Geomatics Engineering

Levelling & Tacheometry

Height-of-instrument levelling, stadia tacheometry and curve geometry — the measurement backbone of surveying.

PART 1

Topic Breakdown & Traps

The Engineering Principle

In levelling, the height of instrument equals the known RL plus a backsight; any point's RL is HI minus its foresight. Tacheometry finds horizontal distance from a staff intercept via the multiplying constant. A circular curve's length follows from its radius and central angle.

The Core Formula Matrix

Height of instrument:

HI = RL_{B M} + BS

Reduced level:

RL = HI - FS

Tacheometry (horizontal sight):

D = K S + C

(

K = 100, C = 0

typical).

Curve length:

L = \frac{π R Δ}{180}

(

Δ

in degrees).

The ‘IIT Traps’

⚠
Backsight adds, foresight subtracts. HI rises by BS; RL of a point falls by FS.
⚠
Tacheometry constant. $K = 100$ multiplies the staff intercept; the additive $C$ is usually zero.
⚠
Radians vs degrees. Convert $Δ$ when using $L = R Δ$ .

📚 Standard references

Surveying Vol. I & II — B.C. Punmia, A.K. Jain & A.K. Jain

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

The RL of a benchmark is

100.000 m

and the backsight on it is

1.250 m

. The height of instrument is _____ m.

Q2MEDIUM1 Mark · NAT

A tacheometer (

K = 100, C = 0

) reads a staff intercept of

1.2 m

on a horizontal sight. The horizontal distance is _____ m.

Q3HARD2 Marks · NAT

A circular curve of radius

300 m

has a central angle of

4 0^{\circ}

. Its length is _____ m.