Quote:
Originally Posted by Patrick Johnson
So that's an 8% CB speed increase for a 47% cue weight increase. And since speed is squared in the kinetic energy equation, does that mean it would take only a 7% speed increase to do the same thing?

The fact that the kinetic energy goes up as the square of velocity doesn't have anything to do with the percentage change, I think. The speeds are all proportional. Changing the stick weight changes the proportionality constant.
The general nature of the problem is that if you begin with a very light cue (one ounce) you will have a poor result because the cue bounces off the cue ball and the energy transfer is poor.
For a six ounce cue, the energy transfer is perfect  the cue stops dead  but not much energy is in the cue stick. The cue ball will be moving the same speed as the stick except for about 10% loss due to the tip, etc.
For 18 ounces, the ball will leave at maybe 140% of the speed of the stick. (Due to the square relationship mentioned above, that's actually twice the energy.) The stick will probably be going slower than for six ounces, though.
For 36 ounces, there will be a problem for most people getting the stick up to speed so there will be a net loss.
For 180 ounces, there will be a problem getting the stick up to speed for everyone, and the ball speed will be less than twice the stick speed. (Twice is the upper limit but practically it's less because of the loss of energy in the tip.) 180 ounces is a bad choice. It would be interesting to see someone try it, though.
Exactly where the maximum ball speed is reached for a particular player for the full range of stick weights depends on a lot of things but mostly I think it is how strong he is and what he is used to.
The general theory of how all this must work says that weights close to the best weight (say + 2 ounces) will not be drastically different. A 2ounce difference is about 10% in weight and that is expected to cause something like a 12% difference in ball speed.
This is the same kind of very general physical situation that makes the halfball follow angle vary so little with cut angle. The smooth maximum happens when you have two contrary effects. In the case of the follow angle you have the angle of deflection to the side which increases with a fuller hit, but you have the follow which tends to take the ball straighter ahead for a fuller hit. The result for the halfball follow angle is that it is almost the same for changes in cut angle of +15 degrees depending on how much change you want to allow in the cue ball deflection angle.