Folks, I don't know how to post a message to Ac44ck so I'll post it here.
The radius needs to be included in the equation:
1) In the central Angle equation, the chord has units of length which is divided by a scalar "2" causing one to attempt to take the arcsin of a length. By adding the radius back in the equation the length units cancel and one can then take the arcsin of a dimensionless number.
2) The next equation on Great Circle Distance includes the radius. From a standpoint of parallel development, shouldn't this radius be set to one and dropped out of the equation as well? It doesn't seem correct to me to do so; the equations become degenerate and useless since the distance now becomes equal to the great circle angle.
- 1) Agreed, a radius is need in the central angle equation. That radius is '1' because the delta values were calculated for a unit sphere.
- 2) When the chord length for the unit sphere is scaled to a distance on the surface of the Earth, the Earth radius is needed and used.
- If more discussion is needed, please use the talk page for the article. - Ac44ck (talk) 06:07, 18 February 2013 (UTC)