The curvature of the earth's surface is taken into account if the extent of survey is more than:
🗺️ Plane vs. Geodetic Surveying: The Core Difference
The fundamental decision in any large survey is whether to treat the Earth as a flat surface or as a sphere. This choice defines the two main branches of surveying.
Plane Surveying: Assumes the Earth is flat. The curvature is ignored. This method is simpler but only accurate for small areas.
Geodetic Surveying: Takes into account the true curved shape of the Earth (a spheroid). All lines are treated as arcs, and calculations involve spherical trigonometry. This is essential for large areas where precision is paramount.
🔍 Why the ~260 km² Threshold?
The limit for plane surveying exists because as the area increases, the error caused by ignoring the Earth's curvature becomes too significant. The value of 260 km² represents a widely accepted point where this error can no longer be ignored for accurate work.
- Below this limit: The difference between a curved arc and a straight line on the Earth's surface is negligible for most practical purposes.
- Above this limit: The discrepancy becomes significant. For example, the sum of angles in a large triangle on the Earth's surface will exceed 180°. This is known as "spherical excess," and it must be accounted for with geodetic methods.
A Note on the Exact Value
While this question uses 260 km², you may see other sources cite 250 km². Both values are correct in context and represent the same principle. Different engineering bodies and textbooks use slightly different standards, but the accepted range is generally 250-260 km².
📊 Quick Comparison Table
| Feature | Plane Surveying | Geodetic Surveying |
|---|---|---|
| Area Limit | Less than 260 km² | Greater than 260 km² |
| Earth's Curvature | Ignored (Treated as flat) | Considered (Treated as a spheroid) |
| Mathematics Used | Plane geometry and trigonometry | Spherical trigonometry |
| Accuracy | Less accurate for large areas | Highly accurate |
| Typical Use | Property lines, building layouts, local roads | Mapping nations, large infrastructure projects |