Surveying
Surveying covers chain and compass work, levelling, theodolite and tacheometry, curves and modern positioning. BTSC JE questions are usually reduction-of-levels, bearing conversions and chain corrections.
Core rules
- Representative fraction RF = map distance/ground distance; a scale of 1:1000 means 1 cm = 10 m.
- Chain correction: ca = (L′ − L)/L × measured length; area correction uses twice the linear error.
- Whole-circle bearing to reduced bearing: in NE quadrant RB = WCB; in SE, RB = 180° − WCB; in SW, RB = WCB − 180°; in NW, RB = 360° − WCB.
- Height of instrument method: HI = RL of BM + backsight; RL of station = HI − foresight.
- Curvature correction = 0.0785 d² m and refraction = 0.0112 d² m; combined correction is about 0.0673 d² m, subtractive.
Worked example
A backsight of 1.585 m is taken on a benchmark of RL 100.000. HI = 100.000 + 1.585 = 101.585 m. A foresight of 0.750 m gives RL = 101.585 − 0.750 = 100.835 m. The instrument is shifted; a new backsight of 1.200 m on the same station gives new HI = 100.835 + 1.200 = 102.035 m. A foresight of 2.100 m then gives RL 99.935 m.
Traps
Adding foresight instead of subtracting; mishandling an inverted staff reading; applying the wrong bearing quadrant; ignoring temperature and sag corrections in precise chain work.