Tacheometry without staff, procedure

Tacheometry is a method of surveying in which horizontal distances and elevations are found from optical measurements made with a tacheometer (a theodolite with stadia hairs) and a graduated staff, without chaining. It is used for contouring, topographic and detail surveys in rough ground.

Can the survey be done without a staff? Yes

The staff only provides a known length to be subtended at the instrument. Any known length, or a reflectorless instrument, can replace it:

1. Tangential method with a ranging rod: paint (or tie bands on) two targets on a ranging rod or pole a known distance $s$ apart (for example 1.5 m), and hold the rod vertical on the point. Measure the vertical angles $\theta_1$ (upper mark) and $\theta_2$ (lower mark):

$$D=\frac{s}{\tan\theta_1-\tan\theta_2},\qquad V=D\tan\theta_2$$

2. Subtense method: hold a ranging rod or tape of known length $l$ horizontal and perpendicular to the line, and measure the horizontal angle $\beta$ it subtends: $D=\frac{l}{2}\cot\frac{\beta}{2}$.
3. Reflectorless total station: the distance to the ground is measured directly by EDM, and the angles are read on the circles.

         Target 2 ●  --
                 |  s | known length (ranging rod)
         Target 1 ●  --
 O ------------------- D
  \ theta2  theta1

Procedure (tangential method)

1. Set up, centre and level the theodolite on the control station, and measure the height of the instrument.
2. Hold the marked ranging rod vertical at the first detail point, with the lower mark at a measured height $h$ above the ground.
3. Read the horizontal circle (bearing) and the vertical angles to the two marks.
4. Compute $D$ and $V$, and the RL: $\text{RL}=\text{RL of axis}+V-h$.
5. Repeat for all details, check against a known point, and plot each point by its bearing and distance.