Area Under a Curve

Subject Area: Pre-Calculus or Calculus

Grade Level: 11 - 12

National Mathematics Standards:

Investigate the area under a curve and the rate of change.

Objectives:

Use the idea of area between curves to make inferences about the forces of pressure on the wing area of an airplane given altitude changes.

The software package FoilSim, which allows you to generate a data set of information to investigate this force, was created at NASA Glenn Research Center. FoilSim is an interactive program that determines the airflow around various shapes of airfoils. As changes occur in the parameters of airspeed, altitude, angle of attack, thickness and curvature (camber) of the airfoil, and the size of the wing area, FoilSim calculates the lift. This software may be downloaded off the World Wide Web at FoilSim Download for Macintosh, MS-Windows 3.x, 95, or NT platforms.

Shown below is a screen shot from the program showing the controls and displays. The values of the variables may be changed by using the slider or the input box to the left of the slider.

To use the slider:

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

To use the input box:

Select the value in the input box, type in the new value, and press Enter or Tab when finished. The button on the slider will move to a position corresponding to the value entered in the box. (Note: This is the easier method to use when specific values are needed.)

To begin the activity, click on the Area Under a Curve Activity.

Assessment:

You, as individuals or in cooperative groups, will be evaluated on:

• The feasibility of your answers.
• Your explanations for given questions.

Evaluation:

You will be evaluated on the graphs created and their comparison to the graphs in FoilSim.

Submitted by: Christine Nagy Warren, Olmsted Falls High School, Olmsted Falls, Ohio.