Error and Correction in a Closed Traverse by Compass Surveying.

 Hi,

A closed traverse constructed after doing a compass survey can be checked for error by a simple formula.

Working with Interior Angles

As per the geometry, in a closed traverse with 'n' number of sides the total sum of the interior angles = (2*n - 4) * 90 degrees.

Example: 

Consider a pentagon with five sides and five number of interior angles A, B, C, D and E.

n = 5 (no. of sides)

Sum of the interior angles = (2*n - 4) *90
= (2*5 - 4) *90
= 540 degrees.

If it was a hexagon,

 then n = 6
and sum of interior angles would be
= (2*6 - 4)* 90  = 720 degrees

Apply this check to the closed traverse at hand and see the error.



Error =
Sum of the given (actual) interior angles - Theoretical Sum = 

 Sum of the given (actual) interior angles  - (2*n - 4)*90

Correction = - Error.

Generally the error is equally divided among the interior angles of the traverse.

 Hence, correction for each angle  = - (Error) / n,

  where n is the number of sides of the closed traverse.

Working with Exterior Angles

If the exterior angles are given, then the total sum of the exterior angles = (2n + 4) * 90
Remember, an exterior angle = 360 - interior angle.
For example, exterior angle at any station A = 360 - Int. angle A.

Calculate the Error, E = Total Sum of exterior angle - (2n + 4)*90
Correction = -E
Divide the correction equally for each angle = -E/n.

Thank You!