Apr 13, 2021 8:00 AM

How Many Homes Could You Power With Free Doughnuts?

Krispy Kreme is offering a year of treats to anyone who gets the Covid-19 vaccine. What if they worked off the energy on pedal-powered bike generators?

Should you get a Covid-19 vaccine? Yes, it will protect you and others to help us move past this pandemic and get back to a more normal life. But wait! If you get vaccinated, you can also get a doughnut! At least, that's the deal that Krispy Kreme is offering. Once you get your vaccine, you get a doughnut. And it's not just one doughnut—it's one every day. That's a lot of doughnuts.

OK, so how about some physics estimations to go along with your tasty treat?

Let's say that all the Americans who have a Covid-19 vaccine get (and eat) one doughnut a day. Of course, eating food gives you energy to do stuff—that's how food works. So, suppose that all those humans use that extra energy to pedal stationary bikes. All of the bikes are connected to generators that feed into the power grid. What kind of power output would this produce?

The first thing we need is the number of doughnuts eaten per day. According to the Centers for Disease Control and Prevention, as of April 7, 63 million Americans had been fully vaccinated. (Don't worry too much about the numbers—I'm going to do all my calculations in Python so that you can change the values, if that makes you happy. I'm also going to assume that all these people get their doughnut every day.)

Next, I need to know the amount of energy per doughnut. According to Krispy Kreme's site, a plain glazed is 190 calories. But what the heck is a calorie? Well, the original calorie was created to describe changes in thermal energy for different substances. Later, people used the term to measure the amount of chemical energy your body can gain from eating food. However, there is a problem: For some reason, all food labels list calories—but these are really kilocalories. So that doughnut has 190,000 calories. I guess it just sounds like it's too big of a number for people to consider eating.

There is another unit of energy: the joule. Since this is the preferred unit of energy for physicists, I'm going to use it. To convert between units, 1 calorie is equal to 4.184 joules.

But what does this have to do with your everyday life? Let's consider something you might do without too much effort. Suppose you have a textbook on the floor and you pick it up to put it on a table. Since you are exerting a force on the book over some distance, you have to change the gravitational potential energy of that book. The change in gravitational potential energy is equal to the mass of the book (about 1 kilogram) multiplied by the local gravitational field (g = 9.8 N/kg) and then multiplied by the change in height (about 1 meter). This will give a change in energy of about 10 joules. So that gives you a rough feeling for the amount of energy in a joule.

But what about power? Power is the rate of energy change. It tells you how fast you use energy. As an equation, it looks like this:

Illustration: Rhett Allain

In this expression, if ΔE is the change in energy in units of joules and Δt is the time interval in seconds, then the power will be in units of watts.

We are almost ready to calculate the power of doughnuts. We just need one more estimation: the efficiency. When a person eats a doughnut, only some of the chemical energy becomes useful energy. Also, with a stationary bike generator, some of the energy the human uses to push the pedals also goes into heating up some of the bicycle's moving parts. In the end, only a percentage of the food energy becomes electrical energy. This percentage is the efficiency. I'm just going to make a rough guess that the conversion of doughnut to electrical energy is 25 percent efficient.

That's it. I just need to take the number of doughnuts consumed per day by all 63 million vaccinated Americans and convert that energy to joules and then divide by the length of a day (in seconds). Then, multiply by the efficiency. Here's what I get. Note: this is actual python code. You can see my calculations and even change them if you like.

Illustration: Rhett Allain

You can see that for each human, it's just a measly 2 watts of power. That's around the output for a smartphone (although power values vary based on use). However, once you include all the vaccinated people, we get up to 144 megawatts. In 2019, the average household’s power consumption was about 1,200 watts. That means that you could use all these doughnuts to run 120,000 homes every day. Oh, and you get vaccinated—that's a win.

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