Before you read this, I suggest you read posts 17.16 and 17.31.

We often see birds flying without flapping their wings – they are gliding (post 17.31). In order to glide, their wing cross-sections must be shaped so that air moving over the wing has further to travel than air moving under the wing, so creating an upward force called lift (as explained in post 17.31). To start gliding, the bird must push on its perch. According to Newton’s third law of motion (posts 16.2 and 17.26), the perch pushes back with an equal and opposite force that will have a horizontal component (post 16.50). So, the bird can launch itself with a velocity that has a horizontal component (post 17.4). The moving air creates the lift force and the bird glides (post 17.31).

But there are other forces acting on a gliding bird: (1) gravity (post 16.16), that tends to make it fall, and (2) drag (post 17.17), that makes it move more slowly and so reduces the lift force (post 17.31). When we watch gliding birds that are not soaring in rising air currents (post 17.31), we often see that their height is decreasing. This decrease in height is characterised by their glide angle which is the angle their direction of motion makes with the horizontal (post 17.31).

The table above shows the glide angles of some birds. A glider has a glide angle of only about 1^o (post 17.31), so birds are not as good at gliding but they have other methods of flying.

One other method, that birds share with gliders, is soaring in rising air currents (post 17.31). Some birds, like eagles, vultures and gulls appear to soar a lot of the time they are flying. You can often see these soaring birds turning to stay in the rising air.

But when we think about bird flight we tend to associate it with flapping wings. It is not only living things that fly by flapping their wings – people have made orthopters that fly in this way. However, wing-flapping in orthopters is much simpler than in birds.

Let’s think about the downstroke of a flapping wing when the wing moves from position 1, through horizontal (position 2) to position 3. The bird is pushing down, with its wings, against the pressure, p, of the air (post 17.5). If its wings are not tilted, in position 3 it then exerts a downward force pA on the air, where A is the area of its wings. According to Newton’s third law of motion (posts 16.2 and 17.26), the air then exerts an equal upward force on the bird – so it moves upwards.

But what happens on the upstroke when the wing moves from position 3 to position 1, through position 2. If the upstroke were identical to downstroke, but in the opposite direction, the bird would lose all the height it had gained!

There are three possible strategies for overcoming this problem: (1) partially folding the wings during the upstroke, (2) making the upstroke faster than the downstroke, and (3) changing the tilt of the wing. Different species of birds appear to use these three strategies to different extents. Strategy 1 reduces the wing area from A to A’, so that the downward force pA’ generated on the upstroke is less than the upward force pA generated on the downstroke. Strategy 2 means that the bird is generating an upward force for a longer time than it is generating a downward force. Strategy 3 is much more complicated because different species of birds appear to change the tilt of their wings in different ways when they are flying. To see how an eagle owl (Bubo bubo) changes the tilt of its wings during flight see http://www.dogwork.com/owfo8/.

A simplified way of looking at strategy 3 is shown in the picture above. The bird tilts its wings by an angle θ on the upstroke. The air pressure acts equally in all directions (post 17.5), so the force acting on the wing is still pA’. Because this force acts perpendicular to the wing (the part of the bird that is pushing the air), it now makes an angle of θ to the vertical. The air pushes against the wing in the opposite direction, so the downward component of the force is pA’.cos θ (post 16.50). Since the cosine of an angle is always less than 1 (post 16.50), the downward force is reduced by tilting the wings. Tilting the wings in this way also produces a horizontal component of the force of pA’.sin θ (post 16.50) that tends to accelerate the bird forwards (post 16.13).

When a bird flaps its wings, it does work (post 16.20) and so uses more energy (post 16.21) than in gliding and soaring. A pigeon uses about ten times more energy when it is flying than when it is resting but a swimming duck uses only three or four times more energy than a resting duck – so flying uses a lot of energy (see appendix). So, it is commonly believed that large birds (like eagles) tend to gain height by soaring, instead of by wing-flapping, to conserve energy. However, it seems to me that the grey heron (Ardea cinereal), which is a very large bird, nearly always flaps its wing when it is flying. Perhaps the heron compensates for this use of energy by spending most of the time standing still looking for fish to catch.

Flying is easy for a bird – but it gives us a lot to think about!

 

Related posts

17.31 Gliding and soaring
17.26 Rockets
17.16 Why does a plane fly?

 

Appendix

The ideas about energy use by flying and swimming birds come from J. Ackerman, The Genius of Birds, Corsair, London, 2016, p. 50. It is based on results in the original scientific papers listed below.

R.L. Nudds & D.M. Bryant, The energetic cost of short flight in birds, Journal of Experimental Biology, vol. 203 (2000), pp. 1561-1572.
http://jeb.biologists.org/content/jexbio/203/10/1561.full.pdf

P.J. Butler, Energetic costs of surface swimming and diving of birds, Physiological and Biochemical Zoology, vol. 73 (2000), pp. 699-705.
http://www.journals.uchicago.edu/doi/pdfplus/10.1086/318111