Department of Zoology, University of Washington, Seattle Washington 98195-1800.
Integr Comp Biol. 2002 Nov;42(5):1044-9. doi: 10.1093/icb/42.5.1044.
Flapping flight and swimming in many organisms is accompanied by significant bending of flexible wings and fins. The instantaneous shape of wings and fins has, in turn, a profound effect on the fluid dynamic forces they can generate, with non-monotonic relationships between the pattern of deformation waves passing along the wing and the thrust developed. Many of these deformations arise, in part, from the passive mechanics of oscillating a flexible air- or hydrofoil. At the same time, however, their instantaneous shape may well emerge from details of the fluid loading. This issue-the extent to which there is feedback between the instantaneous wing shape and the fluid dynamic loading-is core to understanding flight control. We ask to what extent surface shape of wings and fins is controlled by structural mechanics versus fluid dynamic loading. To address this issue, we use a combination of computational and analytic methods to explore how bending stresses arising from inertial-elastic mechanisms compare to those stresses that arise from fluid pressure forces. Our analyses suggest that for certain combinations of wing stiffness, wing motions, and fluid density, fluid pressure stresses play a relatively minor role in determining wing shape. Nearly all of these combinations correspond to wings moving in air. The exciting feature provided by this analysis is that, for high Reynolds number motions where linear potential flow equations provide reasonable estimates of lift and thrust, we can finally examine how wing structure affects flight performance. Armed with this approach, we then show how modest levels of passive elasticity can affect thrust for a given level of energy input in the form of an inertial oscillation of a compliant foil.
在许多生物中，扑翼飞行和游泳伴随着柔性翅膀和鳍的显著弯曲。翅膀和鳍的瞬时形状反过来又对它们能够产生的流体动力有深远的影响，翅膀上的变形波的模式与产生的推力之间存在非单调关系。这些变形中有许多部分是由于柔性空气或水翼的被动机械振动引起的。然而，它们的瞬时形状很可能是由流体负载的细节决定的。这个问题——即瞬时机翼形状和流体动力负载之间的反馈程度——是理解飞行控制的核心。我们要问的是，机翼和鳍的表面形状在多大程度上受到结构力学和流体动力负载的控制。为了解决这个问题，我们使用计算和分析方法的组合来探索由惯性弹性机制引起的弯曲应力与由流体压力力引起的应力之间的关系。我们的分析表明，对于某些组合的机翼刚度、机翼运动和流体密度，流体压力应力在确定机翼形状方面的作用相对较小。几乎所有这些组合都对应于在空气中移动的机翼。这个分析提供了一个令人兴奋的特点，即对于线性位流方程可以合理估计升力和推力的高雷诺数运动，我们可以最终研究机翼结构如何影响飞行性能。有了这种方法，我们然后展示了在给定的能量输入水平下（以柔性箔片的惯性摆动的形式），适度的被动弹性如何影响推力。
