# Non-productive work while running

1. Sep 11, 2011

### spotmeter

Many runners twist in their upper body while they run. You can see this by watching the logo on their tee-shirt move sideways. You can also see it when their arms cross in front of their body instead of moving straight forward and back.

We have found that runners do this because of tightness in their shoulders. When they bring their right arm back, for instance, tightness in their right shoulder will twist their shoulders to their right, throwing their left arm across their body.

Less well known is that they also swing their right leg to their left to counter the twisting to their right in their upper body. In some cases, they may even cross over the midline.

We would like to be able to compute the amount of extra work, or extra energy expended, to twisting and counter-twist like this while running.

We are able to quantify the amount of lateral movement of the arms and legs with a biomechanical analysis of a runner, but we don't know how to quantify the amount of work or energy expended.

Any help very much appreciated.

2. Sep 11, 2011

### Ken G

It sounds to me like you want to analyze the runner's body in terms of two counter-rotating pieces, with their associated moments of inertia, that maintain zero net angular momentum. The kinetic energy of rotation gets stored in some kind of twisting potential, and then some is returned when they untwist and some is dissipated. So the two questions there would be, what is the magnitude of the work done by the two pieces on each other (i.e., the magnitude of the stored energy), and what fraction of that is lost when they untwist and prepare for the next step? It seems to me rather a lot gets lost, so the most important question might be the magnitude of the twisting energy we are talking about. That might be characterized by the maximum angular velocity they achieve-- the twisting kinetic energy is Iw2/2, where I is the moment of inertia of each half (upper and lower body), and w is the angular speed of each half. If the model is good, the product of Iw should be about the same for upper and lower halves-- maintaining zero net angular momentum. That means the work done is just the action/reaction torque each half applies on the other half, integrated over twist angle. Whichever part twists more gets more of the work done. What makes it tricky is that the body might generate balancing but opposite forces on the same part (upper or lower), so that work would be done and likely dissipated without showing up in the w. Estimating that contribution would be difficult, and might have to do with the tenseness of the midriff.