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#### I. Lesson Overview

In the Propulsion Department students learn about different types of airplane engines, which provide the thrust necessary for flight. Piston engiens driving propellers and turbine engines (jets, turbofans and turboprops) are covered, with simple animations showing the inside of these engines. Students practice using various formulas to calculate fuel consumption, speed, time and distance and fuel costs of a flight.

#### 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:

• Understand the role of thrust and propulsion in flight.
• Be able to name the two types of airplane engines.
• Understand how a piston engine operates.
• Understand the unit for measuring the power of a piston engine and be able to compare the power of various common engines.
• Define a turbine engine and compare it with a piston engine.
• Understand how a turbine engine operates.
• Understand the differences between a turbojet, turboprop and turbofan engine in terms of operation, top speed, and fuel economy.
• Understand the inverse relationship between fuel economy and top speed for turbine engines.
• Be able to define cruise thrust and takeoff thrust and understand the differences bewteen them.
• Understand the formula for speed, distance, and time, and be able to compute any of these values if given the other two values.
• Understand fuel consumption and be able to calculate the amount of fuel consumed during a flight.
• Be able to calculate total fuel costs given the price of fuel per gallon and the amount of fuel consumed.
• Understand the various factors that go into the operating cost of a plane.
• Understand and be able to use the proper units in any of the formulas taught in this lesson.

#### IV. Time Allotment

30-40 minutes depending on student's reading ability.

#### V. NCTM Process Standards

Standard 1: Mathematics as Problem Solving

• Use problem solving approaches to investigate and understand mathematical content.
• Verify and interpret given results and generalize solutions and strategies to a new problem.
• Students gain confidence using math meaningfully.

Standard 2: Mathematics as Communication

• Interpret and evaluate mathematical ideas presented in written and visual forms.
• Discuss mathematical ideas and make convincing arguments.

Standard 3: Mathematics as Reasoning

• Understand and apply reasoning with graphs.
• Make and evaluate mathematical arguments.
• Apply deductive and inductive reasoning.

Standard 4: Mathematical Connections

• Explore problems and describe results using graphical, physical and verbal math models.
• Apply mathematics to solve problems in science.
• Recognize the value of math in an applied technical situation

#### VI. NCTM Content Standards

Standard 5: Number and Number Relationships

• Represent numerical relationships in 2-dimensional graphs.
• Develop number sense for decimals, fractions, and integers.
• Understand, represnt, and use numbers in decimal, fraction, and integer form in real-world problem situations.

Standard 6: Number Systems and Number Theory

• Understand and appreciate the need for numbers beyond the whole numbers.
• Understand how the basic arithmetic operations are related to one another.

Standard 7: Computation and Estimation

• Compute with whole numbers and decimals.
• Select and use an appropriate method for computing.
• Use computation to solve problems.

Standard 8: Patterns and Functions

• Describe and analyze a variety of patterns.
• Describe and represent relationships with graphs and rules.
• Analyze functional relationsihips to explain how a change in one quantity results in a change in another.
• Use patterns and functions to represent and solve patterns.

Standard 9: Algebra

• Understand the concept of equation and formula.
• Represent situations and number patterns with tables, graphs, verbal rules and explore the interrelationships of these representations.
• Analyze tables and graphs to identify relationships.
• Investigate nonlinear equations informally.
• Apply algebraic methods tools to solve real world and mathematical problems.

Standard 10: Statistics

• Describe data.
• Read and interpret tables and graphs.

Standard 13: Measurement

• Understanding the selection of particular units for different values.

#### VII. Aeronautics Content

• Forces of Flight
• thrust
• drag
• Propulsion
• Parts of an airplane

#### VIII. Prerequisite Skills

• Students should be familiar with simple formulas and how to use them
• Students should be familiar with units of measurement for time, distance, speed, and volume (liquid)
• Students should have some background knowledge about engines and fuel use as they relate to cars

#### IX. Vocabulary

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

#### X. Materials

For helping with calculations:

• paper and pencil, calculator, or an assistive software package such as MathPad

For the hands-on activity for propellers:

• fan
• a long extension cord
• a cart

For the hands-on activity for the turbine engine:

• balloon
• string
• straw
• two chairs

#### 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. 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 activity. Math software such as MathPad can be used by students who are unable to write and need to do math calculations.

1. Investigate other applications of the speed, distance and time formula. Have students create their own problems based on this formula, using examples from flying, driving, and walking.

2. Look at fuel economy and consumption information for different types of vehicles, and have students calculate the operating costs of these vehicles. Are less expensive cars always cheaper over the long run than more expensive cars? What's the difference in fuel consumption between cars, motorcycles, boats, and airplanes?

Do you have ideas for other activities to use with this activity? Send your suggestions to us at planemath@infouse.com.

#### 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. Return to the top of the page