Illustration 15.4: Airplane Lift

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The animation shows the cross section (side view) of a model airplane wing with air moving past the wing (position is given in centimeters and time is given in seconds).   Restart.   Where is the speed of the air greatest? Where will the pressure be higher? How does this explain the lift on an airplane? Using Bernoulli's principle we can find the pressure difference between the top and the bottom wing and it is

ΔP = ρ (vabove2 - vbelow2)/2.

First, find the speed of the air above (once above the wing, the air speed is constant) and below the wing. We can find the average speed easily as the displacement over the time interval, and we find that vbelow = 950 cm/s = 9.5 m/s and vabove = 990 cm/s = 9.9 m/s.

Now we can calculate the pressure difference using our results for the air speed and the density of air, ρ = 1.3 kg/m3. We find that in this case ΔP = 5 Pa. If the surface area of the wing is 0.1 m2, what is the net force (lift) on this wing? Since P = F/A, we find that the net force will be the pressure difference times the area or 0.5 N.

The reason an air flow pattern develops that yields different speeds on the top and the bottom is that the air flowing around the wing moves into nonideal fluid flow. Initially, since the air on top has farther to travel, the air on the bottom of the wing gets to the back of the wing and moves up to "fill" this space, but this instability causes a turbulent wake that eventually allows a new, more stable, air-flow pattern such as the one shown, where air-particles that travel across the top go faster. For a greater difference in pressure, the wing is tilted up (the angle of tilt is called the angle of attack), and this increases the lift.

Note: The format of the time is written in shorthand. For example, a time of 6.00 x 10-3 s, is written as 6.00e-003.

Illustration authored by Anne J. Cox.

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