The biomechanics of flight

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General Aerodynamics

Aerial gliders and flyers, like swimmers, move through a viscous medium and have do deal with the effects of frictional drag expressed by the Reynolds Number. Because air is significantly less dense than water, however, frictional drag is less of a constraint. Almost all flyers are propelled by appendages, and so are analogous to subaqueous flyers. Thus, the major forces constraining them are lift and drag.

The airfoil:

When a fluid moves without turbulence over upper and lower surfaces of a curved airfoil at different speeds, a region of relatively low pressure on the upper surface is created. As a result of this movement, the airfoil experiences two forces:

Modifying lift: In any flying machine, lift can be increased by increasing:

Problems with increasing lift:

Modifying drag: In any flying machine, drag can be diminished by:

Problems with aspect ratio: If we can reduce drag by increasing wing span without sacrificing wing area or increasing wing loading, why not just go for it? Alas, this, too, involves tradeoffs:

The easiest way to limit these forces is to limit wingspan. Thus, a flying machine (be it metal or meat) makes a tradeoff between drag and mechanical shear forces on the wing.

Scaling issues: It goes without saying that in isometrically scaling fliers, wing area (and, therefore, lift) scales up as a square function while mass scales as a cube. Thus, we typically see wings and wing muscles scaling with positive allometry in nature. The critical point is reached when the body can't physically support the wings or the shearing loads that they must bear.

Synopsis of the major trade-offs:

Aerodynamic strategies: So far we have considered only the general issues facing hypothetical "flying machines." What are the actual strategies employed by aerodynamic animals, and who employs them?

Parachuting and Gliding: The use of drag and/or lift in arboreal creatures to arrest and control their falls. Used to:

Parachuting: When the glide angle (angle downward from the horizontal) exceeds 45 degrees. Typically, parachuters are making significant use of drag to reduce the speed of a fall. Parachuters usually induce drag with a thin membrane, the patagium (pl. "patagia"). Employed by:

Parachuting: When the glide angle is less than 45 degrees, then lift is a significant component. The typical glider has a significantly expanded patagium that may be supported on expandable ribs, between fore and hind limbs, or on other similar structures. Wingspan and camber can be varied by repositioning of structures supporting the patagium. Typically, a trailing tail provides stability. Employed by a wide range of living an fossil vertebrates:

In the fossil record we find the remains of vertebrates with probable gliding adaptations. NOTE: all are small, with snout-vent lengths less than 10 cm.:

Powered flight: The ability to move through still air in a level path (i.e. with a glide angle of zero).

Parachuting and gliding impose only the energy cost needed to climb up a tree. Gravity supplies the necessary energy while in flight. Powered flight is different. In terms of energy required per unit time, powered flight is the most expensive mode of locomotion. Why bother? Because it is fabulously efficient means of transport when measured as units of mass over units of distance.

Requirements: Fundamentally, unlike in gliders, the wing must provide both lift and propulsion.

This means that:

In the history of animals, only four groups have evolved powered flight:

Lift enhancement: Depending on the construction of the wing, powered flyers are able to enhance life by several methods:

Scaling issues: Selective pressure to develop maximum flight thrust is such tat in most birds, the major flight muscles already occupy a maximum proportion of overall body mass, regardless of size. Thus, they cannot be scaled up allometrically. This places a limit on the overall size of an exclusively powered flyer of roughly 12 kg. - roughly the size of the largest powered flyers such as white pelican, kori bustard, mute swan.

Adaptations to specialized flight strategies:

Examples of ancient flyers:


A gull-sized pterosaur from the Late Jurassic, fossilized in lagoonal depsits. What modes of flight was it constrained to? (Reconstruction)


A large (5 m wingspan) pterosaur from the Middle Cretaceous, fossilized in shallow marine depsits. What modes of flight was it constrained to?



A large (1 m wingspan) dragonfly-like insect from the Mississippian of Britain, fossilized in shallow marine depsits. Was it able to exploit leading edge vortices and wake capture in the manner of a modern insect?

Evolutionary origins of flight:

It's easy to see how animals falling out of trees would experience selective pressure to arrest, then control their falls, eventually becoming proper gliders. It is very hard to see why a competent glider should start flapping its patagia for powered flight. Indeed, the origins of flight in pterosaurs and bats is enigmatic, however we do know something about insects and birds. That latter will be addressed in a later lecture, so for now, insects: