This activity is one of many great pre-planned lessons for our free Wings Up Program at the National Museum of World War II Aviation. In this program, students are exposed to the same Engineering Design problems as real-life engineers, in order to design aircraft that are best suited for different tasks. At the museum, they will create their own airplanes based on the wing math of WWII-era planes.
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- Rulers (one per student)
- Calculators (if necessary)
- Wing Math Worksheet (Student)
- Wing Math Worksheet (Teacher)
The aspect ratio is the ratio of the wing’s length to its chord line. The mean chord line is the theoretical line running from the leading (front) edge of the wing to the trailing (rear) edge of a wing, and is required to determine aspect ratio. A wing with a high aspect ratio will perform well at slow speeds and produce large quantities of lift, but at the expense of maneuverability and airspeed. A wing with a low aspect ratio on the other hand will have a sleek appearance and allow an aircraft to fly faster, or be more maneuverable. By determining the aspect ratio of an aircraft, students can make inferences about an aircraft’s function.
Determining the aspect ratio of an aircraft wing relies heavily on algebra and geometry skills. In addition, students will calculate the surface area of the wing. Although surface area is not part of the aspect ratio, it is what gives an aircraft its lift, and also plays a role in the performance of an aircraft.
Using the Wing Math Worksheet, work through the first problem with students. Students should use a ruler to measure lines as needed.
Have students complete the remaining problems on the worksheet individually or in groups. Remind them that each wing is different, and that they may have to subdivide a wing into smaller shapes in order to determine length, height, or mean chord length. A sheet with formulas for area of different shapes is included; you may display this or distribute it to students as necessary.
- How does aspect ratio relate to plane function and wing shape? Aircraft that can tolerate slower speeds (cargo carriers, etc.) can have a higher aspect ratio. However, planes that require faster speeds, such as fighters or supersonic craft, must have a lower aspect ratio.
- How can you measure aspect ratio on an actual plane? Students will have access to real WWII aircraft at the museum; however, they may not be able to reach the wing for direct measurement. Discuss ways of approximating.