Engineering Rock Mechanics

432 Appendix 6: Hemispherical projection

plane that passes through the origin (i.e. the centre of the sphere), assuming
the point of projection is the North Pole of the sphere:

North Pole

/' \ plane

/\ : oniu norizontal

E

hemisphere vector

All points on the lower hemisphere can be projected in this way. This type

of projection is called equal angle projection and is used exclusively in rock

mechanics for engineering.

Equal angle projection of a plane: great circles

We regularly use planes in rock mechanics analyses and so it is important

to determine the projection of such features.

The mathematics of the projection are tedious, but the result is simple:

a circular arc is developed.

Plane of projection

......... 0

Inclined plane '...

passing through

origin of

SP'

projection of plane, called a great circle

Generation of small circles

If, instead of the plane itself, we consider a single vector on the plane, we

see that this vector traces a circular path on the surface of the hemisphere

as the inclination of the plane changes. The projection of this trace is

called a small circle.