ATM 21" F/6: response about sagitta equations

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

I took a look in the Neale Howard "Standard 
Handbook for Telescope Making" this morning 
regarding the sagitta equations we discussed. 
I mentioned a discrepancy in the obtained sagitta 
values and that I would check this up. I used an 
exact equation I personally have derived from 
a circle using classical trigonometry and know 
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. 
Further, in the footnote at the bottom of the 
page, he goes on to say that this equation will 
not suffice for focal ratios above F/5 and that 
eq(1) must be used. Accordingly, I would say 
that my original claim is correct and that eq(2) 
cannot be for a parabola, or, Neale Howard 
may be in error. Perhaps I missed something? 
I tried deriving eq(2) myself and could 
not. Richard, if you are certain this is exact, 
and for a parabola, could I (politely) request 
the derivation?

As for the 21" F/6, Ken Lowther used an equation 
at a web site that yielded S = 0.21875". This 
is exactly what I get if I use eq(2). Eq(1) yielded 
S = 0.21885". These values both yield 0.219" to 
the nearest thousandth of an inch, so to this level 
of precision, both equations work in this particular 
case.



Cheers,


Dominic

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

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Dominic-Luc Webb, doktorand


Lab:
Department of Molecular Medicine
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