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Simple Quadrilateral AdjustmentsWorksheet showing simple Compass and Transit Rule adjustments of a traverse

Coordinate of points (and traverse closure)

Poin t East No rth

3 0.000 0.000 m

4 -73.992 0.000 m

4A -65.955 -80.268 m

3A 7.500 -84.084 m

3 -0.039 0.008 m

Closure Error 0.039 0.000126 Rod was not put on Point 3 at end! ! Off by about 3.5 cm

1 in 10,000

Coordinate Adjustment: Compass Rule

Total Length of Traverse 312.643 m

Northing error 0.008 m

Easting error -0.039 m

Elevation error 0.004 m

Corrections Corrected

Poin t TraverseLength East No rth Elevat ion East North Elevat ion

3 n/a n/a 0.000 0.0004 73.992 -0.009 0.002 0.001 -73.982 -0.002

4A 84.429 -0.010 0.002 0.001 -65.935 -80.272

3A 80.670 -0.010 0.002 0.001 7.529 -84.090

3 73.554 -0.009 0.002 0.001 0.000 0.000

Coordinate Adjustment: Transit Rule

Corrections Corrected

Poin t Change in E Change in N East No rth East North

3 0.000 0.000 n/a n/a 0.000 0.000

4 -73.992 0.000 -0.018 0.000 -74.009 0.000

4A 8.037 -80.268 -0.002 0.004 -65.935 -80.272

3A 73.455 -3.816 -0.017 0.000 7.537 -84.088

3 -7.538 84.091 -0.002 0.004 0.000 0.000

Sum of Changes 163.022 168.175

Raw Measurements

This example data set contains a large error.

The reflector was not set up on the final point at the end of the survey!

Instrument Ht Reflector Sta Reflector Ht Face Block Slope Dist V HA F1 Angle F2 Angle Difference

3 1.701 4 1.664 1 1000 74.002 89.04472 360.00000 95.09195 95.09333 -0.00139

1.701 4 1.664 1 1004 74.001 89.04333 359.99972 95.09139 95.09333 -0.00194

1.701 4 1.664 1 1008 74.001 89.04417 360.00028 95.09111 95.09417 -0.00306 rejected

89.04407 360.00000 0.00083 0.00083 95.092501.701 4 1.664 2 1002 74.003 270.95361 180.00111

1.701 4 1.664 2 1006 74.001 270.95333 180.00028

1.701 4 1.664 2 1010 74.001 270.95306 180.00000

74.002 89.04667 -0.00046

1.701 3A 1.664 1 1001 84.426 89.20861 264.90806

1.701 3A 1.664 1 1005 84.426 89.20889 264.90833

1.701 3A 1.664 1 1009 84.426 89.20889 264.90917

89.20880 264.90852

1.701 3A 1.664 2 1003 84.425 270.78889 84.90778

1.701 3A 1.664 2 1007 84.425 270.78972 84.90694

1.701 3A 1.664 2 1011 84.426 270.78944 84.90583

84.426 89.21065 264.90685

4 1.664 3 1.701 1 1012 74.003 90.96000 360.00028 84.28278 -84.28306 -0.000281.664 3 1.701 1 1016 74.003 90.95833 360.00028 84.28194 -84.28111 0.00083

1.664 3 1.701 1 1020 74.002 90.95722 359.99889 84.28500 ######## 0.00333 rejected

90.95852 359.99981 0.00306 0.00195 84.28222

1.664 3 1.701 2 1014 74.002 269.04639 179.99694

1.664 3 1.701 2 1018 74.002 269.04639 179.99806

1.664 3 1.701 2 1022 74.002 269.04583 179.99694

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74.002 90.95380 0.00269

1.664 4A 1.701 1 1013 80.699 88.40611 84.28306

1.664 4A 1.701 1 1017 80.699 88.40333 84.28222

1.664 4A 1.701 1 1021 80.699 88.40333 84.28389

88.40426 84.28306

1.664 4A 1.701 2 1015 80.699 271.59972 264.28000

1.664 4A 1.701 2 1019 80.699 271.60000 264.27917

1.664 4A 1.701 2 1023 80.699 271.60000 264.27861

80.699 88.40009 -84.27926

4A 1.664 4 1.825 1 1024 80.698 91.46694 360.00056 98.69000 -98.69195 -0.00195

1.664 4 1.825 1 1028 80.698 91.47000 360.00194 98.69000 -98.69194 -0.00194

1.664 4 1.825 1 1032 80.698 91.46722 359.99889 98.69167 -98.69222 -0.00055

91.46806 360.00046 0.00167 0.00028 98.69130

1.664 4 1.825 2 1026 80.698 268.52861 179.99778

1.664 4 1.825 2 1030 80.698 268.53028 179.99833

1.664 4 1.825 2 1034 80.698 268.52833 179.99722

80.698 91.47093 0.00222

1.664 3A 1.825 1 1025 73.584 91.65722 98.69056

1.664 3A 1.825 1 1029 73.584 91.65750 98.69194

1.664 3A 1.825 1 1033 73.584 91.65694 98.69056

91.65722 98.69102

1.664 3A 1.825 2 1027 73.584 268.33972 278.68972

1.664 3A 1.825 2 1031 73.584 268.33972 278.69028

1.664 3A 1.825 2 1035 73.583 268.33917 278.6894473.584 91.66046 -98.68981

3A 1.66 3 1.675 1 1037 84.448 90.79750 81.90417 81.90417 81.90361 0.00056

1.66 3 1.675 1 1041 84.448 90.79750 81.90361 81.90333 81.90417 -0.00083

1.66 3 1.675 1 1043 84.448 90.79889 81.90444 81.90306

90.79796 81.90407 0.00111 0.00056 81.90382

1.66 3 1.675 2 1039 84.448 269.19778 261.90222

1.66 3 1.675 2 1046 84.448 269.19889 261.90250

84.448 90.80167 -81.90236

1.66 4A 1.675 1 1036 73.590 88.20972 0.00000

1.66 4A 1.675 1 1040 73.590 88.21083 0.00028

1.66 4A 1.675 1 1044 73.590 88.21028 0.00139

88.21028 0.00056

1.66 4A 1.675 2 1038 73.590 271.78583 179.998611.66 4A 1.675 2 1042 73.590 271.78667 179.99833

1.66 4A 1.675 2 1045 73.590 271.78583 179.99944

73.590 88.21389 0.00120

Coordinate Calculations

In order to calculate the coordinates we have to remember that there is a differnece between the compass direction (Azimuth)

and the mathematical angle. The easiest way to calculate coordinates is to first determin the compass direction for each leg,

and then convert it to an angle. The angle is then used in the coordinate calculations.

For a quadrilateral, you take the direction you are heading (azimuth) and add (180-Interior Angle) where the interior angle is

the angle you turn through.

This calculation is shown below

Step 1: Calculate azimuth of each leg

Station From To Internal Angle Azimuth Angle3 4 3a 95.09250 3 -> 4 270.00000 180.00000

4 3 4a 84.28222 4 -> 4a 174.28222 275.71778

4a 4 3a 98.69130 4a -> 3a 92.97352 357.02648

3a 4a 3 81.90382 3a -> 3 354.87734 95.12266

Closure 0.03016

Error per angle 0.00754 27.14557 seconds

Step 2: Calculate elevation differences betw een stat ions

From To Vertical Difference Averaged Error

3 4 1.270 1.271 -0.002

4 3 -1.272

4 4a 2.213 2.222 -0.017

4a 4 -2.230

3 3a 1.201 1.198 0.0083a 3 -1.194

3a 4a 2.281 2.286 -0.010

4a 3a -2.291

Vertical Closure 0.004 -0.027

Step 3: Average horizontal distances between stat ions

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From To Horizontal Distance Averaged Error

3 4 73.991 73.992 -0.001

4 3 73.992

3 3a 84.418 84.429 -0.022

3a 3 84.440

4 4a 80.668 80.670 -0.004

4a 4 80.671

4a 3a 73.553 73.554 -0.001

3a 4a 73.554

Step 4: Coordinate calculat ions

These are done at the top of this worksheet!

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