Principles of surveying with examples

Surveying is based on two fundamental principles. Every survey, large or small, follows them to control error and to fix points correctly.

1. Working from whole to part.
2. Fixing the position of a new point by at least two independent measurements from points already fixed.

(A third working rule, always check the measurements, supports both.)

Principle 1: Working from whole to part

First a framework of control stations is fixed over the whole area with high accuracy (a few widely spaced stations, using precise instruments). Then the area is divided into smaller parts and the details are surveyed inside this framework with less precise methods.

Reason: errors do not accumulate. If we worked from part to whole, small errors of each part would add up and grow. If a mistake occurs in a small part, it stays inside that part and does not spoil the whole survey.

Example: For a large town map, main triangulation stations are fixed first with a theodolite. Inside each big triangle, smaller chain-survey triangles are laid and the buildings, roads and boundaries are located from them by offsets.

   Whole:  big triangle ABC (precise)
           A /\ 
            /  \ 
           / .. \     Part: small triangles
          /______\    and details inside
         B        C

Principle 2: Location of a point by two independent measurements

A point can be located from two known points A and B by any one of these pairs of measurements:

• two distances (A-P and B-P, intersection of two arcs),
• one distance and one angle (e.g. angle at A and distance AP),
• two angles (angles at A and B, intersection of two lines),
• a perpendicular offset from a known line and the distance along that line.

Example: In chain surveying a tree P near line AB is fixed by measuring the distance along AB to the foot of the perpendicular (chainage) and the length of the perpendicular offset. A third measurement, the tie distance to a point on the line, is taken as a check.