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

[Dominic-Luc Webb molmed <Dominic.Luc-Webb@molmed.ki.se>]

On Thu, 31 Aug 2000, Peter D. Brooks wrote:

> 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


Well, yes, I fully agreed that the difference is 
small. I was nitpicking a small difference at 
the 4th and 5th decimal points. Neale Howard 
explicitly states that the r^2/2R equation will 
not suffice in more extreme focal ratios. I 
then questioned the use of an equation that 
Howard claims does not work for all spheres 
while the exact equation, which he says will 
work in all cases is also very simple...

S = R - (R^2 - r^2)^0.5

If the shorter equation is for a parabola, 
why does Howard claim it will not work to use 
that equation for all focal ratios whilst an 
equation for a sphere will? 


Cheers,


Dominic

North 59 37' 30"
East  17 48' 10"