Traverse Checks Using Deflection Angles

In surveying, a traverse is a series of connected survey lines whose lengths and directions are measured. A closed traverse starts and ends at the same point, forming a closed loop.

To ensure the accuracy of the measurements in a closed traverse, various checks are performed. One common method uses deflection angles.

Deflection Angles in Traverse

A deflection angle is the angle measured from the extension of the preceding line to the succeeding line. It is typically measured either to the right (clockwise) or to the left (counter-clockwise). Deflection angles are very useful in setting out curves and in traversing.

Algebraic Sum Check for Closed Traverse

For a closed traverse, there is a specific relationship that the measured angles should satisfy. When using deflection angles, this relationship provides a check on the accuracy of the angular measurements.

Consider a closed traverse ABCD. As we traverse from one station to the next, we measure the deflection angle at each station. For a complete circuit around the closed traverse, the algebraic sum of all the deflection angles (taking right deflection angles as positive and left deflection angles as negative, or vice versa) must equal 360 degrees. This is because the traverse lines effectively make a full turn (360 degrees) as you traverse the entire loop and return to the starting point.

The check can be stated as:

\(\Sigma \text{Deflection Angles} = \pm 360^\circ\)

The sign (\(+\) or \(-\)) depends on whether the sum of right deflections or left deflections is larger, but the magnitude of the sum of all algebraic deflection angles must be \(360^\circ\).

Therefore, for a closed traverse using deflection angles, the algebraic sum of the deflection angles should be equal to \(360^\circ\).