Derivation of surface shape for inflatable large aperture antennas

Large deployable aperture inflatable antennas are an emerging technology that is being investigated for potential use in science and exploration missions. In particular, for missions to Mars and beyond, large deployable aperture antennas can provide the antenna gain required for high data rate communications, where the necessary antenna diameter exceeds the available volume of typical launch vehicle platforms. Previous efforts have found that inflatable large aperture antennas do not follow a parabolic shape, and so the nominal Ruze equation is not applicable due to the macroscopic shape errors that exist in this type of technology. Therefore, geometric evaluations of the surface profile cannot simply correlate root‐mean‐square shape error with a parabolic surface to antenna gain degradation. Consequently, the focus of this work is to derive an accurate mathematical model of an inflatable large aperture antenna so that its performance can be characterized. That derivation activity is described in this paper through the calculus of variations methodology, augmented with experimental test data obtained with a laser radar system to validate the surface profile model predicted.