The effects of scale on the structural design of bird and bat wings

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)



First Committee Member

Colin J. Pennycuick - Committee Chair


The effects of size on the structural design of the wings of both birds and bats were investigated. The scaling patterns of mechanically important morphological parameters, the mechanical properties of bird and bat wing bone and feather keratin, and the scaling patterns of bending and twisting moments both in gliding flight and on the downstroke in hovering were examined.Geometric similarity prevailed in the scaling patterns of the morphological parameters (body mass, wing span, wing area, wing second moment of area about the shoulder joint, wing moment of inertia about the shoulder joint, second and polar moments of area of cross-sections of wing bones and flight feathers). No morphological parameter scaled exactly as predicted by geometric similarity, however. This was found to be important in maintaining a relatively constant stress level in the humeri of the birds and bats of different size during flight.Both bird and bat bone proved to be less strong and less stiff than typical mammalian bone, with breaking stresses of 1.2 $\times$ 10$\sp8$ Nm$\sp{-2}$ and 7.5 $\times$ 10$\sp7$ Nm$\sp{-2}$, respectively, and maximum stiffnesses of around 9.5 GNm$\sp{-2}$ and 13.1 GNm$\sp{-2}$, respectively. Feather keratin had a mean ultimate stress of 0.134 GNm$\sp{-2}$. The stiffness of bird bone and feather keratin both exhibited a marked dependence on strain rate. Density measurements suggest that both bird and bat wing bone have low calcium contents, which is consistent with the mechanical properties found.The bending and twisting moments scaled approximately geometrically, but not exactly so. The combined difference from geometric scaling in both the morphological parameters and in the applied moments, keeps the stresses in the wing bones relatively constant through the size range investigated. Both birds and bats were found to have adequate safety factors against failure due to bending in gliding (approx. 5.3) and also against failure in hovering flight (1.7). The stress analysis indicated that, while shearing stresses are important, the wings are more likely to fail due to bending stresses.


Biology, Anatomy; Biology, Zoology

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