Surveying and Levelling
Surveying questions in this paper concentrate on converting compass bearings, computing reduced levels by the height-of-instrument method, and identifying the right instrument or correction for a described situation.
Chain survey and bearings
- The base line is the longest line, measured most carefully; triangles should be well conditioned (angles between 30° and 120°). Offsets may be perpendicular or oblique.
- Whole circle bearing (WCB) is measured clockwise from magnetic north, 0° to 360°. Reduced bearing (RB) is 0° to 90° with a quadrant letter.
- Conversion: WCB 120° → RB = 180° − 120° = S 60° E. WCB 250° → RB = 250° − 180° = S 70° W. WCB 300° → RB = 360° − 300° = N 60° W.
Levelling
- Principle: the line of collimation is horizontal, so HI = RL + back sight, and RL = HI − intermediate sight or fore sight.
- Arithmetical check: ΣBS − ΣFS = last RL − first RL.
- Curvature and refraction combined correction = 0.0673 d² (d in km); refraction alone is about one-seventh of curvature.
Worked example
BM RL = 100.000 m. BS 1.585 → HI = 101.585 m. IS 2.345 → RL = 101.585 − 2.345 = 99.240 m. FS 1.870 → RL = 101.585 − 1.870 = 99.715 m. Check: ΣBS − ΣFS = 1.585 − 1.870 = −0.285; last RL − first RL = 99.715 − 100.000 = −0.285. The booking is correct.
Marks-losing traps
- Forgetting that a staff held inverted against a ceiling gives a negative reading.
- Reporting a magnetic bearing as a true bearing without applying declination.
- Mixing the rise-and-fall method with the HI method in one table, so the arithmetic check fails.