メッシュ式宇宙リフレクタの表面精度の検討 長方形膜要素の鏡面誤差

Abstract

The root-mean square (rms) surface error of a rectangular mesh (membrane) elememt subjected to isotropic tension in a faceted reflector surface is analyzed. The rectangular membrane element is assumed to be placed on any place of the reflector surface with an arbitrary angle between the side of the membrane and the direction of the principal curvature of the ideal reflector surface. The boundaries of the membrane are assumed to coincide with elliptic or hyperbolic paraboloidal surfaces. The deflection of the membrane is calculated based on a linear membrane equation. According to the constraints of parameters which determine the boundary deflections of the membrane element, different kinds of rms error optimizations are carried out and corresponding optimum membranes are obtained and compared. Effects of parameters, such as aspect ratio, boundary deflection, size, etc., upon the surface error of each optimum membrane are examined. The optimum membrane, which has minimum surface error among other optimum membranes, is found to give substantially lower errors than those of the best fit flat membrane. Comparison of the rms error of a rectangular membrane element with those of a circular and triangular membrane element of the same area is also made.