Learn primary divisions of survey plane surveying and geodetic surveying spherical triangle and great circle, earths surface

Primary division of survey

The earth is an oblate spheroid of revolutions, the length of its polar axis (12,713,800 metres) being somewhat less than that of its equatorial axis (12,756,750 metres). Thus, the polar axis is shorter than the equatorial axis by 42.95 kilometres. Relative to the diameter of the earth this is less than 0.34 percent. If we neglect the irregularities of the earth, the surface of the imaginary spheroid is a curved surface, every element of which is normal to the plumb line. The intersection of such a surface with a plane passing through the centre of the earth will form a line continuous around the earth. The portion of such a line is known as ‘level line’ and the circle defined by the intersection is known as ‘great circle’. Thus in Fig. 1.1, the distance between two points P and Q is the length of the arc of the great circle passing through these points and is evidently somewhat more than the chord intercepted by the arc. Consider three points P, Q and R (Fig. 1. 1) and three level lines passing through these points. The surface within the triangle PQR so formed is a curved surface and the lines forming its sides are arcs of great circles. The figure is a spherical triangle. The angles p, q and r of the spherical triangle are somewhat more than corresponding angles p′ q′ and r′ of the plane triangle. If the points are far away, the difference will be considerable. If the points are nearer, the difference will be negligible. As to whether the surveyor must regard the earth’s surface as curved or may regard it is as plane depends upon the character and magnitude of the survey, and upon the precision required.

Primary divisions of survey
Primary divisions of survey, Great circle

Thus, primarily, surveying can be divided into two classes:

Primary divisions of survey

1. Plane Surveying

2. Geodetic Surveying.

Plane surveying

Plane surveying is that type of surveying in which the mean surface of the earth is considered as a plane and the spheroidal shape is neglected. All triangles formed by survey lines are considered as plane triangles. The level line is considered as straight and all plumb lines are considered parallel. In everyday life we are concerned with small portions of earth’s surface and the above assumptions seem to be reasonable in light of the fact that the length of an arc 12 kilometres long lying in the earth’s surface is only 1 cm greater than the subtended chord and further that the difference between the sum of the angles in a plane triangle and the sum of those in a spherical triangle is only one second for a triangle at the earth’s surface having an area of 195 sq. km.

Geodetic surveying

Geodetic surveying is that type of surveying in which the shape of the earth is taken into account. All lines lying in the surface are curved lines and the triangles are spherical triangles. It, therefore, involves spherical trigonometry. All geodetic surveys include work of larger magnitude and high degree of precision. The object of geodetic survey is to determine the precise position on the surface of the earth, of a system of widely distant points which form control stations to which surveys of less precision may be referred.