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Cue Ball Speed: Straight rail hit vs rail hit at angle
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Billy_Bob
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Question Cue Ball Speed: Straight rail hit vs rail hit at angle - 06-13-2006, 12:23 PM

For speed control and how far the cue ball will travel after it hits the object ball, I take into account if it is a full ball hit, 3/4, 1/2, 1/4, or thin cut.

And then if outside or inside english when hitting the cushion.

But what I have *not* been considering is the angle at which the cue ball hits the cushion.

Seems to me if the cue ball is hitting the cushion full on or 90 degrees to the cushion, this will slow down the cue ball quite a bit. Whereas if the cue ball is hitting the cushion at a steep angle, the cue ball will retain a larger percentage of its speed.

I tried testing this, but I can't hit the cue ball the same speed each time because I am not a robot.

Anyway are there any rules of thumb for this?


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Talking Rules of Thumb - 06-13-2006, 12:40 PM

Yes, always use your left thumb when measuring.


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06-13-2006, 01:39 PM

Quote:
Originally Posted by Billy_Bob
...
I tried testing this, but I can't hit the cue ball the same speed each time because I am not a robot.
...
Roll it down a ramp. A ramp is easy to make. As far as rail efficiency for a perpendicular hit, I think that's given in one of the Billiards Digest articles in http://www.sfbilliards.com/articles/BD_articles.html along with how it was measured (so you can measure it on your own table).


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06-13-2006, 01:40 PM

Quote:
Originally Posted by Subsonic2u
Yes, always use your left thumb when measuring.
Subsonic, I have to disagree. You should use your right thumb when measuring.
  
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06-13-2006, 02:00 PM

Quote:
Originally Posted by Bob Jewett
Roll it down a ramp. A ramp is easy to make. As far as rail efficiency for a perpendicular hit, I think that's given in one of the Billiards Digest articles in http://www.sfbilliards.com/articles/BD_articles.html along with how it was measured (so you can measure it on your own table).
Assuming that the rail doesn't provide a perfectly elastic collision it only stands to reason that more energy would be lost in a perpendicular hit versus a hit at an angle. The smaller the angle the more distance the ball would travel.


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06-13-2006, 02:39 PM

You're absolutely correct in your observation, and here's why:

Think of the overall velocity of the ball as two components, call them vp for parallel velocity and vo for orthogonal velocity. If the ball is headed to the rail at an 85-degree angle to it, then almost all of its velocity is moving into the rail, and very little is moving along the rail. High vo, low vp. If the ball is headed into the rail at a 5-degree glancing collision, most of its velocity is along the rail, and very little is into the rail. High vp, low vo. A 45-degree hit is half parallel, half orthogonal. You get the idea.

So during a collision, vp is decreased by friction between the rail cloth and the ball. Should be clear enough, a moving object sliding along a stationary object will be slowed by friction.

VO is decreased because some of its energy is absorbed/dissipated as sound, heat, and vibration in the rail, and so only a fraction of the ball's energy in this direction is returned to it as the rail rebounds it.

Both of these decreases in velocity will be more severe if the ball hits the rail at 85 degrees than if it glances off at 5 degrees. VO will be decreased more because it is larger (makes up more of the ball's overall velocity). More sound, more heat, more vibration, more decrease in velocity. VP will decrease more because VO is higher, and thus contact with the rail is longer and involves more pressure between the ball and the rail. The rail compresses allowing longer contact, and more contact and more pressure means more friction. The glancing shot doesn't compress the rail much at all, and only lightly rubs the rail on its way by. Higher vo means vp is subject to more friction.

So that's what you're seeing when you observe that a ball travelling at a given speed and bouncing off a rail will have less final velocity the more perpendicular its path is to the rail.

-Andrew


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06-13-2006, 04:04 PM

Quote:
Originally Posted by Billy_Bob
...Anyway are there any rules of thumb for this?
For the general case of any combination of topspin/draw and sidespin on the ball, I might be wrong but I think it would be tough to come up with something very useful. The problem is similar to throw, and if you've looked at Dr. Dave's (CCB) graphs for throw, it's obvious that you get a wide range of results depending on the state of the ball just before the collision.

Things are a little simpler if the ball is stunned into the cushion with no sidespin. Bob Jewett's 70% mirror system:

http://www.sfbilliards.com/articles/2004-09.pdf

indicates that over the range of incoming angles in which it applies, the ball will lose about 50% of its speed in the direction parallel to the cushion (my inference). This assumes it loses about 30% of its speed in the perpendicular direction. The latter is approximate but pretty reliable I think. We do know that stunned balls bank short, so it's definitely true that they lose more parallel speed than perpendicular speed.

So, the less perpendicular the incoming angle, the more of its speed is in the parallel direction. And since it loses more of this than in the perpendicular direction, it will lose more speed overall as the incoming angle moves away from the perpendicular. There is a relatively simple formula but whose going to calculate.

Jim

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06-13-2006, 04:46 PM

Quote:
Originally Posted by Andrew Manning
You're absolutely correct in your observation, and here's why:

Think of the overall velocity of the ball as two components, call them vp for parallel velocity and vo for orthogonal velocity. If the ball is headed to the rail at an 85-degree angle to it, then almost all of its velocity is moving into the rail, and very little is moving along the rail. High vo, low vp. If the ball is headed into the rail at a 5-degree glancing collision, most of its velocity is along the rail, and very little is into the rail. High vp, low vo. A 45-degree hit is half parallel, half orthogonal. You get the idea.

So during a collision, vp is decreased by friction between the rail cloth and the ball. Should be clear enough, a moving object sliding along a stationary object will be slowed by friction.

VO is decreased because some of its energy is absorbed/dissipated as sound, heat, and vibration in the rail, and so only a fraction of the ball's energy in this direction is returned to it as the rail rebounds it.

Both of these decreases in velocity will be more severe if the ball hits the rail at 85 degrees than if it glances off at 5 degrees. VO will be decreased more because it is larger (makes up more of the ball's overall velocity). More sound, more heat, more vibration, more decrease in velocity. VP will decrease more because VO is higher, and thus contact with the rail is longer and involves more pressure between the ball and the rail. The rail compresses allowing longer contact, and more contact and more pressure means more friction. The glancing shot doesn't compress the rail much at all, and only lightly rubs the rail on its way by. Higher vo means vp is subject to more friction.

So that's what you're seeing when you observe that a ball travelling at a given speed and bouncing off a rail will have less final velocity the more perpendicular its path is to the rail.

-Andrew
This is cool. I've never considered sound as a source of lost energy. Do you think sound has very much effect in this discussion? The best European 3 Cuhsion tables that have 2-1/2" - 3" thick slates, Steel I-Beam support and very heavy, stout rails are SILENT when the balls hit the cushion. These tables are generally faster than even old Brunswicks (pre 1940) converted with European rubber.

I don't believe that the heated slates add much distance or speed unless it's very humid. I might be wrong on this and hard to test given all the other factors present and I've never heard a discussion on the rubber being formulated for the elevated temp.

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06-14-2006, 02:55 AM

A little off topic: The BBC showed a test on a snooker table with a cueball on a ramp (from golf) where they let the cueball hit a rail perpendicular. When the rail was clean the cueball bounced some 3 feet. They repeated the experiment from the exact same spot on the table only this time the RAIL was loaded up with chalk. Guess what happened. The cueball travelled an additional 6 to 8 inches! If you´re going to test some of this out, make sure you know that the rail is clean, it makes a huge difference. I´d love to see the same experiment on a pooltable, cause the rails are obviously different.

gr. Dave
  
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06-14-2006, 07:17 AM

Quote:
Originally Posted by 3kushn
This is cool. I've never considered sound as a source of lost energy. Do you think sound has very much effect in this discussion? The best European 3 Cuhsion tables that have 2-1/2" - 3" thick slates, Steel I-Beam support and very heavy, stout rails are SILENT when the balls hit the cushion.
...
In this discussion I think "sound" only has an appreciable affect if you expand the concept of sound to include inaudible vibrations within the rail materials. Sound is nothing more than vibration, really, and I think a good bit of the energy that a ball loses when rebounding from a rail becomes vibration in the rail. If you construct a table to have less vibration (like the 3-cushion table you mention), I would think that yes, the rails would play noticeably faster.

-Andrew


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06-14-2006, 11:37 AM

Quote:
Originally Posted by 3kushn
... I've never considered sound as a source of lost energy. Do you think sound has very much effect in this discussion? ...
Probably not. Balls make a fair amount of noise when they hit each other -- think break shots -- and ball-ball collisions are far more efficient than ball-cushion collisions.


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06-14-2006, 11:41 AM

Quote:
Originally Posted by Double-Dave
A little off topic: The BBC showed a test on a snooker table with a cueball on a ramp (from golf) where they let the cueball hit a rail perpendicular. When the rail was clean the cueball bounced some 3 feet. They repeated the experiment from the exact same spot on the table only this time the RAIL was loaded up with chalk. Guess what happened. The cueball travelled an additional 6 to 8 inches! If you´re going to test some of this out, make sure you know that the rail is clean, it makes a huge difference. I´d love to see the same experiment on a pooltable, cause the rails are obviously different.

gr. Dave
This effect is seen all the time on brand-new cloth. A ball coming off the cushion after rolling directly into it will still have spin in the direction of the cushion and will slow down more than a ball rolling straight into a normal rail.

I've played on a pool table with sticky rails and shooting cross-table it was possible to hit six cushions as the nose of the rail wound up and released on each contact returning energy to the cue ball.


Bob Jewett
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06-14-2006, 11:48 AM

Quote:
Originally Posted by Bob Jewett
This effect is seen all the time on brand-new cloth. A ball coming off the cushion after rolling directly into it will still have spin in the direction of the cushion and will slow down more than a ball rolling straight into a normal rail.

I've played on a pool table with sticky rails and shooting cross-table it was possible to hit six cushions as the nose of the rail wound up and released on each contact returning energy to the cue ball.
That makes a lot of sense. On new cloth, the cueball doesn't grip the rail well and keeps some of it's topspin and slows down after the contact with the rail, on a dirty rail it grips and loses the spin. Did I understand correctly?

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06-14-2006, 12:32 PM

Quote:
Originally Posted by Double-Dave
That makes a lot of sense. On new cloth, the cueball doesn't grip the rail well and keeps some of it's topspin and slows down after the contact with the rail, on a dirty rail it grips and loses the spin. Did I understand correctly?...
Yes. Of course if you shoot hard enough on new cloth that the cue ball never gets to smooth rolling, you don't see the effect. Lag speed on brand new cloth will show it.


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06-15-2006, 04:58 AM

Quote:
Originally Posted by Bob Jewett
Probably not. Balls make a fair amount of noise when they hit each other -- think break shots -- and ball-ball collisions are far more efficient than ball-cushion collisions.
Bob

Wouldn't the huge difference in friction between 2 balls colliding and a ball hitting a cushion make the difference here?

The vibration explanation makes some sence to me and is maybe one reason that pool tables in general are less accurate than billiard tables. This is a little off topic but I see the vibrations sending a ball in a less than true angle as well as slowing the ball. I suppose there is some vibration in the rubber itself but probably most occurs after the ball leaves.
On the other hand the more resonant rail will resonate on impact.
  
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