Jal said:
You're right about the cueball moving faster than the stick. Ideally, without energy loss, it should take off at 1.5 times the stick's speed when the stick is three times its weight. In reality, the number is about 1.3. If the stick's mass was infinite, it would take off at only two times the stick's speed in a perfectly elastic collision. So you tend to get diminishing returns by increasing mass.
On the other hand, if the stick is extremely light, you can't get up enough speed to make up for its small mass because you have to accelerate your hand/arm too, which limits the speed.
If you knew not only the mass of an individual's hand/arm, but how the mass is distributed throughout its length, you could use physics to come up with an optimum cue weight for that particular individual. Although hand/arm mass plays essentially no role in the collision itself, you would need to know it in order to figure out how much resistance it offers to accelerating it. I don't know of any easy way to get these measurements.
So as a practical matter, the easiest thing to do is to try cues of various weights and see which one works best...but I guess nobody needed to tell you that. It will definitely be different for different individuals. Using robots will not help for obvious reasons.
Jim
Very good post... good description.
I suggest that a player purchase a Break Cue, with a removable "weight bolt", so that adjusting the cue's weight to the nominal best for the player, can be done easily, over time.
My next Break Cue design will have a weight bolt in the shaft, so I can adjust the weight forward or aft. It's just a trial design. I like the shorter Break Cues too... they feel different, but they hit a ton.
I also suggest that a player purchase a cue with a Break Cue shaft, one that has a real Stiff SPINE.... maybe 13.5mm to 14mm in size. The laminated shafts are superb for this application. A Break Cue taper helps out too.
I don't believe a player can make a snap judgement, about a particular weight, because the optimal situation can only be determined by a pure hit on the cueball & a great hit on the rack. Anything less than a pure hit on the Cue Ball is wasted energy & anything less than a great hit on the rack is also energy loss. True judgement is made with experience, over time.
Some of us are not able to break at 30 MPH, but we are capable of a great break, because of our accuracy of hit, which helps out in the consistancy department....
Since the Break Shot is altogether different than the play shot, methodical practice is necessary. The Professionals got a real "eye opener" during the IPT tournaments. Having to break from the box & hit the lead ball gave them a real test. It became very obvious that a dry break & anything less than top play would eliminate you very quickly.
Good Luck...