PDA

View Full Version : New analysis and plots of various throw effects.



dr_dave
07-16-2005, 02:53 PM
FYI, I just completed and posted a detailed analysis of ball friction and throw effects. It can be found in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf) on my website (http://www.engr.colostate.edu/~dga/pool/). Let me warn you ahead of time: It is full of lots of complicated math and physics, so you might not want to look at the whole thing. However, I encourage everybody to look at and comment on the plots and concluding remarks in the last 4 pages of the document, or at least look at some of the conclusions summarized below. The plots compare to experimental, theoretical, and qualitative results presented by Marlow, Sheppard, Koehler, and Jewett. The analysis and results cover both collision-induced throw (CIT) and spin-induced throw (SIT). The effects of cut angle, speed, and spin are also considered.

The model of friction I use is more complete and accurate than any other I have seen presented before. First, I include the effect of speed on friction, based on experimental data from Marlow. And more importantly, I correct an error that appears in many analyses of collisions with friction (e.g., in Shepard's work). The error involves not taking into account the potential loss of relative sliding motion between the CB and OB during impact. I have accounted for this effect, and it significantly affects the results. I hope some of the physics nerds out there will look at this closely and think about it to make sure they agree.

Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects):<ul type="square"> Both CIT and SIT are larger at slower speeds.
CIT increases with cut angle, but levels off at higher cut angles.
CIT is larger for stun shots.
SIT is larger, and most sensitive to sidespin, with stun shots. But SIT is not nearly as sensitive to small amounts of sidespin as some people think. The more accurate model of friction affected these results significantly.
Inside English increases CIT, especially at small cut angles.
Outside English can create SIT that overcomes CIT.
Outside English creates maximum SIT at small cut angles.
"Gearing" outside English results in absolutely no throw.[/list]
Again, there are no big surprises here, but it is reassuring to see a theoretical model shed some light on and improve understanding of all of these effects. Also, an accurate model lets one ask and answer other questions in the future quite readily.

Regards,
Dr. Dave

dr_dave
07-16-2005, 03:27 PM
FYI,

There have been many recent threads dealing with throw effects. FYI, you can find links to them under "throw" in the online discussion threads area of my website (http://www.engr.colostate.edu/~dga/pool/threads.html).

Regards,
Dr. Dave

dr_dave
07-16-2005, 03:29 PM
FYI,
Information concerning the references I cite in my analysis can be found in the pool and billiards physics resources area of my website (http://www.engr.colostate.edu/~dga/pool/physics.html).

Regards,
Dr. Dave

stickman
07-16-2005, 05:59 PM
Although I can't do all the math to get to your conclusions, my practical experience would cause me to agree with your conclusions. The slow speed demonstrates throw in my banks. I tend to use english on my banks rather than cutting the banks, and occasionally use both. Shooting hard severely lessens the effect I usually am looking for. For me, english in any situation at speed, tends to be less effective. Speed of course, also affects bank angles, even without english.

Inside english used on thin cuts for the purpose of position, can be difficult to pocket. The same shot can easily be made with outside english, provided you can achieve a desired position.

I use throw to make shots that are just barely blocked by an opponents balls. Speed of the shot is keenly apparent in these shots. Swerve also has to counted for, but I tend to believe that throw is a greater factor, especially on dirty bar-room tables, with dirty balls. Great research. /ccboard/images/graemlins/grin.gif It's good to have some idea why the balls do the things they do.

Billy_Bob
07-16-2005, 06:00 PM
I only looked at the pictures! /ccboard/images/graemlins/smile.gif

But I think I figured out why I might be having trouble pocketing the ball with long draw shots...

"BOTTOM LINE: collision-induced throw is greater for stun shots"

I think I'll start paying attention to where the object ball is going with these shots, and if it is being thrown away from the pocket...

Leviathan
07-17-2005, 05:00 AM
Thanks, Dave--nice work, and you present it clearly. I think I can use your info to organize and improve my approach to playing backcut banks.--AS

dr_dave
07-17-2005, 05:32 PM
<blockquote><font class="small">Quote dr_dave:</font><hr>Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects):<ul type="square"> Both CIT and SIT are larger at slower speeds.
CIT increases with cut angle, but levels off at higher cut angles.
CIT is larger for stun shots.
SIT is larger, and most sensitive to sidespin, with stun shots. But SIT is not nearly as sensitive to small amounts of sidespin as some people think. The more accurate model of friction affected these results significantly.
Inside English increases CIT, especially at small cut angles.
Outside English can create SIT that overcomes CIT.
Outside English creates maximum SIT at small cut angles.
"Gearing" outside English results in absolutely no throw.[/list]
Again, there are no big surprises here, but it is reassuring to see a theoretical model shed some light on and improve understanding of all of these effects. Also, an accurate model lets one ask and answer other questions in the future quite readily.<hr /></blockquote>
FYI, I just made a slight improvement to how friction is calculated in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf). I now use the relative speed between the balls for calculating the speed-dependant friction (instead of the cue ball speed). The results didn't change much; although, the following additional conclusions can be made (see the plots and comments in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf)):<ul type="square"> CIT is larger for stun shots close to a 1/2-ball hit (30-degree cut angle), per the plot on page 6.
SIT is maximum for stun and a medium amount of sidespin, per the plot on page 7. "Medium" corresponds to a spin-rate factor (see TP A.12 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-12.pdf)) of 0.5, which is much less than the practical maximum of 1.25. Additional sidespin does not result in more throw; in fact, the model predicts a loss in throw with excess sidespin, because friction is less for higher relative speeds between the balls.[/list]Regards,
Dr. Dave

dr_dave
07-17-2005, 05:56 PM
<blockquote><font class="small">Quote Billy_Bob:</font><hr>I only looked at the pictures! /ccboard/images/graemlins/smile.gif<hr /></blockquote>
I don't blame you.

<blockquote><font class="small">Quote Billy_Bob:</font><hr>But I think I figured out why I might be having trouble pocketing the ball with long draw shots...

"BOTTOM LINE: collision-induced throw is greater for stun shots"<hr /></blockquote>
I've certainly noticed this at the table, especially for soft draw shots where the CB spin wears off to stun in time for impact with the OB ... bad situation, especially for dirty of chalk-marked balls.

Regards,
Dave

dr_dave
07-17-2005, 06:03 PM
<blockquote><font class="small">Quote Leviathan:</font><hr> Thanks, Dave--nice work, and you present it clearly.<hr /></blockquote>You are very welcome, and thank you.
<blockquote><font class="small">Quote Leviathan:</font><hr>I think I can use your info to organize and improve my approach to playing backcut banks.<hr /></blockquote>
Now, banks are a whole different story because you need to also worry about (and adjust for) speed, English transfer (from CB spin and cut angle), and the amount of OB roll (based on distance from the cushion and speed). All of this stuff, along with aiming systems, is presented in Chapter 6 of my book. If you have a copy, check it out.

Regards,
Dave

Jal
08-04-2005, 04:00 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> FYI, I just completed and posted a detailed analysis of ball friction and throw effects.... <hr /></blockquote>

There is a fascinating consequence falling out of Dr. Dave's inclusion of the fact that the cueball can (and does) lose its sliding motion across the object ball under some circumstances. Namely, that if you hit a stun shot (or near stun shot), then over a certain range of cut angles the throw is essentially independent of the amount of friction between the balls.

So you could take a ball, rough sand it, smear chalk over the contact area, maybe even embed some nails /ccboard/images/graemlins/smirk.gif, and you would still get the same amount of throw. Not exactly the same since the rolling resistance would be altered a bit, but virtually the same.

The range of angles for which this is true is fairly large, from a full to an almost half-ball hit (0 to 25-30 degree cut). The rougher the balls are, the bigger this range is. But even for clean highly polished balls there is some span of cut angles for which they'll throw just about as much as old abraided ones.

Adding as much as a quarter natural roll spin (follow or draw) doesn't change this range too much. See the graph on page 6 of T_A14.

It's also interesting that the one thing you can do to avoid cling from the just deposited chalk mark - adding a fair amount of follow or draw - does make the throw susceptible to any other potential variations in the friction (i.e. potato chip grease).

Jim

Jal
08-04-2005, 09:13 PM
<blockquote><font class="small">Quote Jal:</font><hr>... Namely, that if you hit a stun shot (or near stun shot), then over a certain range of cut angles the throw is essentially independent of the amount of friction between the balls.<hr /></blockquote>
Acually, it's independent of an increase in the friction over the entire range. It's independent of a decrease over a smaller spread of cut angles, depending on the amount of the drop.

Jim

Fran Crimi
08-05-2005, 09:24 AM
<blockquote><font class="small">Quote dr_dave:</font><hr> I've certainly noticed this at the table, especially for soft draw shots where the CB spin wears off to stun in time for impact with the OB ... bad situation, especially for dirty of chalk-marked balls.

Regards,
Dave <hr /></blockquote>


Danger??? This is the most popular way of slowing down or stopping the cue ball in distance shots. This technique is used so often with so much success that it's ridiculous to use the word "DANGER" to describe it.

Fran

Cane
08-05-2005, 09:36 AM
<blockquote><font class="small">Quote Fran Crimi:</font><hr> Danger??? This is the most popular way of slowing down or stopping the cue ball in distance shots. This technique is used so often with so much success that it's ridiculous to use the word "DANGER" to describe it.

Fran <hr /></blockquote>

Fran, You're absolutely right. This is a MUST shot in the arsenal of even a "once a week" league player. It's a shot that should be mastered and should never be considered a bad situation or danger shot for ANYONE. As a matter of fact, I wish I could play such that most of my shots were ones where the CB is just losing it's low spin and beginning to slide or slightly take on natural roll. Those are, IMHO, the easiest to control.

Of course, I'm a "fanatic" and many are not. I practice with everything from a $4000 cue with MooriIII tips, to a $30 Players cue with a worn out LePro, I have Aramith Super Pro balls, but also have a mixed and matched set of "whatever" brand that have never been cleaned (typical of what you find in many bar boxes), I have 4 different CB's (aramith Logo, red circle, aramith mag and cheap heavy mag CB) that I practice with. I figure I have to be able to perform a shot like that with light CB, heavy CB, dirty OB, Dirty CB, you name it. It's a common and necessary shot.

Later,
Bob

SpiderMan
08-05-2005, 09:39 AM
<blockquote><font class="small">Quote Billy_Bob:</font><hr> I only looked at the pictures! /ccboard/images/graemlins/smile.gif

But I think I figured out why I might be having trouble pocketing the ball with long draw shots...

"BOTTOM LINE: collision-induced throw is greater for stun shots"

I think I'll start paying attention to where the object ball is going with these shots, and if it is being thrown away from the pocket...
<hr /></blockquote>

While this may be a factor, I expect that a far more significant contributor to the miss is the fact that long draw shots must be shot harder than other long shots. Shooting harder than one is accustomed to does tend to play havoc with form, and accuracy. Just my 2 cents, obviously everyone's nemeses are different.

I'm responding with the assumption that by "long draw shot", you are speaking of a significant separation of cue and object balls, and a desire to retain significant backspin at contact.

SpiderMan

Cane
08-05-2005, 09:46 AM
<blockquote><font class="small">Quote SpiderMan:</font><hr>I expect that a far more significant contributor to the miss is the fact that long draw shots must be shot harder than other long shots. Shooting harder than one is accustomed to does tend to play havoc with form, and accuracy. Just my 2 cents, obviously everyone's nemeses are different.

I'm responding with the assumption that by "long draw shot", you are speaking of a significant separation of cue and object balls, and a desire to retain significant backspin at contact.

SpiderMan <hr /></blockquote>

Marty, I agree with you but would like to also add that most people don't hit as close to true center ball as they think they do. On a long draw, if they hit just a little off center, all kinds of bad things can happen.

Later,
Bob

SpiderMan
08-05-2005, 11:14 AM
<blockquote><font class="small">Quote Cane:</font><hr> <blockquote><font class="small">Quote SpiderMan:</font><hr>I expect that a far more significant contributor to the miss is the fact that long draw shots must be shot harder than other long shots. Shooting harder than one is accustomed to does tend to play havoc with form, and accuracy. Just my 2 cents, obviously everyone's nemeses are different.

I'm responding with the assumption that by "long draw shot", you are speaking of a significant separation of cue and object balls, and a desire to retain significant backspin at contact.

SpiderMan <hr /></blockquote>

Marty, I agree with you but would like to also add that most people don't hit as close to true center ball as they think they do. On a long draw, if they hit just a little off center, all kinds of bad things can happen.

Later,
Bob <hr /></blockquote>

And I agree with you (mutual back-slapping here) /ccboard/images/graemlins/grin.gif

That's acutally part of what I was stating - we're more likely to hit the CB at the "wrong" place when shooting hard, vs shooting soft or medium. Particularly if we don't have perfect mechanics, and who does?

I'm not denying the original statement regarding throw being maximum for stun, but I believe that shooting hard increases the likelihood of other factors being overshadowed by the human error.

Damn, Bob, shouldn't you be on the road? BTW, James V and I met in the finals of a tourney last night. He mentioned that he found a snooker case, but you might go ahead and look him up at the Oklahoma event this weekend anyway. He's an interesting character (aren't we all?).

SpiderMan

Billy_Bob
08-05-2005, 11:18 AM
<blockquote><font class="small">Quote Cane:</font><hr> ...most people don't hit as close to true center ball as they think they do. On a long draw, if they hit just a little off center, all kinds of bad things can happen.<hr /></blockquote>

Yes long draw in that the cue ball is quite a distance from the object ball.

I have done this quite a bit (not hitting the cue ball exactly in the center). I am therefore very careful with kick shots, to be sure I am hitting center or left/right of center as needed.

Are long draw shots more sensitive to not hitting exactly in the center? Whereas a long centerball hit would be more forgiving or something?

Cane
08-05-2005, 11:27 AM
<blockquote><font class="small">Quote Billy_Bob:</font><hr> Are long draw shots more sensitive to not hitting exactly in the center? Whereas a long centerball hit would be more forgiving or something?
<hr /></blockquote>

Billy Bob, Well hitting a bit off center with a "medium speed" shot on a center ball hit, the only thing you have working against you is squirt. When using draw, if you hit off center, you can basically masse' the hell out of the ball and make the miss much worse. You hit the ball, you're a little to the left of center, say a 6:30 hit, the CB squirts out to the right a bit, then starts to curve (swerve, masse' whatever term you wish to use) back to the left, at one point in that arc and ONLY one point, it's back in line, but if that point isn't exactly where you contact the OB, then you miss.

So, yes, IMO, the long centerball hit is more forgiving than the long draw shot. Of course, if we could all learn to hit perfect center ball every time, then it wouldn't be an issue, but I've been around this game since I was 8 years old and haven't met anyone yet that hits perfect center ball EVERY time.

Later,
Bob

dr_dave
08-05-2005, 12:18 PM
Fran,

You are correct. "Danger" is too strong a word. I guess I was being overly dramatic to make a point. Maybe "reserved caution, but happy to have a stop shot" would be a better phrase. /ccboard/images/graemlins/smile.gif

Regards,
Dave

<blockquote><font class="small">Quote Fran Crimi:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> I've certainly noticed this at the table, especially for soft draw shots where the CB spin wears off to stun in time for impact with the OB ... bad situation, especially for dirty of chalk-marked balls.

Regards,
Dave <hr /></blockquote>


Danger??? This is the most popular way of slowing down or stopping the cue ball in distance shots. This technique is used so often with so much success that it's ridiculous to use the word "DANGER" to describe it.

Fran <hr /></blockquote>

Jal
08-05-2005, 12:57 PM
<blockquote><font class="small">Quote Fran Crimi:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> I've certainly noticed this at the table, especially for soft draw shots where the CB spin wears off to stun in time for impact with the OB ... bad situation, especially for dirty of chalk-marked balls.

Regards,
Dave <hr /></blockquote>


Danger??? This is the most popular way of slowing down or stopping the cue ball in distance shots. This technique is used so often with so much success that it's ridiculous to use the word "DANGER" to describe it.

Fran <hr /></blockquote>

<blockquote><font class="small">Quote Fran Crimi:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> I've certainly noticed this at the table, especially for soft draw shots where the CB spin wears off to stun in time for impact with the OB ... bad situation, especially for dirty of chalk-marked balls.

Regards,
Dave <hr /></blockquote>


Danger??? This is the most popular way of slowing down or stopping the cue ball in distance shots. This technique is used so often with so much success that it's ridiculous to use the word "DANGER" to describe it.

Fran <hr /></blockquote>

Although he didn't use the word "danger" as I can see, he did imply it. But I'll use it...I think stun shots in general are dangerous. They're a bane especially to the inexperienced player who soon learns to employ them on straight-in shots to avoid the scratch, only to watch the object ball take off in all kinds of strange directions. Unaware of throw, they conclude that these shots require an unusual amount of accuracy. They do, in the sense of hitting the cueball along the vertical center axis, but the "natural" interpretation (sans the throw concept) is that straight shots are the hardest, and they're the hardest because of some aspect of the geometry.

As you and Cane said, you do need to use stop/drag/stun shots frequently, and they're pretty easy once you get your stroke reasonably straight and are aware of the pitfalls. But there are pitfalls and I think that even somewhat experienced players miss routine shots now and then because of them (I certainly do).

Jim

SpiderMan
08-05-2005, 01:38 PM
<blockquote><font class="small">Quote SpiderMan:</font><hr> Damn, Bob, shouldn't you be on the road? BTW, James V and I met in the finals of a tourney last night. He mentioned that he found a snooker case, but you might go ahead and look him up at the Oklahoma event this weekend anyway. He's an interesting character (aren't we all?).
SpiderMan <hr /></blockquote>

BTW, James got one of the coldest rolls I've ever seen in one of our games. I came up dry on a good break, and expected him to run out. He made a nice rail shot and brought the cueball straight into a pack of three that had to be broken out. The cueball somehow went RIGHT THROUGH THE CENTER of the cluster without touching anything, went to the rail on the other side, and rebounded all the way back across to freeze him against one of the balls in the cluster. It's a testament to his fortitude that he didn't cry. Let me know if he's still talking about it in Oklahoma tomorrow /ccboard/images/graemlins/grin.gif

SpiderMan

Cane
08-05-2005, 05:02 PM
Oh, man, that's a roll that HURTS!!! Of course, if I meet up with him, I would NEVER bring it up! LOL

Well, don't have to hit the road until morning for the OK State Championships. I have my big thermos ready downstairs, and will leave here about 7:30 AM for Tulsa. It only takes me a little less than 2 hours to get to Billiard Palace from here. Besides, tonight I've got a local tournament to play in. Man, been a busy week. and a good one. Played in 4 tournaments since Saturday, 3 wins and 1 third place finish. My fault on the 3rd... rated tourney, and the kid that put me out is only going to 4. He made one 9 on the snap and made 2 early 9's (all this in the first three games, so I'm down 3-0 right off the bat), so before I can blink an eye, he's on the hill. I never should have let him see the object ball! I took him lightly, after all, he's just a 4 speed and NO WAY he beats me, right???? WRONG!!! I just let it slip by and before you know it, he gets me 4-6.

I won't take anything lightly tomorrow. I'll play my hardest, meanest game against every opponent. Getting in that "kill 'em all" mode now!

To keep this in line with the thread, I will be using as many stun or stop shots as I possibly can tomorrow! And hitting center ball. If I don't, I'll be back here by 4pm to post on the disaster! LOL

Later,
Bob

dr_dave
08-09-2005, 07:55 AM
<blockquote><font class="small">Quote Jal:</font><hr>There is a fascinating consequence falling out of Dr. Dave's inclusion of the fact that the cueball can (and does) lose its sliding motion across the object ball under some circumstances. Namely, that if you hit a stun shot (or near stun shot), then over a certain range of cut angles the throw is essentially independent of the amount of friction between the balls.<hr /></blockquote>
Jim,

I'm glad somebody noticed that. Good job! FYI, I just posted a new analysis dedicated to friction effects, with even more graphs (the graph haters out there are going to love this /ccboard/images/graemlins/smile.gif ). It can be found at TP A.17 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-17.pdf). Included are graphs that show the effects of increased and decreased friction for various cases of collision-induced and spin-induced throw. Enjoy! Here's a summary of the conclusions:

- For natural roll shots (or draw shots with a natural roll amount of backspin), there is more collisions-induced throw when there is more friction, for all cut angles.

- For stun shots, the amount of friction does not affect the amount of collision-induced throw for small cut angles. However, there is more throw with more friction for larger cut angles.

- For small amounts of sidespin, the amount of friction does not affect the amount of spin-induced throw. However, with larger amounts of sidespin, there is more throw with more spin (up to a point) and with more friction.

Regards,
Dave

dr_dave
08-09-2005, 08:07 AM
<blockquote><font class="small">Quote Jal:</font><hr>It's also interesting that the one thing you can do to avoid cling from the just deposited chalk mark - adding a fair amount of follow or draw - does make the throw susceptible to any other potential variations in the friction (i.e. potato chip grease).<hr /></blockquote>
Jim,

I think the graphs in TP A.17 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-17.pdf) (on page 2) show the effect you are describing. A follow or draw shot would have much less cling (throw) than a stun shot. However, the amount of cling does increase with the amount of friction, at all cut angles, for typical follow and draw shots.

Regards,
Dave

dr_dave
08-09-2005, 08:15 AM
<blockquote><font class="small">Quote Jal:</font><hr> <blockquote><font class="small">Quote Jal:</font><hr>... Namely, that if you hit a stun shot (or near stun shot), then over a certain range of cut angles the throw is essentially independent of the amount of friction between the balls.<hr /></blockquote>
Acually, it's independent of an increase in the friction over the entire range. It's independent of a decrease over a smaller spread of cut angles, depending on the amount of the drop.<hr /></blockquote>
Jim,

I don't think the second graph in TP A.17 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-17.pdf) (on page 2) supports your statement. The amount of throw is independent of changes in friction only for small cut angles. At larger cut angles, the amount of throw increases with more friction and decreases with less friction.

I'm sorry if I misinterpreted your statement. Please let me know if I did.

Regards,
Dave

freddythebeard
08-09-2005, 05:26 PM
Dr. Dave,
What a wonderful set of accurate descriptions of the various effects of throw. It's invaluable information. My pool hat is off to you.
Freddy The Beard Bentivegna

dr_dave
08-10-2005, 09:10 AM
<blockquote><font class="small">Quote freddythebeard:</font><hr> Dr. Dave,
What a wonderful set of accurate descriptions of the various effects of throw. It's invaluable information. My pool hat is off to you.<hr /></blockquote>
Freddy,

Thanks for the supportive words. My hat is also off to you for your "Banking with the Beard" book. Very well done!!!

Regards,
Dave

Jal
08-10-2005, 11:42 AM
<blockquote><font class="small">Quote dr_dave:</font><hr> <blockquote><font class="small">Quote Jal:</font><hr> <blockquote><font class="small">Quote Jal:</font><hr>... Namely, that if you hit a stun shot (or near stun shot), then over a certain range of cut angles the throw is essentially independent of the amount of friction between the balls.<hr /></blockquote>
Acually, it's independent of an increase in the friction over the entire range. It's independent of a decrease over a smaller spread of cut angles, depending on the amount of the drop.<hr /></blockquote>
Jim,

I don't think the second graph in TP A.17 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-17.pdf) (on page 2) supports your statement. The amount of throw is independent of changes in friction only for small cut angles. At larger cut angles, the amount of throw increases with more friction and decreases with less friction.

I'm sorry if I misinterpreted your statement. Please let me know if I did.

Regards,
Dave <hr /></blockquote>

Great work Dr. Dave. As far as I'm concerned, it's manna from heaven.

You didn't misinterpret my statement, as written. By "Actually, it's independent of an increase in the friction over the entire range", I meant the range of cut angles where the cueball is partly rolling across the object ball (i.e., the nearly straight portions of the curves). But it doesn't read that way and I'm sorry for misrepresenting your hard won results.

Jim

dr_dave
08-10-2005, 12:01 PM
Jim,

Thanks for the clarification and nice words.

I'm glad you have joined the CCB. It's nice to have another physics jockey out there.

What is your background and what kind of work do you do? You seem to have a firm grasp of physics principles.

Regards,
Dave
<blockquote><font class="small">Quote Jal:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> <blockquote><font class="small">Quote Jal:</font><hr> <blockquote><font class="small">Quote Jal:</font><hr>... Namely, that if you hit a stun shot (or near stun shot), then over a certain range of cut angles the throw is essentially independent of the amount of friction between the balls.<hr /></blockquote>
Acually, it's independent of an increase in the friction over the entire range. It's independent of a decrease over a smaller spread of cut angles, depending on the amount of the drop.<hr /></blockquote>
Jim,

I don't think the second graph in TP A.17 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-17.pdf) (on page 2) supports your statement. The amount of throw is independent of changes in friction only for small cut angles. At larger cut angles, the amount of throw increases with more friction and decreases with less friction.

I'm sorry if I misinterpreted your statement. Please let me know if I did.

Regards,
Dave <hr /></blockquote>

Great work Dr. Dave. As far as I'm concerned, it's manna from heaven.

You didn't misinterpret my statement, as written. By "Actually, it's independent of an increase in the friction over the entire range", I meant the range of cut angles where the cueball is partly rolling across the object ball (i.e., the nearly straight portions of the curves). But it doesn't read that way and I'm sorry for misrepresenting your hard won results.

Jim <hr /></blockquote>

dr_dave
09-12-2005, 03:04 PM
FYI, I just posted some additional plots in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf) (see pages 6, 9, and 10). If you like looking at plots, check them out. If you don't, you still might be interested in some of the following conclusions derivable from the plots:<ul type="square"> the theoretical plot of throw vs. cut angle for stun shots matches up with Bob Jewett's experimental data (http://www.sfbilliards.com/throw.gif) very well.
For a stun shot, the amount of CIT is independent of speed at small cut angles.
For a stun shot, CIT is largest in the half-ball hit range (30-degree cut angle range).
For a stun shot, at larger cut angles, CIT is larger for slower speeds.
For a half-ball hit, throw is greatest for a stun shot with no sidespin or with outside English with a spin rate factor of 1 (see TP A.12 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-12.pdf)). For outside English with a spin rate factor of 0.5, there is no throw.[/list]
Regards,
Dr. Dave

<blockquote><font class="small">Quote dr_dave:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr>Here are some of the conclusions resulting from the mathematical analysis (which agree with what most people understand about throw effects):<ul type="square"> Both CIT and SIT are larger at slower speeds.
CIT increases with cut angle, but levels off at higher cut angles.
CIT is larger for stun shots.
SIT is larger, and most sensitive to sidespin, with stun shots. But SIT is not nearly as sensitive to small amounts of sidespin as some people think. The more accurate model of friction affected these results significantly.
Inside English increases CIT, especially at small cut angles.
Outside English can create SIT that overcomes CIT.
Outside English creates maximum SIT at small cut angles.
"Gearing" outside English results in absolutely no throw.[/list]
Again, there are no big surprises here, but it is reassuring to see a theoretical model shed some light on and improve understanding of all of these effects. Also, an accurate model lets one ask and answer other questions in the future quite readily.<hr /></blockquote>
FYI, I just made a slight improvement to how friction is calculated in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf). I now use the relative speed between the balls for calculating the speed-dependant friction (instead of the cue ball speed). The results didn't change much; although, the following additional conclusions can be made (see the plots and comments in TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf)):<ul type="square"> CIT is larger for stun shots close to a 1/2-ball hit (30-degree cut angle), per the plot on page 6.
SIT is maximum for stun and a medium amount of sidespin, per the plot on page 7. "Medium" corresponds to a spin-rate factor (see TP A.12 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-12.pdf)) of 0.5, which is much less than the practical maximum of 1.25. Additional sidespin does not result in more throw; in fact, the model predicts a loss in throw with excess sidespin, because friction is less for higher relative speeds between the balls.[/list]Regards,
Dr. Dave <hr /></blockquote>

Bob_Jewett
09-12-2005, 03:52 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> ... <ul type="square"> For a half-ball hit, throw is greatest for a stun shot with no sidespin or with outside English with a spin rate factor of 1 (see TP A.12 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-12.pdf)). For outside English with a spin rate factor of 0.5, there is no throw.[/list]
Regards,
Dr. Dave
<hr /></blockquote>
The last mentioned case, where a stun shot is played with outside english that exactly eliminates throw is particularly interesting. Usually people recommend using outside english in such a situation to eliminate the possibility of skid. The problem shown in the plot is that if you achieve "perfectly cancelling outside," you are also most sensitive to the exact amount of sidespin you have on the cue ball -- a little more and you throw the object ball quite a bit backwards, and a little less and you throw the ball in the normal direction. By contrast, if you use inside english, the cut angle changes only slightly if you have a little more or a little less side spin.

My own feeling is that you have the best chance of pocketing the ball, usually, if you use no side spin and the cue ball has some draw or follow when it arrives at the object ball.

dr_dave
09-12-2005, 04:06 PM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> ... <ul type="square"> For a half-ball hit, throw is greatest for a stun shot with no sidespin or with outside English with a spin rate factor of 1 (see TP A.12 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-12.pdf)). For outside English with a spin rate factor of 0.5, there is no throw.[/list]
Regards,
Dr. Dave
<hr /></blockquote>
The last mentioned case, where a stun shot is played with outside english that exactly eliminates throw is particularly interesting. Usually people recommend using outside english in such a situation to eliminate the possibility of skid. The problem shown in the plot is that if you achieve "perfectly cancelling outside," you are also most sensitive to the exact amount of sidespin you have on the cue ball -- a little more and you throw the object ball quite a bit backwards, and a little less and you throw the ball in the normal direction. By contrast, if you use inside english, the cut angle changes only slightly if you have a little more or a little less side spin.

My own feeling is that you have the best chance of pocketing the ball, usually, if you use no side spin and the cue ball has some draw or follow when it arrives at the object ball. <hr /></blockquote>
Excellent points, Bob. If a person is a little off with the amount of outside English, the ball might throw 1 or 2 degrees. But on the other hand, if the balls are very dirty or if you happen to hit a chalk mark on a ball, the throw will be significantly larger if outside English is not used. I agree with you that if position play does not require stun, then follow or draw is definitely useful because they can decrease the throw significantly.

Also, for the benefit of others, I thought a previous posting from SpiderMan summed up pertinent issues fairly well in another thread (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=200869&amp;page =0&amp;view=collapsed&amp;sb=5&amp;o=&amp;vc=1).

Regards,
Dave

dr_dave
10-04-2005, 10:05 AM
<blockquote><font class="small">Quote from a PM I received:</font><hr>With your analysis of throw (TP A.14), in arriving at the constants for the coefficient of friction relation u=a+be^(-cvrel), I'm thinking you should multiply the speed of the cueball by the sine of the cut angle to get the surface speed along the tangent line. It doesn't change the constants a or b but affects c.<hr /></blockquote>
You make a good point. I read the section in Marlow's book again and decided that you are correct. Thank you for pointing this out ... good job! I've updated TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/index.html) to reflect the change. The throw values did decrease some, but all of the curve trends, and conclusions, are still the same.

Thank you for spotting this,
Dave

dr_dave
02-27-2006, 02:06 PM
<blockquote><font class="small">Quote question via e-mail:</font><hr>
Dr. Alciatore,

I was looking at your theoretical results in TP A.14 "The effects of cut angle, speed, and spin on object ball throw"
(http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf)
and was having trouble understanding one of the graphs I was interested in.

It is at the top of page 7 and is labeled "collision-induced throw vs. cut angle for shots with various amounts of vertical plane spin (follow or draw), compared to stun"

Although I had my guesses, I was unable to discern which of the colored lines corresponded to draw, follow, and stun. Going from top to bottom on the left side of the graph, what do those 4 lines represent?<hr /></blockquote>
The curves represent 100%, 50%, 25%, and 0% spin rates (compared to the natural roll spin rate), so the first is a natural roll shot and the last is a stun shot. The curves apply to both follow and draw shots with comparable spin rates.

<blockquote><font class="small">Quote question via e-mail:</font><hr>Do your equations assume that both draw and follow will induce an identical amount of collision induced throw?<hr /></blockquote>
Yes, if the amount of spin is the same.

<blockquote><font class="small">Quote question via e-mail:</font><hr>If so, I feel that draw tends to induce more throw than follow. Any comment?<hr /></blockquote>
This probably occurs because some of your draw is wearing off on the way to the object ball, so the spin rate is closer to stun than you might think, especially on a slow cloth.

<blockquote><font class="small">Quote question via e-mail:</font><hr>Thank you for the very interesting work you do.<hr /></blockquote>
You are very welcome.

Dr. Dave

dr_dave
10-06-2006, 10:33 AM
FYI, I've been presenting the results of the throw analysis (TP A.14 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/new/TP_A-14.pdf)) in a series of well illustrated, easy to understand articles in Billiards Digest. The first five articles in the series are already available on my website (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html). More will follow over the next few months. I hope you find them interesting and useful in your game.

Regards,
Dr. Dave