physics-based draw shot advice

[dr_dave]

Anyhow, permit me a couple of comments/observations/questions. In all of this I worked out that the points on the graphs are time markers equally spaced in time. There are 40 or 41 points and the total time is 1220 frames times 1/3000 (3000 frames per second). And the whizzing clock seemed to show around .4 seconds duration, even if backwards. So these time markers are about .01 seconds apart. I hope I got this much right.

I'm not sure what you mean by "time markers." Each frame in HSV B.40 is about 0.0003 second (1/3000 of a second) apart.

On Mr. Jewett's graph:

1. There are 3 or 4 points just before the big drop that are very close in the distance direction. That suggests to me that the cue is moving more slowly that at the previous several points, that are farther apart. Yet the speed given on the speed axis is the same for all of these points. I don't understand how this can be. This is even more noticeable on the Dr.'s graph. Am I misunderstanding this?

We didn't calculate speed for every frame except during around tip contact, where the speed changes the fastest. That's why there are more points around tip contact.

2. The voice-over and vertical red rectangle indicate the points that represent the contact time and that speed decreases during that time. From the red rectangle and from the points where speed decreses, it's about 6 or 7 points, or .06 seconds. That's a lot more time that the one-thousandth of a second that you mentioned in an earlier e-mail. Or did I blow the math here or earlier on.

I think we calculated the speed and distance at every frame around tip contact. So 6 frames at 1/3000 sec per frame would give 0.002 second, which is reasonable for a time period that includes tip contact.

3. How do we know that the cue is no longer in contact with the cueball after the cue speeds up again? Perhaps the contact has slowed down the cue, speeded up the cue ball, and now they are moving as one (like my original question about putting the tip against the cue ball, stroking and getting draw).

I have plenty of high-speed video clips showing what happens with the cue and tip. For video references, see:

http://billiards.colostate.edu/threads/cue_tip.html#contact​

4. If instead the cue ball and the cue separate at the bottom of the vertical red rectangle as per the voiceover information, why doesn't the cue then hit the cue ball again?

... because the cue ball moves away much faster than the original cue speed (see the videos mentioned above), and the cue slows during tip contact.

At the very moment of separation I would think that the cue ball is going a teeny tiny bit faster than the cue. But then the cue speeds up according to the graph and the cue ball should begin to slow down due to the cloth. The cue would win the race.

The cue ball is long gone during the cue re-acceleration and deceleration (I have many HSV videos and physics analyses showing this also).

5. Is my assertion that the key speed is that at separation rather than at initial contact correct?

I think it is better to think of the contact speed as the key, because it defines how much momentum the cue has when it hits the ball. The separation speed is less because some of the cue momentum is transferred to the ball.

6. Going back to the drawing board, I would love to see an experiment with Mr. Jewett's lovely pendulum stroke where he hits the draw shot on the early part of his stroke (accelerating) and then does it again on the decelerating ending part of his stroke, both at the same speed. My bet is on the early Mr. Jewett to get the big draw.

I'll take that bet any day. As the video shows, Bob reaches maximum speed at the bottom of the pendulum. It is an irrefutable fact that more cue speed creates more cue ball speed and/or spin.

Regards,
Dave

 

[nickgeo]

Sir--Thanks a lot for your reply; it really helped me to understand how the graphs were constructed and thus what they show. I did not realize that the time or position or frame points were separated by different amounts at the center of the graph than at the the other positions. And it was helpful to realize that at the center the points were at one frame or 1/3000 of a second increments to the next. Maybe this was obvious to most folks, but not to me. Appreciate the help; now I can go through the other material on your interesting site.

As to the bet, I actually did not say that Mr. Jewett would get more draw at a slower speed than at a faster one. I wanted to see his draw by striking the cue ball at a point in his stroke well before his fastest speed, while his cue is accelerating, and compare that to his draw when hitting the cue ball at a point late in his stroke, well after his fastest speed, while his cue is decelerating. Speed should be the same for each draw, but one while accelerating and one while decelerating. If the cue ball only senses speed, as you surmise, then the draw would be the same. Do you have videos of such a direct test?

Nick

 

[dr_dave]

As to the bet, I actually did not say that Mr. Jewett would get more draw at a slower speed than at a faster one. I wanted to see his draw by striking the cue ball at a point in his stroke well before his fastest speed, while his cue is accelerating, and compare that to his draw when hitting the cue ball at a point late in his stroke, well after his fastest speed, while his cue is decelerating. Speed should be the same for each draw, but one while accelerating and one while decelerating. If the cue ball only senses speed, as you surmise, then the draw would be the same. Do you have videos of such a direct test?

Sorry I misinterpreted your bet. I'm glad you agree speed is important.

The only clips I have showing tip contact at different speeds and for an accelerating stroke are:

HSV A.77-A.81 and A.147-A.151​

The tip doesn't seem to stay in contact with the ball any longer with an accelerating stroke.

Regards,
Dave

 

[Jal]

... I wanted to see his draw by striking the cue ball at a point in his stroke well before his fastest speed, while his cue is accelerating, and compare that to his draw when hitting the cue ball at a point late in his stroke, well after his fastest speed, while his cue is decelerating. Speed should be the same for each draw, but one while accelerating and one while decelerating.

Your intuition is not wrong. In principle, the cueball will draw back farther (i.e., have more speed and spin) when you apply a force during impact. It's just that since the impact period is so short (mainly), the effect is essentially negligible. If you had a really, really soft tip such that contact lasted, say, a second, that would be a different story. So would being able to apply something like 100 lbs of force, as opposed to what we actually apply, about 15-20 lbs at the peak of a power stroke (much less throughout most of the rest of the stroke).

That aside, "accelerating through" can, in theory, give you noticeably more draw by generating more cue speed before impact commences. One impact begins, virtually nothing short of a superhuman effort can alter things. And the term "accelerate through" is a misnomer. You can continue to apply force, but the impact will inevitably slow the cue down unless you can muster something on the order of 400 lbs.

If the cue ball only senses speed, as you surmise, then the draw would be the same....

It does sense force, but the force doesn't last long (it takes force acting over time to get things moving). And the entire force that you might be applying with your grip hand is not what the cueball sees; it's only about 1/4'th of that. The force that really gets its attention is the one generated by the impact of the already moving cue, and this can approach 300-500 lbs. That's why cue speed is important, not the relatively meager force generated by our stroking arm.

Jim

 

[Clark_the_Shark]

.....compare that to his draw when hitting the cue ball at a point late in his stroke, well after his fastest speed, while his cue is decelerating.

See, I think this is a wrong assumption. I think the ONLY reason the cue SLOWS DOWN is because it hits the CB or when your arm runs out of room. The cue stops ACCELERATING... but it maintains the same speed until acted upon by the CB or your arm stopping at the end of your stroke. Moving the CB away from the cue say by 10-12 inches, the top of the curve will be very flat and not drop down because the cue has finished accelerating but it is still maintaining its speed.

The only way the cue would "accelerate slower" (decelerate as the coloquial term) is if you put the CB at the last 2 inches of your stroke where your arm is almost at its fully extended follow through point. At any time before that - speed stays the same. At least this is my take on the subject.

 

[dr_dave]

Excellent post!!! Ditto.

Your intuition is not wrong. In principle, the cueball will draw back farther (i.e., have more speed and spin) when you apply a force during impact. It's just that since the impact period is so short (mainly), the effect is essentially negligible. If you had a really, really soft tip such that contact lasted, say, a second, that would be a different story. So would being able to apply something like 100 lbs of force, as opposed to what we actually apply, about 15-20 lbs at the peak of a power stroke (much less throughout most of the rest of the stroke).

That aside, "accelerating through" can, in theory, give you noticeably more draw by generating more cue speed before impact commences. One impact begins, virtually nothing short of a superhuman effort can alter things. And the term "accelerate through" is a misnomer. You can continue to apply force, but the impact will inevitably slow the cue down unless you can muster something on the order of 400 lbs.

It does sense force, but the force doesn't last long (it takes force acting over time to get things moving). And the entire force that you might be applying with your grip hand is not what the cueball sees; it's only about 1/4'th of that. The force that really gets its attention is the one generated by the impact of the already moving cue, and this can approach 300-500 lbs. That's why cue speed is important, not the relatively meager force generated by our stroking arm.

Jim

 

[Jal]

... Moving the CB away from the cue say by 10-12 inches, the top of the curve will be very flat and not drop down because the cue has finished accelerating but it is still maintaining its speed.

The only way the cue would "accelerate slower" (decelerate as the coloquial term) is if you put the CB at the last 2 inches of your stroke where your arm is almost at its fully extended follow through point. At any time before that - speed stays the same. At least this is my take on the subject.

Dr. Dave has gathered some actual plots produced with accelerometers here (see TP A.9):

http://billiards.colostate.edu/technical_proofs/index.html

Apparently, the force applied during a stroke and thus the acceleration of the cue, rises to some peak value and then drops off. It will continue to drop off to below zero, wherein the cue decelerates, unless impact occurs first, in which case it undergoes a dramatic deceleration. I think it's commonly believed that the transition from positive to negative (acceleration to deceleration) happens when the forearm is approximately vertical (perpendicular to the cue or floor). How much control we have over this is an interesting question for some of us.

So it appears that at no time, except momentarily, is the cue moving at a constant speed (zero acceleration), though it comes closest to this around the time of zero acceleration. If you're mathematically inclined, Dr. Dave has applied his usual high-powered analysis to the stroke (see TP B.4 on the same page linked to above).

(As an aside, and very, very, very strictly speaking, according to modern physics, the cue is never moving at an absolutely constant speed, not even for an instant.)

Jim

 

[nickgeo]

All--Thanks for your views and your assistance in helping me understand these issues.

Some 50 years ago I had the privilege of a bit of instruction in varieties of balk line billiards by a couple of seniors who themselves had started playing in the 1890's. As you are probably aware, balk line requires tight control of all three balls on each shot. In pocket play, object ball speed often is not critical--it can be varied to accommodate the needs of cue ball position. Some balk line shots required unusual combinations of slow cue ball speed and lots of draw. For such situations I was taught to stroke with at most a one- or two-inch bridge (cue tip to cue ball distance at inception of forward stroke).

I posit that such a stroke involves a considerably longer contact (20 to 50% ???) with the cue ball than the conventional "hit the cue ball when the cue has achieved its maximum speed" stroke. I suggest that the cue and the cue ball might actually be accelerated together (in contact with one another) by the hand and arm, if only for a brief period, during such a stroke.

The extreme shot that I first described in this thread--cue tip resting on the cue ball, forward stroke from that position, resultant draw--would be a limiting case of this mode of stroke. No "hit," only "carry" or "push." (Please ignore what is legal). The contact described by others in this thread is virtually all hit, essentially no push. Are there any high-speed videos of such a stroke?

It is very difficult to perform the short-bridge draw stroke that I have described. There is almost a panic that sets in that makes one want to shoot it way too hard, rush it, yip it, etc. It's just not natural if you are used to a certain length bridge for all your strokes. No room to take a back swing. This represents a "parameter space" for the stroke that few players apparently inhabit. It is Mr. Jewett's stroke way, way to the left on the curve, practically at the start of his forward motion, and having contact with the cue ball well before he hits his peak speed.

The ratio of draw to speed from this stroke results in nearly v-shaped returns (lacking most or all of the initial lateral curving) from object balls hit moderately off-center. I sometimes am quite surprised by such paths--they are distinct form those of conventional stroking.

Perhaps my physical (not physics) analysis is incorrect. But you might want to experiment with the stroke that I describe, if you have not already. Sorry if you don't have some ivory billiard balls to work with--wish I did.

Thank you for your time!

Nick

 

[Clark_the_Shark]

Dr. Dave has gathered some actual plots produced with accelerometers here (see TP A.9):

I looked at this TP, but it only shows plot points for a cue that is going through practice strokes short of the CB, and after it has hit the CB. Not for a fully swung cue stick with full follow-through with no CB present. Barring the exception that the cue (very strictly) never moves at a constant speed, I still think I may be accurate in my above description unless some other TP is provided. I'm no expert here, not even an amature, but this is how I would see it for sure.

It may be common to believe that full speed happens when the forearm is vertical and drops off, but I still think that even if full speed IS at vertical forearm, that it won't drop off drastically whatsoever, (unless of course you strike a CB or your arm stops at the end of your follow through).

 

[Clark_the_Shark]

Dr. Dave... can you comment on my last two posts?

Thanks.

 

[dr_dave]

Dr. Dave... can you comment on my last two posts?

Thanks.

Sorry. I've been very busy the last few days. I'll take a look.

Dave

 

[dr_dave]

I looked at [TP A.9], but it only shows plot points for a cue that is going through practice strokes short of the CB, and after it has hit the CB. Not for a fully swung cue stick with full follow-through with no CB present. Barring the exception that the cue (very strictly) never moves at a constant speed, I still think I may be accurate in my above description unless some other TP is provided. I'm no expert here, not even an amature, but this is how I would see it for sure.

It may be common to believe that full speed happens when the forearm is vertical and drops off, but I still think that even if full speed IS at vertical forearm, that it won't drop off drastically whatsoever, (unless of course you strike a CB or your arm stops at the end of your follow through).

Check out the plots of speed vs. position data in HSV B.40. With the pendulum stroke, I think the cue would start to slow down (decelerate) gradually past the vertical position. When looking a the graph, imagine removing the ball-impact event. It looks like the curve might tend to be symmetrical with the ball impact event. I haven't measured this, but it makes sense. It would be unnatural for the arm to wait to try to slow all of the speed at the very end of the motion (but we can't be sure without a real test).

Regards,
Dave

 

[jay helfert]

A good follow through is also important in executing a long draw shot. You must go through the cue ball to get the action you need to execute the shot. I didn't read the entire thread but this should be in there somewhere.

P.S. You can hit pretty darn low on the cue ball, as long as you keep your cue level and hit on the center axis (draw a line down the center) of the cue ball. You don't have to stroke that hard either. It will come back!

 

[Clark_the_Shark]

I did look at the video. But I think that some of the points that were stated in above threads would be validated/disproved if we knew how the curve looks without a ball in the cue's way. I think it IS natural for the arm to "wait" till the end, because no force is acting to slow the arm until the elbow runs out of hinge room. So technically, it doesn't "wait" but is physically slowed down by the end of the stroke (elbow motion).

 

[dr_dave]

A good follow through is also important in executing a long draw shot. You must go through the cue ball to get the action you need to execute the shot. I didn't read the entire thread but this should be in there somewhere.

The follow through is a "symptom" of a good stroke. The "action" comes from cue speed and tip offset at CB impact. With good speed and a smooth stroke, a follow through will result. It is best to create the speed with a smoothly accelerating (non jerky) and longer stroke. The follow through doesn't "cause" the draw ... the pre-impact part of the stroke does. For more info, see:

http://billiards.colostate.edu/threads/stroke.html#follow-through​

Regards,
Dave

 

[dr_dave]

I did look at the video. But I think that some of the points that were stated in above threads would be validated/disproved if we knew how the curve looks without a ball in the cue's way. I think it IS natural for the arm to "wait" till the end, because no force is acting to slow the arm until the elbow runs out of hinge room. So technically, it doesn't "wait" but is physically slowed down by the end of the stroke (elbow motion).

I believe slowing would occur before the end of the stroke (with no CB impact), but we can't be sure unless we see real data. However, the real data we do have does show gradual slowing in the latter part of the stroke (after the temporary re-acceleration after CB impact). Look at the curves in the video again. The slowing appears to occur at a similar rate as the speed-up in the beginning of the stroke. The speed is not abruptly stopping at the end.

Regards,
Dave

 

[Clark_the_Shark]

Okay... I agree that it isn't abrubtly stopping at the end. All I'm saying is that the "constant" speed is over a longer period than people generalize than "at the vertical forearm point".

 

[jay helfert]

The follow through is a "symptom" of a good stroke. The "action" comes from cue speed and tip offset at CB impact. With good speed and a smooth stroke, a follow through will result. It is best to create the speed with a smoothly accelerating (non jerky) and longer stroke. The follow through doesn't "cause" the draw ... the pre-impact part of the stroke does. For more info, see:

http://billiards.colostate.edu/threads/stroke.html#follow-through​

Regards,
Dave

Whatever you said, I agree! Actually one thing you mentioned that is important is the speed of the stroke. A slow back swing and an accelerated forward stroke will get the job done. You must be accelerating when you go through the ball for best results, particularly on a long draw shot where there is distance between the cue ball and object ball.

Thanks Dave for this good information.

 

[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.

 

[dr_dave]

A slow back swing and an accelerated forward stroke will get the job done.

Agreed.

You must be accelerating when you go through the ball for best results, particularly on a long draw shot where there is distance between the cue ball and object ball.

I agree with the intent of your message, but see the messages from me and Jal in the previous couple of pages of this thread. Acceleration earlier in the stroke, well before ball contact, is what is important (to build cue speed). Acceleration during tip contact has no practical effect. With a pendulum stroke, there is typically no acceleration at tip contact (see HSV B.40); although, there IS plenty of speed at tip contact with a good power-draw pendulum stroke.

Thanks Dave for this good information.

You're welcome ... and thank you.

Regards,
Dave