Here is the text of their description of a half-ball hit. I would say that as instruction, this is completely broken. It says to shoot a spot-to-spot spot shot as a half ball hit. Another way to say your last point is that some champions have no idea how the balls actually work.
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Bob, you are cherry picking, taking the part of the author's writing as correct that you like, while saying he is in error other places. Perhaps he is in error both places, or even neither. We can look at pool with different perspectives.
Except the half ball hit (the result of half ball aim) actually does result in a 30° cut angle, not 45°.
Misinformation isn't without consequences, even in pool.
pj
chgo
pj, the issue is that neither statement is wrong, just a matter of different perspectives. From a function based perspective it is equally correct or more correct to say that the hit that gives a 45 degree angle is a half ball hit.
The man who won a world championship while saying a half ball hit gives a forty-five degree path has demonstrated his system superior to yours and Bob's unless either of you have won professional world championships I didn't hear about.
Deciding what a half ball hit is based on function as well as other fractional hits is just as valid and possibly more effective than trying to use math. I'm pretty sure that people have been doing just that a lot longer than they have been using math and physics. Marie Antionette was a dedicated cueist. I don't recall her background in math or physics.
I will maintain that a half ball aim doesn't give a half ball hit until the cows come home and a lot longer. If it gave a half ball hit it would give a forty-five degree angle, not thirty.
Another way to say your last point is that some champions have no idea how the balls actually work.
Bob, champions know very well how the balls actually work. Without meaning to offend, you, me, pj, or Mensabum could all be champions or could have at one time if we understood how balls work as well as the champions. Champions at any sport know how things work. Most will turn up their noses at the math and science because it doesn't benefit their performance.
Hu