As a Mechanical Engineer, I understand your math and your conclusions, but do see a few issues. Nothing to do with your calculations, but to do with the equipment. As a pool player, I collect things... like cue balls. I have a collection of about 20 or so different cue balls. Everything from a measles ball to red circles, red dots, blue dots, black circles, every kind of magnetic ball I could find, oversized cue balls (very common on older bar tables) and they all weigh differently and have different density. This has a drastically different effect on, not only cue ball direction of travel after the hit, but on another thing, that as a physicist (I am just making an assumption that you are a physicist) I thought you would calculate in, and that is cling. Cling happens... the slower the roll of the cue ball, the MORE it happens and it changes the point at which the balls "release" from each other, which changes cue ball path. Also, Cue ball path is determined greatly by the "condition" of the cue ball and object ball at impact. I'm not talking about whether they are clean and polished or dirty and rough, although that DOES make a difference, but WHAT the cue ball is doing when it contacts the object ball. A rolling cue ball will NOT release on the 90 degree tangent line from the shot. It varies greatly from 90 degrees to 30 degrees, depending on A) angle of shot and B) speed of the CB. The only way to insure that you get very close to that 90 deg release is to insure that the cue ball is sliding at contact with the OB... no forward roll, no backwards roll... a pure slide.
In any case, as an engineer, I really enjoyed the math and the concept. As a pool player, quite honestly, I didn't find it useful, but that does NOT mean I didn't find it interesting!
Thanks for posting,
Bob
Edit... I just want to be sure I'm clear on one statement that I made... Except on a dead straight in shot, the cue ball ALWAYS leaves the object ball on the "tangent line" or a line 90 degrees from the travel angle of the object ball but, except under certain conditions, that path will almost immediately deviate. The "condition" of the cue ball, as I described it, (sliding, rolling, backspin, etc) determines what it does in that instant after contact.
In any case, as an engineer, I really enjoyed the math and the concept. As a pool player, quite honestly, I didn't find it useful, but that does NOT mean I didn't find it interesting!
Thanks for posting,
Bob
Edit... I just want to be sure I'm clear on one statement that I made... Except on a dead straight in shot, the cue ball ALWAYS leaves the object ball on the "tangent line" or a line 90 degrees from the travel angle of the object ball but, except under certain conditions, that path will almost immediately deviate. The "condition" of the cue ball, as I described it, (sliding, rolling, backspin, etc) determines what it does in that instant after contact.
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