Unifying constructal theory for scale effects in running, swimming and flying
Unifying constructal theory for scale effects in running, swimming and flying
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DOI：
10.1242/jeb.01974
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发表时间：
2006-01-01
影响因子：
2.8
通讯作者：
Marden, JH
中科院分区：
文献类型：
--
作者：
Bejan, A;Marden, JH
生物学家认为，跑步、飞行和游泳之间存在着明显的根本区别，因为运动和动物的形式是如此不同：四肢和翅膀与身体的波动，中性浮力与负重的身体，等等。在这里，我们展示了所有形式的运动都可以用一个单一的物理理论来描述。该理论是对流动系统以破坏最小有用能量(火用、食物)的方式进化的原理的引用。这种优化方法以令人惊讶的直接方式提供了观察到的速度和身体质量(M-b)之间的关系提高到1/6，以及频率(步幅、拍打)和M-b(-1/6)之间的关系，并说明了为什么这些关系适用于跑步、飞行和游泳。动物的运动是一种优化的两步间歇：在有用能量的垂直损失(抬起体重，随后下降)和与周围介质的摩擦导致的水平损失之间实现最佳平衡。该理论预测了动物设计的其他特征：斯特鲁哈尔数常数，该常数适用于跑步、飞行和游泳，动物马达的力输出与质量之间的比例，以及只有当身体雷诺数超过约30时才会发生波动游泳和拍打飞行的事实。这一理论和被称为构造理论的一般工作现在一起表明，动物运动(跑步、飞行、游泳)和流体涡流运动(湍流结构)都是优化的间歇运动形式。
Biologists have treated the view that fundamental differences exist between running, flying and swimming as evident, because the forms of locomotion and the animals are so different: limbs and wings vs body undulations, neutrally buoyant vs weighted bodies, etc. Here we show that all forms of locomotion can be described by a single physics theory. The theory is an invocation of the principle that flow systems evolve in such a way that they destroy minimum useful energy (exergy, food). This optimization approach delivers in surprisingly direct fashion the observed relations between speed and body mass (M-b) raised to 1/6, and between frequency (stride, flapping) and M-b(-1/6), and shows why these relations hold for running, flying and swimming. Animal locomotion is an optimized two-step intermittency: an optimal balance is achieved between the vertical loss of useful energy (lifting the body weight, which later drops), and the horizontal loss caused by friction against the surrounding medium. The theory predicts additional features of animal design: the Strouhal number constant, which holds for running as well as flying and swimming, the proportionality between force output and mass in animal motors, and the fact that undulating swimming and flapping flight occur only if the body Reynolds number exceeds approximately 30. This theory, and the general body of work known as constructal theory, together now show that animal movement (running, flying, swimming) and fluid eddy movement (turbulent structure) are both forms of optimized intermittent movement.