Direct Thrust Efficiency for the L’Garde Sail Surface with a Linear Reflectivity Model

Abstract

A measure of propulsive efficacy for the grooved L’Garde solar sail surface — the photonic thrust efficiency in the context of an equivalent smooth (i.e., not grooved) sheet — is numerically assessed for thrust in the surface normal direction, and the dependence of this metric on the illumination incidence angles (in the directions along and across the grooves) is found to have some remarkable counter-intuitive characteristics. The study is based on a simple but powerful reflectivity model which, despite being a straightforward approximation to the full optical formulation, has received little attention in the past. This model, referred to as “linear” thrust model, simplifies analysis at the cost of only a minor loss of detail shown to be insignificant in the context of other common approximations. A result of this simplification is rigorous proof that the L’Garde sail surface groove contour shapes well approximate the classic catenary curve — the hyperbolic cosine function. The insight here offered contributes both to a practical appreciation of photonic thrust models and to the better understanding of some of the thrust characteristics of the L’Garde solar sail.