1.8M mirror mass


The 1.8M LAT Mirror is estimated to weigh 2420 lbs. ***(+/- 128 lbs.)
Jump to Mark Thein's estimate. (2430 lbs.)


The mass of the glass was determined in the following matter.

(At the moment we are not able to weigh the glass directly.) Therefore.
We need to know the density of the glass and the volume of the glass.
As it turns out. We have some chips that were accidently knocked out from the mirror blank.

** speculum; The part of the glass which is "silvered" the "actual" mirror.
** sagitta; The depth of the speculum. (our mirror the sagitta is 1.6 in.)
***error(s);The most sensitive measurements to total mass error is the thickness. (+/- 1 mm.) The next most sensitive measurement (due to its poor quality) is the volume of the shard; which gives us a density error of +/-0.27. Assuming that all the error (>90%) are in these two measurements, gives a total weight error of +/- 128lbs


Mark Thein did more work.

Rick:

I calculated the volume of the glass by using the Volumes-by-Cylindrical-Shells method of integration.

First I came up with the formula for the cross-section of the glass with the curve as a parabola. The equation of the parabola is Y=X^2/(4*fl)+ T with fl being the focal length in cm and T being the thickness of the glass at the center, which is 17.3cm.

Next I plugged the formula into the volume equation V=the integral from 0 to 90 of 2*pi*X*f(x) with 90 being the edge radius in cm.

The volume equation for the glass is then V=(pi*X^4)/(8*fl)+T*pi*X^2.

After placing 17.3 for T, 519.1125 for fl and 90 for X the volume is 489684 cm^3. Multiply by 2.25 to get grams and you get 1.102194*10^6g or 1102.194Kg or 2430lbs.

This result is close to yours. This volume equation can be used for any parabolic mirror with a flat back.

Mark Thein


Rick Powell rick(AT)group70(DOT)org