Pointing error in passively stabilized spacecraft caused by thermal bending

Abstract

An important component of passively stabilized earth orbiting spacecraft is a long thinwalled cylinder that points at all times towards the earth. When the cylinder is exposed to the sun, the side facing the sun heats up more than the far side causing it to bend away from the sun. In general, the differential thermal expansion produces stresses in the material of the boom; however, there is a particular distribution that does not produce stresses. Equations for determining the bending radius are derived for the no-stress and the general cases. Sample calculations are presented; although the results obtained for the two cases do not, in general, differ very much, there are instances for which the discrepancy is significant. Nomenclature a = absorptivity A = area of boom cross section, in.2 d = boom diameter, in. e = external emissivity #i = internal emissivity E = Young's modulus of elasticity, psi / = moment of inertia, in.4 k = thermal conductivity, Btu-ft/hr-ft2-°F K = integer m = number of sides of equilateral polygon M = couple, Ib-in. P — force, Ib R = radius of curvature, in. RL = radius of curvature according to the linearized theory, in. Ri = projection of the distance between center fiber and edge of the z'th element on the axis b-b (Fig. 4), in. <s = boom thickness, in. t = temperature, °F £nax = maximum temperature, °F tmin = minimum temperature, °F At = tmax tmin