Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 203

Fig. 5.22 Orthographic
projection of the arc
element on a parallel

Fig. 5.23 Traversing the
geodesic

normals to the surface at each point do not intersect, and normal section planes do
not coincide. Thus, lateral bending of geodesics arises, which is represented by the
torsion at each point (see Fig. 5.24 ). Therefore, the geodesics on the ellipsoid are
curves with both curvature and torsion except for the meridian and equator.
If an elastic band is stretched between two points on an absolutely smooth
ellipsoid, then this tightly stretched rubber band is the geodesic between two points.
The direction of the compressive stress exerted by the rubber band on the ellipsoid
at each point is the principal normal to the curve. The direction of the anchorage
force provided by the ellipsoid at this point is the normal to the surface. When the
rubber band goes slack, the principal normal to the curve coincides with the normal
to the surface. Therefore, due to the existence of elasticity, the rubber band will
always represent the shortest path between two points.

The Geodesic Lies Between Two Reciprocal Normal Sections

In general, on the surface of the ellipsoid, the geodesic lies between two reciprocal
normal sections and is close to the direct normal section. In addition, it divides the
angle between the reciprocal normal sections at a ratio of approximately 2 to
1, i.e. can range from 0.001 00

to 0.002 00 in first-order triangulation when S is around 35 km. Corrections need to be

ʼ : ʳ ﾼ 2 : 1, as shown in Fig. 5.25 . The value of ʳ