M7 Air Locomotion

Topic

Active flight—involving the flapping of wings—is unique among mammals to bats, whose membranous wings (patagia) are extremely deformable compared to the rigid wings of other flying creatures.

The active flight enabled by these wings combines two aerodynamic conditions: the lift generated by the wings must exactly match the bat's weight to maintain level flight (without ascending or descending), and the thrust produced must exactly match air resistance to maintain constant speed.

The total mechanical power a bat must generate to sustain level flight varies with speed: it reaches a minimum at a specific optimal speed and increases both below and above that point, tracing a U-shaped curve. This occurs because the air resistance acting directly on the body and wings increases with the cube of the speed, whereas the additional resistance associated with generating lift decreases as speed rises; at low speeds, this latter type of resistance dominates, while at high speeds, the former dominates.

Bat flight takes place within a specific airflow regime around the wing: a dimensionless number comparing the relative importance of inertial versus viscous air forces falls within the order of magnitude of 10,000 to 100,000—a range where viscous and inertial effects are comparable, with neither clearly dominating the other.

Precisely because their wings are so deformable, bats can actively modulate wing shape during each stroke—a feat impossible for conventional rigid wings. This active modulation allows them to harness vortices that form along the wing's leading edge during each stroke; these vortices provide additional lift but do not form on the rigid wings of other flying creatures. The frequency at which a bat beats its wings also has an optimal value that coincides with the natural resonant frequency of its own musculoskeletal system; flapping near this resonant frequency allows the bat to sustain flight with the least possible active muscular effort.

The patagia mentioned earlier serve a different function in mammals that do not actively flap their wings: in flying squirrels, this same membrane acts as a broad, short wing that enables gliding between trees without any flapping, relying solely on the airflow over the membrane during the descent.

The horizontal distance the animal covers for every meter of descent during a glide is determined by the glide ratio—the quotient of the lift generated by the membrane and the air resistance (drag) it produces while gliding. Flying squirrels achieve glide ratios of between two and five meters of horizontal travel per meter of descent, whereas gliding bats—with their aerodynamically more efficient membranous wings—achieve ratios of between six and ten, covering much more horizontal distance for every meter of altitude lost.

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