Kwong, M., Xi, F., and Alighanbari, H., "Stability-Based Motion Planning for a Modular Morphing Wing," SAE Technical Paper 2013-01-2323, 2013, doi:10.4271/2013-01-2323.
Aircraft wing geometry morphing is a technology that has seen recent interest due to demand for aircraft to improve aerodynamic performance for fuel saving. One proposed idea to alter wing geometry is by a modular morphing wing designed through a discretization method and constructed using variable geometry truss mechanisms (VGTM). For each morphing maneuver, there are sixteen possible actuation paths for each VGTM module. This paper proposes a method to find an optimal actuation path from the point of view of the longitudinal static stability.To do so, we locate the aerodynamic center (ac) and the center of gravity (cg) of each VGTM module which is first determined according to its morphed shape. Then, the ac and cg of the entire modular morphing wing can be determined and the stability margin can be computed. The two suggested methods to obtaining the ac for each VGTM module are the integration method and the geometry method. The integration method treats each VGTM module as a full half-wing and applies existing theory for determination of ac for full half-wings, and under similar assumptions, a piece-wise defined equation can be derived where each piece is a VGTM module. The geometry method solves for the location of the ac by determining the location of the mean aerodynamic chord of each VGTM module and further applying airfoil theory. If an assumption is made that the airfoil shape remains constant for all VGTM modules, then a mass axis can be drawn from wing root to wing tip based on the airfoil shape. If the wing has taper, then only airfoil size will change, and a uniform mass distribution will be applied based on the given parameters of each VGTM module and a cg can be determined for the module. The ac and cg of the entire modular morphing wing is determined on the roll axis of the aircraft as a common reference point and longitudinal static stability margin is determined.Ideally, since there are sixteen actuation paths for each VGTM module, a three module morphing wing would have a total of 163 permutations of actuation paths for one morphing maneuver. A search loop is then designed to obtain the static margin of all possible actuation paths where the optimal path will be the one with the most stable static margin. To simplify the analysis, all three modules are assumed to morph in unity during a wing morphing maneuver, and the search loop is designed to obtain the static margins and selecting the actuation path of the most stable static margin for the morphing wing. A case study of a three module morphing wing is provided to demonstrate the actuation path selection process as described above.