draw shot spin vs. spin-to-speed ratio

[dr_dave]

As Mike Page and Colin Colenso pointed out in the draw shot physics thread, there are some cases where spin-to-speed ratio is more important than spin. I decided to take a closer look at this and share the results. All of the detailed analysis, graphs, and conclusions can be found here:

TP B.9 - Draw shot spin vs. spin ratio​

With a straight draw shot (with no cut angle), the amount of draw is determined solely by the amount of CB spin at contact with the OB. This is the topic of TP B.8. In TP B.9, I look at both spin and the spin-to-speed ratio. Examples where spin-to-speed ratio is more important than spin are when ...

1. ... you don't want to hit the OB too hard (e.g., to leave the OB by a pocket if you can't or don't want to pocket it, or to increase the effective size of the pocket), while still maximizing draw (e.g., to achieve position for the next shot or to play a safety).
   
2. ... you want to keep the draw angle as narrow as possible when there is a cut angle (e.g., to avoid a ball or a pocket, or to get straight up or down the table better).

Here are the results of the analysis:

1. Generally, to get more spin at contact with the OB, you must hit the CB harder and lower. However, as you approach the miscue limit, you get a smaller gain in spin. And for longer drag distance shots, the amount of spin actually decreases as you approach the miscue limit (see Graphs A and I). See TP B.8 for more info and results.
   
2. More tip offset results in a greater spin-to-speed ratio at OB contact (except for long drag shots, especially if conditions are "sticky" (see Graphs B and J). So to get a better spin-to-speed ratio, hit as low as you can on the CB without being at too high a risk of miscuing.

The graphs mentioned above can be found in TP B.9.

I don't think there are any huge surprises here, but hopefully some people while find the results interesting or useful.

Regards,
Dave

 

[btoneill]

Damn...

I'll I can say is that made my head hurt... And I actually understood a good portion of the math... Maybe I didn't forget everything I learned in Calc...

 

[dr_dave]

Damn...

I'll I can say is that made my head hurt... And I actually understood a good portion of the math... Maybe I didn't forget everything I learned in Calc...

I probably shouldn't include links to the math and physics stuff since only a few people in the world probably find it interesting. Hopefully, people who don't like the math and physics can just read the conclusions (and maybe look at a graph on two).

Regards,
Dave

 

[btoneill]

I'd leave it all in there, but maybe put a link in the PDF at the top to send someone straight to the conclusions if they don't like the math. Not sure what you used to typeset it (LaTeX?) and if it supports doing links like that when sent through Distiller...

Even though I only understood about 60% of the math completely, was still very insightful. I am curious where the friction/resistance/efficency numbers came from (not that I doubt them in the least, just curious if you got those number from previous experiments or if it's actually published somewhere).

Thanks,
Brian

 

[CreeDo]

Here's some for ya Dave

1. I've been using a rule of thumb that for low outside on rail cuts, you get better results if you focus on the draw if the cut is less than 45 degrees, and with sidespin if it's more than 45. Can you confirm?

2. At what cut angle does the draw effect (same situation) become so negligible as to be pointless?

3. If a player wants maximum "climb" in this situation, does adding a touch of draw help or hinder the sidespin's effect? In other words, assuming the ball is within an inch of the rail, will adding more draw get better results or will it dilute the sidespin and make the angle off the rail less nice?

 

[dr_dave]

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

I'd leave it all in there, but maybe put a link in the PDF at the top to send someone straight to the conclusions if they don't like the math. Not sure what you used to typeset it (LaTeX?) and if it supports doing links like that when sent through Distiller...

Thanks for the idea. I use MathCAD. I don't think it can do links within a document, but I will check.

Even though I only understood about 60% of the math completely, was still very insightful. I am curious where the friction/resistance/efficency numbers came from (not that I doubt them in the least, just curious if you got those number from previous experiments or if it's actually published somewhere).

I have a summary of physical parameter values here:

http://billiards.colostate.edu/threads/physics.html#properties​

I have found these in various publications (many are listed and linked here), and I have done many of my own tests to verify the numbers. The tip efficiency number comes from TP A.30.

Regards,
Dave

 

[dr_dave]

Here's some for ya Dave

1. I've been using a rule of thumb that for low outside on rail cuts, you get better results if you focus on the draw if the cut is less than 45 degrees, and with sidespin if it's more than 45. Can you confirm?

2. At what cut angle does the draw effect (same situation) become so negligible as to be pointless?

3. If a player wants maximum "climb" in this situation, does adding a touch of draw help or hinder the sidespin's effect? In other words, assuming the ball is within an inch of the rail, will adding more draw get better results or will it dilute the sidespin and make the angle off the rail less nice?

Those are great questions. I wish I had great answers. I'll add it to my "list."

Regards,
Dave

 

[btoneill]

What would be really interesting is to see the effects of a heavier and/or oversized coin-op cue ball on spin/draw/stun/etc. Mainly because the ball is typically 1/8" larger, the point of contact between the CB and OB will induce spin (I believe anyways) as the CB will contact the OB 1/16" above it's center.

Brian

 

[frankncali]

thanks Dave

Much of your stuff goes over my head but I think there are some out here that appreciate it. I do find some of it interesting and get a bit of knowledge from it.

One question I have always wondered is how bridge heights correlate to the cue balls reaction off the OB. or if it changes at all.

How much does raising one's cue for a draw shot affect the outcome? Is it ever better to do so at times.

I have heard things like "the lower you cue the faster the draw reaction"

 

[dr_dave]

One question I have always wondered is how bridge heights correlate to the cue balls reaction off the OB. or if it changes at all.

How much does raising one's cue for a draw shot affect the outcome? Is it ever better to do so at times.

I have heard things like "the lower you cue the faster the draw reaction

I'm working on this over the next few days. I'll post something when I'm done.

Regards,
Dave

 

[TheBook]

Having a engineering degree but probalbly not the great in theory but more in practice I always have liked the hands on approach and demonstration. I have aways felt that a picture is worth more than a 1000 words.

Henry Ford was a great inventor and engineer but also had the show me attitude. Having one of the worlds largest private railroads he got tired of replacing the wooden track ties. He came up with a idea of making them out of concrete thinking that they would last longer. All of his engineers told him that it won't work. He didn't believe them. He constructed about a mile of track using concrete ties. The train ran about 20 feet and derailed. He looked at it and said I guess it won't work.

I worked and retired from Ford. Whenever we were stuck or came up with something new someone would always ask "What would Henry do?'

Therfore I have one question. How does Efren feel about all of this pool theory? :rotflmao1:

 

[enzo]

i dont know if this will help anybody or add to the conversation, but the way ive always looked at it is this.....

when you have a strait in shot, and the cb is 1 foot from the ob.... to draw back eight feet, your best bet is to stroke it pretty soft and smooth and get back there.....

now, if you have a strait in shot and the cb is 6 feet from the ob, you will need to hit the cb harder to get back the desired 8 feet. the reason being you can't hit it so soft and smooth because the spin will dissipate on the way there. so you have to hit it harder. but there is a huge consequence to having to hit it harder. more of the backspin is lost upon impact with the ob as it is a relatively more forceful impact. so, you have to have more spin on this shot than you would on the one desribed above, even though you are drawing back the same distance.

so, with distance you're fighting both the cloth and the loss of spin on impact due to the hard hit.

 

[Patrick Johnson]

Dave surprises me yet again:
...for longer drag distance shots, the amount of spin actually decreases as you approach the miscue limit

A little barrage of questions, Dave:

Do you mean decreases for the same force applied?

Can more spin be retained by hitting the shot at the miscue limit but harder?

When going for maximum draw distance, hitting the cue ball hard, is it still advisable to hit above maximum offset (assuming you can hit both reliably)?

pj
chgo

 

[dr_dave]

...for longer drag distance shots, the amount of spin actually decreases as you approach the miscue limit

A little barrage of questions, Dave:

Do you mean decreases for the same force applied?

First of all, remember we are talking about the spin on the CB when it arrives at the OB (not off the tip). All comparisons assume everything else is constant. So in looking at different offsets, I am assuming the cue speed is the same for each shot. More speed always gives you more spin.

Can more spin be retained by hitting the shot at the miscue limit but harder?

Yes. More speed always gives you more spin (at a given tip offset).

When going for maximum draw distance, hitting the cue ball hard, is it still advisable to hit above maximum offset (assuming you can hit both reliably)?

As you get closer to the miscue limit, additional offset does not give more spin at OB contact. In fact, for longer shots (with more drag distance), more offset gives you less spin at OB contact (for a given cue speed). See Graph G on page 13 of TP B.8. It tells the whole story.

Regards,
Dave

 

[jsp]

Some great info again Dr. Dave. Thanks.

I do have another (may or may not be relevant to the thread) question regarding spin-to-speed ratio on draw shots. There was a thread a few months back that discussed the subject of elevation and its impact on spin-to-speed ratio. In that thread, I hypothesized that for the same tip offset the CB spin-to-speed ratio would be higher than with a completely level cue. Others have argued the opposite is true. The two competing factors are the greater cloth friction on the ball at impact (with an elevated cue) vs. the smaller translation speed. Not sure which one wins out. You have any thoughts on this?

 

[dr_dave]

Some great info again Dr. Dave. Thanks.

I do have another (may or may not be relevant to the thread) question regarding spin-to-speed ratio on draw shots. There was a thread a few months back that discussed the subject of elevation and its impact on spin-to-speed ratio. In that thread, I hypothesized that for the same tip offset the CB spin-to-speed ratio would be higher than with a completely level cue. Others have argued the opposite is true. The two competing factors are the greater cloth friction on the ball at impact (with an elevated cue) vs. the smaller translation speed. Not sure which one wins out. You have any thoughts on this?

I'm working on an analysis for this now. I don't want to comment until I am done. I'll post something when I have results.

Regards,
Dave

 

[Patrick Johnson]

Some great info again Dr. Dave. Thanks.

I do have another (may or may not be relevant to the thread) question regarding spin-to-speed ratio on draw shots. There was a thread a few months back that discussed the subject of elevation and its impact on spin-to-speed ratio. In that thread, I hypothesized that for the same tip offset the CB spin-to-speed ratio would be higher than with a completely level cue. Others have argued the opposite is true. The two competing factors are the greater cloth friction on the ball at impact (with an elevated cue) vs. the smaller translation speed. Not sure which one wins out. You have any thoughts on this?

Masse shows us that elevation can increase the spin/speed ratio, so I guess the question is how much elevation is necessary. I think more elevation = higher spin/speed ratio but any amount of elevation works to some degree.

I think the more important question is how does it affect your shotmaking? More elevation increases cue ball curving on offcenter hits, magnifying stroke errors. A very accurate stroke is probably a necessity for using elevated draw - but with a very accurate stroke elevated draw is probably unnecessary.

pj
chgo

 

[Jal]

Masse shows us that elevation can increase the spin/speed ratio, so I guess the question is how much elevation is necessary....

I'll be very interested in what Dr. Dave comes up with (might have to eat some crow), but according to my math, there is in fact a minimum elevation required to increase the spin/speed ratio beyond what you'd get with a "level" cue. It depends on the amount of tip offset, cloth coefficient of sliding friction (say 0.2), and cloth/bed coefficient of restitution (say 0.6). Using these numbers and an effective tip offset of (2/5)R, for example, the minimum elevation would be about 20.4 degrees.

If the math is correct, a smaller elevation doesn't help, but doesn't do any real harm either. You only see a drop in the ratio (compared to level) of about 2 percentage points or so. Elevating to 30 degrees increases it by 5%, while you have to jack up 40 degrees for a 17% gain.

I don't want to put words in his mouth, but I think Bob J. has observed that the miscue limit of (1/2)R is expanded with masse type shots. (I rarely practice them so I can't say from experience.) This would be because of an increased coefficient of static friction between the tip and the ball. The coefficient is greater (presumably) because of the increased pressure of the more violent collision.

A more difficult question is the related issue of ball hop, as far as absolute spin retention at the OB.

Jim

 

[claymont]

What's this little guy mean :=

 

[Patrick Johnson]

What's this little guy mean :=

That's the universal smilicon for "I am the walrus." Since you're the only one, I'm not surprised you haven't seen it.

pj <- regretably not the walrus
chgo