Scale effects on the stresses and safety factors in the wing bones of birds and bats.

The effects of scale on the estimated stresses and safety factors in the humeri of several bird and bat species were investigated. This was accomplished by estimating the lift distribution across the wings at two extremes of flight, gliding flight and the downstroke in hovering, finding the center of lift on the wings at these two extremes and calculating the applied bending and twisting moments. This information, along with measurements of mechanically important morphological variables, allowed for estimates of bending and shearing stresses in the humeri for both gliding flight and on the downstroke in hovering. The stresses in flapping flight other than hovering should fall somewhere between these two values. It was found that the stresses in the humeri are not scale-dependent and that the bending stresses are slightly lower than those found in the limbs of terrestrial animals, while the shearing stresses are larger than those in terrestrial limbs. The breaking stress of bird and bat wing bone was also investigated. Both materials were found to have a lower breaking stress than that of typical long bone material. The ratio between the breaking stress of the material and the estimated stresses was defined as the safety factor. Bird humeri have safety factors that are generally greater than those of bat humeri. This is because bat bone has a lower breaking stress than does bird bone, although the estimated stresses in the wings are similar. The mean safety factor against failure due to bending in gliding flight was 6.63 for birds and 3.99 for bats. In hovering, the mean safety factors against failure due to bending were 2.22 for birds and 1.41 for bats. The safety factors against failure due to shearing stresses were estimated to be seven times greater than those against failure due to pure bending stresses.