Christopher…
I don’t know if this advances the discussion with respect to sprinting, but if I understand your question, while the earth’s gravity is a downward force, an object (it’s center of mass) can be moved in a horizontal direction by the force of gravity if it is touching the ground. A simple example is a walking stick balanced at vertical and then released. The force of gravity and the ground force will cause the stick to rotate as it falls, and as it rotates, the center of mass moves both vertically and horizontally. When the stick comes to rest, depending on friction and other second order affects, the center of mass may have moved horizontally on the order of L/2 where L is the length of the stick.
While I understand your example – I’m unsure of it’s application. If the same walking stick were held horizontally, then released, it would essentially fall straight down. So as gravity is present in both of these examples, it would seem that the key is that the bottom of the stick is in contact with the ground. This contact creates a pivot point (hinge moment) as the bottom is fixed while the top rotates. While this indeed creates positive horizontal displacement of the COM – does in not likewise produce a negative vertical (downward) displacement of the COM (I’m assuming the COM travels in an arc about the pivot point)?
Obviously at max velocity – this pivot point is not stationary (it moves with each step) and is only present for less than .10 seconds (for elite sprinters) while the foot is in contact with the ground.
Assuming that the COM does indeed have negative displacement, would not the COM have to be raised for this process to repeat itself for the next stride (assuming we don’t want the athlete to face plant)? And if so, would this not require a vertical force to re-raise the COM so that it may “fall” again (sorry JC, I don’t think you can lean forward at the ankles and be dragged along by gravity)?
What am I missing?