Surveying is broadly classified as Plane and Geodetic Surveying depending upon the extent of the area covered.
The shape of the Earth is not exactly a spheroid; instead, it is an Oblate Spheroid with a major axis of 12,756,750 meters in length and a minor axis of 12,713,800 meters. The difference between these two axes is 42.95 Km.
If we take three points such as P,Q and R as shown in figure 2, we can connect these points in two ways :
Blue Triangle PQR – It shows that we have connected points P,Q, and R by lines running along the surface of the Earth.
Green Triangle PQR – It shows that we have connected these points directly without considering the curvature of the Earth.
figure 2: Showing points P,Q and R on the Earth’s Surface
So, what is the difference between the Blue and Green triangle ?
The Blue triangle is called a Spherical Triangle whereas the Green triangle is called as Plane Triangle. When the area is small, the difference between the area covered by the Plane and Spherical Triangle is negligible but as the area increases, this difference increases. Therefore for larger areas, it is not suitable to ignore the curvature of the Earth.
The surveying in which Earth’s curvature is not taken into consideration is called Plane Surveying. In this, the area is generally less than 250 sqkm, the impact of curvature is negligible hence the error due to curvature can be safely neglected.
Surveying in which Earth’s curvature is taken into consideration is called Geodetic Surveying. In this, the area surveyed is greater than 250 sqkm and the impact of curvature is high.
What are the impacts of Earth’s curvature on observations ?
If the distance between two points, say P and Q, is 12 Km along the surface of the Earth (blue line), then the difference between the distance along the surface of the Earth and along the chord PQ (green line) is 1 cm.
In figure 2, the difference between the sum of all angles of spherical and plane triangle is 1 second.