When to use deflection angle traversing

A deflection angle is the angle between the prolongation of the previous line and the next line, measured to the right (R, clockwise) or to the left (L, anticlockwise).

When it is suggested

Traversing by deflection angles is preferred:

• For route and open traverses such as roads, railways, canals, pipelines and transmission lines, where the lines run in one general direction and the deflections are small.
• When the deflection angles are needed directly for setting out curves (the angle of deflection at the intersection point).
• For long, narrow route surveys where the direction changes gradually, because small deflections are quick to measure, book and plot.
• For preliminary and reconnaissance work, as the angle sum is easy to check for a closed route: $\Sigma R-\Sigma L=360^\circ$.

It is not suggested for closed polygons with many short sides, where included angles are simpler and have a direct geometric check, $(2n-4)\times90^\circ$.

Sketches and field procedure

 Left deflection (L)
                    C
                   /
                  /  d (anticlockwise)
 A-------------B - - - - - - prolongation of AB

 Right deflection (R)
 A-------------B - - - - - - prolongation of AB
                  \  d (clockwise)
                   \
                    C

1. Set up and level the theodolite at B. With the horizontal circle set to zero on face left, sight the back station A using the lower clamp.
2. Plunge (transit) the telescope so that it points along the prolongation of AB.
3. Loosen the upper clamp, sight C and read the angle. If C lies to the right of the prolongation, it is a right deflection; if to the left, a left deflection.
4. Repeat on the other face and take the mean.

Each deflection is booked with R or L, and the bearing of a line is found from

$$\theta_{BC}=\theta_{AB}+d_R\quad\text{or}\quad\theta_{BC}=\theta_{AB}-d_L$$

Check for a closed traverse: $\Sigma d_R-\Sigma d_L=\pm360^\circ$.