joe_meadmaker wrote on Oct 6
th, 2020 at 11:01pm:
IronGoober wrote on Oct 6
th, 2020 at 2:27am:
It makes sense if you think about how pitchers get maximum velocity, they have maximum path length of their throw.
I'm curious about how much of a difference the forward step makes. Like you (and definitely others), I use a forward step when slinging. What happens to the results if you don't take that step and just use a rotation of the body? If you recreate this experiment, I would be interested to see that comparison.
Concerning the path length of the 'drive', I tend to think of it this way. We've seen various use of the 'simple pendulum' analogy, but there is more to be squeezed from that.
We know the 'period' of a simple pendulum (twopi sqrt(L/g)) which is the time it takes to swing back from an extreme position in its swing back to the same place. We also know it takes a little longer for wide swings, but actually not very much.
In the analogy with the sling, rather than 'g' due to gravity it is due to the acceleration of the hand, the 'pivot' of the pendulum. Consider how far that point has to move from rest during a half swing of the pendulum and you arrive at a 'notional drive length', say D, which is straight and a multiple of the length of the sling.
The result is
D = (1/2) (pi k)
2 L,
making D about five times the length of the sling. Most importantly it is independent of the acceleration applied.
Having got the foot in the door with that, we need to look at what freedom we have to alter the dynamics in practice. One thing is curving the drive path, but the other thing is to have the 'pendulum' already swinging about the pivot. In that case the time the pendulum is in the lower half of its possible motion is decreased. So by increasing the initial angular rotation about the pivot, considering the situation at the beginning of the power stroke of the action we can apply the same acceleration pattern and use a shortened drive length.
So, the argument here is that the early part of the sling action is to set this initial rotation for the sling to tune the physically realizable path length to the sling length.
Hope that makes some sense.
There is another wrinkle in all this. The actual path length can be 'folded' if the drive is actually started when the hand is moving backwards, rather than at rest, so there is a suggestion that the effectiveness of the throw could be increased by recognizing that. If you want an analogy to that folding, we throw things up in the air and they come back to the same height, ie. havn't moved at all in height during a period of acceleration.