The math of a perfectly centered break shot

[DeadStick]

This is pretty interesting:

http://mathoverflow.net/questions/1...erfectly-aligned-pool-ball-rack/156407#156407

A few of the images:

 

[RFranklin]

All racks

do you have one for 9 and 10 ball.

 

[Jude Rosenstock]

This is pretty interesting:

http://mathoverflow.net/questions/1...erfectly-aligned-pool-ball-rack/156407#156407

A few of the images:

Although we all know that the real world isn't perfect and we can never expect to see results like this, I agree, it's still very interesting. One thought I just had by watching this experiment is how the second-ball break in 8-ball works. I mean, I've done it and got fairly good at it but never really thought about *which* ball(s) I needed frozen. This diagram gives a great illustration of how you can predict the distribution of force throughout the rack and perhaps give you a better understanding of what can help/prevent pocketing balls.

 

[ChicagoJoe]

Interesting. I'd be interested in an app or program where you could change gaps in-between balls, break speeds, and angles.

 

[DeadStick]

Interesting. I'd be interested in an app or program where you could change gaps in-between balls, break speeds, and angles.

Technically, you could do that with Virtual Pool 4, but it'd be tedious. Easier than real life, however, since you can move a ball directly against another one without moving the other one.

 

[ctyhntr]

This confirms what I learned from watching Joe Tucker's racking secrets DVDs, where I learn to read the gaps.

do you have one for 9 and 10 ball.

 

[Cdryden]

Perfect? Pfft, the 8 ball isn't even in the right spot!

Seriously though, thanks for posing this. Very interesting.

 

[JBB2388]

Very interesting indeed

 

[rayjay]

Interesting, I enjoy a math debate.

 

[Bob Jewett]

Technically, you could do that with Virtual Pool 4, but it'd be tedious. Easier than real life, however, since you can move a ball directly against another one without moving the other one.

I don't know whether VP4 models the contact time of the balls. That requires a very short time step in the simulation (around 1 microsecond) and slows things down a lot. In the past, VP has treated each ball-ball contact as instantaneous and determined by a simple formula. That doesn't get the right answer for when balls are frozen.

 

[CreeDo]

Cool to note that the middle ball (in this case the orange 5 ball) moves *upward* on a perfect break.
I think that's because it rebounds off the larger mass of balls behind it,
which act as a single big mass if they're all frozen.

This is exactly what you see very often with a magic rack, the center ball creeps upwards
towards the breaker by a few inches. And it also proves that if that ball flies
away from the breaker (like towards the corner pocket) there was a gap.
If the rack is tight, you're not going to get a golden break unless something rebounds
off the rail to kick a ball in.

 

[shinobi]

And it also proves that if that ball flies
away from the breaker (like towards the corner pocket) there was a gap.
If the rack is tight, you're not going to get a golden break unless something rebounds
off the rail to kick a ball in.

I have watched a lot of older pool matches and it was ridiculous how often the 9 ball used to go in, in some tournaments. Before Sardo, Magic Rack, and apparently qualified referees...

I saw golden breaks 6 times out of 9 breaks. Straight into the corner, again and again. Naturally, the commentators got excited, as if it was an act of skill.

 

[logical]

Perfect? Pfft, the 8 ball isn't even in the right spot!

Seriously though, thanks for posing this. Very interesting.

Those are TV balls, the 8 is orange.