Bob Jewett said:The stick transfers energy to the cue ball by compressing like a spring along its whole length. The compression wave happens at the speed of sound in the stick, which is about 13000 feet per second. This speed is the fastest that the butt can learn of something colliding with the tip. Some people make the mistake of thinking of the cue stick as being perfectly rigid and incompressible, but it's not. So, the shot proceeds like this: the stick is coming forward and the tip meets the ball. The tip starts to compress, force and acceleration of the cue ball start to build up. The ball also starts to compress, since it too is not incompressible. The ball has started to move, but is not up to the speed of the stick yet, and the stick has started to slow down as its energy is transferred to the cue ball. This continues until the tip (and ferrule and joint and butt) reach maximum compression along the length. At this exact point some amazing things are happening. The stick and ball are moving at the same speed. The force between stick and ball are at their maximum. The compression along the length of the stick (including the tip) is at its maximum. The energy stored in the spring-like compression of the tip (and stick and ball) are at their maximum. For a typical ball and stick, the speeds of the ball and stick are 75% of the original stick speed.
After this point of maximum compression, the ball is pushed forward from the tip by the compression of system. The ball starts to move even faster from this force and the stick continues to slow down. This "unwinding" process continues until the ball finally leaves the tip. At that point, the ball is going at about 130% of the original stick speed, and the stick has slowed down to about 50% of its original speed. (The 130% would be 150%, but the tip is not perfect in springing back to its original shape, and energy is lost.)
Now the hand comes in. Human flesh makes a much "softer" spring than the leather of a tip or the wood that is compressed along the length of the stick. Think of the tip as about the stiffest car spring you can imagine and your hand like a rubber band. The cue ball is gone by the time your hand -- which is still moving forward at full speed -- can wind up even a little. As the hand winds up on the stick and relaxes, which takes about 20 milliseconds, the hand is slowed to about 80% of its initial speed and the stick goes from 50% back up to 80% of its initial speed. Of course this re-acceleration of the stick by your hand is useless in that the cue ball is long gone.
How does a heavier stick affect things? It changes that 130% number. The formula is in Byrne's Advanced book, and somewhere in my columns in Billiards Digest and certainly in Ron Shepard's paper and Dr. Dave's book. A heavier stick through the spring action, puts slightly more energy into the cue ball.
As for how the weight of the stick affects the squirt, I think the answer is that it doesn't, much. Squirt is caused by the spinning cue ball pushing the stick to the side during the contact time of an off-center hit. The amount of squirt is determined by the mass that is being pushed to the side. Since the stick is very floppy side-to-side (as compared to length-wise compression), only the front part of the stick can participate in the squirt during the 1 millisecond or so of contact time. A heavier stick will increase the contact time a little, and that will increase the squirt a little, but I think this effect is pretty small.
Phrased technically, the transverse wave has a very slow propagation velocity along the length of the stick, and so the joint and butt cannot participate in the sideways push that causes squirt.
You should find Mike Page's discussion of his experiment with vise grips on the shaft which determined how much of the shaft participates in squirt.
As Fred mentioned, a major problem with some of the Jacksonville Project was that Iron Willie had too stiff a grip -- like vise grips -- and too hard a bridge. I have heard that Predator's current cue testing robot has fixed those problems to hold the cue more like a human at both ends.
As for some of your other questions, in theory the squirt should depend on stiffness of the cue since that should change the speed of the transverse wave. In practice, "end mass" seems to be a much better indicator of squirt than stiffness. There are stiff cues with little squirt and stiff cues with lots of squirt. A major red herring along the path of squirt studies was the fact that carom cues tend to be stiff but have relatively low squirt. They usually have smaller tips than pool cues.
Excellent! Thanks for such a thorough description. I'm beginning to see the light.
One thing I don't get is if the sideways shaft pushing from the spinning cueball causes squirt, and this happens too quickly for the rest of the cue to take part, when does the slower full-stick system-compression/force-transfer stuff take place on an offcenter hit? Afterwards?
If the cue is still in contact long enough to transfer its shotward force to the cueball, why isn't squirt affected during this time? Is squirt decided, over and done with, after only the inital stage of contact?