The physics of the break

[ineedaspot]

Most of what happens on a pool table can be understood pretty well with "high-school" physics. That doesn't mean it's simple, but it does mean that friction and collisions between rigid bodies cover most of what goes on. The break is different, though, because a lot of balls are colliding at the same time.

I came across an interesting post on a physics forum about what happens during the break. Pretty cool if you're into this kind of thing. Don't know if it's been cross-posted here before:
http://physics.stackexchange.com/qu...d-break-of-a-perfectly-aligned-pool-ball-rack

Basically, to simulate the break right, you have to take into account that the balls aren't absolutely stiff, but they compress and overlap slightly when they collide with each other. Using that assumption they get a pretty realistic mathematical simulation of a perfectly centered 8-ball break:

Here's a chart of how the forces propagate through the rack in the first 0.2 milliseconds after contact:

Another interesting thing is they illustrate how changing the stiffness of the balls changes the break dynamics. If you make the balls ultra-stiff, then you get a totally different outcome where basically all the energy goes back to the the two corner balls:

 

[Hits 'em Hard]

As a note, all these calculations and graphics were done without the calculations of friction being applied. Pointless information that only exists as a theoretical.

 

[jsp]

As a note, all these calculations and graphics were done without the calculations of friction being applied. Pointless information that only exists as a theoretical.

I wouldn't say theory is "pointless information".

 

[Hits 'em Hard]

I wouldn't say theory is "pointless information".

And you don't understand what I said. With your words there, yes theory is good. Applied theory that has no real world application is useless. Why do we want to understand how a frictionless environment affects the balls when we will never exist in a frictionless environment?

 

[ineedaspot]

As a note, all these calculations and graphics were done without the calculations of friction being applied. Pointless information that only exists as a theoretical.

True, it doesn't account for friction, which in this case would mean primarily contact-induced-throw. The question then is how much does contact-induced throw change the outcome of the frictionless model.

There are also a lot of other things it doesn't take into account. For example, in reality, the balls aren't perfectly spherical. They also aren't all identical. They also aren't all equally close to each other in the rack, even in a "tight" rack. You also never hit the head ball precisely square. And so on.

None of this makes it pointless, it just makes it an approximation, which is what any model of reality is anyway. There's contact-induced throw in other shots besides the break. It doesn't make the no-throw model pointless -- for a lot of shots, you can mostly ignore contact-induced throw (i.e. if the angle is small or if you hit the shot hard). And even when you can't, the no-throw model is usually pretty close, so you can adjust slightly for throw and get a good prediction.

 

[bdorman]

As a note, all these calculations and graphics were done without the calculations of friction being applied. Pointless information that only exists as a theoretical.

Most of what physicists and mathmaticians do is only theoretical and pointless. One of the most brilliant mathmaticians of the 20th century, Paul Erdos, was once asked if any of his work had practical application; his answer was "Of course not. What a silly question."

While it may be pointless and theoretical, it's still interesting.

Other the other hand, we eagerly await your calculations that include friction.

 

[Kim Bye]

It might be a simplification of break physics, but you can build on this model and add more information and thus get a more realistic result.
It would be really cool if you made a more accurate model and made a small program or app,so we could experiment with a break simulator. I would pay to have such a program or app.

 

[iateyourlunch]

Thanks for link! Anyone else bothered by black ball in the wrong spot?

 

[KMRUNOUT]

And you don't understand what I said. With your words there, yes theory is good. Applied theory that has no real world application is useless. Why do we want to understand how a frictionless environment affects the balls when we will never exist in a frictionless environment?

Because abstraction is the basis for almost all human knowledge, particularly physics and especially mathematics. Friction is one of many forces at work. Understanding each force individually is extremely important to understanding the aggregate effect of multiple forces. If you don't undersrand why, its best to ask...but your question sounded sarcastic and rhetorical. If you instead are claiming that it *isn't* important, then now is the time when you should quietly bow out of physics type discussions.

KMRUNOUT

 

[bdorman]

Thanks for link! Anyone else bothered by black ball in the wrong spot?

It's league play

 

[conetip]

Thanks for link! Anyone else bothered by black ball in the wrong spot?

Not at all.
It makes it, all the more real .You know for sure the person doing the simulation is not a pool player, and the info presented is least likely to be biased or influenced to present a particular outcome.
Great thread and info all the same.

 

[dr_dave]

Most of what happens on a pool table can be understood pretty well with "high-school" physics. That doesn't mean it's simple, but it does mean that friction and collisions between rigid bodies cover most of what goes on. The break is different, though, because a lot of balls are colliding at the same time.

I came across an interesting post on a physics forum about what happens during the break. Pretty cool if you're into this kind of thing. Don't know if it's been cross-posted here before:
http://physics.stackexchange.com/qu...d-break-of-a-perfectly-aligned-pool-ball-rack

Basically, to simulate the break right, you have to take into account that the balls aren't absolutely stiff, but they compress and overlap slightly when they collide with each other. Using that assumption they get a pretty realistic mathematical simulation of a perfectly centered 8-ball break:

Here's a chart of how the forces propagate through the rack in the first 0.2 milliseconds after contact:

Another interesting thing is they illustrate how changing the stiffness of the balls changes the break dynamics. If you make the balls ultra-stiff, then you get a totally different outcome where basically all the energy goes back to the the two corner balls:

Thank you for posting this. It is interesting to see what the break would look like if everything were perfect (balls, rack, hit, etc.). Obviously, this is not the case in the real world. If it were, the game would definitely be less interesting.

Regards,
Dave

 

[DogsPlayingPool]

Thanks for link! Anyone else bothered by black ball in the wrong spot?

Didn't even notice that. I was too busy thinking I'd hope my opponent chose solids.


It's an interesting physics exercise, but I'm not even sure a break simulator app would be of much benefit. Once the balls start colliding all bets are off. And every table racks different and breaks different, so where and when they spread and collide with each other is so variable I doubt a simulator would be very useful. But who knows.

Still, cool little gif that kept me momentarily mesmerized. :thumbup:

 

[theattendant]

This is pretty cool to see, even if it's real world application isn't great. It gives a different look at things.

 

[MitchAlsup]

Thank you for posting this. It is interesting to see what the break would look like if everything were perfect (balls, rack, hit, etc.). Obviously, this is not the case in the real world. If it were, the game would definitely be less interesting.

It would be interesting to do a MonteCarlo simulation of a large variety of CB impact points, CB spin, and tightness of each ball in the rack; say 100,000 individual breaks amalgamated into something meaningful, if that is possible.

 

[Bob Jewett]

As a note, all these calculations and graphics were done without the calculations of friction being applied. Pointless information that only exists as a theoretical.

It's traditional in the discussion of analyses of physical systems for the critic to estimate a bound on the accuracy introduced by the simplification or reduction that they object to. Do you have an estimate for the error introduced by the failure to include friction? Are you referring to the ball-cloth friction or the ball-ball friction? I think ball-cloth can safely be ignored but ball-ball could have a small influence in the resulting speeds.

 

[Bob Jewett]

It would be interesting to do a MonteCarlo simulation of a large variety of CB impact points, CB spin, and tightness of each ball in the rack; say 100,000 individual breaks amalgamated into something meaningful, if that is possible.

I think that Virtual Pool does something like this but at least through VP3 the ball-ball contact time was assumed to be zero and the consequences of three-ball interactions (such as for the "ten times fuller" system) were missing. Nine ball breaks in VP are not all the same.

 

[K2Kraze]

The simulation has the balls placed in the following layout / rack for all examples:

1
2 3
4 5 6
7 8 9 10
11 12 13 14 15

Which is why the black 8-ball is where it is. The diagrams below the deflection angles and speeds show it. Hope that clears up any questions - the way I'm reading and evaluating the data that is.


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