Wing flapping with minimum energy

The interesting article by Archer, Sapuppo and Betteridge leads to the problem of determining the optimum lift distribution along the wing during flapping motion. Adopting the assumptions made in Ref. 1, the problem may be reduced to one of minimising the induced drag for a specified, periodically varying, bending moment at the wing root. The wing-root bending moment should be of primary importance to a bird or, for that matter, to a mechanical flapping-machine, since it is at this point that most of the flapping energy is introduced.