On 14 Dec 2004 09:52:31 -0800, "Robert Clark"
wrote:

I'm a little confused by what you quoted above. That was only used to
say if you have 30m by 30m mirror (taken square for simplicity.) Then
this could be made up of 900 segments each 1 meter wide.
I assume you were actually referring to this earlier passage:

"We can also see from the formula that if a mirror is scaled up by a
constant factor k in radius and thickness, then the deflection is
changed by a factor of k^2. Then since .2664^2 =.071, we can get the
same level of stability from a diamond mirror as a Zerodur one that is
.2664 times as big. So a diamond mirror 8*.2664 = 30 meters wide would
have comparable stability against deformation to a current Zerodur
mirror 8 meters wide."

Several references give the deflection amount according to the
material and size. Here's one:

Mirror Structural Design.
http://astron.berkeley.edu/~jrg/Mirr...ure/node1.html

It shows the deflection is proportional to (diameter)^4/(thickness)^2.
So if the dimensions are increased uniformly by a factor k, the
deflection goes up by k^2. By replacing low expansion glass by diamond
you want to see how much you can increase the size when taking into
account diamonds greater strength ratios so that you don't incur
greater deformation. You therefore take the square-root of the increase
in material strength to see by what factor you can uniformly scale up
the size of the mirror.



Bob Clark

According to Marks' Handbook, the deflection of a circular plate of
stiffness Y supported at the edge and subject to a uniform pressure P
is
Defl = (r^2/t^2)*P/Y
But the gravity pressure goes up as the weight, g* rho*(area*t)/area =
rho*t
so Defl = (r^2/t^2)*rho*t/Y = (rho/Y)*(r^2/t)
From this if you double the radius the stiffness must go up by 4 and
you have to take into account the density rho of the material. Y/rho
is a sort of specific stiffness, being c^2 for a particular material
(m/l).

But you don't have to have the same deflection, you could allow
yourself a double deflection for doubling the radius, since
%error = defl/radius.
John Polasek

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