Mine Development & Surveying

Underground Surveying & Correlation

Bearings and lengths from coordinate differences, and the closing error that measures a traverse's accuracy.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Underground survey lines are tied to the surface by correlation (transferring bearing and coordinates down a shaft). Once partial coordinates (latitude

Δ N

and departure

Δ E

) are known, the line's length is the hypotenuse and its bearing is the arctangent of departure over latitude. A closed traverse should return to its start; any residual

(\sum Δ N, \sum Δ E)

is the closing error, whose magnitude gauges the survey quality.

The Core Formula Matrix

Line length:

L = Δ N^{2} + Δ E^{2}

.

Bearing:

θ = tan^{- 1} (\frac{Δ E}{Δ N})

(measured from north).

Closing error:

e = (\sum Δ N)^{2} + (\sum Δ E)^{2}

The ‘IIT Traps’

⚠
Bearing uses departure over latitude ( $Δ E /Δ N$ ), then is reckoned from north — not $Δ N /Δ E$ .
⚠
Closing error is the vector magnitude, combining both component misclosures, not their simple sum.
⚠
Watch the quadrant. The signs of $Δ N$ and $Δ E$ place the bearing in the correct quadrant (N–E, S–E, etc.).

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

A survey line has

Δ N = 30 m

and

Δ E = 40 m

. Its length is:

Q2MEDIUM2 Marks · NAT

For the same line (

Δ N = 30 m

Δ E = 40 m

E), the whole-circle bearing is ______ degrees. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

A closed traverse fails to close by

\sum Δ N = 0.06 m

and

\sum Δ E = 0.08 m

. The closing error is ______ m. (Round off to two decimal places.)