Hello All:

Here are a few comments that may be helpful in this discussion.

First, the horizontal force at top speed should not actually average to zero because of the aerodynamic drag component. I don’t know of a value of drag area for a runner but lets just assume 0.6m^2 (for reference a racing cyclist in an aerodynamic position is about 0.2m^2 so my value of 1 may be high). Given a top speed of an elite sprinter of around 12.8 m/s the aerodynamic drag force at sea level would be around 0.5 * 1.2 * 0.6 * 12.8^2 = 59N. This would be average force for flight (~0.12s) and ground contact time (~0.08s) but the runner can only produce force during ground contact so average propulsive force during ground contact would be 59 *(0.2/0.08) = 147 N. This would be average for the ground contact phase. I have made some assumptions here so this number could off. I’ll try to find a better number for a runner’s drag area and redo the calculations when/if I find one. Anyway, 147 N is not large but its not zero.

EDIT: By the way, 147N moving at 12.8 m/s indicates average forward power during ground contact is around 1882 Watts. Expressed in that way, propulsive forces take on added importance.

Second, horizontal forces are important for force direction. Specifically, the line of action of the total ground reaction force vector must pass through the whole body center of mass or else there will be a net toque which causes the body to develop angular acceleration. When you slip on ice, the ice doesn’t provide any horizontal force so you only have a vertical force which is directed in front of you center of mass. Hence you rotate backward and fall on your ass. In order to run forward, you must put your foot down in front of your center of mass and so the ground reaction force vector must include a backward acting horizontal component. Later in the support phase, as you have moved past your foot the horizontal component must act forward, again to direct the ground reaction force through your center of mass.

Another way to think about the horizontal and vertical ground reaction forces would be to think of the leg as a spring. It must touch down out in front of your center of mass and it will compress in a line from the center of pressure to the center of mass. When you think about it this way, talking about horizontal and vertical forces separately misses the point.

Okay, that was a lot and I hope I wrote in English.

Cheers,

Jim