Similarity Criteria and Associated Design Procedures for Scaling Solar Sail Systems

T HE NASA In-Space Propulsion program has promoted the development of solar sail propulsion technology through the development of subsystems, operations tools, analytical and computational models, and ground-based testing. Solar sails can potentially provide low-cost propulsion and operate without the use of propellant, allowing access to non-Keplerian orbits through constant thrust. A solar sail is a gossamer structure: a membranebased large, lightweight structure. The primary objective of the sail is to convert emitted solar pressure into thrust on a spacecraft. This solar pressure is extremely small, however, on the order of 9 N=km at 1 astronomical unit, resulting in a need for the sail to bevery large and lightweight to achieve reasonable accelerations. The solar sail development process consists of a progression through ground-based testing and flight demonstration to yield a system ready to perform a specific science mission. The science missions envisioned will require sails on the order 2000 to 10; 000 m (or larger); sail size will be dictated by the mass and mission scope of the craft, while flight demonstrations and ground testing will be conducted at significantly smaller sizes [1,2]. For this reason, the ability to understand the process of scalability, as it applies to solar sail system models and test data, is crucial to the advancement of this technology. Because of the significant size of solar sails, the search for scalable sail designs or scaling laws that assist in testing and analyzing solar sail structures are fairly common in the literature. For example, scalable solar sail designs have been proposed by researchers, including Murphy [3], Gaspar et al. [4], Murphy and Murphey [5], and Greshik [6]. Here, the term scalable design seems to imply solar sail designs that retain a basic geometric relationship over various sizes, each tested to validate analytical models [3,4], or architectural design based on a set of sail panels sized to meet engineering requirements and numbered to meet the mission requirements [6]. Alternatively, several researchers develop scaling laws that govern the design of solar sails at larger sizes while maintaining similarity; that is, amodel can be built that represents the behavior of a prototype existing at a different scale. For example, Holland et al. [7] observed a set of scaling properties for inflatable structures (boom) based on geometric parameters, while Greschik et al. [8] andZeiders [9] offer scaling laws for dimensional analysis of solar sail structures. One way to perform dimensional analysis is through a process of nondimensionalizing a set of governing equations. None of the preceding contributions appear to use this approach. This Note is intended to provide an illustration of deriving the similarity conditions or criteria based on nondimensionalization of the governing equations for a model of the solar sail system. The similarity criteria will define the requirements needed to achieve similarity between a prototype and model solar sail design. The complete number of similarity criteria will be demonstrated through nondimensionalization of the governing equations for the solar sail system following the method of dimensional analysis as demonstrated for a variety of applications in [10–12]. This model will apply to a four-quadrant sail design as presented in [3,6,9]. The model will account for arbitrarily large sail deflection, sail–boom interaction, and the onset of buckling in the boom. The effects of wrinkling in the sail and nonlinear buckling behavior of the boom are two examples of higher-order effects not considered in this model. The results show a set of four independent similarity criteria that must be satisfied. A procedure is offered to demonstrate the use of these similarity criteria to guide the design of a model for ground testing.