SEED Science

Power to the Pedal!

Math Puzzles of the Month
Power to the Pedal!

Have you ever wondered whether the power of a bicycle could be harnessed to do useful work—other than pleasurably moving you from place to place? This puzzle may help you decide whether this is a) possible and b) practical.

Sami comes from a remote village without electricity. The last time he returned home for vacation, he brought his laptop computer with him. Sami also loves to ride his bike. His cousin is a clever electrician, so Sami wants to know if he can rig up a generator for his bike that would provide enough power for him to use his laptop computer. The generator and bicycle would have to be mounted on a stationary stand so that all the pedal power would go to generating electricity.

Resources

There are many Web sites with information about generating power from bicycles. Here are a few that will get you started for information on producing electricity by pedaling:

A man named Michael Bluejay has set up a comprehensive Web site for finding out about electrical power uses of various home appliances:

The following page has specific information you can use:

Let’s assume that the technical problems have been solved and that Sami is a good cyclist with strong legs and is used to taking long bike rides.

Here are a few specific questions you might try to answer:

  1. About how much power can Sami expect to generate while pedaling?
  2. How much power is needed to run Sami’s laptop?
  3. Would it be better for him to use his computer while pedaling (it’s a stationary bicycle, remember) or to charge his laptop battery, then get off the bike and use the laptop? How many hours of pedaling would it take to charge the battery?
  4. The One Laptop Per Child project is developing low-cost laptop computers for use in developing countries. How many hours of pedaling would it take to charge one of those computers?

Extra Challenge

How many hours of pedaling would it take to run various household appliances: TV, radio, refrigerator, washing machine, and so forth?

Background

Fermi questions

This puzzle is the third in a series devoted to examples of “Fermi questions” named in honor of the Nobel laureate and nuclear physicist Enrico Fermi. Fermi used to give his students problems that involved large numbers, estimates, and approximations. He expected his students to be able to simplify the numbers and do all their calculations on a small piece of paper. They are sometimes called “back of the envelope” problems. You can find many examples on the Web if you search for “Fermi questions.”

Fermi questions involve making many assumptions, approximations, and simplifications to try to get a reasonable answer quickly. Your answer doesn’t have to be exactly correct—maybe there is no exact answer, because the problem is vague or conditions can vary. A Fermi question does not give you all the information you need; you need to look things up and/or make assumptions.

Electric power

The rate at which electric power is used is measured in watts, a product of the voltage, V, in volts and the current, A, in amperes. For example, the power adaptor for a Toshiba laptop says that it produces 15 volts of electricity at a current of 5 Amps. This results in a power usage of 15 x 5 = 75 watts. However, as you may know, a computer rarely needs to run on its maximum power—75 watts is the most this computer will use. Most of the time it will draw much less. The rate of power use is 75 watts. The maximum power may be needed when saving data on a hard drive or downloading graphics. When the computer is idle, and especially when it’s “sleeping,” it may use only a few watts.

To find the total power used by an appliance, multiply the wattage by the time it’s used. A 100-watt lightbulb will use 100 watt-hours of power every hour. (It doesn’t use any power when it’s turned off!)

After you’ve tried this for yourself, check our solution.


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