RainmanTime
Super Moderator
You might be surprised, Kerr.
In general, the faster that things happen in a dynamic event, the smaller your "integration time constant" has to be to model it accurately. What this means is that I would have to evalute the equations of motion for a figher aircraft much more rapidly than for a commercial passenger jet. As a typical example for a naturally unstable fighter airplane, our simulations of these typically must evaluate ALL the equations of motion (DOFs) at least 100 times each second (and don't think this is just ONE calculation...each DOF involves hundreds of calculations). A highly stable commercial passenger jet MIGHT be able to get by evaluating its equations at 20 times each second. Because the playing area of a pool table is relatively small as compared to the velocities the balls can achieve, I would not try to build a simulation of a pool game with an integration time step of anything less that 10 milliseconds (i.e. 100 times per second), and it may have to be quite a bit lower.
Whereas we do NOT model elastic (or inelastic) collisions for aircraft, we would have to include some measure of inelastic collision modeling for the pools balls contacting each other, and the rails. In other words, start adding more DOFs. And now it is possible that all 16 balls (15 targets and 1 cue) could all be in motion at the same time. So however many DOFs you have for the balls (absolute minimum of 6 DOFs per rigid ball), you now multiply by 16.
All of the above had not even addressed accuracy of any physical measurements that may impact the playing field... believe it or not, the ambient temperature and pressure will have a measurable effect on the motion. Once you start addressing the accuracies on how well you know something so that you can then try to model it, THAT is when the computational intensity of the problem REALLY starts to take off.
Could it be done? Sure it could. But the question one must ask is: What would be the REQUIRED accuracy that you would accept for a solution? In reality one could spend a LOT of time and money (engineers are not cheap these days!) :D on such a simulation and STILL not get to a point where I could positively predict whether a specific ball would stay on the table or fall into a pocket with a high degree of confidence.
In my opinion, I tend to find that the "general public" thinks tasks such as this are a lot simpler than they really are. It is a bit like enjoying a smoked sausage on your grill one afternoon at the beach and thinking "what a glorious, tasty, and simple product." But then there is the old adage of how you never want to see sausage being made! :eek:
Of course we know that we have video games that simulate pool tables already. But I think we all should know that if you were to compare the results of such a program against a real table (even if all the geometry and masses matched what the program was built to), the confidence (or probability) that the computer program reflects real life would likely be below 50%. In other words the fidelity of that game program is VERY VERY LOW.
RMT
