I had an interesting conversation over lunch about exercise efficiency. It all started as I was explaining how I hate running. Then we started talking about how running used far more energy than cycling and one thing led to another. Anyway, I brought up the fact that a bicycle is one of the most energy efficient forms of transportation and quoted my usual random figure about the miles per gallon equivalent of bicycles and cars.

I have always been unsure of the exact MPG equivalents so I looked it up and found the above equation on Wikipedia.

Go ahead and read everything at the link for a full explanation but I’ve quoted the variables I’ll use here:

Where *P* is in watts, *g* is Earth’s gravity, *V*_{g} is ground speed (m/s), *m* is bike/rider mass in kg, *s* is the grade (m/m), and *V*_{a} is the rider’s speed through the air (m/s). *K*_{1} is a lumped constant for all frictional losses (tires, bearings, chain), and is generally reported with a value of 0.0053. *K*_{2} is a lumped constant for aerodynamic drag and is generally reported with a value of 0.185 kg/m.

I’m also going to use the same values for *V*_{g} (ground speed) and *V*_{a} (air speed) and assume there is no wind just to simplify it a bit.

I weigh 210 pounds or 95.25 kilograms, I can peddle at 15 miles per hour or 24.14 kilometers per hour which is about 6.7 meters per second. So here we go with the math:

**P = (9.8 x 95.25 x 6.7 x 0.0053) + (0.185 x 6.7**^{3})

or

**P = 89.54 watts**

Simple, at 15mph on a flat road without any wind I am generating 89.54 watts of power. If we go back to the Wikipedia article for some numbers we can assume that the human body converts food calories to energy with about 24% efficiency or every kilojoule of energy to the peddles requires about 1 kcal of food.

**Human Efficiency = 89.54 x .24**

so

**Human Efficiency = 372.08**

Assuming the loss in efficiency I’m using 373.08 watts of food energy to get 89.54 watts to the peddles. Next we’ll convert watts to kilocalories per hour by multiplying by 0.86 to convert it to food energy. (A kilocalorie is the equivalent to 1 calorie of food.)

**Calories per hour = 373.08 x 0.86**

so

**Calories per hour = 320.85**

So i’m using about 320.85 calories per hour to travel by bicycle on a windless flat road. Now lets get to the final answer. We’ll use 31,000 kcalories of energy per gallon of gas and do some simple division.

**Calories Per Mile = 320.85 / 15**

which is 21.39

** **** Mile Per Gallon = 31,000 / 21.39**

** **** ****1 449.28 MPG**

In a nutshell, I’m getting 1,449.28 mpg when I’m peddling the bicycle around. I’m glad I finally calculated all that and know the answer.

…and back to the original discussion on why running sucks, it uses nearly three times as much energy to travel the same distance:

On firm, flat, ground, a 70 kg person requires about 30 watts to walk at 5 km/h. That same person on a bicycle, on the same ground, with the same power output, can average 15 km/h, so energy expenditure in terms of kcal/(kg·km) is roughly one-third as much. Generally used figures are

- 1.62 kJ/(km∙kg) or 0.28 kcal/(mi∙lb) for cycling,
- 3.78 kJ/(km∙kg) or 0.653 kcal/(mi∙lb) for walking/running,
- 16.96 kJ/(km∙kg) or 2.93 kcal/(mi∙lb) for swimming.

You can do you’re own math with that information. I still hate running.