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## Wing Shape Investigations

 Subject Area(s): Algebra I/Geometry Grade Level: 8-10 National Mathematics Standards:                     National Technology 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.  Technology research tools: Use content-specific tools, software and simulations (e.g., environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research; select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems. Problem-Solving and Decision-Making Tools: Routinely and efficiently use on-line information resources to meet needs for collaboration, research, publications, communications, and productivity. Objectives: After reading the explanation given below, use FoilSim to investigate the effects that wing shape have on the generation of lift. Several popular misconceptions about lift will be explored. A wing does not need curvature to generate lift.

FoilSim is an interactive simulation software package that examines the airflow around various shapes of airfoils. As you change parameters such as 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 the NASA Glenn Research Center.

FoilSim II is a Java applet program that executes inside the browser of your computer. It is available on the World Wide Web at http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html. You can also download the program to run off-line.

Shown below is a screen shot from the program's controls and displays. You may change the values of the variables by using the slider or the input box on the left 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 arrow.
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 Shape 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 camber and lift. Submitted by: Herb Schilling, NASA Glenn Research Center, Cleveland Ohio

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