Tangential tacheometry, total station procedure

Tangential tacheometry

In tangential tacheometry the horizontal distance is found from vertical angles only. Two targets (vanes) are fixed on a staff a known distance $s$ apart, and the vertical angles $\theta_1$ (upper vane) and $\theta_2$ (lower vane) to them are measured with a theodolite. For two angles of elevation:

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

The RL of the staff point is the RL of the axis $+V-h$, where $h$ is the height of the lower vane above the staff point. (For two depressions, $D=s/(\tan\alpha_1-\tan\alpha_2)$; for one elevation and one depression, $D=s/(\tan\theta+\tan\alpha)$.) It is useful when the theodolite has no stadia hairs, or when the distance is too large for the stadia intercept to be read accurately.

Field procedure of a tacheometric survey by total station for a topographic map

1. Control: establish control stations by traverse, with known coordinates and RL (from GPS or an existing control network).
2. Set up the total station over a control station, centre and level it, and measure the HI. Enter the job name, station coordinates (N, E, RL), HI and corrections (temperature, pressure, prism constant).
3. Orient the instrument: sight a known back-sight station and enter its coordinates (or azimuth), so that the horizontal circle is oriented to grid north. Check by measuring another known point.
4. Measure details: a reflector (prism) on a pole of height $h_r$ is held on each point, and $h_r$ is entered in the instrument. Aim the telescope at the prism and press measure; the total station records the horizontal angle, the vertical angle and the slope distance, and computes $N$, $E$ and RL automatically.
5. Code the points with feature codes (road, building, tree, stream, spot level), and take all break lines, boundaries and enough spot heights, radiating from the station; check by re-sighting the back-sight before moving.
6. Move to the next control station and repeat, tying the surveys together with common points.
7. Download the data to a computer, process it in software to make a Digital Terrain Model, interpolate the contours and draw the topographic map with a scale, north arrow and legend.