Levelling and Contouring
Core concepts
Levelling determines relative heights. Know the instruments (dumpy, tilting, auto level), the staff, and the terms: benchmark, reduced level (RL), back sight (BS), intermediate sight (IS), fore sight (FS), height of instrument (HI), change point, and the line of collimation. Master the height of instrument (collimation) method and the rise-and-fall method.
Understand curvature and refraction corrections (combined ≈ 0.0673 D² m with D in km), and how to eliminate errors by balancing BS and FS distances. Learn the sources of error: parallax, bubble, staff verticality, refraction, and settlement of the instrument.
Contouring: contour lines join points of equal elevation. Know characteristics (contours never cross except at overhangs, close spacing = steep slope, uniform spacing = uniform slope, V-shape points upstream in valleys) and the methods: direct, indirect (grid, cross-section, radial), and interpolation.
Traps in questions
- Arithmetic check: ΣBS − ΣFS = last RL − first RL. A mismatch signals an arithmetic error.
- Rise and fall: rise when next staff reading is smaller; fall when larger.
- Curvature correction is always subtractive; refraction is additive; combined is subtractive.
- Contours of different elevations never meet; they may coincide at a vertical cliff.
Worked example / rule of thumb
BS 1.50 (RL 100.00) → HI = 101.50. FS 1.80 → RL = 99.70. If the next BS is 1.20, new HI = 99.70 + 1.20 = 100.90. Rule: RL = HI − staff reading; new HI = RL at change point + new BS.
For contour interpolation, use proportional distance between two known spot levels along a line.