MILLER, L.A.*; PESKIN, C.S.; University of Utah; Courant Institue of Mathematical Sciences: Wing flexibility, clap and fling, and flight in the smallest insects

The immersed boundary method was used to model rigid and flexible wings performing an idealized two-dimensional ‘clap and fling’ stroke. We calculated lift coefficients as functions of time for Reynolds numbers ranging from 8 to 128. The results for stiff wings show that the lift generated during constant translation following ‘fling’ is substantially higher than the lift generated during constant translation. This effect becomes greater with decreasing Reynolds number, and could explain why all tiny insects use the ‘clap and fling’ mechanicsm of lift generation. For a Reynolds number of 8, lift coefficients following two-winged fling during the translational phase are about 70% higher than the one-winged case at the beginning of translation. When averaged over the entire translational part of the stroke (not including rotation), lift coefficients in the two-winged case are 35% higher during a 4.5 chord translation following fling. Drag coefficients produced during fling, however, are also substantially higher for the two-winged case than the one-winged case, particularly at lower Reynolds numbers. The results for flexible wings show that lift is also significantly enhanced during pure translation following fling. If the wings are sufficiently flexible, the drag forces produced during fling are much lower than those produced by a rigid wing. If the leading edge of the wing is rigid and the trailing edge is flexible, the lift forces generated during fling are comparable to the rigid case, while the drag forces produced are significantly lower. This result suggests that asymetries in wing stiffness can reduce drag while maintaining lift during clap and fling.