Surveying and Measurement
What the exam tests
This domain tests levelling, horizontal control, traversing, setting out, distance and angle measurement, and the reduction of field observations. You should be able to reduce levels, compute coordinates or bearings, assess misclosure, and choose appropriate instruments and checks.
Core rules
- Height of instrument (HI) method: HI = known reduced level (RL) + backsight. New RL = HI − foresight or intermediate sight.
- Rise and fall method: rise = previous staff reading − current reading; fall = current reading − previous reading. Apply arithmetic checks to the reduced levels.
- A closed levelling traverse should start and finish on known or check points; misclosure must be within the specified tolerance.
- Bearings are measured clockwise from north. Whole-circle bearings avoid quadrant ambiguity; reduced bearings need a quadrant letter.
- Traverse coordinates: ΔE = L sin θ and ΔN = L cos θ for a whole-circle bearing θ measured from north.
- Instrument errors include collimation error, parallax, vertical staff error and refraction; use balanced backsights and foresights and keep sight lengths similar.
Worked example
A benchmark has RL 100.000 m. A backsight of 1.450 m is taken on the benchmark, then a foresight of 2.100 m on a new point. Find the new RL. HI = 100.000 + 1.450 = 101.450 m. New RL = 101.450 − 2.100 = 99.350 m. The new point is lower than the benchmark by 2.100 − 1.450 = 0.650 m, which agrees with 100.000 − 99.350 = 0.650 m.
Traps
Adding a foresight instead of subtracting it; reversing backsight and foresight; ignoring the arithmetic check; using a staff that is not vertical; allowing parallax; mixing degrees and radians; and reporting a bearing without stating its reference direction. In setting out, a small angular error becomes a large positional error over a long distance.