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RE: RE: Geometry Of Evacuated Membranes

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Posted by Tom Leech on October 29, 2000 04:44:23 UTC

hi robert, finally found my way into the log in maze. i would like to make a correction to your entry. you stated that the curve would be a catenoid (catenary) which it would be if the forces acting on the surface were all in the same direction alnog the axis of the drum head. however, as the drum is evacuated, the surface takes a curve, and the atmospheric pressure outside the drum head acts perpendicular to the drumhead surface at each point on the surface. the outside if the drumhead is in effect a very small sector of a very large sphere (baloon) in effect. ie, the evenly distributed forces on the drumhead are no longer parallel to each other, but all point to a common radial center. anyway. the difference between the two (catenary/spherical) only become large for large curvature. the difference between a long focus sphere and a porabola is very tiny also, but what a difference it makes when one is talking in wave lengths of light. this thought that the guy had was important because it has been the genisis of such technology as celestrons correctors for their sct's and the warping harnesses of off axis telescope secondaries, and elastically deflected primary mirrors both during figuring, and the parabolization of spherical mirrors as was recently reported on in s&t. i cant seem to keep my notes short, tom leech

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