## BSCI392 9-26-07 The biomechanics of flight

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:

• Lift: The upward acceleration caused by the pressure differential.
• Drag: The airfoil also experiences posteriorly directed drag. In addition to the form and frictional drag discussed for swimmers, the airfoil experiences significant induced drag, caused by the formation of vortices at wingtips, as air rushes from below into the low-pressure region above the wing. For flying animals and aircraft, the energy used to form these is a significant energy sink.

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

• Camber: the mean "height" of the airfoil perpendicular to its length.
• Angle of attack: the angle between the orientation of the airfoil and its direction of motion.
• Wing area: For flyers of the same weight, greater wing area results in diminished wing loading, the ratio of weight/wing area. This is good because the wings must support the mechanical load of the entire flying machine.

Problems with increasing lift:

• Stalling: Under most circumstances, lift only happens when air flows smoothly across the wing. If the angle of attack becomes too great, the air flow separates from the airfoil, resulting in the turbulent backflow of entrained air forward onto the upper surface. When this happens, lift disappears. The stall speed, the minimum speed at which an object can stay airborn, is inversely proportional to the amount of lift it generates.

• Vortex generation: All other things being equal, however, as lift increases, so does the tendency to create vortices. Thus, flight involves tradeoffs between lift and drag.

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

• Reducing camber
• Reducing angle of attack
• Reducing wing area

But also

• increasing wing span: For a given wing area, a greater wing span results in smaller vortices and reduced induced drag. Of course, for a given wing area and loading, increasing the wing span results in a wing with a higher aspect ratio (recall from our discussion of thunniform caudal fins.)

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 wing as a lever: The wing is subject to mechanical forces, especially shear. Indeed, the force of lift acts to shear the wing off of the body. As the wingspan increases, so does that shearing force's leverage. Eventually, a critical point is reached at which the wing skeleton (be it bone or titanium alloy) fails and the wing breaks.

• Turning loads: So far we have only considered the balanced forces of lift and weight on the wing. If the machine climbs, lift exceeds weight, perhaps considerably. Entering a tight turn places lateral loads on the wing, such that its material feels the vector sum of a number of forces. SO, a highly maneuverable flying machine needs, especially, to be able to withstand sheering forces.

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:

• Increased lift vs. stalling risk
• Lift vs. (vortex-) induced drag.
• Reducing drag by increased wingspan vs. increased shearing loads.

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:

• Move from tree to tree without having to climb down and back up
• Facilitate low-energy movement from the trees to the ground.

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:

• The wing must be able to move so as to provide forward thrust. (Typically done as in subaqueous flyers, through the induction of lift on the forward surface as the wing is flapped.) In all powered flyers, the wingtips function as propellors, rotating so that lift will be concentrated on the leading surface. In birds, individual flight feathers are asymmetrical and rotate similarly.
• It must be structured so that its shape and position can be finely controlled.
• Structural support must be concentrated at the leading edge of the wing, where bending loads are the most severe.
• Wings must be long enough to avoid excessive induced drag
• Their structure must be very light but capable of withstanding significant bending forces
• They must be moved by a powerful muscular system
• the creature's weight must be minimized.

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

• Pterygote (winged) insects: (Starting ~325 mya) Employ two pairs of wings made of two stiff, flexible cuticle layers with blood vessels sandwiched in between, serving as structural elements.

• Pterosaurs: (Starting ~225 mya) Forelimbs support a patagium of varying proportions by means of an enlarged fourth finger. The unique pteroid bone supports the leading edge in front of the forearm. The patagium is invested with parallel collagen fibers, giving it the mechanical characteristics of a folding fan.

Pterosaurs' limb skeletons were hollow and invaded by pneumatic cavities. Their flight muscles arose from large sternums similar to those of birds.

• Birds: (Starting ~150 mya) Forelimbs support a wing formed of overlapping contour feathers. The outer wing consists of primary flight feathers supported by a hand with three coosified fingers.

Modern birds' limb skeletons are hollow and invaded by pneumatic cavities. Their flight muscles originate on large sternums. Uniquely, both the depressors and elevators of the wing arise from this region.

• Bats: (Starting ~50 mya) Fore and hind limbs support a flexible membranous patagium. The outer wing is supported by elongate digits II through V.

Whereas birds' and pterosaurs' limb skeletons are hollow, those of bats are solid but extremely slender. Among bats, the wing depressors originate on the sternum while the elevators arise from the scapulae.

Lift enhancement: Depending on the construction of the wing, powered flyers are able to enhance life by several methods:
• Variable camber: The camber of membrane wings is easily altered.
• Bats can depress their thumb and digit II to lower the leading edge, while curling fingers IV and V to increase curvature of the trailing edge.
• Pterosaurs could depress their pteroid bone and digits I - III to lower the leading edge. Fossils indicate that the membrane was invested with muscles, giving the trailing edge some flexibility.
Variable camber doesn't work well in a bird's non-membranous wing, however they have other options.:
• Slotted outer wing margins: In birds whose primaries project out individually from the wingtips, the formation of wingtip vortices is suppressed and each feather acts as a separate small, lift-generating wing.
• Leading edge flaps:

Large aircraft operating near stall speeds often extend leading edge flaps that create a slot through which air is directed across the wing surface more precisely. Birds have an analogous structure, the alula. This is the homolog to the thumb, and supports a tuft of feathers that can be elevated to create a leading edge slot.

Insects perform none of these tricks, but have their own:

• Leading edge vortex:

Aeronautical engineers have long known that in the very beginning of a stall, a powerful vortex forms at the wing's leading edge. As the stall progresses, this vortex detaches from the wing surface, initiating the general current detachment of the stall. During the moment before its detachment, the vortex greatly increases the lift force. For aircraft or vertebrate flyers, this moment is too fleeting to matter, however insects, with their rapid wingbeats, are able to exploit it by redirecting it outward, so that it dissipates before detaching.

• Wake capture: Wingtip vortices are, by definition, updrafts. In vertebrates, their energy is lost to the flyer that creates them (although others following along will use it - the source of the familiar V-formation of birds.) Many insect wingbeats are sufficiently rapid for the flyer to recapture the energy of its own wingtip vortices. (More information)

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:

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:

• Low aspect ratio, low-load wing
• large alula and slotted tips in birds
• high camber in bats.

High-speed flight:

Typical of birds and bats that pursue prey at high speed (swallows and molossids) and of large heavy birds who must cope with high wing-loading and are limited to high speeds (ducks). Characteristics:

• High aspect ratio, high-load wing
• Unslotted tips in birds
• Low camber in bats.

Hovering:

Terrifically energetically expensive. Characteristic of some nectar feeders and some small birds of prey. Characteristics:

• High aspect ratio, high-load wing
• Rigid wing skeleton capable of significant rotation at the shoulder.
• Wing mass concentrated proximally.
Hummingbirds are the champions. When they hover, they are the only symmetrical vertebrate aerial flyers. Other hoverers include phyllostomatid and long-eared bats, sunbirds, and the kestrel.

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:

• Thermal soaring:

Over warm land, rising columns of air form, with the fastest currents toward the center. Birds that ride thermals must be able to turn tightly in order to stay as near the center of the thermal as possible. Thus, their wings must bear heavy loads. In order to avoid the shearing loads that would go with a high aspect ratio wing, they typically opt for shorter wings with slotted tips. (E.G.: turkey vulture)

• Slope soaring:

When the wind encounters a large obstacle (E.G.: a cliff, ship, or large wave) a standing updraft is formed on its windward side. If the obstacle is elongate, slope soarers can ride it considerable distances in more or less straight lines. Many terrestrial thermal soarers also slope soar, but slope soaring specialists are usually sea birds with long, high aspect ratio, high-load wings. (E.G.: waved albatross) >Dynamic soaring: Dynamic soarers exploit the fact that wind speeds diminish closer to the ground. This happens in a series of steps:

• A bird approaching the ground while gliding downwind at a constant ground speed experiences increasing airspeed and lift - because the air around it is slowing down relative to the ground while the bird is not.
• Using this increased lift, the bird rises and turns into the wind. Again, the air speed increases because, as the bird rises, facing upwind, it encounters stronger winds.
• When it has reached a height at which the winds are effectively constant, and its drag has slowed it down, reducing its lift, it turns downwind and starts over.
For practical purposes, dynamic soaring can only be done over the ocean, so it is practiced by the same long winged birds that specialize in slope soaring.

Examples of ancient flyers:

Rhamphorhynchus:

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

Pteranodon:

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

Meganeura:

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:

• Arthropods ancestrally possessed biramous appendages with a walking branch and a gill-bearing branch. Insect wings are thought to have evolved from the upper gill-bearing ramus of the thoracic appendages.
• These may have originally been used as heat, gas, or water exchange organs in primitive adult insects. Indeed, the primitive winged insects typically have, in addition to the two proper wing pairs, a pair of small winglets - pronota in front. Thus, a pair of "wings" for each pair of thoracic legs.
• Such structures would be well suited for modification as parachuting structures, but why start flapping?
• A second hypothesis is that they were used as a means of propulsion for insects that were standing on the surface tension of bodies of water.
• Consistent with the fact that primitive living insects (E.G. mayflies) spend most of their lives as aquatic nymphs and transform into weakly flying air-breathing adults only to mate.
• Some living stoneflies use them for this purpose but are unable to fly in a level path.