March 08, 2010

Power Output: The Energy Flow Rate

As my studies continue here at UNT, I notice myself beginning to think more like an engineer. This time I really mean it. The other day I calculated the power output of my body. The calculations were pretty messy, but it was worth it just to get a quantitative comparison of my body to an electric motor. The calculation itself is quite easy actually, just messy.


When I go to the gym, I typically ride the stationary bike for about 30 minutes. Sometimes I run on the treadmill, but the type of activity here is unimportant. What I want to highlight is the area on exercise equipment that displays the amount of calories you have burned during a workout. I typically burn around 300-400 calories every 30 minutes, depending on the type of exercise, sometimes it’s more, but for the purposes of this discussion we’ll say it’s 400.

In my studies, I learned that the calorie is a unit of energy. Energy is what makes everything work. Energy manifests itself in several different forms. Electricity, heat, magnetism, and mechanical work are the simplest forms of energy. The calorie is just one of many different ways to quantify these said forms of energy. Calories can also be expressed in a unit called Joules. There are approximately 4.18 Joules in 1 calorie. A unit of power called the watt is commonly used to quantify power, and watts are a measure of the amount of Joules per second. So I figured that if I simply took my total amount of calories burned in thirty minutes, multiplied by 4.18, and then divided by the number of seconds in thirty minutes that I would have my body’s power output during my workout. The numbers were staggering.


400 times 4.18 is 1672. That’s the number of Joules. 1672 divided by 1800, which is the number of seconds in thirty minutes, is 0.928. My body’s power output is only 0.928 Watts. You gotta be kidding me! To compare, a common light bulb runs at about 40 Watts, more than forty times my body’s power output. And to think, I could only keep that pace for thirty minutes, light bulbs can last for years.
These kinds of calculations humble me. The capability that we now have to harness energy is astounding. You can clearly see that the human body is no match to the power output of an electric motor. We even measured a quarter-sized motor in my lab class that ran at around 1- 1.5 Watts, and as long as the motor has power it will continue to run assuming no friction or other unforeseen electrical problem. At that power output, my body could probably only run for about an hour. I wonder if there is any way to battery power a human…

Arnold figured it out.