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Investigating Velocity Effects at Takeoff

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Subject Area(s):

Algebra I

Grade Level:


National Mathematics Standards:








National Technology Standards:

Mathematics as Problem Solving:

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.

Mathematics as Reasoning:

Students will be able to make and test conjectures.


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


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.



  • After reading the explanation given below, use FoilSim to complete the activity to determine the constant in a "direct variation to a square" equation.
  • Then use the constant to extrapolate to other situations and verify the results of the equation using FoilSim.

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 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.

Image of FoilSim Interface

To begin the problem, click on Investigating Velocity Effects.


You, or you and your partner(s), will be evaluated on the accuracy or feasibility of your answers and your ability to explain how you arrived at your decisions.


You will demonstrate the ability to use information found on the World Wide Web and in FoilSim to complete the activities and discuss your findings.

Submitted by:

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

Related Pages:
Lesson Index
Aerodynamics Index


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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, May 13 02:38:38 PM EDT 2021

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