WALKER, J.A.: Swimming in air, flying under water: Physical constraints on the design of oscillating wings, fins, legs, and feet at intermediate Reynolds numbers

Why do some animals swim by rowing appendages back and forth while others fly by flapping them up and down? One answer lies in the sharply divergent physical environments encountered by small, slow animals, and large, fast animals. Flapping appendages allow large animals to move through a fluid environment quickly and efficiently. As size and speed decrease, however, viscous drag dominates the force balance. Consequently, the geometry of appendage motion allows a rowing, but not flapping, appendage to exploit large skin-friction drag for thrust generation. I used both a comparative analysis and a mathematical model to address the question “At what scale does a rowing appendage work more efficiently than a flapping appendage?” The comparative analysis suggests that flapping flight is less effective than rowing at Re less than 50 -100. A simple quasi-steady, blade-element model of virtual oscillating appendages has several important results. First, the mechanical efficiency of both rowing and flapping decrease dramatically with scale. Second, at Re 1, rowing appendages are much more efficient than flapping appendages. At Re 10, flapping appendages are more efficient than rowing appendages only if high reduced frequencies are allowed. Third, flapping appendages are much more efficient than rowing appendages at commonly found reduced frequencies when the scale increases to about Re 200. These results suggest at what scale we might find aquatic animals flying under water or aerial animals swimming in air.