Re: ATM 21" F/6: response about sagitta equations

["Peter D. Brooks" <pdbrooks@pacbell.net>]

Dominic-Luc Webb molmed wrote:
> to be correct:
> 
> S = R - (R^2-r^2)^0.5   eq (1)
> 
> Richard Schwarz claimed that:
> 
> S = r^2 / 2*R    eq (2)
> 
> is exact, but for a parabola. On page 15, Neale
> Howard claims that this same equation is an
> approximation for a circle, and not a parabola.

Both true.  I took up Richard's challenge, (was going to anyway) and the
difference in saggita between a sphere and a parabola is:

DeltaS = sqrt(abs(r^2 - (r^4/4R^2)))

Where R >> r, the difference is vanishingly small.

Pete