Wing Shapes and Areas
 

Subject Area(s):

Algebra I/Geometry

Grade Level:

8-10

National Mathematics Standards:

Mathematics as Problem Solving:

  • Students will be able to apply integrated mathematical problem-solving strategies to solve problems from within and outside mathematics.
  • Students will be able to use, with increasing confidence, problem-solving approaches to investigate and understand mathematical content.

Mathematics as Communication:

  • Students will be able to express mathematical ideas orally and in writing.

Mathematical Connections:

  • Students will be able to recognize equivalent representations of the same concept.

Algebra:

  • Students will be able to use tables and graphs as tools to interpret expressions, equations, and inequalities.

Geometry from a Synthetic Perspective:

  • Students will be able to represent problem situations with geometric models and apply properties of figures.

 

Objectives:
  • After reading the explanation given below, use FoilSim to determine the weight of the aircraft that can be lifted by a pair of wings of each type.
  • Design a unique planform of a wing to lift a plane weighing 11500 pounds.

About FoilSim:

FoilSim is an interactive simulation software package that determines the airflow around various shapes of airfoils. As you change the parameters of  airspeed, altitude, angle of attack, thickness and curvature of the airfoil, and size of the wing area, the software calculates the lift. The package was created at NASA Glenn Research Center to illustrate an example of their research.

Macintosh or MS-Windows 3.x, 95, or NT versions of FoilSim are available for downloading off the World Wide Web at FoilSim Download.

Shown below is a screen shot from the program showing the controls and displays. You may change the values of the variables by using the slider or the input box on the left side of the slider.

To use the slider:

  1. Click the mouse pointer on the arrows at the ends of the slider.
  2. Click the mouse pointer anywhere between the slider and the arrows.
  3. Drag the slider with the mouse.

To use the input box:

Simply select the value in the input box, key in the new value, and press Enter or Tab when finished. The button on the slider will move corresponding to the value typed in the box.

To begin working on the problems, click on Wing Area Investigations.

Assessment:

You, or you and your partner(s), will be evaluated on the accuracy or feasibility of your answers and creativity in design.

Evaluation:

You will demonstrate the ability to use information found on the World Wide Web and in FoilSim to complete calculations involving area and lift and to design a unique wing planform.

Submitted by:

Paula L. Phillips, North Olmsted High School, North Olmsted, Ohio


Please send any comments to:
Web Site Related: Dale Morris (Dale.J.Morris@grc.nasa.gov), Technology Related: Tom Benson(Tom Benson@lerc.nasa.gov)