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 Supersonic Dream Classroom Activity

Objective
To understand how fuel use affects the mass of different planes during flight and to determine the per person fuel cost of a transatlantic flight for seven airplanes.

• copy of the "Fueling the Burn" student handout (PDF or HTML)
• copy of the "Aircraft Specifications" student handout (PDF or HTML)
• copy of the "Graphing Mass Change" student handout (PDF or HTML)
• calculator

1. Passengers on the Concorde could arrive at their transatlantic destination twice as fast as regular jet travelers. But how much fuel did the Concorde use to accomplish that feat? How did the Concorde's fuel use compare to that of other aircraft? How did the Concorde compare in fuel cost per passenger for a transatlantic flight to some more common jets? Students will explore these questions and others in this activity.

2. Organize students into teams. Provide each team with copies of the student handouts and review the activity with students. (You may want to note to students that the statistics represent actual specifications for commercial aircraft.)

3. Use the board to complete a sample graph of the data for one aircraft (see the "Aircraft Specifications" student handout to find out how to determine the calculations):

• Calculate how much fuel is burned after one, two, and three hours and record the mass changes.

• Plot these points and draw a line that passes through the points.

• Calculate the percent change in mass of the aircraft after three hours of travel.

4. Some students may think that mass is actually lost as a plane's mass changes during flight. Make sure students understand this is not true. Explain to students that energy can neither be created nor destroyed. (Energy present in a system remains constant.) In terms of this activity, fuel is burned and converted into energy to fly the plane. Some energy is dissipated as heat; fuel (mass) is lost from the plane, but not from the universe.

5. Have students complete their calculations and fill in their data tables. (Note: If you would like, you can also have students calculate the slope of the line [slope = rise/run]. The slope indicates fuel burn in relationship to the mass of the plane.)

6. Now have students consider what it costs per passenger to fly across the Atlantic. (Figures provided in the charts are based on presumptions that the planes are flying the same distance under the same conditions.) As the weight per gallon of jet fuel varies during different seasons and in different climates, students are given the conservative estimate for the weight of one U.S. gallon of jet fuel (2.715 kilograms). Ask teams to complete the calculations on the "Passenger Counts" chart and display their results in a bar graph.

7. Discuss the results as a class. Ask students why it is important to consider how fast an aircraft burns fuel. Why is it important to consider take-off weight? Why is it important to consider the percent change in mass of an aircraft in flight? What are some factors that have an effect on aircraft fuel consumption? Which plane has the highest per passenger fuel use? Which has the lowest? (See Activity Answer for more information.)

8. Note to students that the amount of fuel burned per hour and the number of passengers are only two of many variables that must be taken into account when determining a plane's economic efficiency. Have students name three additional factors that would contribute to determining if an airplane is an economical investment for an airline company (i.e., safety record of the plane, speed at which the plane travels, and repair and maintenance costs).

9. As an extension, have students compare the fuel burn of military aircraft. How is it different from that of commercial aircraft? What might account for the differences in fuel burn?

The Federal Aviation Administration completes calculations for aircraft hourly fuel burn and considers how fuel burn increases when there is additional weight on a plane. (Hourly fuel burn calculations include an average of climb, cruise, and descend fuel burn rates.) Extra weight can impact fuel burn because the engines must work harder to maintain flight.

Students can infer from their graph the rate of fuel burn in relationship to the average take-off mass of an aircraft. The Concorde's fuel burn rate is greatest.

It is important to consider how fast an aircraft burns fuel because fuel has mass and alterations in mass impact flight. Because the mass of the plane has changed after the first hour of flight, there could be a slight difference in rate of fuel burn after each successive hour. (This difference is not calculated in this activity.) The fuel burn rate also has implications for the range in which an aircraft can fly.

It is important to consider the percent change in mass of an aircraft in flight because balance is an important aspect of flight. Changes in mass have an effect on the balance of some planes.

The initial mass of the plane affects how much fuel burn is needed to produce a increase in percent mass change. A greater amount of fuel burn per hour is required to increase the percent mass change for more massive planes than for less massive planes. This is why the slope of the line for Boeing 747-100 is greater than for Airbus 300-600 even though the percent mass change is the same.

Three major factors that have an effect on aircraft fuel consumption are the mass of the plane, speed of the plane, and resistance (wind). Based on fuel calculations alone, the Boeing 737-4 is the most fuel efficient per passenger; the Concorde is the least fuel efficient per passenger.

Graphing Mass Change

Fuel Burn

 Aircraft Type Engines Average Take-off Mass with Fuel (kg) Fuel Burn Rate (gal/h) Weight of Gallon of Fuel (kg) Mass of Fuel Burned (kg/h) Hour 1 Mass of Plane (kg) Hour 2 Mass of Plane (kg) Hour 3 Mass of Plane (kg) Boeing 747-100 4 340,190 3,638 2.7215 9,901 330,289 320,388 310,487 Boeing DC-10-3 3 259,450 3,130 2.7215 8,518 250,932 242,414 233,896 Concorde 4 185,062 6,771 2.7215 18,427 166,635 148,208 129,781 Airbus 300-600 2 161,022 1,678 2.7215 4,567 156,455 151,888 147,321 Boeing 727-200 3 95,026 1,844 2.7215 5,018 90,008 84,990 79,972 Boeing 737-4 2 64,636 792 2.7215 2,155 62,481 60,326 58,171 BAE 146-2 4 40,993 817 2.7215 2,223 38,770 36,547 34,324

 Aircraft Type Mass of FuelBurned After3 Hours (kg) PercentMassChange Boeing 747-100 29,703 8.73 Boeing DC-10-3 25,554 9.85 Concorde 55,281 29.87 Airbus 300-600 13,701 8.51 Boeing 727-200 15,054 15.84 Boeing 737-4 6,465 10.00 BAE 146-2 6,669 16.27

Passenger Counts

 Aircraft Type Fuel Burn Rate (gal/h) Average Airborne Speed (km/h) Amount of Fuel Burned (gal/km) Passengers and Crew Distance per Passenger per Gallon (km/gal) Distance Traveled (km) Gallons per Passenger (London to New York) Boeing 747-100 3,638 825.6 4.4 423 96.1 5,547 57.7 Boeing DC-10-3 3,130 828.8 3.8 283 74.5 5,547 74.5 Concorde 6,771 2,160.0 3.1 109 35.2 5,547 157.6 Airbus 300-600 1,678 740.3 2.3 274 119.1 5,547 46.6 Boeing 727-200 1,844 703.3 2.6 157 60.4 5,547 91.8 Boeing 737-4 792 664.7 1.2 150 125.0 5,547 44.4 BAE 146-2 817 463.5 1.8 92 51.1 5,547 108.6

Gallons Per Passenger

Web Sites

NOVA Web Site—Supersonic Dream
www.pbs.org/nova/concorde/
Find articles, interviews, interactive activities, and resources in this companion Web site to the program.

How Concordes Work
www.howstuffworks.com/concorde.htm
Describes how the Concorde worked and compares it to other jets.

Last Concorde Flights Touch Down
www.cnn.com/2003/WORLD/europe/04/10/biz.trav.concorde.quest/
Includes a special report that covers the rise and fall of the Concorde.

Concorde History
www.concordesst.com/history/historyindex.html
Presents a time line and key events section and includes photographs that span more than 20 years of the plane's history.

Books

Calvert, Brian. Flying Concorde. Osceola, Wisconsin: Motorbooks International, 2002.
Portrays the history and production of the Concorde and contains technical specifications of the aircraft.

Endres, Gunter. Concorde. Osceola, Wisconsin: Motorbooks International, 2001.
Examines Concorde's history, design production, and service.

Grant, R.G. Flight: 100 Years of Aviation. New York: Dorling Kindersley Publishing, 2002.
Presents an historical view of aviation that includes photos focusing on aircraft design.

Owen, Kenneth. Concorde: Story of a Supersonic Pioneer. London: Science Museum, 2002.
Traces the development of the Concorde.

The "Fueling the Burn" activity aligns with the following National Science Education Standards and Principles and Standards for School Mathematics.

Grades 5-8

 Science Standard B:Physical Science

Transfer of Energy:

• In most chemical and nuclear reactions, energy is transferred into or out of a system. Heat, light, mechanical motion, or electricity might be involved in such transfers.

Motions and forces:

• The motion of an object can be described by its position, direction of motion, and speed. The motion can be measured and represented on a graph.

Mathematics Standards:

• Algebra
• Data Analysis and Probability

Grades 9-12

 Science Standard B:Physical Science

Chemical reactions:

• Chemical reactions may release or consume energy. Some reactions such as the burning of fossil fuels release large amounts of energy by losing heat and by emitting light. Light can initiate many chemical reactions such as photosynthesis and the evolution of urban smog.

Conservation of energy and the increase in disorder:

• The total energy of the universe is constant. Energy can be transferred by collisions in chemical and nuclear reactions, by light waves and other radiations, and in many other ways. However, it can never be destroyed. As these transfers occur, the matter involved becomes steadily less ordered.

Mathematics Standards:

• Algebra
• Data Analysis and Probability

Classroom Activity Author

Developed by WGBH Educational Outreach staff.

 Supersonic Dream Original broadcast:January 18, 2005

 Major funding for NOVA is provided by Google and BP. Additional funding is provided by the Howard Hughes Medical Institute, the Corporation for Public Broadcasting, and public television viewers.

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