On the left in the picture above: When a person stands still, gravity pulls down and ground reaction force pushes up with equal force. A GRF vs time graph shows a steady line equal to the force of gravity. On the right: Sprinting has a flight phase in which neither foot is on the ground. During flight, gravity accelerates the body downward. So during stance a sprinter has to overcome gravity and accelerate the body upward to avoid falling. The resulting up and down motion is known as vertical oscillation. This requires quick spikes of vertical force on each foot contact (shown on the GRF vs time graph).The ability to generate these spikes in vertical force determines max velocity.

- Contact distance is the horizontal distance covered by the center of mass during one foot contact, from touchdown to toe-off. In the example above, contact distance is 1 meter.
- Contact time is determined by how quickly the necessary upward acceleration can be produced. In the example above, 1/10 of a second is required. This means the body can move 1 meter horizontally in 1/10 of a second, AKA an average velocity of 10 meters per second during stance.
- If this theoretical sprinter improves vertical force application so that only 1/11 of a second is required to produce the necessary upward acceleration, the body can then move at a horizontal velocity of 11 meters per second. This is how max velocity is improved.

It is important to avoid misconceptions when talking about increasing vertical force. One mistake is thinking that this calls for a more dramatic stride producing greater vertical oscillation, basically what happens when you consciously run with really long strides. The problem with doing this is that both ground time and air time increase, which means stride rate (the number of steps taken per second) decreases. The graph on the right in the picture above shows what this might look like in a force curve. The red curve has higher peak force than the black curve, but it takes more time, so it does not produce greater velocity (unless the black curve represents running short and choppy).

What is actually needed is the same vertical oscillation but achieved in less time. The graph on the left above shows the required change in force application. The red curve yields higher velocity because the higher peak force gets the sprinter off the ground in less time. In beginners this change may come from altering technique, but long term this change comes from developing the capacity of the athlete to apply force really fast.

These claims are not just my belief. We have data on this. The graph below is from "Are running speeds maximized with simple-spring stance mechanics?" It shows clearly the change in vertical force application required to achieve higher velocity.

## What about increasing stride rate and length?

Improving ground force application improves speed through some combination of stride rate and length changes. Exactly what those changes are will vary, and we really do not need to be concerned with the exact details. Here is an example scenario:- With improved vertical GRF, contact time gets shorter while air time stays the same. So the total time required for one stride is shorter. Therefore stride rate increases.
- With shorter contact time and assuming the same contact distance, the body is able to move at a higher horizontal velocity (reference the second picture above). Since air time stays the same, higher velocity means the body travels farther during flight. Therefore stride length also increases.