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:

Saving Electricity [4]

The following page has specific information you can use:

How much electricity do computers use? [5]

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:

About how much power can Sami expect to generate while pedaling?
How much power is needed to run Sami’s laptop?
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?
The One Laptop Per Child [6] 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!)

Course:

Math [7]

Result/Solution(s)

Any solutions we find will be approximate—which is perfect for a Fermi question. People pedal at different rates; different generators harness that power with different degrees of efficiency; different computers have different power requirements. So our answers may not be the same as what you came up with.

1. About how much power can Sami expect to generate while pedaling?

Different Web sites we’ve looked at estimate that a good cyclist can generate between 50 and 100 watts at a steady rate. Let’s estimate that our generator is only 50% efficient. So if 75 watts is an average rate, then the generator output would be about 37 watts.

2. How much power is needed to run Sami’s laptop?

Michael Bluejay’s Saving Electricity Web site rates laptop computers at an average of 15–45 watts. Let’s take a middle value of 30 watts as the average amount needed for Sami’s laptop.

3. Would it be better for Sami 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?

Since the average output of Sami’s generator is about 37 watts, he should have no problem using his 30-watt computer, as long as he can keep pedaling. However, it would be difficult for him to use his computer while pedaling. If he can get someone else to pedal for him, this won’t be a problem.

Let’s do some estimates about how long it would take Sami to charge his battery. Suppose an average laptop battery can power the computer for four hours before running down. At 30 watts, this means the battery would have a power capacity of 4 x 30 = 120 watt-hours. At his average output rate of 37 watts, Sami can generate 120 watts of power in 120 / 37 = 3.24, or 3 1/4 hours.

If he wanted to use his computer for one hour, his pedaling time would be 30 / 37 = 0.81 hours or about 49 minutes.

4. The One Laptop Per Child project is developing very low-cost laptop computers for use in developing countries. How many hours of pedaling would it take to charge one of those computers?

It’s worth a visit to this project’s Web site just to read about this amazing effort, which seems to be nearing fruition. (The goal is to produce these at a cost of $100 each, but current projected costs are running closer to $150.)

According to hardware specs on the Web site, the voltage will be between 10 and 25 volts, with a maximum current draw of 500 mA (that’s 0.5 A). Batteries are rated for 22.5 watt-hours. The goal, as stated on the Web site, is to have a computer that can run for a whole school day on a charge.

We know that Sami can generate 37 watts on his stationary bike. So he can charge the battery in 22.5 / 37 = 0.61 hours, or about 36.5 minutes.

But how long will it take the little giant to use up 22.5 watt-hours? Based on the maximum power requirements listed in the specs, the laptop could draw a maximum 25 V x .5 A = 12.5 watts. Since this is the maximum power use, the average rate will be less, maybe half, or 6.25 watts. This means it would use up 22.5 watt-hours in 3.6 hours, or 3 hours 36 minutes.

So by these estimates, Sami could use his computer for more than 3 1/2 hours with only 49 minutes of pedaling!

Here's an extra challenge: How many hours of pedaling would it take to run various household appliances, for example the TV, radio, refrigerator, washing machine, and so forth?

With the Web resources and your level of knowledge, you should be able to find answers for any of these—no sweat!

Math Puzzle [8]