Engineering Surveying

An alternative consideration is a level surface, at all points normal to the direction of gravity. Such a surface would be formed by the mean position of the oceans, assuming them free from all external forces, such as tides, currents, winds, etc. This surface is called the geoid and is the equipotential surface at mean sea level. The most significant aspect of this surface is that survey instruments are set up relative to it. That is, their vertical axes, which are normal to the plate bubble axes used in the setting-up process, are in the direction of the force of gravity at that point. Indeed, the points surveyed on the physical surface of the Earth are frequently reduced to their equivalent position on the geoid by projection along their gravity vectors. The reduced level or elevation of a point is its height above or below the geoid as measured in the direction of its gravity vector (or plumb line) and is most commonly referred to as its height above or below mean sea level (MSL). However, due to variations in the mass distribution within the Earth, the geoid is also an irregular surface which cannot be used for the mathematical location of position.

EThe mathematically definable shape which best fits the shape of the geoid is an ellipsoid formed by rotating an ellipse about its minor axis. Where this shape is used by a country as the surface for its mapping system, it is termed the reference ellipsoid. Figure 1.1 illustrates the relationship of the above surfaces.

The majority of engineering surveys are carried out in areas of limited extent, in which case the reference surface may be taken as a tangent plane to the geoid and the rules of plane surveying used. In other words, the curvature of the Earth is ignored and all points on the physical surface are orthogonally projected onto a flat plane as illustrated in Figure 1.2. For areas less than 10 km square the assumption of a flat Earth is perfectly acceptable when one considers that in a triangle of approximately 200 km2 , the difference between the sum of the spherical angles and the plane angles would be 1 second of arc, or that the difference in length of an arc of approximately 20 km on the Earth’s surface and its equivalent chord length is a mere 10 mm.