Mine Development & Surveying

Traverse & Circular Curves

Latitude/departure of a survey line and the tangent length & arc length of a simple circular curve.

PART 1

Topic Breakdown & Traps

A traverse fixes positions by measuring the length and bearing of connected lines; each line's change in northing is its latitude (

l cos θ

) and its change in easting is its departure (

l sin θ

). To join two straight alignments smoothly — a haul road or rail bend — a circular curve of radius

R

is inserted through a deflection angle

Δ

. Its tangent length

T

(from the intersection point to where the curve begins) and its arc length

L_{c}

follow directly from

R

and

Δ

Latitude / Departure of a line of length

l

at bearing

θ

Latitude = l cos θ, Departure = l sin θ

Tangent length of a circular curve:

T = R tan (\frac{Δ}{2})

Length of curve (arc),

Δ

in degrees:

L_{c} = \frac{π R Δ}{180}

R

= curve radius,

Δ

= deflection (intersection) angle.

⚠
Latitude uses cosine, departure uses sine. Bearings are measured from the north–south meridian, so the cosine gives the N–S (latitude) component. Swapping them is the classic traverse error.
⚠
**Tangent uses $Δ/2$ , arc uses full $Δ$ .** $T = R tan (Δ/2)$ but $L_{c} = π R Δ/180$ — don't mix the half-angle into the arc formula.
⚠
Degrees vs radians. $L_{c} = π R Δ/180$ already converts $Δ$ from degrees; using radians here double-converts.

PART 2

Q1BASIC1 Mark · MCQ

A survey line is

100 m

long with a whole-circle bearing of

N 3 0^{\circ} E

. Its departure (easting component) is:

Q2MEDIUM2 Marks · NAT

A circular curve of radius

R = 300 m

connects two straights meeting at a deflection angle

Δ = 4 0^{\circ}

. The tangent length is ______ m. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

For the same curve (

R = 300 m

Δ = 4 0^{\circ}

), the length of the curve (arc) is ______ m. (Round off to two decimal places.)