Why running English for multiple rails kicks?

[nataddrho]

They take the 70% number and convert it to the parameter theta, which is the angle from the center of the cue ball up to the (single, ideal) point where the ball contacts the cushion. The angle theta then appears prominently in most of the following equations.

I am thinking, that the greater value of theta the more downward force component will be generated by the rail forcing the ball into the cloth, which will cause cloth friction to reduce momentum of the ball.

If you are saying that they are over-estimating the rail height, and the actual true rail height is closer to the center of the ball, then the rebound velocity should be greater then their analysis? Not less?

I also think what I am trying to understand from this paper is that the rail itself, does not absorb energy (mostly). All energy is absorbed by cloth-ball friction (rail cloth and table cloth). The only place energy can go is into either heat, permanent deformation (inelastic collision) or back into the ball. Have you found this not to be true?

 

[Bob Jewett]

I am thinking, that the greater value of theta the more downward force component will be generated by the rail forcing the ball into the cloth, which will cause cloth friction to reduce momentum of the ball.

If you are saying that they are over-estimating the rail height, and the actual true rail height is closer to the center of the ball, then the rebound velocity should be greater then their analysis? Not less?

I also think what I am trying to understand from this paper is that the rail itself, does not absorb energy (mostly). All energy is absorbed by cloth-ball friction (rail cloth and table cloth). The only place energy can go is into either heat, permanent deformation (inelastic collision) or back into the ball. Have you found this not to be true?

I'm not saying that they will get more velocity with a correct rail height. I'm saying that their analysis is broken. If a correct rail height in their analysis gives a higher rebound speed, then they violate conservation of energy because they are already near 100% . But you would have to plug a real value into their equations and see what the result is. It is possible it would give a lower rebound speed. As I said, if it gives the same speed at all heights, the analysis is very clearly broken. Rail Height Matters!

In order to get a 98% or so COR the analysis must have essentially no friction.

A 70% rail height assumption is totally and completely broken. No pool or carom rail is that high. Only someone who knows nothing about pool would ever suggest such a height.

A 70% height is a very, very special height. That is the center of percussion of the ball. It is the height to hit for smooth rolling from the start. The use of that particular height is very, very suspicious.

 

[Pubo]

This discussion is simply brilliant! Thank you so much Bob and nataddrho I hope more keeps coming. I'll read the paper carefully to catch up haha

 

[nataddrho]

I'm not saying that they will get more velocity with a correct rail height. I'm saying that their analysis is broken. If a correct rail height in their analysis gives a higher rebound speed, then they violate conservation of energy because they are already near 100% . But you would have to plug a real value into their equations and see what the result is. It is possible it would give a lower rebound speed. As I said, if it gives the same speed at all heights, the analysis is very clearly broken. Rail Height Matters!

In order to get a 98% or so COR the analysis must have essentially no friction.

A 70% rail height assumption is totally and completely broken. No pool or carom rail is that high. Only someone who knows nothing about pool would ever suggest such a height.

A 70% height is a very, very special height. That is the center of percussion of the ball. It is the height to hit for smooth rolling from the start. The use of that particular height is very, very suspicious.

Here is another paper, where the rail height is 64% of the ball diameter (epsilon). The results include sliding and sticking during collision impulses. Though they unfortunately don't provide a plot, they claim their measured values match their theoretical values... COE of ball-rail is 0.6-0.95 depending on a few factors.