### Should you walk or run when it's hot out?

Thanks to global warming, I've gotten the pleasure of walking to work in excruciatingly hot conditions recently. As I was walking to my office yesterday, I started thinking "it's so hot - I should hurry inside to get to the air conditioning." But of course, if I hurried then I would burn more energy and heat myself up even further!

Despite the wide body of literature available on whether one should walk or run in the rain, I couldn't find any suggestions on whether to walk or run in the heat. So I decided to do some investigating.

For a 150 pound person, walking at three miles per hour (a moderate pace) burns 230 Calories per hour. Walking at four miles per hour (a brisk walk) burns 350 Calories, and five miles per hour (a near run / slow jog) burns 544.

In 30°C temperature (~85°F), the sun gives off 400 Watts per square meter of heat from solar radiation, about half of which is immediately reflected (depending on your skin color and clothing). While most peoples' body surface area is around 1.8m2, only about half of your body will be directly receiving the sunlight, so we'll assume that you're getting ~200 Watts of power from the sun, which equates to 172 Calories per hour.

Lastly, we need to consider convection (or "wind chill"). The "wind chill factor" can be approximated as $8.3\sqrt{w}$, with $w$ the wind speed in meters per second. Skin temperature stays fairly constant around 34°C, meaning that in our 30°C weather there will be a temperature differential of 4 degrees. Change in heat is the product of the temperature difference, wind chill factor and body surface area. For a standard person, this gives us $$\frac{dQ}{dt}=8.3\times \sqrt{w}\times 4 \times 1.8 = 59.8\sqrt{w}$$ which we can integrate to find our total heat loss.

If you walk at three miles an hour, you will gain 230 C/hr from the exercise, and spend 1/6 of an hour outside to walk 1/2 of a mile. While outside, you will gain 172 C/hr from the sun, but lose 60 C/hr from convection, for a total gain of 112 C/hr. If we multiply this all out, we find that you will gain a total of 57 Calories of heat from your exercise.

Repeating the calculations gives us that you increase by 56 Calories when walking at four miles per hour, and 64 Calories when walking at five.

So my recommendation is what you would probably expect: a brisk walk will cool you off a little, but don't jog or you'll just end up soaked in sweat.

(All numbers and formulae taken from Physics of the Human Body. See this gist for a small octave/matlab script if you want to play around with the numbers. It would be interesting to consider the effects of humidity and higher temperatures, if you're up for it.)