I read a manual by Ralph Mann and in it he stated that as speed increases it gets harder to apply vertical force. My question is: why is more vertical force need to go faster and how do you go about doing it?
As one increases speed it is harder to increase vertical force output because the faster you run the shorter ground contact time becomes. Consequently, it becomes increasingly more difficult to apply vertical forces (or horizontal forces for that matter) because you have less and less time to apply those forces. This is one of the reasons it is not recommended for long jumpers to attempt to takeoff at angles that are mathematically ‘optimal’ because to produce the vertical forces necessary to do so would require the individual to slow down so that they’d have a long enough time on the ground to apply the vertical forces necessary to takeoff at the mathematically ‘optimal’ angle (somewhere in the neighborhood of 40 degrees). Slowing down enough to set up a higher takeoff angle would have a far more detrimental effect on the distance of the jump than taking off at an angle that is substantially less (more than 20 degrees less) than the ‘optimal.’
Vertical forces are important for Vmax running because at maximum velocity the system acts very much like a spring or a bouncing ball. Forward momentum is developed through the acceleration / drive phase and at maximum velocity the net propulsive forces are 0. The vertical forces are what keep the system going (keep the ball bouncing). Without high vertical forces the system ceases to act as a spring-mass model and deceleration occurs.
At it’s most basic level we can think of it like this: the acceleration phase develops forward momentum—> the body will now tend to stay at a constant velocity unless acted on by external forces (gravity, air resistance, friction, etc.). These situations of course do not occur on earth but this statement will be most relevant to the sprinter / coach if they aim to get the system to act as a perfect spring (forces in = forces out). To do this a sprinter needs high vertical forces to keep the ball bouncing. Without the high vertical forces the system becomes less and less perfectly elastic (not to be confused with the concept of the same name typically used in sprinting) and the sprinter will decelerate more and more.
You maximize vertical force output through proper sprint mechanics and force, rate of force, and power development.
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