How planes generate lift!

Any textbook that talks about airplanes always discusses the four forces affecting a plane: lift, weight, thrust and drag: Three of those forces are obvious to us. For example, everyone weighs himself or herself on the bathroom scale every morning, so weight is easy to understand. Weight is what keeps us on the ground.

Household fans produce thrust (at least a little) in the same way a propeller does, so that concept is familiar.

Anyone who has ever stuck his or her hand out the window of a car on the freeway has felt the effects of drag.

But lift - there's something uncommon. If lift were easy we could stick out our arms and fly like a bird! But obviously it is not that easy. To understand lift you need to understand how wings work.

If you read an aerodynamics textbook, you will find many different explanations of lift: Bernoulli's principle, vortex circulation, fluid dynamics, etc. are discussed. None of these explanations are particularly satisfying unless you have a Ph.D. in mathematics. However, it is possible to get a good basic understanding of lift using the simple idea of action and reaction, or Newton's 3rd law.

The following is from HowStuffWorks.com.

Let's say that you were to build an airplane's wing out of flat sheets plywood - no fancy airfoils, just a flat wing. A typical small airplane, like the one shown here, has wings that are 40 feet long and about 4 feet wide:

Say you made the wing for this plane out of five 4'x8' sheets of plywood arranged as a 40' x 4' sheet. If you were to angle the plywood wing slightly (giving it an "angle of attack") and move the wing through the air, you can imagine that the wing would cut a "slice of air". The action of the wing is much like a knife cutting a slice from a block of cheese. The following figure shows the slice of air being cut off of the larger block of air by a slightly angled plywood wing:

In this picture the wing is moving from right to left, and it is cutting off a slice of air as it goes. The thickness of the slice is controlled by the angle of the wing. If the front of the wing is 4 inches higher than the back, the slice is 4 inches thick.

What's interesting is that, by thinking about what is happening to the slice, you can actually learn a lot about lift. You know that rocket engines are reaction engines. That is, they "throw" mass in one direction and take advantage of the equal and opposite reaction. See the rocket engine article for a complete explanation. The simplest way to think of a wing is this: A wing works by exactly the same action/reaction principle. The mass that a wing is throwing is the weight of the air-slice it is carving off. The air-slice has mass, and in the process of getting carved it is "thrown" downward. The wing reacts to the air-slice's mass being thrown, and it rises.

That may be hard to believe, so let's look and see if this action/reaction idea actually works. Let's assume a flat plywood wing that is 40 feet long and 4 feet wide. Let's assume that its front edge is 4 inches higher than the back edge, so a 4-inch slice is being carved off. Let's also assume the wing is slicing through the air at the rate of 100 miles per hour.

First let's figure out the mass of the air that this wing is carving off. 100 MPH is equivalent to 147 feet per second. So in one second the wing carves off a slice of air 147 feet long, 40 feet wide and 4 inches thick. That's about 1,955 cubic feet of air.

Air really does have weight, and one cubic foot of air weighs about 35 grams. Therefore, the 1,955 cubic foot slice of air that the wing produces every second weighs almost 160 pounds!

Force = mass * acceleration. The upward force on the wing is determined by figuring out the acceleration that the wing applies to the 160 pound slice. The wing is definitely accelerating it: as the wing is cutting off the slice, it moves it downward by 4 inches. It takes the wing 4 feet (the width of the wing) to move the air downward by 4 inches.

Since the wing is moving at 146 feet per second, it takes only 0.027 seconds to move 4 feet. Therefore, the slice is moving downward at a velocity of 4 inches per 0.027 seconds (12.3 feet per second) once the wing passes by, and it took 0.027 seconds to accelerate it from zero to that speed. So the air in the slice is being accelerated at a rate of about 448 feet/second2.
Now we can calculate the upward force from the wing:

Upward force = 160 pounds * 448 feet/second2 / 32 feet/second2 = 2,240 pounds!

Wow! There is 2,240 pounds of upward force being generated by the slice of air this wing carves off. The 32 feet/second2 in the divisor, by the way, is the acceleration that earth's gravity generates. To calculate pounds of upward force we divide by gravity's acceleration.

2,240 pounds of upward force is a lot. The interesting thing to note is that the small airplane pictured above has wings that are about 40 feet long and 4 feet wide, it cruises about about 100 MPH, and it weighs about 2,000 to 2,200 pounds once it is loaded with fuel and passengers. What an amazing coincidence!

So, why aren't all wings simply big flat sheets of plywood? There are three reasons:

1. A big flat sheet of plywood carving off a slice of air would create a tremendous amount of drag. The triangle-shaped area behind the wing is a big vacuum, and as the vacuum sucks in air to replace the slice it creates drag.

2. It would be hard to make a 40-foot long sheet of plywood that has any strength.

3. If you run the equations we just ran using the parameters of a 747, you will find that you need to carve off about a 6-foot-thick slice of air to get the lift you need. That's not so unreasonable when you consider how wide a 747's wing is - the angle of attack would be about 20 degrees. But it would still create a lot of drag. One interesting thing to note - the small plane weighs 2,000 pounds and has 40 foot wings, while the 747 weighs 800,000 pounds and has 211 foot wings. The 747 weighs 400 times as much but its wings are only 5 times longer. That indicates there might be another force at work.

Vocabulary

Aerodynamics: the study of the motion of air and the effect of moving air on obstructions

Angle of Attack: The angle formed by the tilt of the flying disk and the line parallel to the ground.

Angular Momentum: A rotating body's resistance to change in its orientation and rate of rotation. This is similar to gyroscopic inertia.

Bernoulli's principle: The pressure in a fluid decreases as the speed of the fluid increases.

Drag: The force that resists the motion of the aircraft through the air.

Fluid: a substance tending to flow and conform to the outline of its container

Force: A measurable push or a pull in a certain direction.

Lift: the force that allows for upward motion on a flying object. An upward force resulting from decreasing the pressure on the top of an object by increasing the velocity of the air flowing over the top of it. This is the force that opposes the weight force of the plane. The difference between the lower pressure on top of the wing, and the higher pressure beneath the wing, results in lift.

Newton's Third Law: for every action there is an equal and opposite reaction.

Pressure: the force exerted over a surface divided by its area

Thrust: a force created by the engine that pushes an aircraft through the air. Thrust acts against the force of drag.

Weight: the force of gravity acting on an object. The weight force pulls an aircraft toward the Earth. Weight is balanced by lift.

Wind tunnel: an enclosure in which a steady current of air can be maintained for the purpose of testing lift and friction

Velocity: the rate of change of displacement of a moving body with time