Mine Development & Surveying

Levelling & Tacheometry

Reduced levels by the height-of-instrument method and distances from stadia readings — fixing elevation and range in the field.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Levelling determines the reduced level (RL) — the height above a datum — of points by sighting a graduated staff. In the height-of-instrument (HI) method, a backsight onto a benchmark of known RL fixes the instrument's collimation height; any foresight is then simply subtracted from that height to give the new point's RL. Tacheometry speeds up surveying by reading the stadia interval (the gap between the upper and lower cross-hairs on the staff) to compute distance directly — no chaining required — with a small correction for any inclination of the line of sight.

The Core Formula Matrix

Height of instrument:

H I = R L_{B M} + B S

(backsight).
Reduced level of a point:

R L = H I - F S

(foresight).

Tacheometric distance (stadia, line of sight inclined at angle

θ

D = K S cos^{2} θ + C

K

= multiplying constant (usually 100),

S

= staff intercept (upper − lower hair),

C

= additive constant (≈ 0 for modern internal-focusing instruments).

Vertical component:

V = \frac{1}{2} K S sin 2 θ

. For a horizontal sight (

θ = 0

D = K S

The ‘IIT Traps’

⚠
Backsight adds, foresight subtracts. $H I = R L + B S$ , then $R L_{n e w} = H I - F S$ . Reversing the roles inverts every level.
⚠
** $cos^{2} θ$ , not $cos θ$ .** The horizontal tacheometric distance carries the square of the cosine; using a single cosine over-estimates the distance.
⚠
Staff intercept = upper − lower. $S$ is the difference of the outer stadia readings, not the middle (axial) reading.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

A benchmark has

R L = 100.000 m

. A backsight of

1.250 m

is taken on it, then a foresight of

0.750 m

on a change point. The RL of the change point is:

Q2MEDIUM2 Marks · NAT

A tacheometer (

K = 100

C = 0

) reads stadia hairs of

1.500 m

(upper) and

0.700 m

(lower) on a vertical staff with a horizontal line of sight. The horizontal distance to the staff is ______ m. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

The same tacheometer (

K = 100

C = 0

) reads a staff intercept of

S = 1.250 m

with the line of sight inclined at

θ = 5^{\circ}

above horizontal. The horizontal distance is ______ m. (Round off to two decimal places.)