IronGoober wrote on Jul 28
th, 2021 at 3:03pm:
Ok, so my method of estimating velocity must be incorrect of looking at the motion of the sling. Can anyone point out where I'm going wrong with it? I calculate about 50 m/s release speed.
I was looking at the last 2 frames before you release, the sling travels about 1/4 turn.. if it is 30" and your hand moves about a foot, that is over 1m in radius.
2*pi*(1m) = 6.724m
divide by 4 to get distance traveled in a single frame,
(6.724m / 4)*(1/30 s) = 50.42 m/s.
I thought just looking at the video you could get a decent estimate of release velocity, but it seems that is not correct, because 50.4 m/s only goes 258.7m MAX (without any drag).
Maybe adding in the distance traveled by the hand is wrong?
I would guess that the projectile continues to accelerate a lot towards the point of the release. So the average speed of the last 1/4 turn might be significantly slower than the actual speed at point of release (think how much you would spoil the power of a shot by releasing a 1/4 turn early).
I think the way you did the calculation more or less holds up in a rough sense, though it's true the reality is much more complex, you don't just have a straight rotor from the shoulder out to the projectile, it's more of a rotor around the hand which experiences a ton of angular acceleration due to the force from the hand. So it doesn't quite act the same way you would expect a big rotor to.