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How is an ellipsoid used to represent the shape of the Earth in surveying?

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surveying Figure 1: Photogrammetric photographs from two short, overlapping flight strips arranged for supplying mapping details. Photo-control points are shown on only one photograph; shading indicates a typical terrain feature such as a lake (see text).

In surveying and geodesy, an ellipsoid is used as a simplified mathematical model to represent the Earth's size and shape for geodetic calculations.12

While the geoid—a surface defined by mean sea level and gravity—more accurately represents the Earth's physical shape, it is irregular due to mass distribution and gravity anomalies, making it unsuitable for direct geometric modeling. To overcome this, surveyors use a reference ellipsoid, which is an oblate spheroid generated by rotating an ellipse about its minor axis.231

This geometric figure allows for consistent horizontal control and coordinate systems in large-scale surveys where the Earth's curvature is a significant factor. By defining the Earth as an ellipsoid, surveyors can perform complex calculations more easily than with the irregular geoid. The ellipsoid is specified by two parameters, such as the semimajor axis (equatorial radius) and the flattening, which accounts for the Earth's polar compression of approximately 21 kilometers.312