Steady state energy vs. energy rate

[Bill Foster]

I went for a run and measured time and distance. I wanted to estimate how many calories I used.

Suppose a ran a distance $$x$$ in an amount of $$t$$ time.

if my mass is $$m$$, then my stead state average energy would be

$$E=\frac{1}{2}m\frac{\Delta{x}^2}{\Delta{t}^2}$$

But what is the rate at which I am using energy?

Or what is the total energy used in either distance $$x$$ or time $$t$$?

Total energy used, or work, can be gotten from $$W=Fx$$, and the rate of energy used from $$P=Fv$$. But I don't know what the force $$F$$ is.

 

[Shooting Star]

If you stand still for one hour at a stretch, you'll probably be exhausted. Our body doesn't use or conserve energy quite like the sliding blocks or rolling balls of elementary mechanics.

The average force you have to overcome during running comes from various sources. One is obviously the air resistance. Another is the friction between muscles in your body -- the two legs don't act like double pendula. You also move your arms and other parts of the body relative to each other.

But the most significant energy loss would be this way: with every step, your centre of gravity rises and falls, and the co-efficient of restitution with the ground is not unity. So, with every step energy is lost and to bring back the CG to the same height, you have to expend energy. That's why making shoes for runners has become such a science -- the more spring your shoe has, the less energy you spend.

Think about it and I'm sure you'll find other sources of spending energy. It won't be very easy to find the average force F.