How does the velocity of the previous stride affect the current stride?
In every stride except for the first stride, the runner’s center of mass already has horizontal velocity. How does this affect the simple example of project motion of the center of mass? If we consider the simple object rather than the runner, there are three cases that could occur with the object already having horizontal velocity. Before the object is released into the next free-fall, it could have positive, zero, or negative horizontal acceleration. After any acceleration is applied, and once it is in free-fall, it either has a new velocity or the same velocity. It travels a path independent of any previous parabolic paths. The horizontal velocity of the object is determined by what happens before it is in free-fall.
This analysis of the simplified example can be applied to a runner. Although there may be movements that can be made while in free-fall to increase horizontal velocity, to simplify the analysis, let’s ignore any of these components. One obvious component that determines the horizontal acceleration of the runner’s center of mass is the speed of the foot when it contacts the ground. If the foot is moving slower than the ground, there will be a net negative (backward) change in the velocity of the runner’s center of mass. If the foot is moving the same speed as the ground, the ground will not decrease the runner’s speed, but air resistance would contribute to a net decrease in the runner’s speed. Therefore, the foot must be moving faster than the ground to be able to create positive horizontal acceleration. This is necessary to prevent negative acceleration due to the ground and also the negative acceleration due to air resistance. Some people have the perspective that to maintain top speed, you just have to push down into the ground “like a pogo stick” and let the horizontal velocity carry you along at top speed. From the above analysis, it appears that only pushing down into the ground would actually result in lower velocities because the foot would not be moving at least the speed of the ground.