A disclosed method reduces a wave drag on an airfoil traveling at a speed. At least a portion of the airfoil is configured to be selectively moveable between a first position and a second position. The first position is a neutral position, and the second position generates a shock wave near to the leading edge of the airfoil. The method includes the steps of maintaining the airfoil in the first position when the speed is less than a first limit and moving the airfoil to the second position when the speed is greater than a first limit.

An airfoil body may include a plurality of tubercles along a leading edge of the airfoil body and a plurality of crenulations along a trailing edge of the airfoil body, wherein at least one of a position, a size, and a shape of the plurality of tubercles and the plurality of crenulations varies in a non-periodic fashion. The non-periodic fashion may be according to a Fibonacci function and may mimic the configuration of a pectoral fin of a humpback whale. The tubercles and crenulations may be defined with respect to a pivot point. The spanwise profile, including the max chord trailing edge curvature, may closely follow divine spirals and related Fibonacci proportions. The spanwise chord thickness may vary in a nonlinear pattern. Related methods are also described.

Morphable active corrugate structure and aeronautical wings are provided herein including one or more skins or envelopes, and a sheet having independently actuable hinge domains attached to the one or more skins or envelopes and independently actuable facet domains, each of the hinge domains and facet domains configured with through-thickness differential expansion coefficients, wherein differential strains in at least one of the hinge domains or the facet domains cause the sheet to expand or contract along a flexible axis of the sheet, wherein the sheet is attached to the upper and lower skins at respective upper and lower of the hinge domains.