD
|
S
|
15
|
30
|
0
|
W
|
720.48
|
+195.500
|
+5523.970
|
+9407.904
|
+5523.174
|
+9407.772
|
|
DE
|
N
|
1
|
42
|
0
|
W
|
203
|
+358.300
|
+5517.948
|
+9610.815
|
+5517.052
|
+9610.666
|
|
EA
|
N
|
53
|
0
|
0
|
W
|
647.02
|
+307.000
|
+5001.214
|
+10000.201
|
+5000.000
|
+10000.000
|
LINEAR MISCLOSURE
The hypotenuse of a right triangle whose sides are the misclosure in latitude and the misclosure in departure.
TRAVERSE PRECISION
- The precision of a traverse is expressed as the ratio of linear misclosure divided by the traverse perimeter length.
- expressed in reciprocal form
- Example
0.89 / 2466.05 = 0.00036090
1 / 0.00036090 = 2770.8
Precision = 1/2771
1 / 0.00036090 = 2770.8
Precision = 1/2771