What is surveying?
Surveying is measuring points on or near the ground, and drawing them on a plan or map at a smaller scale. Civil engineers use it to plan (where should the road go?), to design (how high, how wide?) and to set out (mark the plan back on the ground with pegs).
Main kinds: plane surveying (small area, ground treated as flat) and geodetic surveying (very large area, the curve of the Earth counts). Two basic measures are distance and angle; a third is height (levelling).
Two golden rules: work from the whole to the part (fix big frame first, then details) and check every measurement.
Distance surveying: the tape
Distance on the ground is measured along the horizontal. Ways to measure:
- Pacing: count steps (rough, quick).
- Chain or tape: a steel tape of 20 or 30 m is laid again and again. Count the tape lengths and add the last part.
- EDM (electronic distance measurement): an instrument sends light or a laser to a reflector and finds distance from the time taken: d = speed × time ÷ 2. Total stations do this.
For a long line, use ranging: fix ranging poles at the ends and put middle poles exactly on the line by sighting. Then every tape lies on a straight line.
Corrections to measured distance
A measured length may be wrong because of the ground and the tape.
- Slope correction: if the tape lies along a slope of angle θ, horizontal distance H = L cos θ. The correction is L - H, always taken off.
- Sag: a tape held in the air hangs in a curve, so it reads too long. Pull it tight.
- Temperature: a steel tape grows longer in heat, so readings become too small.
- Wrong length of tape (worn, bent) or mistakes in counting.
Measure each line twice (forward and back) and take the average if they agree.
Angle surveying
An angle tells which way a line goes. Instruments:
- Compass: gives the bearing of a line, the angle from north, clockwise, 0° to 360°.
- Theodolite: a telescope on a stand that turns on a horizontal plate (reads horizontal angles) and a vertical plate (vertical angles). It is set up exactly over a peg and levelled with its bubbles.
To measure a horizontal angle: sight the first point, set the reading to zero; turn the telescope to the second point; read the angle. Repeat on both faces of the instrument and average to cancel errors. For a closed shape with n sides, the inside angles must add to (n - 2) × 180° — a handy check.
Try it: pace your school ground
Measure 10 m with a tape. Walk it normally and count steps. Work out pace length = 10 ÷ steps. Predict: how many steps for the whole ground? Walk and count, then check with a tape.
Key formulas and definitions
- Horizontal distance H = L cos θ (L measured along the slope)
- Total length = (full tapes × tape length) + last part
- EDM: distance = speed of light × time ÷ 2
- Interior angles of an n-sided closed figure: (n - 2) × 180°
- Scale: ground distance = map distance × scale number
Worked examples
1. Three full 20 m tapes and a last part of 7.5 m are laid. Total?
3 × 20 + 7.5 = 67.5 m.
2. A tape on a 10° slope reads 50 m. Find the horizontal distance. (cos 10° = 0.985)
H = 50 × 0.985 = 49.25 m. Slope correction = 0.75 m.
3. The angles of a triangular plot are 62°, 55° and x. Find x.
Sum is 180°. x = 180 - 62 - 55 = 63°.
4. A closed traverse has 5 sides. What should the sum of inside angles be?
(5 - 2) × 180 = 540°.
5. A pace is 0.75 m. A student takes 120 paces. Distance?
120 × 0.75 = 90 m (approx).
6. A line measured forward is 80.04 m and back 79.96 m. Best value?
Average = (80.04 + 79.96) ÷ 2 = 80.00 m. The difference of 0.08 m is small.
Common mistakes
- Using the slope length as the plan distance. Always reduce to horizontal.
- Forgetting to count the number of tapes.
- Letting the tape sag in the air and still taking the reading.
- Confusing bearing (from north, clockwise) with an angle between two lines.