Surveying
Surveying tests chain and tape corrections, levelling, theodolite work, traversing and curve setting.
Core rules
- Tape correction: temperature correction = Lα(T − T0); pull correction = (P − P0)L/(AE); sag correction is negative for unsupported tape.
- Levelling: height of instrument HI = RL + backsight; RL = HI − foresight. Rise or fall is the difference between consecutive staff readings.
- Curvature and refraction: combined correction ≈ 0.0673D² m with D in km; curvature is subtracted and refraction partly cancels it.
- Simple circular curve: tangent T = R tan(Δ/2); length L = πRΔ/180; mid-ordinate M = R(1 − cos Δ/2).
- Theodolite traversing: angular misclosure is distributed; latitude = L cos θ and departure = L sin θ.
Worked example
A circular curve has R = 300 m and deflection angle Δ = 40°. Find T, L and M. T = 300 × tan(40/2) = 300 × tan20° = 300 × 0.3640 = 109.2 m. L = π × 300 × 40/180 = 209.4 m. M = 300(1 − cos20°) = 300(1 − 0.9397) = 18.1 m. These are the standard setting-out elements before pegging the curve.
Traps
Using the whole deflection angle in T instead of Δ/2; working in radians in a formula expecting degrees; adding instead of subtracting curvature correction; confusing latitude with departure; correcting slope distance after instead of before computing coordinates.