Question

A perfectly adjusted tacheometer is set at a point A having Reduced Level (RL) of 80.50 m and the following readings are taken to the staff held at point B having RL of 80.10 m.

The height of the instrument from the ground above point A is \underline{\hspace{1.8cm}} m (Rounded off to 2 decimal places).

Hint:

With VC $=0^\circ$, the line of sight is horizontal, so the middle-hair reading equals the height difference between HI and staff station ground. For a perfectly adjusted tacheometer, use $K=100$, $C=0$.

Answer 1

For a perfectly adjusted tacheometer, the multiplying constant $K=100$ and the additive constant $C=0$. The vertical circle is $0^\circ$, hence the line of sight is horizontal.
Stadia intercept: $s=2.20-1.80=0.40$ m.
Distance $AB=Ks+C=100(0.40)+0=40$ m (not directly needed below).
With a horizontal line of sight, the central hair reading equals the difference between the height of instrument (HI) and the ground at B: $r_m=\dfrac{2.20+1.80}{2}=2.00$ m $⇒$ HI $= \text{RL}(B)+r_m=80.10+2.00=82.10$ m.
Therefore, height of instrument at A above the ground at A is \[ \text{HI}-\text{RL}(A)=82.10-80.50=1.60\ \text{m}. \]