# Reverse Throw

#### Robert Raiford

##### The Voice of CaromTV
Silver Member
I see the logic and agree with the modification. But the "sin(cut angle)" threw me off for a while - shouldn't that be cos(cut angle)?
I intentionally mistyped that just to see if you were paying attention...yeah, that's what happened...
One difficulty in easily accounting for inelasticity is that the coefficient of restitution (I realize your "alpha" isn't the COR, directly) varies, I believe, with the CB speed component along the impact line. Thus, so will alpha. I'm basing this on tests done by Cushioncrawler (Cue Chalk Board). I have them on another semi-defunct computer, but I believe I remember that the greater the speed, the smaller is the COR. This, of course, makes it cut angle dependent as well.
That's actually Coriolis' "alpha", not mine He wrote in the days before COR was standardized. I did it that way to alter your diagram in the spirit of his approach using his constant loss fraction assumption.

He didn't describe any experiments attempting to establish the validity of that assumption, but I'm sure he was aware it was an approximation that was useful for introducing the idea graphically into the constructions of how the ideal case is affected. Remember, his constructions were there to help guide the lay reader's intuitions in support of the introductory summary section of the book. (Interestingly, he did describe experimentally suspending cues and balls from cords to attempt measurements from controllable tip/ball collisions, but he lamented the slower-than-actual-play max cue speeds he could attain that way.)
Dr. Dave has described the departures from the predictions as well. I think a significant one is squirt. Although it may be relatively small in the inclined plane of the cue, it's projection onto the horizontal plane magnifies it considerably at the steep inclinations used with masse shots.

Jim
Yeah, Coriolis totally missed the ball when it came to squirt. It's one of the reasons I suspect that he wasn't such a good player himself to have missed it. It's painful with our current understanding to read his argument about how if the cue stroking line and the CB path weren't parallel, it would be "impossible to play with any confidence...but we recognize from experience that the two directions are in fact the same." As Dr. Dave once said, "Coriolis was brilliant, but he didn't have a high speed camera."

Robert

#### dr_dave

##### Instructional Author
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I briefly corresponded with David Nadler in 2007. Mostly, it was me thanking him for all of that tedious hard work he put into the translation, but I did try to be productive and include a few corrections that he was nice enough to include in the errata pdf available from his site for the book.

Unfortunately, he didn't seem very interested in diving into the details of corrections based on the content, such as the obviously mistakenly drawn location of point L in figure 24 of Coriolis' original that he reproduced when recreating the figures for the book. I never got a reply to my last email, so I didn't pursue it further. I greatly appreciate the tremendous effort he put into it, and the last thing I want to do is bug the guy with anything that may be taken as criticism as opposed to being helpful.

However, I don't mind bugging you - especially, when you asked so nicely Here's a .doc file I created at the time with some nicely formatted errata through p.65 (about halfway through Ch.2):

RaifordCoriolisErrata.doc

As you can see, there's 7 pages worth of corrections just for the beginning alone. I was going to go through the entire book like that and send it to him, but I wasn't as sure as you are that it would be received so positively after his lack of response. The rest of the corrections are still only penciled in the margins of my copies of the English and French texts. I hope to eventually pretty them up and put them online for the benefit of other readers, but it'll have to wait until I have more free time. Now that I know there are at least 2 interested parties, that may even actually happen

Robert

UPDATE: I just viewed the errata doc file in LibreOffice/OpenOffice, and the equations aren't reproduced well. I suggest using MS Word to view it, if possible.
Thank you for posting the corrections. I've already written them into my copy of the book. I would also like to see the additional corrections if you can find time to summarize and post them.

Thanks again,
Dave

PS: Great job with spotting all of those errors! You should be a technical editor in your next life.

Silver Member

#### Jal

##### AzB Silver Member
Silver Member
....That's actually Coriolis' "alpha", not mine He wrote in the days before COR was standardized. I did it that way to alter your diagram in the spirit of his approach using his constant loss fraction assumption.

He didn't describe any experiments attempting to establish the validity of that assumption, but I'm sure he was aware it was an approximation that was useful for introducing the idea graphically into the constructions of how the ideal case is affected. Remember, his constructions were there to help guide the lay reader's intuitions in support of the introductory summary section of the book. (Interestingly, he did describe experimentally suspending cues and balls from cords to attempt measurements from controllable tip/ball collisions, but he lamented the slower-than-actual-play max cue speeds he could attain that way.)
Dr. Dave, in several of his technical documents, uses an average value for COR of 0.94. That would make alpha 0.03 and your adjustment: BC' = 0.97BC.

One way, perhaps, to measure COR is to freeze two balls together, then aim the cueball directly at their mutual point of contact, slightly favoring one of the balls such as to cut it at a touch less than 30 degrees. It turns out that for idealized balls, the cueball would come off the second ball at a very consistent angle close to 120 degrees from the perpendicular to the line of centers of the two frozen balls. For instance, if the first ball is cut at 25 degrees, the angle works out to 119.73, and if the first cut is 28 degrees, the rebound angle is 119.96. Given the inelasticity of the first collision, the actual angles should be even closer to 120 degrees, except, of course, for the COR of the second collision (assuming well-matched ball masses.)

In the spirit of Cushioncrawler's data, but lacking the actual numbers, I made a bald guess and assumed COR to be a linear function of speed: = 1 at 0 MPH and 0.88 at 25 MPH along the GB-OB line of centers, just to get a rough idea of what the deviations from the C-B-A predictions might look like. Here are a couple of samples for a briskly hit cueball.

Yeah, Coriolis totally missed the ball when it came to squirt. It's one of the reasons I suspect that he wasn't such a good player himself to have missed it. It's painful with our current understanding to read his argument about how if the cue stroking line and the CB path weren't parallel, it would be "impossible to play with any confidence...but we recognize from experience that the two directions are in fact the same." As Dr. Dave once said, "Coriolis was brilliant, but he didn't have a high speed camera."
I don't know if it's just that we're so used to the idea of squirt now, but after all his detailed analysis, its pretty surprising, almost shocking, that he would have not noticed it.

Jim

#### dr_dave

##### Instructional Author
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When the balls are close enough to each other and/or you're hitting hard enough such that the cueball doesn't lose any significant backspin on the way to the object ball (or gain more topspin), there is a method of determining the cueball's direction once it reaches natural roll after the collision. I call it the Bottom-Center-Arrow method, or B-C-A for short, in that it's easy to remember.

Imagine a circle centered on the ghostball with the bottom of the circle running through the center of the cueball. This circle represents the face of the cueball from the shooter's perspective. To determine the CB's roll direction after the collision for any vertical offset (no sidespin applied), draw a line from the center of the real cueball parallel to the line of centers between the ghostball and the object ball. This will intersect the tangent line at 90 degrees, call it point A. Thus, we have a triangle with the CB at vertex B (bottom of the circle), the ghostball at C (center of the circle) and point A from which we'll draw an arrow such that it intersects the vertical axis of the large circle. This yields the CB's direction once roll sets in, given that vertical tip offset on the face of cueball. Here's a diagram:

View attachment 216279
Jim,

Again, excellent job coming up with this. I have verified the math and physics for this part (but not the inside English adjustment stuff, but I'm confident your results are valid). It is beautiful how this works out. I'm surprised I didn't discover this myself many years ago when I looked at this stuff closely. Again, good job!

FYI, I've added a quote of part of your post (with credit to you) to the following FAQ page, with a link back to your AZB post:

Thanks again for posting this,
Dave

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#### Jal

##### AzB Silver Member
Silver Member
Jim,

Again, excellent job coming up with this. I have verified the math and physics for this part (but not the inside English adjustment stuff, but I'm confident your results are valid). It is beautiful how this works out.
Appreciate the nod, Dr. Dave. And, of course, I'm relieved that you arrived at the same result!

I'm almost as sure of the inside english adjustment for friction. (The answer was not what I expected, and thus, I've been over the algebra many times.) However, it's difficult or impossible for me to construct it graphically in my head and I haven't set down to do the same on paper. So there is some slight lingering doubt, although I'm pretty convinced at this point that the result is correct.

I'm surprised I didn't discover this myself many years ago when I looked at this stuff closely....
The vegetative life, consisting mainly of time, does occasionally have its rewards.

Thanks for the generous words!

Jim

#### Patrick Johnson

##### Fish of the Day
Silver Member
When the balls are close enough to each other and/or you're hitting hard enough such that the cueball doesn't lose any significant backspin on the way to the object ball (or gain more topspin), there is a method of determining the cueball's direction once it reaches natural roll after the collision. I call it the Bottom-Center-Arrow method, or B-C-A for short, in that it's easy to remember.

Imagine a circle centered on the ghostball with the bottom of the circle running through the center of the cueball. This circle represents the face of the cueball from the shooter's perspective. To determine the CB's roll direction after the collision for any vertical offset (no sidespin applied), draw a line from the center of the real cueball parallel to the line of centers between the ghostball and the object ball. This will intersect the tangent line at 90 degrees, call it point A. Thus, we have a triangle with the CB at vertex B (bottom of the circle), the ghostball at C (center of the circle) and point A from which we'll draw an arrow such that it intersects the vertical axis of the large circle. This yields the CB's direction once roll sets in, given that vertical tip offset on the face of cueball. Here's a diagram:

This is great stuff, Jim! I imagine with practice you could use this visualization at the table. Do you?

pj
chgo

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#### Jal

##### AzB Silver Member
Silver Member
This is great stuff, Jim! I imagine with practice you could use this visualization at the table. Do you?

pj
chgo
Thanks Patrick. Over the last year or so I haven't been able to get to the pool room. When I get back, I do plan on trying to form these visualizations as a matter of habit. If nothing else, though, I think the construction is good for "theoretical" purposes, i.e., seeing what you can and cannot do with the cueball, particularly with draw (we have the 30-degree rule for near max follow, of course.)

Perhaps one immediately useful conclusion (although not obvious from the diagram), is that the ideal limit for draw (zero ball-ball friction, effective tip offset of 1/2 R below center) results in the cueball's roll direction being twice the cut angle from straight back at you (i.e., measured from line B-C). This applies to all cut angles, but friction and the slightly inelastic nature of the ball-ball collision makes this unattainable in the real world....unless the CB is lighter than the OB.

You can also see why departures from the intended vertical tip offset result in greater variations in the cueball's roll direction when hitting near stun at small cut angles: point A is close to the vertical axis B-C.

But I can't claim that it's helped my game thus far (as I've had no game).

Jim

#### dr_dave

##### Instructional Author
Gold Member
Silver Member
This is great stuff, Jim! I imagine with practice you could use this visualization at the table. Do you?
I've tried it out at the table some. It takes a little practice to get comfortable with using the system, and drag effects require lots of judgement and feel, but it does work fairly well.

One of these days, I'll write up an article for BD explaining and showing examples of how the system is applied (with credit to Jim). This might help the people who don't quite get Jim's diagram and description.

I still prefer using the tangent line (90 degree rule), natural angle (30 degree rule), and maximum reasonable draw (trisect system) as my main references, and then adjust between those. It is also important to have a good feel for speed effects.

Regards,
Dave

PS: It sure is refreshing to see some substantive content and discussion on AZB for a change.

#### Patrick Johnson

##### Fish of the Day
Silver Member
I still prefer using the tangent line (90 degree rule), natural angle (30 degree rule), and maximum reasonable draw (trisect system) as my main references, and then adjust between those.
Yes, I do that too. Establishing known references (particularly limits) is a really useful method for all kinds of things. It's also a primary way aiming systems work.

pj
chgo

#### francophile

##### New member
Robert,

I did include the corrections you sent me back in 2007 in coriolisbilliards.com/errata_list.html.

I can't get the link to your doc file to work. If you could send it to david@coriolisbiliards.com, I'd be much obliged.

Thanks very much,

Silver Member
................

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#### Robert Raiford

##### The Voice of CaromTV
Silver Member
Robert,

I did include the corrections you sent me back in 2007 in coriolisbilliards.com/errata_list.html.

I can't get the link to your doc file to work. If you could send it to david@coriolisbiliards.com, I'd be much obliged.

Thanks very much,

Sorry I'm replying so late to this, David, but I somehow missed your reply to this thread. I've emailed the errata doc file to your email, as requested. Please let me know if you have any problems receiving or reading it.

Thanks again for your hard work in producing the English translation. We know it was a labor of love, and we greatly appreciate it!

Robert

##### AzB Silver Member
Silver Member
Too many people worry about throw.

#### JoeyA

##### Efren's Mini-Tourn BACKER
Silver Member
When the balls are close enough to each other and/or you're hitting hard enough such that the cueball doesn't lose any significant backspin on the way to the object ball (or gain more topspin), there is a method of determining the cueball's direction once it reaches natural roll after the collision. I call it the Bottom-Center-Arrow method, or B-C-A for short, in that it's easy to remember.

Imagine a circle centered on the ghostball with the bottom of the circle running through the center of the cueball. This circle represents the face of the cueball from the shooter's perspective. To determine the CB's roll direction after the collision for any vertical offset (no sidespin applied), draw a line from the center of the real cueball parallel to the line of centers between the ghostball and the object ball. This will intersect the tangent line at 90 degrees, call it point A. Thus, we have a triangle with the CB at vertex B (bottom of the circle), the ghostball at C (center of the circle) and point A from which we'll draw an arrow such that it intersects the vertical axis of the large circle. This yields the CB's direction once roll sets in, given that vertical tip offset on the face of cueball. Here's a diagram:

View attachment 216279

The relevant point here is that friction, amongst other things, has an effect on this idealized geometry. Below is plot of the deviations from this ideal due to CB "throw" at various vertical offsets and cut angles.

View attachment 216278

(Note:the discontinuities in some of the curves are transition points from partial to full sliding during the collision.)

As you can see, the largest departures happen at close to stun at smallish cut angles. But these deviations can be essentially eliminated by applying an amount of inside english determined as follows. Swing the vector going from (3/5)R below center to the desired vertical tip offset, parallel to the direction of the line of centers between the ghostball-object ball. The location of the tip of this vector yields the amount of inside english to use (as seen on the large circle epesenting the face of the CB) in order to negate the effects of friction. A couple of diagrams should help, one for draw, one for follow:

View attachment 216280

View attachment 216281

I should note that the above correction assumes that a certain component of the CB's spin (i.e., along the ghostball-object ball line of centers) is unaffected by the collision. While this is certainly not exactly true, I believe it's true enough compared to the effect of the friction on the CBs other spin component along the tangent line. Also, the use of the inside english will generate another deviation: post-impact swerve.

There are other deviations due to mismatched ball weights and the less than perfect elasticity of the collision, but I'll leave it at that for now, since we're discussing CB throw.

Jim

YES! This clears up everything.

#### naji

##### AzB Silver Member
Silver Member
Does anyone know how much reverse throw is applied to the cue ball when throw is applied to the object ball?

In order to throw the ball you have to use stun shot with or without side english, with stun shot CB goes 88 degrees direction from aim line, if you happen to stun with little follow or draw angle changes a little up and down. Like other poster says CB will have friction induced spin

Due to stun, CB will not throw, its path is well known, try with combination shots

With lots of follow or draw shots, throw is there but not much especially on clean balls

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#### naji

##### AzB Silver Member
Silver Member
... and too many people miss too many shots because they don't fully understand (or know how to intuitively compensate for) all of the different squirt, swerve, and throw effects.

Regards,
Dave

Agree 100% Dave, it took me years to know how little smudge on OB or CB, or cloth type can be a game changer. Thanks to you.

Was playing a guy one pocket, he scratches, and put a ball on the spot, did not look, and missed it badly, it happened again, this time i noticed the ball is smudged with chalk different than other balls, i cleaned the ball and made it.

Also so many trick bank shots can be made with dirty balls, and impossible with clean balls.

#### Bob Jewett

##### AZB Osmium Member
Staff member
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Too many people worry about throw.

Yes, this is true. You have to "internalize" throw -- take it into your game in such a way that the use of it and compensation for it is completely automatic. See the ball, make the ball. No worries.

The real question for some of us is whether understanding throw better speeds that internalization.

#### Jdale

##### AzB Silver Member
Silver Member
Does anyone know how much reverse throw is applied to the cue ball when throw is applied to the object ball?

"little fishes bite if you got good baits" Taj Mahal.
Nice post