Plane Table Surveying and Minor Instruments
Core concepts
Plane table surveying plots detail in the field without separate field notes. Know the equipment: plane table, alidade, plumbing fork and plumb bob, spirit level, compass, and U-fork with plumb bob. Understand the three operations: orientation (by compass or by backsight), centering, and levelling.
Master the four methods: radiation, intersection (triangulation), traversing, and resection. For resection, learn the three-point problem and its solutions: trial and error, Bessel's graphical method, and the Lehmann method. Understand the triangle of error and how the Lehmann rules guide its resolution.
Minor instruments include the clinometer (measures slope angle), hand level, Abney level, box sextant, planimeter (measures area on a map), and pantograph (reduces/enlarges drawings).
Traps in questions
- Orientation error is the most serious plane table error; always re-orient before resecting.
- Intersection requires the table to be set at two known stations; radiation requires one station only.
- Resection fixes the table's own position; intersection fixes a new point.
- Planimeter gives map area; multiply by the scale factor squared to get ground area.
- The Abney level measures angles of elevation; the box sextant measures horizontal or vertical angles up to 120°.
Worked example / rule of thumb
A planimeter reading on a map at 1:1000 gives 25 cm². Ground area = 25 × (1000)² cm² = 25 × 10⁶ cm² = 2500 m². Rule: ground area = map area × scale².
For the three-point problem, the Lehmann rules place the table's plotted position inside or outside the triangle of error depending on whether the station lies inside or outside the great triangle.