If you cut a wing from its leading (front) edge to its trailing edge (back), the "cutaway" illustrated in the Figure 1 is what you would see. Aeronautical engineers call this an airfoil.

Figure 1. Airfoils click for copyright

The top and bottom halves of the first airfoil are identical — this is referred to as symmetric. The airfoil on the right is not symmetric: its top and bottom halves are different. The difference in the bottom from the top means this airfoil is cambered.

The four forces of flight are lift, weight, thrust and drag. Lift and weight are opposites and will counteract one another. Likewise, thrust and drag will counteract one another.

The top of a plane's wing is longer than the bottom because it is curved (see Figure 2). This means air will travel faster over the top of the wing than under it. As a result, the air moving over the top has less time to push on the wing, creating less air pressure than air passing below the wing. In the diagram below, the air moving under the wing moves slower and exerts more pressure/force on the wing than does the air moving over the wing. Since there is more force under the wing than above it, the net result is that the wing rises up, creating lift. This principle forms the basis of winged flight.

Figure 2. How a wing produces lift. click for copyright

There are flaps on the front and back edges of the wing. During takeoff and landing, pilots extend the flaps on the back edge of the wing. The flaps increase the curve of the wing, which maintain the lift at slower speeds. After takeoff, the pilot retracts (puts back in) the flaps. Engineers continuously test their designs of wings to determine the lift, and in so doing, they must consider the following when testing:

• The amount of air diverted by the wing is proportional to the speed of the wing and the air density.
• The vertical velocity of the diverted air is proportional to the speed of the wing and the angle of attack.
• The lift is proportional to the amount of air diverted times the vertical velocity of the air.
• The power needed for lift is proportional to the lift times the vertical velocity of the air.

• Copy all worksheets.
• Preload computers to the following website: http://www.swe.org/iac/LP/wind_tunnel.html

1. Discuss Bernoulli's Principle and introduce the concept of lift.
2. Explain the difference between a symmetric and cambered (asymmetric) airplane wing.
3. Direct students' attention to the worksheet and website. Have students read the background information silently to themselves. Allow 10 minutes, and discuss the reading.
4. Have students break into pairs.
5. Be sure to model the process. Students may find it difficult to grasp how the model runs. The model depicts velocity lines flowing over different wing types. Velocity lines that are close together above the wing demonstrate lift; lines that are the same distance apart above and below the wing demonstrate no lift.

1. Pick an Airfoil Shape from Column #1.
2. Pick an Angle Of Attack from Column #2.
3. Click "Run Tunnel."
4. Close the window when you are done with this activity.
5. Have students complete the worksheet. Be sure they try several models to decide which causes the most or least lift.
6. Be sure to model the process. Students may find it difficult to turn the English sentences into math equations. The worksheet walks students through the process step-by-step.
7. Discuss with the students that the phrase "proportional to something " means "equal to some number multiplied by something." More specifically we can say "is proportional to" means K times something where K is the constant of proportionality.
8. Assign Math Worksheet 2 for students to complete for homework. (This worksheet may not be appropriate for lower grades.)

Discussion Question/Answer: Ask students questions and have them raise their hands to respond. Write answers on the board

• If you arm wrestle someone, who wins? (Well of course, the person who exerts the most force wins!)
• What happens if both "wrestlers" push with the same force? (Their arms do not move.)
• How does this relate to lift? (Lift occurs when the force under a plane is greater than the force pushing down on the plane (weight). This is the same as arm wrestling since the person who exerts the most force pushes the other arm in that direction.)
• Describe the force of lift and how it affects airplane flight. (The students should understand Bernoulli's Principle — that lift is caused when the air is pushing harder from below the wing than above the wing.)

Worksheet: Have the students record observations and comments on their Windy Tunnel worksheet. After students have finished their worksheet, have them compare answers with their peers. Discuss as a class.

Figure drawing/Race: Draw an airfoil on the board (see Figure 1 for sample airfoils). Have two students come to the board and race who can draw (with chalk or whiteboard marker) the top or the bottom of the airfoil the fastest. The student who "wins" completes the drawing (gets to the end of the airfoil) first. Which student was the fastest? Will that airfoil create lift or not?