Flapping Flight

An additional mode of flapping propulsion is flapping flight utilized by birds. Unlike undulatory swimming, flapping flight involves oscillating (flapping) wings rather than tails. Wings are familiar features from both birds and airplanes, but birds use their wings quite a bit differently than do airplanes. Whereas airplanes use their wings only for generating lift, leaving the job of generating thrust to a separate propulsion system, birds' wings generate both lift and thrust.

As described in the discussion of propellers, wings accelerate fluid away from them to generate a reaction force. If the fluid is accelerated down, lift is the result. If it is accelerated backwards (as in the case of propellers), thrust is the result. To generate both lift and thrust, birds must use their wings as a cross between a wing (lifting surface) and a propeller by accelerating fluid both down and backward. To control the direction of the force on their wings, birds vary two parameters: the stroke-plane angle and the pronation angle (see the figure below). The stroke-plane angle can be measured either relative to the horizontal (δ_h) or relative to the axis of the bird body (δ_b). It describes the angle of the wing-tip path during the down stroke. The pronation angle (φ) describes the rotation angle of the wing relative to the axis of the bird body.

(A) WEa, wingtip elevation at the start of downstroke; WEb, wingtip elevation at the end of downstroke; δb, stroke-plane angle relative to the body; δh, stroke-plane angle relative to horizontal. (B) φ, pronation angle of the wing (negative when above the body axis as shown); α, angle of attack of the wing; β, body angle relative to horizontal. Adapted from Tobalske, B.W., W.L. Peacock, and K.P. Dial (1999) "Kinematics of flap-bounding flight in the zebra finch over a wide range of speeds," J. Exp. Biol. 202, 1725-1739.

To illustrate how birds coordinate δ and φ to generate both lift (F_L) and thrust (F_T), let's focus on a wing downstroke since this is where most of the action takes place anyway. For slow speed flight, the primary force birds must contend with is gravity since drag is low due to the low forward speed. For this situation the stroke-plane angle relative to the horizontal (δ_h) is small (< 90°) as shown on the left below. This has two effects. First, it gives the wing forward velocity relative to the bird, so more force can be generated despite the slow flight speed (note that U is the is the vector sum (addition) of V₀ and W and recall that the force on a wing depends on velocity squared). Second, it allows a modest angle of attack (α) to be achieved to be achieved with a smaller pronation angle. A small pronation angle is beneficial because a larger fraction of produces lift (vertical force) and a modest angle of attack is helpful because if α is too large, the "drag" on the wing (F_||, not shown) can become large, reducing efficiency (see the discussion of thunniform propulsion).

To contend with the increased drag in high-speed flight, birds use a larger pronation angle and a larger stroke-plane angle (approaching 90°) during the downstroke. The large pronation angle converts more of to thrust and the large stroke-plane angle allows a positive angle of attack to be achieved at the large pronation angle. The net effect is an increase in the thrust force with sufficient lift to maintain flight.

Wing downstroke during slow and fast flight. The wings are shown midway through the downstroke. Flow velocities are shown from the point of view of someone sitting on the wing. V0 is the flight speed of the bird, W is the velocity of the wing, and U is the air velocity seen by the wing. Click here for a review of vectors.

During the upstroke, birds tend to fold their wings in toward their body (adduction). This is especially pronounced at low speed where often no significant lift is generated on the upstroke. The reason for adduction on the upstroke relates to the difficulty in generating beneficial forces during the upstroke in low flight speed. To illustrate, a possible upstroke scenario is illustrated below. Notice the large, negative pronation angle required in order to get a positive angle of attack (required to avoid generating a down force during the upstroke). The result is very little lift generation, but substantial drag (back force, F_D) generation. To avoid this scenario, birds essentially avoid using their wings during the upstroke during low-speed flight. In high speed flight, the situation is not quite as bad and many birds do not fold their wings as much on the upstroke. The payoff is lift production on the upstroke with a small drag penalty from the negative pronation angle. The movie below illustrates how this all works together in the flight of a Thrust Nightingale (species Luscinia luscinia)

As cruise speed increases, many birds do not change their flapping frequency significantly. Instead, they steadily increase the stroke-plane angle (increase thrust) and align their bodies more with the flight direction (decrease form drag) as speed increases. It is likely that maximum bird flight speed is determined by the limits on stroke-plane angles and downstroke speeds (W) that can be achieved by birds.

To change speed, birds adjust their flapping roughly as follows. To accelerate, they use a downstroke similar to high-speed flight and an upstroke similar to low-speed flight (large thrust, low drag). To decelerate, they tend to keep their wings spread (adduction is minimized) and use an upstroke similar to high-speed flight (larger drag).

Many variations and modifications to the basic scheme described here exist. Most notably, birds also use their tails to help enhance lift in different flight situations and many birds do not always flap continuously during "steady" flight (giving the so-called "flap-bounding" flight mode). Nevertheless, the basic features described above encompass the primary physics governing bird flight and propulsion. The description also holds, in general terms, for flight of most large insects, although the precise features of the flow over the wings are somewhat different since most insects do not have airfoil-shaped wings.

Because birds combine both lift and propulsion into one action, it is difficult to discuss propulsive power and efficiency separate from lift production. Some estimates, however, indicate that around 25% of the power expended by birds in flight is directly related to generating thrust.