Plane-table surveying
A plane table is a drawing board on a tripod. The surveyor fixes paper on it, levels it, and draws lines to targets with a sighting ruler (alidade) while standing in the field. Distances are measured with a tape and drawn to scale straight away. The map is made on the spot, so nothing can be forgotten. It is good for small areas in dry weather.
Angle measurement
Direction between two lines is an angle. A theodolite has a telescope that turns round a vertical axis (to read horizontal angles) and a horizontal axis (to read vertical angles). Aim at the left target, read; aim at the right target, read; the difference is the angle. Angles are in degrees; 1 degree = 60 minutes.
Traverse surveying
A traverse is a series of connected lines whose lengths and angles are measured. In a closed traverse the last line returns to the first station. For n sides the sum of interior angles must be (n - 2) x 180 degrees. Any difference is the angular error, and a gap at the end is the error of closure. A small error is spread over all stations; a big one means re-measuring.
Levelling
Levelling finds the height difference between points. A level gives a horizontal line of sight. A staff (a long ruler) is read at two points. The first reading on a point of known height is the back sight (BS); the next reading on the new point is the fore sight (FS).
Height difference = BS - FS. If positive, the new point is higher. Reduced level (RL) of new point = RL of known point + BS - FS.
Control points and satellite positioning
Control points are marks whose position and height are known very accurately (survey pillars). Every small survey is tied to them so that maps join without gaps.
GNSS (such as GPS, NavIC, Galileo) uses satellites that send their position and time. A receiver measures how long each signal took; with four satellites it solves for latitude, longitude, height and its own clock error. Survey receivers use special methods to reach centimetre accuracy.
Key formulas and definitions
- Height difference = BS - FS
- RL of new point = RL of old point + BS - FS
- Sum of interior angles of closed traverse = (n - 2) x 180 degrees
- Angle = reading on right target - reading on left target
- 1 degree = 60 minutes
Worked examples
1. BS = 1.30 m on a point of RL 100.00 m. FS on the next point = 2.10 m. Find its RL.
RL = 100.00 + 1.30 - 2.10 = 99.20 m.
2. Reading on left target = 25 degrees, on right target = 85 degrees. Find the angle.
85 - 25 = 60 degrees.
3. A closed traverse has 5 sides. Find the sum of interior angles.
(5 - 2) x 180 = 540 degrees.
4. Measured interior angles of a quadrilateral traverse: 91, 88, 92, 87 degrees. Find the angular error.
Sum = 358 degrees. Correct sum = (4 - 2) x 180 = 360. Error = 2 degrees (short).
5. RL of A = 50.00 m. BS = 2.40, FS = 1.15 to point B. B is higher or lower? Find RL.
BS - FS = 1.25 (positive), so B is higher. RL = 50.00 + 1.25 = 51.25 m.
6. Going from A to C through B: BS on A = 1.50, FS on B = 1.20 (change point), BS on B = 2.00, FS on C = 2.90. RL of A = 200.00. Find RL of C.
RL of B = 200.00 + 1.50 - 1.20 = 200.30. RL of C = 200.30 + 2.00 - 2.90 = 199.40 m. Check: total BS = 3.50, total FS = 4.10, difference = -0.60; 200.00 - 0.60 = 199.40.
Common mistakes
- Reading the staff upside down or at the wrong mark.
- Mixing up BS and FS: BS is the first reading on the known point.
- Using (n + 2) x 180 or n x 180 for the angle sum. It is (n - 2) x 180.
- Thinking GPS needs only one satellite. Four are needed for position and height.