Calculating energy requirements for heavy runners

[andrewdickson]

Hi All...

This is my first time, be gentle.

It was a long time ago that I studied stage 1 physics during my biochemistry degree (yes, I know biochemistry was a cop-out) and I am having trouble figuring out a way to express the energy requirements for different body weight runners. Basically someone quoted F=MA to me to describe why a man weighing 90kgs running at a constant speed of 4m/s would require more force than a man weighing 60kgs also running at a constant speed of 4m/s. Now I know that it is obvious that the bigger bloke must exert more force but it seems that F=MA is not the formula to show this. What I really want to do is work out the relationship between body weight and force required to move that body weight at a constant speed.

Any ideas?

Thanks all,
Andrew (from New Zealand)

 

[tiny-tim]

Welcome to PF!

Hi Andrew! Welcome to PF!

Basically someone quoted F=MA to me to describe why a man weighing 90kgs running at a constant speed of 4m/s would require more force than a man weighing 60kgs also running at a constant speed of 4m/s. Now I know that it is obvious that the bigger bloke must exert more force but it seems that F=MA is not the formula to show this. What I really want to do is work out the relationship between body weight and force required to move that body weight at a constant speed.

Yes, at constant speed, the acceleration (A) is zero, so F = MA doesn't help at all!

At constant speed, the forces must balance, so the horizontal force from the muscles must equal the air resistance.

So weight doesn't come into it, though frontal surface area certainly does.

But I don't know how the horizontal force relates to the energy … it presumably depends on lots of physiology-type things.

 

[SteveW]

F = MA is indeed the short explanation, but not very useful in prediction. Every stride contains a vertical component that is an acceleration against gravity. Also muscles do not generate a constant force, but create a series of accelerations. You'll never get to an accurate math analysis without knowing and accounting for all the masses and motions of the individual body parts.