Calculating Your Effective Pivot Point.

[Colin Colenso]

My original post (further below) had overlooked some things and was incorrect. So here is the improved formula and reasoning as seen in post #20 of this thread.

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.

This figure will be different for each cue on each table. It brings the slickness variable into the formula.

My prefered cue on my table has PPe* 13.7 inches. (This could change with humidity changes). It's PPi is 9.5 inches, so my K value for my cue on my table at the moment is (13.7 - 9.5)/15 = approx 0.28.
0.28 is the adjustment needed at distance 1 foot and speed factor 1.
The number 15 is derived from the PPe* being at 5 foot at speed factor 3. 5x3 = 15.
PPe* could use any shot as a basis with a different numerator, but 5 foot is a good number because it is about the length of the cue, it can be played with little elevation and it is long and slow enough to provide a decent difference with PPi, hence giving it a reasonable margin of error. PPe* can vary by around 2 inches depending on cloth slickness. It is a number that can be derived pretty accurately within half a dozen hits on a new table.

So for any shot my PPe = 9.5 + D x V x 0.28

So if I have a shot at speed factor 2 over 4 feet my PPe = 9.5 + 2.24 = approx 11.7 inches.

Below is a chart with PPe's for the full range of speeds and distances for my cue. You should be able to plug data into this formula and get PPe's that correspond to those in the chart.

Note: The key to making this formula simple was creating the methodology of the speed factor. In the chart below, the speeds are divided into 6 markings, rather than the 5 for speed factors 0-4, so I will need to redo the graphics and make some clearer statements and do some measurements regarding defining the speeds in a way that others can immitate.

General Speed Factor Rules are:
0 = Max speed, would bounce about 5 rails.
1 = Firm speed, would bounce 4 rails and back to starting position.
2 = Medium speed, would bounce 3 rails and back to starting position.
3 = Slow-Medium speed, would bounce 2 rails and back to starting position.
4 = Slow speed, would bounce 1 rail and back to starting position at center table.

----------------------------------------------------------------------
Original Post​

Following on from some other discussions regarding finding the required pivot point, for Back Hand English, which takes into account swerve, I did some further testing today and fiddled around with equations until I got something which I think is a pretty accurate guide for various cues and cloth conditions.

I would appreciate if some people would trial this formula on the table with their own cues and give some feedback, or make any suggestions as to improving the nature of this equation.

Note: This is not a formula based on the physics of swerve, squirt, friction and the likes, it is an equation that roughly imitates the data produced in experiments.

Here is the Effective Pivot Point Equation - 14 Oct 2008
PPe = PPi + [(D-V) x K]

Where K = PPe*/10

Note that (D-V) has a minimum value of zero.

PPe* = The measured effective pivot point for a shot over 5 feet length hit at speed 2. Where speed 2 is approximately the speed required to hit the CB 2 rails and back to its starting position. A relatively slow shot. On my own cue and table PPe* is just under 14 inches.

PPi = The Intrinsic Pivot Point. Estimated by finding the effective pivot point for a shot over 5 feet hitting at maximum velocity, such that swerve has insignificant influence on the shot. My cue's PPi is 9.5 inches. Low squirt cues are 12 to 14 inches.

D = Distance in feet between CB and OB.
V = Velocity Factor, such that 1 travels one table length including 1 bounce of a rail, 2 = 2 table lengths including 2 rail bounces. etc. 5 represents a near maximum power shot.

PPe tells you the required effective pivot point for any shot after you enter the distance and expected shot velocity.

K provides the equation with a factor that takes into account the slickness of the cloth. Each time you play on a different table, you'd need to establish a new K value. A sticky table will have higher K values. Also, low squirt cues will have higher K values. For my table and cue the K value is about 1.5, which means at the lowest speed I need to extend my pivot point 1.5 inches for every foot of extra distance and I reduce the pivot point by 1.5 inches for every number up the velocity scale I increase the shot.

I hope those who use a little BHE will find this equation useful.

Any questions or suggestions?

Please no suggestions telling me to stop thinking so much. Please respect that getting this equation to where it is has taken a lot of thinking, reading, arguing and testing over the years. So if you're not interested, just keep on walking and avoid the thread please.

Colin

 

[JimS]

I knew that. :groucho:

 

[Patrick Johnson]

Following on from some other discussions regarding finding the required pivot point, for Back Hand English, which takes into account swerve, I did some further testing today and fiddled around with equations until I got something which I think is a pretty accurate guide for various cues and cloth conditions.

I would appreciate if some people would trial this formula on the table with their own cues and give some feedback, or make any suggestions as to improving the nature of this equation.

Note: This is not a formula based on the physics of swerve, squirt, friction and the likes, it is an equation that roughly imitates the data produced in experiments.

Here is the Effective Pivot Point Equation - 14 Oct 2008
PPe = PPi + [(D-V) x K]

Where K = PPe*/10

Note that (D-V) has a minimum value of zero.

PPe* = The measured effective pivot point for a shot over 5 feet length hit at speed 2. Where speed 2 is approximately the speed required to hit the CB 2 rails and back to its starting position. A relatively slow shot. On my own cue and table PPe* is just under 14 inches.

PPi = The Intrinsic Pivot Point. Estimated by finding the effective pivot point for a shot over 5 feet hitting at maximum velocity, such that swerve has insignificant influence on the shot. My cue's PPi is 9.5 inches. Low squirt cues are 12 to 14 inches.

D = Distance in feet between CB and OB.
V = Velocity Factor, such that 1 travels one table length including 1 bounce of a rail, 2 = 2 table lengths including 2 rail bounces. etc. 5 represents a near maximum power shot.

PPe tells you the required effective pivot point for any shot after you enter the distance and expected shot velocity.

K provides the equation with a factor that takes into account the slickness of the cloth. Each time you play on a different table, you'd need to establish a new K value. A sticky table will have higher K values. Also, low squirt cues will have higher K values. For my table and cue the K value is about 1.5, which means at the lowest speed I need to extend my pivot point 1.5 inches for every foot of extra distance and I reduce the pivot point by 1.5 inches for every number up the velocity scale I increase the shot.

I hope those who use a little BHE will find this equation useful.

Any questions or suggestions?

Please no suggestions telling me to stop thinking so much. Please respect that getting this equation to where it is has taken a lot of thinking, reading, arguing and testing over the years. So if you're not interested, just keep on walking and avoid the thread please.

Colin

Interesting stuff, Colin, if only to you and me. Let me see if I understand the concept:

1. When speed range (1-5) equals or exceeds shot distance in feet (1-5), then swerve is negligible.

2. When speed range is less than shot distance in feet, then swerve is a factor and increases your pivot length by a fixed amount (the "K factor") per "extra" foot of shot distance (D-V, the "K-multiple").

3. You calculate the K factor for the cloth by shooting a shot with a K-multiple of 3 (distance = 5 feet; speed range = 2) and then dividing the total effective pivot length for that shot by 10.

I have a couple of questions about calculating the K factor:

- For your K-calibrating shot, why not just divide the added pivot length by 3? Why divide the whole effective pivot length by 10?

- Why not shoot 5 K-calibrating shots at K-multiples of 1-5 instead of just one at K-multiple 3?

- Is dividing the entire effective pivot length by 10 (rather than dividing the added pivot length by 3) a way of approximating the results of shooting 5 shots rather than one (averaging the results)?

pj
chgo

P.S. It seems to me that speed, distance and cloth condition could be combined into one factor by comparing actual shot speed with the speed necessary for a stop shot.

Consider that:

1. A stop shot is a familiar combination of shot speed, distance, cloth condition and CB hit (vertical axis height) that causes the CB to reach the OB just before it transits from sliding to rolling.

2. Swerve primarily happens as the CB transits from sliding to rolling.

Once you've figured out how to hit stop shots at various distances on the table, you could calculate how much to add to the pivot length for shots slower than stopshot speed by visualizing how much closer the OB would have to be for a stop shot at the slower speed. For instance, like this:

Shot Distance = D; Stop Distance = 4/5 x D: Add 10% to pivot length
Shot Distance = D; Stop Distance = 3/5 x D: Add 20% to pivot length
Shot Distance = D; Stop Distance = 2/5 x D: Add 30% to pivot length

etc.

P.P.S. This stopshot concept could also be used for those, like myself, who don't use BHE. For instance, I might aim like I would without any swerve, but adjust so that I'm aiming at the closer "ghost object ball" that's at "stopshot distance". I'll have to give this a try...

 

[jrt30004]

i was told there would be no math..........

 

[Colin Colenso]

1. When speed range (1-5) equals or exceeds shot distance in feet (1-5), then swerve is negligible.

pj
chgo

Patrick,
Straight away you found a flaw that I had overlooked by only checking the formula on examples where D was greater than V. A rushed job, but I think an improvement in structure than my previous attempt.

Your other suggestions seem well worth considering too. Let me get back to the math and the data to try to refine the formula in a way that doesn't make it too complex yet comes up with numbers close to my experimental data.

As I've said before, when I use BHE I have certain base points (from experimentation) I refer to, from which I make adjustments, but making a wholistic formula that is accurate has advantages. I figured it's hard for me to see where I am going wrong sometimes, so getting some good math brains on the task will help me to refine the formula.

Thanks,
Colin

 

[Patrick Johnson]

Patrick,
Straight away you found a flaw that I had overlooked by only checking the formula on examples where D was greater than V.

Did I? I thought you had covered it by saying D-V can't go below zero.

Your other suggestions seem well worth considering too. Let me get back to the math and the data to try to refine the formula in a way that doesn't make it too complex yet comes up with numbers close to my experimental data.

I'm intrigued by the idea of using a stop shot as a "unified adjustment factor". I'll try to refine that idea.

pj
chgo

 

[Colin Colenso]

Your other questions.

Patrick,
I obviously need to adjust some parts of the equation thanks to points you've raised. However, I think i can answer a few of your other questions. See below;

3. You calculate the K factor for the cloth by shooting a shot with a K-multiple of 3 (distance = 5 feet; speed range = 2) and then dividing the total effective pivot length for that shot by 10.

I have a couple of questions about calculating the K factor:

- For your K-calibrating shot, why not just divide the added pivot length by 3? Why divide the whole effective pivot length by 10?

- Why not shoot 5 K-calibrating shots at K-multiples of 1-5 instead of just one at K-multiple 3?

- Is dividing the entire effective pivot length by 10 (rather than dividing the added pivot length by 3) a way of approximating the results of shooting 5 shots rather than one (averaging the results)?

I chose the shot using a speed of 2 at a distance of 5 because it just so happened to form almost a perfect 10 multiple of the difference in PPe per unit of speed and that this measurement reflects both the cue squirt characteristic and the cloth slickness characteristic. I could have used any speed/distance PPe, which would provide similar data, but the speed 2, distance 5 feet measure seems appropriate and provides an easily divisible number. It was just something I noticed from the data.

Also, I should mention that the data comes out to about 1.1 inches PPe adjustment (from memory) per foot, so is not perfectly equivalent to shifts in velocity factor which are about 1.5 per unit of velocity. So (D-V) has a variation that would need adjustment at extremes. I hope to find a simplistic way to work this into the formula or as an adjustment at extremes.

P.S. It seems to me that speed, distance and cloth condition could be combined into one factor by comparing actual shot speed with the speed necessary for a stop shot.

Consider that:

1. A stop shot is a familiar combination of shot speed, distance, cloth condition and CB hit (vertical axis height) that causes the CB to reach the OB just before it transits from sliding to rolling.

2. Swerve primarily happens as the CB transits from sliding to rolling.

Once you've figured out how to hit stop shots at various distances on the table, you could calculate how much to add to the pivot length for shots slower than stopshot speed by visualizing how much closer the OB would have to be for a stop shot at the slower speed. For instance, like this:

Shot Distance = D; Stop Distance = 4/5 x D: Add 10% to pivot length
Shot Distance = D; Stop Distance = 3/5 x D: Add 20% to pivot length
Shot Distance = D; Stop Distance = 2/5 x D: Add 30% to pivot length

etc.

That's a very interesting approach and I will think more about how or if i can use that approach in developing the equation and/or establishing useful constants.

Thanks again,
Colin

 

[Colin Colenso]

Did I? I thought you had covered it by saying D-V can't go below zero.



I'm intrigued by the idea of using a stop shot as a "unified adjustment factor". I'll try to refine that idea.

pj
chgo

What I meant is that it makes no sense for D-V to be a negative number. I just couldn't think of a way to represent that in an equation. Where swerve doesn't come into play, such as shots from 5 feet and less, shot at maximum speed, then the intrinsic pivot point is the minimum bridge length.

I'm also interested in your stop shot idea and will put more thought into it. Any ideas you present are welcomed.

Colin

 

[Colin Colenso]

1. When speed range (1-5) equals or exceeds shot distance in feet (1-5), then swerve is negligible.

To clarify;
If speed is 3 and distance is 3 feet, then the PPe is longer (by about 2 inches) than with speed 5 and distance 5 feet where the PPe is basically the same as the PPi. This is something I overlooked in the above equation and have to rethink.

Colin

 

[Patrick Johnson]

To clarify;
If speed is 3 and distance is 3 feet, then the PPe is longer (by about 2 inches) than with speed 5 and distance 5 feet where the PPe is basically the same as the PPi. This is something I overlooked in the above equation and have to rethink.

Colin

I think this is the kind of thing the stop shot concept might help with. I don't know yet how to use it, but starting with stop shot speed as the baseline for each shot would automatically calibrate for each specific shot distance. The challenge is figuring out how to translate slower-than-stop shots into pivot length add-ons.

pj
chgo

 

[SpiderWebComm]

i was told there would be no math..........

Ha... that reminds me...

"I was told...there'd be no math."

 

[Colin Colenso]

I think this is the kind of thing the stop shot concept might help with. I don't know yet how to use it, but starting with stop shot speed as the baseline for each shot would automatically calibrate for each specific shot distance. The challenge is figuring out how to translate slower-than-stop shots into pivot length add-ons.

pj
chgo

Patrick,
My first concern (idea) with using a stop shot is that it brings draw, hence elevation into shots. While my testing indicates normal elevations can be dealt with, without too much problem, when using it as the set constant method, I'm not so sure it is the best way, but I have to try some of the tests and see what kind of K vakue they could produce.

FWIW: Some experiments show that using draw with english show that when a CB is hit as the same speed of CUE, (not cue ball) that the pivot point is similar to the same cue speed shot played middle ball. However, that draw english shot may travel only around half the distance as other shots hit with the same initial cue speed. So it kind of cancels out.

So when I use draw english over 5 feet I can use a PPe which equates to the PPe of playing a standard shot of one speed level higher.

That's just something I think I'll have to keep in mind when testing and thinking about your stop shot methodology to develop benchmarks and constants.

nb. While I'm happy with my test data, as being fairly accurate, the difficult part is developing a simplistic equation with appropriate benchmarks and constants that accords with it. When I get time I'll post a/some graphs that summarize my data.

Colin

 

[Mike Templeton]

These guys must be watching the Big Bang Theory on Monday nights on CBS.

 

[devindra]

Too much thinking and maths. When you guys simplify it in a couple of sentences then I will read.

 

[Patrick Johnson]

Too much thinking and maths. When you guys simplify it in a couple of sentences then I will read.

It's not really for you. It's an ongoing conversation from another thread (or two). Just ignore it.

pj
chgo

 

[devindra]

It's not really for you. It's an ongoing conversation from another thread (or two). Just ignore it.

pj
chgo

Ok. I just want to know the basics of adjusting.

 

[Jal]

...Here is the Effective Pivot Point Equation - 14 Oct 2008
PPe = PPi + [(D-V) x K]

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

 

[Colin Colenso]

The PP Data Charts

Below are the charts I've constructed showing the PPe for various speeds and 3 different cues.

The chart on the right demonstates the variation that would occur due to cloth slickness. The low lines are for a super slick cloth, the upper lines are for a very grippy / sticky table. The middle line is for my own table which is probably a little slicker than intermediate due to the CB and cloth having been siliconed a month ago.

Anyway, that variation of slickness is the reason I have the K in the formula.

The tricky part is getting an equation between D and V that creates numbers pretty close to that line without using something like y = (1.1D - 1.4V) x 0.357K (just made up numbers) which would be too hard for most to use as a rule of thumb.

Maybe some mathematicians can look at this data and find a way to represent it in a better way?

Note: PPi (Intrinsic Pivot Point) is the value to the left. The left axis are in inches.

This chart is for 5 feet between CB and OB.
As distance decreases the lines flatten.
As the distance increases the lines get steeper.​

 

[Colin Colenso]

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

Jim,
I expect there will need to be a few 'if' type adjustments. I'm not trying to make a comprehensively accurate formula, just a pretty good rule of thumb that works for most common shots.

I've played around testing the differences with different offsets and using top and bottom but haven't found the variations to be highly significant.

Can you explain more about the sideways migration per foot travelled when hitting above center? Are you saying it causes the swerve to start earlier than with draw or that it creates more swerve than draw?

Colin

 

[Colin Colenso]

New Improved Formula

I got a bit confused with my first formula because I was only comparing it to my data at 5 feet CB-OB separation.

If been playing around with various ways to approach this and 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.

This figure will be different for each cue on each table. It brings the slickness variable into the formula.

My prefered cue on my table has PPe* 13.7 inches. (This could change with humidity changes). It's PPi is 9.5 inches, so my K value for my cue on my table at the moment is (13.7 - 9.5)/15 = approx 0.28.
0.28 is the adjustment needed at distance 1 foot and speed factor 1.
The number 15 is derived from the PPe* being at 5 foot at speed factor 3. 5x3 = 15.
PPe* could use any shot as a basis with a different numerator, but 5 foot is a good number because it is about the length of the cue, it can be played with little elevation and it is long and slow enough to provide a decent difference with PPi, hence giving it a reasonable margin of error. PPe* can vary by around 2 inches depending on cloth slickness. It is a number that can be derived pretty accurately within half a dozen hits on a new table.

So for any shot my PPe = 9.5 + D x V x 0.28

So if I have a shot at speed factor 2 over 4 feet my PPe = 9.5 + 2.24 = approx 11.7 inches.

Below is a chart with PPe's for the full range of speeds and distances for my cue. You should be able to plug data into this formula and get PPe's that correspond to those in the chart.

Note: The key to making this formula simple was creating the methodology of the speed factor. In the chart below, the speeds are divided into 6 markings, rather than the 5 for speed factors 0-4, so I will need to redo the graphics and make some clearer statements and do some measurements regarding defining the speeds in a way that others can immitate.

General Speed Factor Rules are:
0 = Max speed, would bounce about 5 rails.
1 = Firm speed, would bounce 4 rails and back to starting position.
2 = Medium speed, would bounce 3 rails and back to starting position.
3 = Slow-Medium speed, would bounce 2 rails and back to starting position.
4 = Slow speed, would bounce 1 rail and back to starting position at center table.

Colin