Plane and geodetic surveying; principles

Plane surveying

Plane surveying is the type of surveying in which the earth's surface is treated as a plane, so the curvature of the earth is neglected. The level line is taken as a straight line, the angles of a triangle sum to $180^\circ$ and plane trigonometry is used. It is suitable for areas up to about 250 km$^2$ (about 15.8 km $\times$ 15.8 km), where the difference between an arc and its chord is negligible. Examples: road, canal, building-site and small town surveys.

Geodetic surveying

Geodetic surveying is the type of surveying in which the curvature of the earth (its spheroidal shape) is taken into account. Precise instruments and methods are used, the lines are treated as arcs and spherical trigonometry is used. It is used for large areas above about 250 km$^2$, for fixing widely spaced control points (latitude, longitude, elevation) and for national mapping. The angles of a triangle sum to more than $180^\circ$ (spherical excess).

Principles of surveying

The two basic principles are:

1. Working from whole to part. A strong main framework (control network) of a few stations is first established over the whole area with high accuracy. The smaller parts and details are then surveyed inside it with less accurate methods. Errors are therefore controlled, and a mistake in one part does not spread to the others. Working from part to whole would let errors accumulate and grow.

   Example: a main triangulation or main traverse is made first, then chain lines and offsets locate the details inside each triangle.

2. Location of a point by at least two measurements from fixed reference points. A new point is fixed relative to two known points by two distances (linear intersection), two angles (angular intersection), a distance and an angle, or a perpendicular offset and a chainage. A third measurement is taken as a check.

   Example: Point C is fixed from A and B by measuring distances AC and BC; the check is the distance from C to a point on AB.

Other working rules follow from these: take every measurement twice or by a different method (as a check), and keep the accuracy of the work consistent with the purpose of the map.

 Point C fixed from A and B
        C
       /|\ 
    b / | \ a      by distances a and b
     /  |  \ 
    A---+---B      check: tie distance