Calculating
Cadet
Horsepower

Objective

This is a fun activity designed to allow participants to discover their horsepower by expending energy and then calculating the horsepower.  And, once you can compute your horsepower, you'll determine how much horsepower it takes to move your car, your plane, and your space shuttle.

Time Requirement

Allow 30 minutes minimum for 20 cadets, more time for discussion is good.

Materials

• Part of this activity must be conducted on a stairway
  
• A bathroom scale would be helpful, but not necessary if participants know their weight
  
• A stopwatch, or a watch with a second hand
  
• A calculator can be handy to check the answers, but it's better to have the cadets do the math manually just like in the good ol' days

Background

• Horsepower is a standard unit of power equal (in the United States) to 746 Watts.  This is nearly equivalent to the English gravitational unit (called one horsepower) of 550 foot-pounds of work per second.
  
• James Watt devised this formula for computing horsepower:

Horsepower =

Foot-Pounds Seconds X 550

• It is still used today for calculating the horsepower of engines.
  
• Another way to calculate horsepower is:

Horsepower =

Distance (in feet) X Weight (in pounds) Speed (in seconds) X Constant (550)

• Using either of these formulas, a horsepower-hour is equal to 1,980,000 foot-pounds, the amount of energy used to do one hour's worth of work at one horsepower.
  
• The engine of a small motor-bike produces between 30 and 50 horsepower; a medium-sided car engine creates between 100 and 300 horsepower.
  
• How much horsepower can a cadet produce?

Procedure

1. Divide the group into teams of two.

2. Measure the distance up a staircase.  Determine the number of steps that equals ten feet vertical rise, and mark that step with a piece of masking tape.  (If you only have an eight-foot staircase, you can alter the math accordingly.

3. One person on each team starts as the stair-climber.  The other is the timer/recorder.

4. Each person records their weight, either from using the scale or from memory. (Senior members may want to be observers only for this activity! *wink*)

5. The stair-climber, beginning at the bottom of the stairs, climbs up the stairs as swiftly (and safely!) as fast as he or she can go.  The timer/recorder times the climb from the start to the time that the climber passes over the mark at the ten foot level.  The time is recorded.

6. Team members change places, and the timer/recorder becomes the climber.  Complete the task as before, and record the results.  (If you want to get the cadets all sweaty, repeat the procedure a number of times and take the average time!)

7. Using the formula, calculate each person's horsepower output.  For foot-pounds, use the cadet's weight multiplied by ten feet.

Assuming a cadet weight of 120 lbs.,  and a time of 3.5 seconds to climb 10 vertical feet:

 

Horsepower

=

120 X 10 3.5 X 550

=

1,200 1,925

=

0.6233

Discussion

Compare horsepower among members of the group.  Which cadet has the most horsepower?

• Would this be a good way to determine how much energy a person could expend in a day?  Why or why not?

• How much horsepower does it take to move these objects?

  • Find the weight of a typical automobile, a Cessna 172, and the space shuttle.

  • Calculate the horsepower needed to move the car 5,280 feet in one minute (one mile at 60 miles per hour). 

  • Calculate the horsepower for the Cessna to reach 5,000 feet altitude in ten minutes.

  • Calculate the horsepower needed for the shuttle to reach 100 miles (528,000 feet!) up (in orbit) in five minutes.

Instructor Notes

• The fueled weight of a Saturn SL2: 2,470 pounds

• The fueled weight of a Cessna 172 Skyhawk: 1,678 pounds

• The fueled weight of the space shuttle: 4,500,000 pounds (approx.)

Other Interesting Facts:

• The Saturn gas tank holds 12 gallons.  Each gallon weighs 6.7 pounds.

• The Cessna 172 gas tank capacity is 42 gallons, again at 6.7 pounds per gallon.

• Fuel for the space shuttle is contained in two solid rocket boosters, each weighing approximately 181,000 pounds, and an external fuel tank with an approximate weight of 66,000 pounds.  The approximate weight of the solid fuel is 1,111,000 per booster.  The liquid oxygen weighs in at 1,361,936 pounds and the liquid hydrogen weighs 227,641 pounds.  (See table below)

Space Shuttle Component	Weight (lbs.)
Solid Booster	181,000 X 2
External Fuel Tank	66,000
Solid Fuel	1,111,000 x 2
Liquid Oxygen	1,361,936
Liquid Hydrogen	227,641
Orbiter	260,000
Total	4,500,000 (approx.)

Factoids:

A Saturn needs about .2 pounds of fuel to travel one horizontal mile.

A Cessna uses about 12 pounds of fuel to reach 5,000 feet, about one mile up.

The space shuttle uses about 3,811,577 pounds of fuel to reach an orbit 100 miles up, or 3,115 pounds to climb each mile.

Adapted from: Aerospace 2000, Volume 3
Published by the Aerospace Education Training Directorate
National Headquarters, Civil Air Patrol.