Calculating Your Effective Pivot Point.

Jal said:
Colin,

I know it's a work in progress and you want to avoid complicating it too much, but I think a couple of things need to be added in some way, shape or form.

Cue elevation and tip location above or below center are, me thinks, pretty critical factors. They both affect the direction of the cloth friction force, and in turn how quickly the ball swerves for a given cueball speed. Higher stick elevation and/or hitting above center result in more sideways migration per foot traveled, and not in a minor way.

If I missed a premise that fixes these variables, my apology.

Jim
Click to expand...
Jim,
I did quite a bit of testing tonight and found that when hitting the CB with follow and english it had a significant effect on most shots.

My early estimations are that a high follow contact adds about an additional 40% to the value that is added to the PPi. Hence if the VDK part comes to 3 inches, I need to add about 1.2 inches to get an accurate PPe.

I figure the 40% diminishes as the initial contact approaches center ball.

I usually execute longer shots hitting near center level english, so I had not noticed this effect on most testing shots. However, on rail shots closer to the OB where I hit the CB higher I have noticed a tendency to have too short a pivot distance.

I did some trialing with draw and didn't find a similar anomoly. Seems to me draw works pretty much the same as center ball english use, except that I need to be conscious of the tendency to think a shot struck with draw is hit softer than it actually is struck. On shots with draw, I've found we tend to hit the cue ball harder (with faster cue action) than we realize.

Your advice regarding high hitting seems spot on. Thanks for making me pay more attention to it. It seems to be a factor that comes up pretty regularly and definitely needs to be accomodated.

Colin
 
Colin Colenso said:
Jim,
I did quite a bit of testing tonight and found that when hitting the CB with follow and english it had a significant effect on most shots.

My early estimations are that a high follow contact adds about an additional 40% to the value that is added to the PPi. Hence if the VDK part comes to 3 inches, I need to add about 1.2 inches to get an accurate PPe.

I figure the 40% diminishes as the initial contact approaches center ball.

I usually execute longer shots hitting near center level english, so I had not noticed this effect on most testing shots. However, on rail shots closer to the OB where I hit the CB higher I have noticed a tendency to have too short a pivot distance.

I did some trialing with draw and didn't find a similar anomoly. Seems to me draw works pretty much the same as center ball english use, except that I need to be conscious of the tendency to think a shot struck with draw is hit softer than it actually is struck. On shots with draw, I've found we tend to hit the cue ball harder (with faster cue action) than we realize.

Your advice regarding high hitting seems spot on. Thanks for making me pay more attention to it. It seems to be a factor that comes up pretty regularly and definitely needs to be accomodated.

Colin
Click to expand...
Colin,

It'll take a while before I absorb the new posts you've put up, so let me just add a few comments on the high/low stuff. I did a nervous calculation to see what the numbers say.

The rate at which the cueball swerves depends on the direction of the friction force with the cloth, which in turn depends on the relative surface velocity between the ball and the cloth (velocity has direction as well as magnitude of course). The friction is in the anti-direction (180 degrees) to the surface velocity. One fortunate fact is that it always points in the same direction as the cueball curves.

To check the numbers, I compared two shots with the same amount of side offset of 1/4R. One is hit additionally at 1/4R above center, while the other is hit 1/4R below center. Let's suppose that the cue elevation is 2 degrees for the first shot. How much then do you have to elevate the cue on the second shot to get the friction in the same direction as the first shot? If I didn't screw up the math, it turns out to be about 8.6 degrees.

More likely, if a player is elevating at 2 degrees on the first shot, he'll be elevating at about 3 degrees on the second shot (joint about the same height above the cushion, say) . Comparing the direction of surface velocity for the two shots, it's about 3.33 degrees off of straight ahead for the first one, and 1.15 degrees for the second (with elevations of 2 and 3 degrees, respectively).

The sideways drift of the cueball per foot is proportional to these angles (technically, the tangent of these angles), so the cueball should swerve at about three times the rate for the follow shot compared to the draw shot.

A complicating factor is ball bounce, which will be at least a little different for both shots. Once the cueball settles down though...

This adds to your task, I guess, and I'm sorry about that. After your initial response, I was thinking that maybe the modest differences in cue elevations might bring the friction directions more in line...but apparently not.

Jim
 
Jal said:
Colin,

This adds to your task, I guess, and I'm sorry about that. After your initial response, I was thinking that maybe the modest differences in cue elevations might bring the friction directions more in line...but apparently not.

Jim
Click to expand...
Hey Jim,
It's not your fault the world doesn't move exactly according to my formulas....or is it? lol

Anyway, I'm glad you alerted me to this effect. Fact is, this early swerve with high english is something every player needs to be aware of.

I guess I have learned over the years to play the english lower and let natural roll gather as the CB travels to the OB. Hence I hadn't noticed it in most of my testing.

However, I had noticed that shorter cross table shots, where the CB is closer to the rail and I needed to hit the CB higher. e.g. Potting almost straight shots into the center pocket with IE. On these shots my bridge never seemed long enough and I tended to think it might be the elevation and the throw, but it just didn't feel right.

Anyway, last night, after realizing the high english effect I started playing thise shots adding about 2 inches to my bridge pivot and was making them better than I ever had.

A lot of shots can be played without using high english. I suspect most players using standard english methods tend to avoid slow to medium speed high english shots like the plague too. Perhaps more testing will lead to an accurate method for adjusting for high english.

Colin
 
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Colin Colenso said:
Hey Jim,
It's not your fault the world doesn't move exactly according to my formulas....or is it? lol

Anyway, I'm glad you alerted me to this effect. Fact is, this early swerve with high english is something every player needs to be aware of.

I guess I have learned over the years to play the english lower and let natural roll gather as the CB travels to the OB. Hence I hadn't noticed it in most of my testing.

However, I had noticed that shorter cross table shots, where the CB is closer to the rail and I needed to hit the CB higher. e.g. Potting almost straight shots into the center pocket with IE. On these shots my bridge never seemed long enough and I tended to think it might be the elevation and the throw, but it just didn't feel right.

Anyway, last night, after realizing the high english effect I started playing thise shots adding about 2 inches to my bridge pivot and was making them better than I ever had.

A lot of shots can be played without using high english. I suspect most players using standard english methods tend to avoid slow to medium speed high english shots like the plague too. Perhaps more testing will lead to an accurate method for adjusting for high english.

Colin
Click to expand...
Appreciate the feedback Colin. Those near rail shots can be tough - any english is really amplified as far as swerve is concerned. When you get to 2/5R above center, the friction force becomes oriented at 90 degrees to the forward direction. I guess I knew this in a theoretical way before you, yet why is it that you would sink ten of these shots to my one?

I read your other posts and want to extend my thanks for all the work and then letting us in on it. You (and Mr. Johnson) really know how to present the info with some very nice graphics. I hope you get more feedback from others.

It's purely a matter of preference, but if I were using your equation, I would probably substitute (5-V) for V, to help relate the speed to the number of cushion bounces. Memory ain't so good these days.

Jim
 
A diagram showing how the calculations are done on the shot. Perhaps of aid to those who think better when they see things visually.
 

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Jal said:
Appreciate the feedback Colin. Those near rail shots can be tough - any english is really amplified as far as swerve is concerned. When you get to 2/5R above center, the friction force becomes oriented at 90 degrees to the forward direction. I guess I knew this in a theoretical way before you, yet why is it that you would sink ten of these shots to my one?

I read your other posts and want to extend my thanks for all the work and then letting us in on it. You (and Mr. Johnson) really know how to present the info with some very nice graphics. I hope you get more feedback from others.

It's purely a matter of preference, but if I were using your equation, I would probably substitute (5-V) for V, to help relate the speed to the number of cushion bounces. Memory ain't so good these days.

Jim
Click to expand...
Jim,
(5-V) is a great idea!
I have corresponding throw charts for speeds 1 through 5 for every cut angle, slowest to fastest so making a Speed Factor, which runs 0 to 4 even confuses me.

The (5-V) might not look as simple or as neat but it will be less confusing when the entire system is put together.

btw: What can you tell me about this swerve amplification factor as we hit further or lower down the ball? Should there be a similar effect with extreme low draw?

Is it possible that the effect reduces as we move downward on the CB while elevation is increasing, hence some cancelling out?

I would like to know more about this so I can test it and see where adjustments should be incorporated.

Colin
 
Predicting a pool shot is like predicting the weather... there are way to many constantly changing variables to ever account for all of them... by the time you list them all ... half of them have changed..

you can have a reasonable expectation as to what will happen...but it is impossible to construct an infallible mathematical model that will function all the time everywhere without fail..

there are simply to many variables...
 
Jal said:
To check the numbers, I compared two shots with the same amount of side offset of 1/4R.

One is hit additionally at 1/4R above center, while the other is hit 1/4R below center.

Let's suppose that the cue elevation is 2 degrees for the first shot. How much then do you have to elevate the cue on the second shot to get the friction in the same direction as the first shot? If I didn't screw up the math, it turns out to be about 8.6 degrees.

More likely, if a player is elevating at 2 degrees on the first shot, he'll be elevating at about 3 degrees on the second shot (joint about the same height above the cushion, say) . Comparing the direction of surface velocity for the two shots, it's about 3.33 degrees off of straight ahead for the first one, and 1.15 degrees for the second (with elevations of 2 and 3 degrees, respectively).

The sideways drift of the cueball per foot is proportional to these angles (technically, the tangent of these angles), so the cueball should swerve at about three times the rate for the follow shot compared to the draw shot.

Jim
Click to expand...
Jim,
Does this suggest 3 times more curve in the initial stages or for the total curve path.

I thought swerve was coming about mainly as a result of the coriolis masse' diagrams. I'm still don't understand this other source of swerve. Are they like vectoral components such that we can add them to coriolis type swerve forces.

Sorry if my questions are a bit strange, just trying to find a way to grasp this concept a bit better.

Colin
 
softshot said:
Predicting a pool shot is like predicting the weather... there are way to many constantly changing variables to ever account for all of them... by the time you list them all ... half of them have changed..

you can have a reasonable expectation as to what will happen...but it is impossible to construct an infallible mathematical model that will function all the time everywhere without fail..

there are simply to many variables...
Click to expand...
*ALERT* *ALERT**ALERT*
Engineers everywhere, all your quests are in vain. Softshot hath spoken.:grin:
 
Colin Colenso said:
*ALERT* *ALERT**ALERT*
Engineers everywhere, all your quests are in vain. Softshot hath spoken.:grin:
Click to expand...


ouch......:thumbup:

list every single variable involved in a pool shot... professor....
 
softshot said:
ouch......:thumbup:

list every single variable involved in a pool shot... professor....
Click to expand...
Such a list is not relevant to this thread unless you can suggest some particular variables that I am overlooking in these equations.

What I can say, is that I am able to measure the nature of the most significant of these variables and apply that knowledge to a system that allows me to make many english shots with a higher degree of accuracy and consistancy than I was able to when just guessing how to deal with those variables.

Go try it out. You might be surprised.

Colin
 
Colin Colenso said:
Jim,
Does this suggest 3 times more curve in the initial stages or for the total curve path.

I thought swerve was coming about mainly as a result of the coriolis masse' diagrams. I'm still don't understand this other source of swerve. Are they like vectoral components such that we can add them to coriolis type swerve forces.

Sorry if my questions are a bit strange, just trying to find a way to grasp this concept a bit better.

Colin
Click to expand...

I believe Jim must be saying that, although Coriolis predicts the final rolling angle of a CB hit higher to be less than the final rolling angle of a CB hit lower, a CB hit higher curves sooner than a CB hit lower.

Sorry if I got you wrong and confused things, Jim.

pj
chgo
 
squerve effects

Patrick Johnson said:
I believe Jim must be saying that, although Coriolis predicts the final rolling angle of a CB hit higher to be less than the final rolling angle of a CB hit lower, a CB hit higher curves sooner than a CB hit lower.

Sorry if I got you wrong and confused things, Jim.
Click to expand...
FYI, my March '08 article covers this topic in detail with lots of illustrations.

Good work Colin, Jal, and Patrick! I've been too busy this week to keep up with the discussion and contribute, but I'll try to find some time soon.

Regards,
Dave
 
Jal said:
I want to extend my thanks for all the work and then letting us in on it. You (and Mr. Johnson) really know how to present the info with some very nice graphics. I hope you get more feedback from others.
Click to expand...
Ditto!

Dave
 
Colin Colenso said:
What can you tell me about this swerve amplification factor as we hit further or lower down the ball? Should there be a similar effect with extreme low draw?

Is it possible that the effect reduces as we move downward on the CB while elevation is increasing, hence some cancelling out?
Click to expand...
Colin,

You might check out my March '08 article. It describes and illustrates the various "squerve" effects fairly well.

Regards,
Dave
 
more ideas

Colin Colenso said:
think I have come up with the best and most accurate so far.

PPe = PPi + DVK​

D = Distance from CB to OB (or target) in feet.
V = Velocity Factor where 0 is maximum speed and 4 is slow, or one table length roll including bouncing off one rail.

K = (PPe* - PPi)/15​

PPe* is the pivot point required for a 5 foot shot at speed factor 3, which is medium slow, enough to bounce 2 rails back to the original position.
Click to expand...
Colin,

I applaud your efforts with all of this. And thank you for pointing out the problem with the procedure in my November '07 article for measuring "natural pivot length." With a short-distance shot the effects of throw are too large, even if Silicone spray is used to reduce throw. Your procedure practically eliminates throw from the measurement entirely, giving a much better measurement of the "natural pivot length" (without using messy Silicone spray). FYI, I've changed my "pivot length" FAQ page to clarify this and recommend your procedure instead:


I love your idea to compensate for throw separately and address "squerve" (the net effects of squirt and swerve) only with the BHE pivot. I think your idea to vary BHE pivot length to make squerve adjustments is a real contribution. Kudos to you!

My first reaction to the formulas is that not many people will accept it because they will perceive it as too complex. I don't see any easy ways around this, unless a small set of "calibration shots" can be created to define a set of benchmark pivot lengths (and account for the given table conditions). Then every shot would fall somewhere between the benchmarks, making it easy for people to estimate (through judgment instead of calculation) a pivot length between the benchmarks pivots (e.g., the speed and distance for this shot are about halfway between these two benchmarks, so I'll split the difference on the pivot length).

Also, some people might not like changing their bridge length so much, and some people might prefer much shorter bridge lengths. A possible solution here is to use a combination of BHE and FHE with a fixed bridge length. So instead of varying the bridge length, one would instead change the amount they pivot with each hand. For a short pivot, you pivot just with the back hand. For a long pivot, you pivot just with the front end. For a pivot in between, you pivot partly with the back hand and the rest with the front hand. The only variable would be the percentage you pivot with one hand (e.g., pivot 25% with the back hand and the rest with the front hand). More food for thought.

Regards,
Dave
 
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