Thanks for pointing this out Clark. I'm still learning. :wink:
physics-based draw shot advice
- Thread starter dr_dave
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Thanks for pointing this out Clark. I'm still learning. :wink:
If you look at the accelerometer plots in TP A.9 again,
http://billiards.colostate.edu/technical_proofs/new/TP_A-9.pdf,
they definitely do show the acceleration passing through zero and continuing on to negative values without any appreciable delay. Aside from the unpleasantness that occurs at impact, the deceleration phase roughly mirrors the acceleration phase before impact, except that it's flipped over into the negative region. The first graph of John Pizzuto's stroke (page 4) clearly shows the cue decelerating before impact. And it almost reaches as low a valley before impact as the positive acceleration rose to a peak. (As Mr. Pizutto observed when he first presented them, this is not the ideal way to stroke. You generally want impact to occur when the cue's acceleration is around zero, or still positive.)
But we may be talking about two different things, acceleration versus speed. When you say that in the absence of an impact (no cueball in the way), there is sort of a delay before the cue slows down, that is true, no argument. Its speed does tend to "flatten out" for a period because its acceleration/deceleration is close to zero, as TP A.9 shows. But its acceleration doesn't hesitate to transition to deceleration. It's just that it takes a while for the effect of the deceleration to build up, i.e., slow the cue down appreciably. All of this takes place continuously, of course - its speed is never absolutely constant.
Hope we're on the same page now, or do you still disagree?
Jim
Attempt to accelerate through the cue ball or not.
Quote:
Originally Posted by Clark_the_Shark
Jay, not to be rude here, but you really should read this entire thread before posting... The things you say have been covered already. Especially the debunking of your statement that "you must be accelerating when you go through the ball for best results".
It's simply not true.
Thanks for pointing this out Clark. I'm still learning.
While there is no doubt that it is physically impossible to accelerate through the cue ball, I continue to believe that an effort to accelerate the movement of your cue through the cue ball is a very good thing.
This attempt to accelerate through the cue ball is something that helps one to provide a more complete stroke. With no attempt to accelerate through the cue ball, you will most likely provide a less than desired and inconsistent stroke.
JoeyA
Quote:
Originally Posted by Clark_the_Shark
Jay, not to be rude here, but you really should read this entire thread before posting... The things you say have been covered already. Especially the debunking of your statement that "you must be accelerating when you go through the ball for best results".
It's simply not true.
Thanks for pointing this out Clark. I'm still learning.
While there is no doubt that it is physically impossible to accelerate through the cue ball, I continue to believe that an effort to accelerate the movement of your cue through the cue ball is a very good thing.
This attempt to accelerate through the cue ball is something that helps one to provide a more complete stroke. With no attempt to accelerate through the cue ball, you will most likely provide a less than desired and inconsistent stroke.
JoeyA
I agree with this. Though I have a slightly hard time making out what exactly is happening with the cue during the first 3 pages of graphs, though I "assume" that it's his warmup strokes before actual cue striking. In which case the waves make sense because you are forcing your arm to slow down and stop before it strikes the CB. And usually this motion is very smooth which makes sense given what I am seeing.
You'll have to forgive the apparent difficulty in explaining things to eachother via the internet as you are right, it's hard to see if two people are talking about two different things or not. So for that I appologize.
I think the distinction here is that his graph shows that the cue DECELERATES from an accelerating motion. In other words, the cue's speed doesn't slow, its acceleration slows. What I am talking about is the fact that once a cue (your arm) reaches its max speed, of course it stops accelerating, but it maintains speed (or that its speed stays relatively constant - of which I know the technicality here) for a longer period than you stated earlier about what people assume is happening. Does this make sense? Or am I restating what you said?
I think maybe these graphs (and people's knowledge - myself included) could be enhanced if we could see a "speed vs. time" graph overlay.
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I think that is excellent advice, especially for power draw shots. Even though I know I can't "accelerate through the ball," and even though I know my pendulum stroke has little or no acceleration at tip contact, I still sometimes tell myself: "accelerate smoothly into [and even through] the ball" (and it usually helps me get the power I want). For me, I think it helps me be smoother and less jerky.
Regards,
Dave
You present an interesting and tough challenge from a physics point of view. On the one hand, it's not hard to show that a change in contact time, by itself, will not change the cueball's speed and spin due to the magnitude of the impact force generated by the already moving cue. That is, this part of the total force acting on the cueball doesn't get to act over a longer period without being proportionally diminished. However, applying a significant force to the cue with the grip hand during impact (significant compared to the impact force from the moving cue) might change the shape of the impact force-time curve. This can either increase or decrease the effect this force, depending on how it's shape is altered. I don't know the answer to this. But, imo, generating a "significant" force with the grip hand (compared to the impact force), probably isn't going to happen.
In order to get the cueball to draw back at a sharper angle, you have to increase the spin/speed ratio at impact. You can only do this by increasing the effective tip offset (as Dr. Dave has been discussing). I'm very skeptical that this can be done "better" with the technique you describe (short bridge and a "push"), than with a normal stroke. I wonder if anyone can come up with a reason why this might be true?
So while I'm skeptical, proving or disproving it is not easy. As you say, it's something best done at the the table. Have you tried to get the same effect with a normal stroke?
Jim
This is my best attempt at what I think is going on. I think that most people believe, as you said Jal, that max speed happens at vertical forearm. I don't disagree here, but rather I just extend that speed with no losing of speed until much later than others are postulating.
What I also postulate, as I think NickGeo was trying to say with him describing the Bob Jewitt scenario of moving the CB to a different point in his stroke, is that a cue ball will have the same amount of draw (with the same tip position of course) at BOTH A & D, and likewise, at both B & C. And that we are all in agreement that speed is the factor, not acceleration as has been so elegantly detailed by Dr. Dave.
The ONLY point I'm trying to make here is that I believe that from points B - C are a little longer than people speculate/assume because the CB is usually struck in this area and we don't know for sure because no one has done the analysis.
What I also postulate, as I think NickGeo was trying to say with him describing the Bob Jewitt scenario of moving the CB to a different point in his stroke, is that a cue ball will have the same amount of draw (with the same tip position of course) at BOTH A & D, and likewise, at both B & C. And that we are all in agreement that speed is the factor, not acceleration as has been so elegantly detailed by Dr. Dave.
The ONLY point I'm trying to make here is that I believe that from points B - C are a little longer than people speculate/assume because the CB is usually struck in this area and we don't know for sure because no one has done the analysis.
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Yes, you're right about them showing the warmup strokes, and confusing the issue a bit (they did it to me at first).
You should read some of the miserable opaque stuff I've written!
We're probably in agreement, more or less, and I may have not stated things in the best way earlier. The only thing we might still differ on is that the cue doesn't start slowing down at all until the forearm nears the end of its arc, if that's your position? From the graphs, it seems pretty clear that it does start slowing down immediately after reaching peak speed, i.e., as acceleration changes to deceleration. But, it does take time for the effect of this deceleration to accumulate as a large change in speed.
Agreed. Dr. Dave has a theoretical curve on page 2 here (graph on the left):
http://billiards.colostate.edu/technical_proofs/new/TP_B-4.pdf
It has the same general shape as the acceleration vs time curve, except it goes from zero to a peak during the same time interval as the acceleration goes from zero to a peak and then back down to zero again. If you continued this graph past the moment of impact, it would mirror what went on before impact. In other words, it would be symmetrical about impact. Since it's peaking at impact, the cue's speed is "stable" or virtually constant at this time. But it does begin dropping off immediately, just not much at first.
Jim
I don't think "at all", but rather just later than you suppose. The "mirror" quotation above I believe is speculation until we can see actual plotted points. That's all I'm saying.
Given the accelerometer graphs, which is actual data, albeit only a few examples, and that the acceleration shows no delay in transitioning from positive to negative and continuing downward, I think it's pretty clear that a companion plot of speed vs time would resemble Dr. Dave's theoretical graph. This is a mathematical inference, which follows from the definitions of speed and acceleration. Of course, we're assuming the accelerometer graphs are representative.
Thanks for taking the time, by the way, to present your graph. I guess we sort of disagree on its flatness between points B and C. I would say that it should not be as flat as indicated, based on the few accelerometer examples (and inferences from the math). But I think everyone would agree that you would get the same amount of draw at points A and D, and B and C.
Not to throw a wrench in the works, but "accelerating through", misnomer though it may be, can, in theory, produce more speed and spin, by generating more cue speed before impact. If you did nothing else but stretched the force-time curve out in time, so that impact occurred while the cue was still positively accelerating, you would get more cue speed. And this, despite the fact that you've taken some of the acceleration away from the early part of the stroke. It has to do with the fact that the cue's speed is equivalent (mathematically) to the area under the curve, and you get more area by stretching it. Another way of looking at it, is that you want to delay peak force until the cue has built up some considerable speed. This yields more kinetic energy, which is equal to the sum of the magnitude of the applied force times each small interval of space it passes over on the way to the cueball. You want it to be passing over as many small spaces as possible when the force is large. But its main virtue, probably, is that it surely prevents one from significantly decelerating before impact.
Jim
Thanks for taking the time, by the way, to present your graph. I guess we sort of disagree on its flatness between points B and C. I would say that it should not be as flat as indicated, based on the few accelerometer examples (and inferences from the math). But I think everyone would agree that you would get the same amount of draw at points A and D, and B and C.
Not to throw a wrench in the works, but "accelerating through", misnomer though it may be, can, in theory, produce more speed and spin, by generating more cue speed before impact. If you did nothing else but stretched the force-time curve out in time, so that impact occurred while the cue was still positively accelerating, you would get more cue speed. And this, despite the fact that you've taken some of the acceleration away from the early part of the stroke. It has to do with the fact that the cue's speed is equivalent (mathematically) to the area under the curve, and you get more area by stretching it. Another way of looking at it, is that you want to delay peak force until the cue has built up some considerable speed. This yields more kinetic energy, which is equal to the sum of the magnitude of the applied force times each small interval of space it passes over on the way to the cueball. You want it to be passing over as many small spaces as possible when the force is large. But its main virtue, probably, is that it surely prevents one from significantly decelerating before impact.
Jim
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I'll bet you can get more draw with a two-inch stroke than you can with a normal stroke, but you need a little help - about a five pound hammer should do it.
Lay the stick down with its butt over the edge of a padded rail and its shaft resting on a padded support with the tip about 1/4" off the cloth. Place the CB just about touching the tip. Hold the butt down firmly on the rail padding so it won't go anywhere and whack the stick on the butt with the hammer. Instant superdraw.
Wish I had a cue I didn't mind whacking and a video setup... Why, this sounds like a job for Mike Page, Pool Scene Investigator!
pj
chgo
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If you were surprised by this and some of your other results, then you haven't been studying your Coriolis!
This and much more was derived almost 200 years ago in his masterwork of billiard physics, Théorie mathématique des effets du jeu de billard published in 1835. Luckily for you guys, there's an English translation by David Nadler available now. (I slogged my way through the original French years ago with a dictionary and grammar reference and my brain is still aching.)
This stuff was also revisted by Régis Petit in Billard : Théorie du jeu, which is really just a chapter-by-chapter restatement of most of Coriolis' results in more modern notation.
I've attached an image of figures 8-10 from Coriolis for reference:
- Figure 8 shows spin vs tip offset and how max rpms aren't at max offset.
- Figure 9 shows ball speed vs tip height, and how it peaks around %20 above center.
- Figure 10 is a composite of 3 graphs of distance vs tip height. The first (I's) shows distance to the sliding/stun state (peak around %30 below center); the second (Q's) shows distance to natural roll (peak around %10 below center); and the third (K's) are just the distance to parabola vertices used in his constructions in figures 6-7.
For comparison, I also attached Petit's version of figure 10 which is a little easier to read out of context.
Robert
Attachments
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Maybe the math shows that, but the drawing doesn't. The bottom arrow, which (if I read the graph right) points at maximum rpms (maybe even slightly less), is just about at 1/2R from centerball. I think that's about maximum offset.
Thanks for posting this, by the way. Very interesting.
pj
chgo
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You are both right and wrong in how you're reading the graph.
He is indeed pointing at slightly less than 0.5R offset there, but due to his assumptions in his stick-ball interaction about kinetic energy losses and such, he calculates the miscue limit to be ~0.6R. Therefore, he is showing it as less relative to his maximum. (As you probably noticed, this drawing shows no table line because it could be sidespin as well.)Whether you agree with the details of those assumptions numerically is a separate issue from the qualitative result of max RPMs occurring at less than max offset, which he does show.
Of course, sometimes a much more relevant idea to actual play is the spin/speed ratio, which does continue to increase with increased offset. Coriolis discussed that as well.
You're welcome! Now where are those coveted PJ greenies I can't seem to find in my inbox, eh?
Robert
Must've been a software glitch. :wink:
They're in your box now (don't spend 'em all in one place).
pj
chgo
Coriolis brilllance
Thank you for the excellent post. I do need to go back and read the Nadler translation again. I was fortunate to be a reviewer for Nadler's translation. I had seen Coriolis' French document on microfilm a while ago, but I didn't get much out of it because I don't know French. When I read Nadler's draft, I actually found quite a few small errors and inconsistencies. I'm not sure they were in Coriolis' original work, but they are fixed in Nadler's published book. I agree that Coriolis analyzed almost everything that can be analyzed. We have learned a lot since then (e.g., with the help of high-speed video), but his contributions were monumental. That's too bad his book wasn't translated to a more universal language (e.g., English) earlier.
I will look back at Coriolis' coverage of draw shots, but I still think my analysis has some interesting graphs and results that Coriolis did not present. I'm sure if he had had access to the same computer tools I have, he would have done even more.
To me, one of Coriolis' most brilliant (and useful) contributions was the masse shot aiming method.
Regards,
Dave
Thank you for the excellent post. I do need to go back and read the Nadler translation again. I was fortunate to be a reviewer for Nadler's translation. I had seen Coriolis' French document on microfilm a while ago, but I didn't get much out of it because I don't know French. When I read Nadler's draft, I actually found quite a few small errors and inconsistencies. I'm not sure they were in Coriolis' original work, but they are fixed in Nadler's published book. I agree that Coriolis analyzed almost everything that can be analyzed. We have learned a lot since then (e.g., with the help of high-speed video), but his contributions were monumental. That's too bad his book wasn't translated to a more universal language (e.g., English) earlier.
I will look back at Coriolis' coverage of draw shots, but I still think my analysis has some interesting graphs and results that Coriolis did not present. I'm sure if he had had access to the same computer tools I have, he would have done even more.
To me, one of Coriolis' most brilliant (and useful) contributions was the masse shot aiming method.
Regards,
Dave
If you were surprised by this and some of your other results, then you haven't been studying your Coriolis!
This and much more was derived almost 200 years ago in his masterwork of billiard physics, Théorie mathématique des effets du jeu de billard published in 1835. Luckily for you guys, there's an English translation by David Nadler available now. (I slogged my way through the original French years ago with a dictionary and grammar reference and my brain is still aching.)
This stuff was also revisted by Régis Petit in Billard : Théorie du jeu, which is really just a chapter-by-chapter restatement of most of Coriolis' results in more modern notation.
I've attached an image of figures 8-10 from Coriolis for reference:
- Figure 8 shows spin vs tip offset and how max rpms aren't at max offset.
- Figure 9 shows ball speed vs tip height, and how it peaks around %20 above center.
- Figure 10 is a composite of 3 graphs of distance vs tip height. The first (I's) shows distance to the sliding/stun state (peak around %30 below center); the second (Q's) shows distance to natural roll (peak around %10 below center); and the third (K's) are just the distance to parabola vertices used in his constructions in figures 6-7.
For comparison, I also attached Petit's version of figure 10 which is a little easier to read out of context.
Robert
I use it all the time, and am still amazed at how well it works. It has transformed masse shots for me from "wing and a prayer" to "man with a plan".
pj
chgo