Re: [ATM] Stripping to re-figure?

["Jeff Baldwin" <bald@centurytel.net>]

I used the disk method of revolution about an axis from integral calculus, 
I'm pretty sure this is correct.  If the radius of the mirror is r and the 
radius of curvature is R, then the volume ought to be V = pi*r^4/(4R).  The 
larger the mirror or the faster the mirror, the further it will differ from 
a sphere's sagitta's volume, but for most small mirrors it ought to be 
fairly close.  For a sphere I am using the same method and the formula I get 
is V = pi[r^4/(4R)-r^6/(24R^3)].  For an 8" f/6 I am getting a volume of 
2.094393 in^3 using the parabolid formula, and 2.093787 in^3 using the 
spheroid formula, really close.  For a 24" f/4 I am getting a volume of 
84.82293 in^3 using the paraboid formula and 84.76771 in^3 using the 
spheroid formula.  So even with a fairly large fast mirror, the formulae are 
close enough to each other to be useful.  Fun to check these out!
JBald

Jeff and Glenda Baldwin
Beaver WA
http://home.centurytel.net/bald


>I found something slightly different at
> http://mathforum.org/dr.math/faq/formulas/faq.sphere.html,
> being to lazy to derive the formula myself.
>
>  Spherical Cap = The portion of a sphere cut off by a
> plane.
>     Radius of sphere: r
>     Radius of base: r1
>     Height: h
>     Surface area: S
>     Volume: V
>
>          r = (h^2+r1^2)/(2h)
>          S = 2*Pi*r*h
>          V = (Pi/6)*(3*r1^2+h^2)*h
>
> --- Jeff Baldwin <bald@centurytel.net> wrote:
>
>> You can calculate the sagitta volume of the mirror,
>> V=pi*r^4/(4R),  whee r
>> is the radius of the mirror, R is the ROC of the
>> center zone, and determine
>> how much to pour onto the mirror, let it sit
>> overnight, then dispose of it
>> properly.  The stuff works great and no rubbing is
>> required.
>> JBald
>>
>> Jeff and Glenda Baldwin
>> Beaver WA
>> http://home.centurytel.net/bald
>>
>
> Guy  Brandenburg
> Washington, DC
> My home page:
> http://home.earthlink.net/~gfbranden/GFB_Home_Page.html
> 

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