# Physics Behind Energy Expenditure?

1. Jun 17, 2014

### Jimmy87

Hi, I have been reading some research online which seems to all conclusively say that the energy a person expends during a workout is indpendent of their running speed (http://www.runnersworld.com/weight-loss/mythbusting-running-mile-always-burns-same-calories). It only depends on things like your weight, fitness levels etc. So if two people the same weight, height and fitness ran 5 miles then it wouldn't matter who ran it the fastest - they would both expend the same energy. I was just wondering if this fact comes from any fundamental laws of physics? Would there be any equations that could prove that a quicker running speed over a shorter distance is the same as a slower running speed over a longer distance?

2. Jun 17, 2014

### Born2bwire

The energy needed, at its simplest, is dependent only on their mass, distance traveled, and change in altitude. The energy needed does not depend on the speed as long as the distance is the same. For real life, the efficiency of the body to produce this energy would be the extra factor and this is probably what they mean by fitness. Perhaps the speed that you run may change this efficiency but that is a biological question and they seem to think it is not as significant.

Edit: To explain this more fully, energy is a force acting through a distance. Walking is like a controlled fall. We move our legs back and forth, but with a steady gait this is a pendulum motion so we do not have keep up a strong force to keep it going. Most of the force we exert is to lift our body back up so that we can fall forward again. So the work we do against gravity is not affected by the speed since the force of gravity is set by your mass. However the number of times we have to lift will be related to the length of your gait and the number of strides you take. So to first approximation, the speed is not a large factor.

Last edited: Jun 17, 2014
3. Jun 18, 2014

### CWatters

As I understand it running involves the storage and release of energy in the legs in much the same way that energy is stored and released in a spring. You only burn energy because the process of storing and releasing energy isn't 100% efficient (ignoring air resistance and the like).

The article suggests that in some cases less energy is consumed when running faster. Perhaps that's because when running faster you take fewer longer strides to cover the distance - so there are actually fewer cycles of the spring.