Analytic design methodology for flexible wing parametrization and spanwise load estimation

Presented is an analytic study of aerodynamic loading along a high aspect ratio wing, typical for airliners, under passive aeroelastic deformation. Such a highly non-planar, curved wing is feasible using the latest composite material technology, and is expected to enhance airliners aerodynamic performance at transonic cruise conditions, given it allows lower induced drag, similar to a wingletted wing. Also, gust and manoeuvring loads can be partially alleviated by the structure elasticity, hence the concept is of great interest for the airliner industry. A major problem to designing highly flexible wings is their constantly shifting shape and, as a result, their hardly predictable, non-constant lift force generated. This paper provides an attempt to precisely estimate load distribution along the statically inflected wing at different stages of its deformation, using mathematical parametrization of the curved wing shape to relate its geometry to aerodynamic loading and structural stiffness in a closed form function. This is achieved using the geometric dependency of local angles of attack on local wing curvatures, therefore load distribution is a function of the parametrized deformed wing shape. Spanwise load distributions in turn can be coupled with structural stiffness distributions using cantilever beam theory.