Kirkpatrick S J
Department of Biology, University of Miami, Coral Gables, FL 33124.
J Exp Biol. 1994 May;190:195-215. doi: 10.1242/jeb.190.1.195.
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.
研究了体型大小对几种鸟类和蝙蝠肱骨估计应力及安全系数的影响。通过估计在两种极端飞行状态下（滑翔飞行和悬停时的下拍）翅膀上的升力分布，找到这两种极端状态下翅膀上的升力中心，并计算施加的弯曲和扭转力矩来实现这一研究。这些信息，连同对机械上重要的形态变量的测量，使得能够估计滑翔飞行和悬停时下拍时肱骨的弯曲和剪切应力。除悬停外的扑翼飞行中的应力应介于这两个值之间。研究发现，肱骨中的应力与体型大小无关，弯曲应力略低于陆生动物肢体中的应力，而剪切应力则大于陆生肢体中的应力。还研究了鸟类和蝙蝠翼骨的断裂应力。发现这两种材料的断裂应力均低于典型长骨材料的断裂应力。材料的断裂应力与估计应力之比被定义为安全系数。鸟类肱骨的安全系数通常大于蝙蝠肱骨的安全系数。这是因为尽管翅膀中的估计应力相似，但蝙蝠骨骼的断裂应力低于鸟类骨骼。鸟类在滑翔飞行中因弯曲而失效的平均安全系数为6.63，蝙蝠为3.99。在悬停时，鸟类因弯曲而失效的平均安全系数为2.22，蝙蝠为1.41。因剪切应力而失效的安全系数估计比因纯弯曲应力而失效的安全系数大七倍。
