The Biomechanics of Flight

John Merck

General Aerodynamics

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: But also

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 and give every flyer wings like a high-performance sailplane? 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 yet another tradeoff, this time between induced drag and mechanical shear forces on the wing.

Synopsis of the major trade-offs:


Flying squirrel from From the Depths
Parachuting and gliding: Creatures like gliding frogs, snakes, squirrels, etc. store potential energy as they climb to their launch sites, then exchange it for the kinetic energy for propulsion. Once they take off, they can use only the stored energy of gravity.

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 transported over units of distance.

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

This means that:

Diversity of powered fliers:

In the history of animals, only four groups have effectively slipped the surly bonds of Earth:
Lift enhancement: Depending on the construction of the wing, powered flyers are able to enhance life by several methods:

Reduction of induced drag: Depending on trade-offs with other demands of flight, fliers use a range of strategies.

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.

Selective pressure to develop maximum flight thrust is such that 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 allometricallys. 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:

Anything bigger must cheat.

Adaptations to specialized flight strategies:

Northern mockingbird from Surveymonkey

Slow flight and maneuverability:

Typical of birds and bats that maneuver through branches and other obstacles and have no pressing need for speed (passerines and vespertilionids). Characteristics:

High-speed flight:

Typical of:


Soaring: Many larger bodied birds get around the size limitations of the scaling of muscle mass by exploiting rising air masses in which they can glide (with a glide angle greater than zero) while still rising relative to the ground. To soar in a straight path, the optimum form is a low-load high aspect ratio wing, however many soarers are not like this. This disparity is because there are three distinct ways to soar:


Confusciusornis sanctus from Wikipedia

Item 1: Confusciusornis sanctus

Rhamphorhynchus muenster by Ronald Day from Flickr

Item 2: Rhamphorhynchus muensteri

Archaeopteryx lithographica from David Hone's Archosaur Musings

Item 3: Archaeopteryx lithographica

Pteranodon longiceps from Wikimedia

Item 4: Pteranodon longiceps