Scaling the Shape, Motion, and Function of Oscillating Wings, Fins, Legs, and Feet

0119643Jeffrey A. Walker当一个物体（如立方体）被缩小到越来越小的尺寸时，其表面积与体积的比例会成比例地增加。这种比例关系对动物如何在空气和水中移动有很大的影响，因为惯性（质量）和摩擦力分别是体积和面积的函数。比果蝇稍大或稍快的动物（约2毫米长）生活在一个由惯性主导的世界里。在这个世界上，摆动的机翼或鳍片产生旋转的漩涡，这是由于流体在流过时与推进结构“分离”造成的。这些分离产生了异常大的力，对具有刚性机翼的飞机造成了严重破坏（它们是失速的来源），但最近的工作表明，分离和有时涡流可以被具有振荡附件的动物利用。比果蝇稍小或稍慢的动物生活在这样一个世界里，摩擦力是推进结构产生的净力的重要组成部分。摩擦力削弱了涡流，延迟或完全阻止了分离。因此，一个大的摩擦组件，必须对小型游泳和飞行动物的设计产生深远的影响，事实上，小型动物的推进附肢在不同的分类群（节肢动物门，脊索动物门和软体动物门），解剖学（触角，翅膀，鳍，腿，脚），行为（游泳和飞行）和流体介质（空气和水）之间表现出显着的趋同性。目前的建议的目的是调查如何小，振荡的附件产生的力量在空气或水中，如何推进机制的规模（大小和速度）的变化，以及如何最佳设计的附件的规模变化。将在跨越相关大小范围的各种小动物群体中测量爬行形状和运动，包括海蝴蝶（减少或失去外壳的游泳蜗牛），小黄蜂和水甲虫。将在一系列尺寸范围内测量振动板上的力，这些力复制了在小动物的振动附肢中发现的条件。尽管在小尺度下具有振荡附肢的动物游泳或飞行的事实包括所描述的动物物种的大部分，但关于振荡附肢在该范围的低端如何工作以及力产生机制如何随尺寸和速度缩放的知之甚少。拟议的研究将是第一个系统地研究在这个重要的尺寸范围内附属物形状，运动和功能的缩放。

0119643Jeffrey A. WalkerWhen an object, such as a cube, is reduced to smaller and smaller sizes, its surface area to volume ratio increases proportionally. This scaling relationship has large consequences on how animals move through air and water because inertia (mass) and friction are functions of volume and area, respectively. Animals slightly larger or faster than a fruitfly (about 2 mm long) live in a world dominated by inertia. In this world, oscillating wings or fins create swirling vortexes that result from the fluid "separating" from the propulsive structure as it flows by. These separations create unusually large forces that wreak havoc for airplanes with rigid wings (they are the source of stall) but recent work has shown that the separations and sometimes the vortices can be exploited by animals with oscillating appendages. Animals that are slightly smaller or slower than a fruitfly live in a world where friction results in a significant component of the net force generated by a propulsive structure. Friction weakens vortices and delays or entirely stops separation. A large friction component, then, must have profound effects on the design of small swimming and flying animals and, indeed, the propulsive appendages of small animals show remarkable convergence among diverse taxa (the phyla Arthropoda, Chordata, and Mollusca), anatomy (antennae, wings, fins, legs, feet), behaviors (swimming and flying) and fluid media (air and water). The objective of the current proposal is to investigate how small, oscillating appendages generate forces in air or water, how the propulsive mechanisms change with scale (size and speed), and how the optimal design of an appendage changes with scale. Appendage shape and motion will be measured in various groups of small animals that span the relevant size range including the sea butterflies (swimming snails with reduced or lost shells), small wasps, and water beetles. Forces on oscillating plates that replicate the conditions found in oscillating appendages of small animals will be measured across a range of sizes. Despite the fact that animals swimming or flying with oscillating appendages at small scales comprise a large portion of described animal species, little is known about how oscillating appendages work at the low end of this range and how the force generating mechanisms scale with size and speed. The proposed research will be the first to systematically study the scaling of appendage shape, motion, and function in this important size range.