Flight: adaptations and the lift equation
Birds as living dinosaurs, the anatomical adaptations for powered flight, why the 'equal transit' explanation of lift is wrong, and calculations with the lift equation L = ½ρv²ACL.
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Birds evolved from maniraptoran theropod dinosaurs about 150 million years ago; the Jurassic fossil Archaeopteryx combined teeth and a long bony tail with modern-style flight feathers. Today there are over 10,000 identified species.[1]
Flight is costly: birds are endothermic with a high metabolic rate. Air sacs connected to the lungs give a one-way flow of air through the lungs, and gas exchange works by a cross-current system.[1]
Mass is reduced by pneumatic (hollow) bones strengthened by struts called trabeculae, and by a keratin beak instead of heavy jaws and teeth. The flight muscles attach to a deep keel on the sternum: the pectoralis major powers the downstroke, and the supracoracoideus the upstroke.[1]
Primary feathers give thrust on the downstroke; secondary feathers give lift. Flight feathers are asymmetrical and curved, so air flowing over them generates lift.[1][4]
The 'equal transit' theory of lift is wrong: flat paper wings fly, and air over the top reaches the trailing edge first. Lift comes from the wing turning the flow: the upper flow is faster and, by Bernoulli's equation, at lower pressure; the pressure difference produces lift.[7]
Lift can be modelled by L = ½ ρ v² A CL, where ρ is air density (about 1.229 kg/m³ at sea level), v the airspeed, A the wing area and CL the lift coefficient, usually found by experiment. Because lift depends on v², doubling the speed gives four times the lift.[6][8]
Try it: Modelling a wing with the lift equation
You need
- Paper or thin card, ruler, scissors
- Drinking straw, sticky tape, thread or thin string
- Battery-powered hand-held fan
- Metre rule, retort stand and clamp
- Electronic balance (0.01 g)
Safety
Use a battery-powered fan with a guard; keep fingers and hair away from the blades. Clamp the stand securely. Take care with scissors.
What to do
- Make a cambered wing: fold a 10 cm × 20 cm sheet so that the top surface is curved and the bottom flat, and tape the trailing edge. Push a straw vertically through the wing near its front third.
- Hang a thread vertically from the clamp through the straw and fix the bottom end, so the wing can slide up and down the thread.
- Measure the mass of the wing and calculate its weight (W = mg, with g = 9.8 N/kg). Measure its area A in m².
- Hold the fan level with the wing at 60 cm, 40 cm and 20 cm. Record whether the wing rises and how far. Repeat each distance three times.
- When the wing just lifts off, lift ≈ weight. Rearrange L = ½ρv²ACL to estimate the product v²CL needed, using ρ = 1.229 kg/m³.
- Turn the wing upside down and repeat. Does it still lift? What does this tell you about the 'equal transit' idea?
What happens, and why?
The cambered wing turns the air from the fan; the faster flow over the top is at lower pressure, and when the pressure difference times the area exceeds the weight, the wing rises. Closer to the fan the air is faster, and lift rises with v². Real wings and fans give uneven airflow, so the estimate is rough: the lift coefficient for a real wing is found by experiment. If an inverted or flat wing still lifts when tilted, the path-length explanation cannot be right.[6][7][8]
Play: Adaptations for flight
What does this adaptation mainly do?
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