# Running Heat Model

From Fellrnr.com, Running tips

This page gives details of the mathematical model of the heat generated and lost while running. This model is used in a number of calculators:

Other calculators may be added in the future.

## Contents

# 1 Basic Heat Calculation

The basic heat calculation is from

- Heat produced from running. This is dependent mainly on your weight.
- Heat lost (or gained) from convection. This is mostly dependent on your surface area (calculated from weight and height), and the air temperature.
- Heat lost (or gained) from radiation. This is mostly dependent on your surface area and the air temperature.
- Heat lost from evaporation of sweat. This is mostly dependent on your surface area, the air temperature and humidity.

# 2 Important caveats

These calculations make lots of assumptions.

- Your running efficiency may be different to the average. A higher efficiency will produce less heat at a given pace, a lower efficiency will produce more heat.
- The only air movement is assumed to be from running through still air.
- Any wind can make a significant difference, with a headwind or crosswind cooling your off. A tailwind less than twice your running pace will reduce your cooling; it takes a tailwind of at least twice your running pace to cool you off more than still air, but of course a tailwind will reduce the energy required to run.

- The calculations assume negligible clothing. If you are wearing more than the absolute minimum clothing, this will impair your ability to cool off.
- It is possible to actively cool off with ice, which will allow you to tolerate higher temperatures.
- Any direct sun will increase the heat stress and dark clothing will make this worse.
- Remember that All models are wrong.

# 3 Advanced notes on calculations

These notes are for those with an interest in the underlying details.

- There are multiple formulas for calculating water vapor pressure which produce slightly different results.
- The calculation of skin temperature is not straightforward. The calculator uses a combination of Neilson's approach and the Mehnert formula.
- The various formulas for calculating the surface area of the skin appear to give similar results.

# 4 References

This calculator is based on Olympics in Atlanta: a fight against physics and Advantages of a smaller bodymass in humans when distance-running in warm, humid conditions