Geomatics Engineering

Theodolite & Traverse

Angles and bearings, latitudes and departures, and the closing error of a traverse — the backbone of horizontal control surveys.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A traverse is a connected series of lines whose lengths and directions are measured. Each line is resolved into a latitude

L cos θ

(N–S) and departure

L sin θ

(E–W) from its bearing. For a closed traverse the algebraic sums of latitudes and departures should be zero; any residual is the closing error, distributed by Bowditch's rule.

The Core Formula Matrix

Latitude:

Lat = L cos θ

Departure:

Dep = L sin θ

Closing error:

e = (\sum Lat)^{2} + (\sum Dep)^{2}

Bowditch (compass) rule: correction

\propto

length of each line.

The ‘IIT Traps’

⚠
Latitude uses cosine, departure uses sine of the bearing measured from the meridian (N–S).
⚠
Watch the quadrant signs. Northings/Eastings are positive; southings/westings negative when summing.
⚠
Closing error is the resultant of the two misclosures, not their simple sum.

📚 Standard references

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

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

A survey line is

100 m

long with a whole-circle bearing of

30°

. Its latitude is _____ m.

Q2MEDIUM1 Mark · NAT

For the same line (

100 m

, bearing

30°

), the departure is _____ m.

Q3HARD2 Marks · NAT

A closed traverse has

\sum Lat = + 0.3 m

and

\sum Dep = - 0.4 m

. The closing error is _____ m.