Information for Teachers and Parents Back to Airfoils

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Table of Contents

  1. Lesson Overview
  2. Hypertext Outline of Lesson
  3. Objectives
  4. Time Allotment
  5. NCTM Process Standards
  6. NCTM Content Standards
  7. Aeronautics Content
  8. Prerequisite Skills
  9. Vocabulary
  10. Materials
  11. Teacher Tips
  12. Additional Activities
  13. Accessibility

I. Lesson Overview

In the Airfoils Department, students learn how airfoils, or the shape of the cross section of a wing, are related to the amount of lift that wing is capable of generating. Mathematical concepts related to airfoils and lift are introduced and students are given experiences and opportunities to answer questions pertaining to these concepts (symmetry, chord, lines, function tables, patterns, square numbers, formulas, graphs of relationships). A culminating wind tunnel activity allows students to experiment with the variables of speed and airfoil coefficients of lift to see the effect on lift and drag.

II. Hypertext Outline of Lesson

This purpose of this outline is to help you navigate to specific parts of the lesson without having to go through every page. The section titles link to the first pages of that section, and the numbers in parentheses refer to the page number where that section starts.

III. Objectives

At the end of this lesson, students will:

IV. Time Allotment

30-40 minutes, depending on student's reading ability and familiarity with geometric terms and formulas.

V. NCTM Process Standards

Standard 1: Mathematics as Problem Solving

Standard 2: Mathematics as Communication

Standard 3: Mathematics as Reasoning

Standard 4: Mathematical Connections

VI. NCTM Content Standards

Standard 5: Number and Number Relationships

Standard 8: Patterns and Functions

Standard 9: Algebra

Standard 10: Statistics

Standard 12: Geometry

VII. Aeronautics Content

VIII. Prerequisite Skills

IX. Vocabulary

Vocabulary words are linked to the activity pages on which they're defined.

X. Materials

For the string activity:

Other materials:

XI. Teacher Tips

This lesson can be completed individually but will move faster and be more fun if two or more people work together. The lesson can be done in under an hour if the students are good readers. There are several good breaking places in this lesson--after symmetry lesson, after lift and airfoil (prior to function tables) and before the wind tunnel activity.

Pair up students if someone is unable to hold or manipulate objects. Students who are unable to write can provide verbal input on project or make choices during the activity. In the string activity, tape or anchor the string down at one end if a student is unable to use both hands.

XII. Additional Activities

1. Students create a data chart for the wind tunnel activity. Students fill in values for speed and lift as they explore the characteristics of the symmetrical and asymmetrical airfoils with the wind tunnel, and then determine what pattern exists. Students then describe in writing the relationship between speed and lift.

2. Students create models of airfoils using clay, paper mache or another malleable substance. Students make examples of symmetrical and asymmetrical airfoils, showing the chord line on each model.

3. Students draw symmetrical and asymmetrical shapes on pieces of paper and cut them out. Then, they test for symmetry by folding and manipulating the shapes to find the line of symmetry. Students may also use a mirror to view the mirror images of any half-shapes they might make.

4. Students visit an airplane museum, sketching the airfoil shape of different planes. They can also research the speed and function of these planes. Students then provide rationales for why different airplanes have different airfoil shapes.

Do you have ideas for other activities to use with this activity? Send your suggestions to us at

XIII. Accessibility

The interactive Shockwave portions of this activity, such as the wind tunnel, are accessible through both the keyboard and the mouse. Students can use the spacebar to cycle through all the entry options on the screen, which will be highlighted by a small yellow bar next to the option. Students then use the up or down arrows to change an option, or press Return or Enter to select a button.

All the pages maintain a consistent grid of 6 buttons along the bottom of the page, which should be accessible through a ClickIt! overlay for IntelliKeys. For more information on using assistive technology, please refer to the document "Making PlaneMath Accessible" on the main PlaneMath parent/teacher page.

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