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How a wing lifts

Air and fluids · level 6, lesson 5 of 6

A question to start

An airliner weighs hundreds of tonnes, yet its wings hold it up on nothing but air. How does a wing push up on a plane?

The idea

A wing is shaped and tilted so that it turns the air flowing past it downwards. Two ways of looking at it give the same answer:

  • Newton's third law. The wing pushes air down, so the air pushes the wing up.
  • Pressure. The air speeds up over the curved top of the wing, so the pressure there is lower (Bernoulli). Under the wing, the pressure is a little higher. The difference, over the wing's area, is the lift.

The tilt of the wing into the flow is its angle of attack. More tilt turns more air down and gives more lift, up to a point: tilt it too far and the flow breaks away from the top, and the wing stalls.

liftlower pressurehigher pressureair turned down

How much lift a wing gives grows with the air density, the wing area and the speed squared. That is the bad news for wings on Mars: with air 75 times less dense, a wing needs far more speed or far more area to hold up the same weight.

Worked examples

1. Turning air down. A wing pushes 100 kg of air down each second, giving it a downward speed of 5 m/s. The force on the air is its change in momentum each second: \(100 \times 5 = 500\) N. So the lift is 500 N.

2. A pressure difference. A wing of 16 m² has an average of 600 Pa less pressure on top than underneath. Lift \(= 600 \times 16 = 9{,}600\) N, enough to hold up a mass of about 980 kg on Earth.

3. On Mars. To give the same lift, the same wing needs the same \(\tfrac12\rho v^2\). With \(\rho\) 75 times smaller, \(v^2\) must be 75 times bigger, so the speed must be about \(\sqrt{75} \approx 8.7\) times higher.

Try it

  1. Which way does a wing push the air?
  2. Use Newton's third law to explain lift.
  3. A wing turns 40 kg of air down each second to a downward speed of 6 m/s. Find the lift.
  4. What happens if the angle of attack is too big?
Answers
  1. Downwards.
  2. The wing pushes air down, so the air pushes the wing up with an equal force.
  3. \(40 \times 6 = 240\) N.
  4. The flow breaks away from the top and the wing stalls, losing most of its lift.

Common mistake

"The air over the top must meet the air underneath at the back, so it goes faster." There is no such rule; the air over the top actually gets to the back first. The top air is faster because the wing's shape and tilt bend the flow, and the lift comes from turning the air down.

Where it leads