Aerodynamic Lift Explained by Joseph F. Alward, PhD
University of the Pacific Stockton CA 95207
October, 2013
Figure 1 shows a cross-section of an airfoil in a wind tunnel just after the air stream is turned on. The airstream has just encountered the leading edge of the wing.. The air pressure above and below the wing is initially equal to atmospheric pressure, P0, before the air stream reaches it.
If it were not for the fact that a reduced pressure is about to be created above the wing, the airstream above the wing would follow the broken-line path in Figure 1.
Observe the dots that are near the surface of the wing in Figure 1. These dots represent air molecules that are initially at rest above the wing in the wind tunnel, before they are met by the onrushing airstream. These air molecules are about to be swept away from the wing's surface and become part of the the airstream by a process called "entrainment."
"Entrainment" happens when the onrushing air molecules collide with the air molecules (shown as dots in Figure 1) above the wing, knocking some of them upward and to the right. The entrainment of the those air molecules in the airstream is illustrated in Figure 2; some of the air that was once close to the wing's upper front surface is now gone, swept into the airstream.
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Figure 1
Figure 2
In Figure 2, the air molecules near the front top of the wing are now entrained in the airstream. They leave below a region close to the wing that is depleted of air molecules, and therefore at a pressure P that is lower than the air at the higher pressure P0 above it. The air at the higher pressure P0 is pushed toward the lower pressure region just above the wing's surface. This bending of the air to follow the wing's contour is the so-called "Coanda Effect."
What Causes Lift?
The air under the wing is still at atmospheric pressure P0, so there is a net upward force on the wing equal to (P0- P) A, where A is the effective area of the affected wing's surface. This force is shown as F1 in Figure 2.
Another cause of aerodynamic lift occurs when the airstream initially moving to the right below the wing collides with the bottom of the wing and is deflected downward and to the right. This is illustrated in Figure 2. The downward component of the force by the wing on the air (not shown) is paired according to Newton's Third Law with an equal but opposite upward force (F2) by the air on the wing. This upward force on the wing, together with F1, is responsible for most of the lift the wing experiences. Note: the force vectors F1 and F2 are not necessarily drawn to scale, that is, no claim is made here about the relative strengths of the forces.
It's a lot more complicated than this. A more comprehensive description of the aerodynamic lift involves vortices, but that discussion is beyond the scope of this discussion, which is intended mainly for elementary physics courses.
The YouTube video below illustrates the Coanda effect.
A screen capture from the video, shown below with my notes added, shows the direction the smoke would have traveled (straight red line) if it were not for the fact that entrainment of air near the wing into the streaming smoke reduces the pressure above the wing, allowing the normal (and higher) pressure air above the smoke stream to push the smoke toward the wing. The lower red curve shows the direction along which the streaming air actually travels.
The lower pressure above the wing allows the normal (and higher) air pressure below the wing to contribute a lift to the wing. This lift, caused by the pressure difference, is only part of the lift that the wing experiences, as I described above. Part of the remaining lift is due to the vertical component of the momentum transferred to the bottom of the wing by the air stream (not shown) colliding with the bottom of the wing.
Does the air travel over the top of the wing more rapidly than the air traveling under the wing?
Yes. The reason the air over the top of the wing is traveling more rapidly is that the air pressure above and in front of the leading edge of wing, shown as Point A in the figure below, is at normal (and higher) pressure, while the air farther back above the wing, at Point B, is at a lower pressure. The air at the higher pressure at A is thereby accelerated toward the lower pressure region, and this accounts for the higher speed of the air above the wing.
The pressure drop just above the wing, accounts for the increased speed of the air above the wing, relative to the speed below the wing. The speed increase is caused by the higher pressure air at the leading edge of the wing being accelerated along the top of the wing toward the lower pressure area farther back.
Misusing Bernoulli's Equation
It is the fact that air is traveling faster over the top of the wing than the air below the wing (Note 2) that has misled many persons to offer a popularized, over-simplified (and completely wrong) explanation of airplane lift. They falsely claim that Bernoulli's equation accounts for airplane lift. Their incorrect argument goes something like this: Bernoulli's equation (shown below for a fluid of density ρ, ignoring elevation differences and friction),
ΔP = ½ρ Δ(v2)
shows that wherever there is a speed difference in fluid flow, there is an associated pressure gradient. (So far, so good.)
Where they go wrong, apparently, is when they seem to argue that however one might cause a fluid speed change, this would (somehow magically) be the cause of a pressure gradient. (This is like saying that however one might cause an acceleration, a force would result, thereby getting the effect before the cause.)
As we saw above, the higher speed air over the top of the wing is caused by a pressure difference, not vice-versa.
Bernoulli's Equation
Bernoulli's Equation is just Newton's Second Law applied to an incompressible fluid in which friction is ignored: A fluid element will accelerate if a net force is acting on it. This net force may arise either from a pressure gradient, or gravitational force, or both. In the derivation below, elevations differences are assumed to be zero, and friction is ignored.
The element of fluid in Figure 3 has density, ρ, width dx, area A, and velocity v = dx / dt
Assume the pressure difference between the left and right sides of the element is dp.
ma = F
Consider two points 1 and 2 in the tube, and
let ΔP = P2 - P1.
ΔP = ½ρ (v22 - v12)
or
ΔP = ½ρ Δ(v2)
Figure 3
Bernoulli's equation derivation above began with a cause-effect equation: acceleration is caused by force, and ends with the same result applied to fluids--speed change is caused by a pressure difference. In other words, Bernoulli's equation contains no more information or insight into the behavior of fluids than does Newton's Second Law. The equation no more predicts that speed differences cause pressure differences than does Newton's Second Law predict that accelerations cause forces. It is exactly the reverse: net forces cause acceleration, and pressure gradients cause speed changes.
Exploring the physics of air pressure with the wind bag
The content below was taken from www.arborsci.com.
The drawing is from Paul G. Hewitt's wonderful introductory level physics textbook, Conceptual Physics. As Hewitt explains, the air breathed into the bag entraps (or, "entrains") the surrounding air, that is, the breathed air drags adjacent air molecules along with it, which in turn drag other adjacent molecules. This entrainment of air above the airplane wing is at the heart of the explanation above of aerodynamic lift.
The filling of the bag below doesn't illustrate aerodynamic lift, of course; it only serves as an example of entrainment.
The following additional information about the operation of the air bag is provided in Hewitt's textbook:
"The long plastic bag demo nicely illustrates Bernoulli's principle. Tie a knot in the end of the 2 meter x 25 cm (8 ft x 10 in) bag and stretch it out on a smooth surface. If you were to blow it up by placing it firmly to your mouth, many lung-fulls of air would be needed. But when you hold it in front of your mouth and blow, air pressure in the stream you produce is reduced, entrapping surrounding air to join in filling up the bag. So you can blow it up with a single breath! This is especially effective after your students have counted many of their own breaths in attempting to fill up the bag!" -Paul G. Hewitt, Conceptual Physics
Joseph F. Alward
JFAlward@aol.com
Any comments and criticisms will be very welcome.
