The earth is curved, but a drawing sheet is flat. Every survey has to deal with that mismatch, and there are only two honest ways to do it — ignore the curvature because the area is small enough, or account for it because it is not.
That choice is exactly what separates plane surveying from geodetic surveying. This post covers both, the numbers that decide between them, and why the distinction matters.
The Two Divisions
Surveying is divided primarily into Geodetic surveying and Plane surveying.
| Geodetic Surveying | Plane Surveying | |
|---|---|---|
| Area involved | Large areas of the earth’s surface | Relatively small areas |
| Curvature of earth | Taken into account | Ignored — earth assumed flat |
| Trigonometry used | Spherical trigonometry | Plane trigonometry |
| Carried out by | Department of National Survey of India | Engineers on individual projects |
Plane Surveying in Detail
- Relatively small areas are under consideration, and it is assumed that the earth’s surface is flat.
- Measurements plotted will represent the projection on the horizontal plane of the actual field measurements.
What “Projection” Means Here
This is the key idea, and it is easily read past.
Suppose you measure along the ground from A to B. The earth’s surface between them curves, so the true distance follows an arc. But when that measurement is plotted on a flat sheet, it appears as a chord — the straight line between the two points.
For example, AB is plotted as AB’. If the actual area on the curved surface is ABC, the projected area becomes A’B’C’.
The arc AC is projected as the chord A’C’.
Every plane survey therefore contains this small, unavoidable distortion. The question is simply whether it is large enough to matter.
How Big Is the Error? The Key Numbers
If arc AB = 18.5 km, then chord A’B’ will be 1.52 cm shorter than arc AB.
Take a moment to appreciate that number, because it explains the entire justification for plane surveying.
Over a distance of 18.5 kilometres, the difference between the curved surface distance and the straight chord is just 1.52 centimetres. That is about the width of a thumb, across a distance you would drive in twenty minutes.
As a proportion, 1.52 cm in 18.5 km is roughly one part in a million — far smaller than the errors that ordinary survey instruments and field conditions introduce anyway. There is no point correcting for curvature when your tape and your theodolite are less accurate than the correction.
The Area Limit
For surveys up to 195.5 km2 in area, this discrepancy is not serious, and therefore plane surveying will be adequate.
This figure — 195.5 square kilometres — is the single most asked number in this topic. It is the practical boundary between the two branches of surveying.
To picture it, 195.5 km2 is roughly a square of side 14 km. Almost every engineering project ever undertaken falls comfortably inside that, which is why almost all practical surveying is plane surveying.
The Precaution
However, precautions are required when connecting such a survey to control points established and coordinated by geodetic surveys.
This warning matters. A plane survey is internally consistent — its own measurements agree with one another. But the moment you tie it into the national geodetic framework, the two systems are using different assumptions about the shape of the earth, and the mismatch has to be handled properly.
Where Each Type Is Used
Plane Surveys
Plane surveys are done for engineering projects such as:
- Factories
- Bridges
- Dams
- Location and construction of canals
- Highways
- Railways
Geodetic Surveys
Geodetic surveying is done for fixing widely spaced control points, which may afterwards be used as necessary control points for fixing minor control points for plane survey.
Geodetic survey is carried out by the Department of National Survey of India.
The Relationship Between Them
Read those two descriptions together and the structure of Indian surveying becomes clear.
Geodetic surveying builds the national skeleton — a network of widely spaced, highly accurate control points covering the whole country, with curvature properly accounted for. Individual engineers do not do this work; the Survey of India does.
Plane surveying then hangs off that skeleton. An engineer surveying a dam site starts from a nearby geodetic control point, and works locally on the flat-earth assumption. The national framework supplies accuracy at large scale; plane surveying supplies detail at small scale.
This is exactly the principle of working from whole to part, applied at national level.
Control Points
Control points are points of known coordinates. They are used as a reference for taking other measurements during surveying.
Every survey needs something to measure from. Control points are that reference — positions already established to a known accuracy, from which all subsequent work is built up.
Lengths in the Two Systems
| Survey Type | Lengths Determined | Using |
|---|---|---|
| Geodetic | AB, BC, CA — the true curved lengths | Spherical trigonometry |
| Plane | A’B’, B’C’, C’A’ — the projected chord lengths | Plane trigonometry |
The mathematics differs because the surface differs. On a sphere, the angles of a triangle sum to more than 180 degrees; on a plane, exactly 180. Spherical trigonometry handles the first case, plane trigonometry the second.
Quick Revision Notes
- Surveying divides primarily into geodetic and plane surveying.
- Geodetic: large areas, curvature taken into account, uses spherical trigonometry.
- Plane: small areas, earth assumed flat, uses plane trigonometry.
- In plane surveying, measurements plotted are the projection on the horizontal plane of the actual field measurements — an arc is plotted as a chord.
- Arc of 18.5 km gives a chord 1.52 cm shorter.
- Plane surveying is adequate for areas up to 195.5 km2.
- Precautions are needed when connecting a plane survey to geodetic control points.
- Plane surveys serve factories, bridges, dams, canals, highways and railways.
- Geodetic surveying fixes widely spaced control points used later for minor control points in plane surveys.
- Geodetic survey in India is carried out by the Department of National Survey of India.
- Control points are points of known coordinates used as a reference.
Mistakes Students Commonly Make
- Misquoting the area limit. It is 195.5 km2, not 195 or 200.
- Swapping the trigonometries. Geodetic uses spherical; plane uses plane trigonometry.
- Saying the chord is longer than the arc. A chord is always the shorter straight-line distance.
- Confusing the two numbers — 18.5 km is the arc length and 1.52 cm is the discrepancy.
- Assuming geodetic surveying is done by project engineers. It is carried out by the Department of National Survey of India.
- Forgetting the precaution about connecting plane surveys to geodetic control points.
- Thinking plane surveying is simply careless. It is a justified simplification whose error is smaller than instrument accuracy over the permitted area.
Conclusion
Plane and geodetic surveying differ on one question — does the curvature of the earth matter here? Below about 195.5 km2 it does not, because an 18.5 km arc differs from its chord by only 1.52 cm, which is less than ordinary survey error. Above that, curvature must be handled with spherical trigonometry, and that work belongs to the Survey of India. The two are not rivals but partners: geodetic surveying builds the national framework of control points, and plane surveying fills in the detail within it.
Frequently Asked Questions
What is geodetic surveying?
Surveying in which large areas of the earth’s surface are involved and the curvature of the earth is taken into account.
What is plane surveying?
Surveying in which relatively small areas are considered and the earth’s surface is assumed to be flat.
Up to what area is plane surveying adequate?
Up to 195.5 square kilometres, beyond which the discrepancy caused by curvature becomes serious.
What is the discrepancy over an 18.5 km arc?
The chord will be 1.52 cm shorter than the arc.
Why is that discrepancy acceptable?
Because 1.52 cm over 18.5 km is roughly one part in a million, which is smaller than the errors ordinary survey instruments and field conditions introduce in any case.
What trigonometry is used in each type?
Spherical trigonometry in geodetic surveying, and plane trigonometry in plane surveying.
Who carries out geodetic survey in India?
The Department of National Survey of India.
What is the purpose of geodetic surveying?
To fix widely spaced control points, which are then used to establish the minor control points needed for plane surveys.
What are control points?
Points of known coordinates, used as a reference for taking other measurements during surveying.
What precaution applies when connecting a plane survey to geodetic work?
Care is required when connecting a plane survey to control points established and coordinated by geodetic surveys, because the two are based on different assumptions about the earth’s shape.