Effects of Tip Hardness

Andrew Manning said:
A question for the Bob Jewett and Dr. Dave crowd:

Has there been a scientific study of the effects of tip hardness on CB impulse, duration of contact, and location of miscue limit?
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You can find info and experimental results related to these topics here:


Regards,
Dave
 
Andrew Manning said:
Only if the force between the two is equal.
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What I meant to imply is that with equal shaft speeds prior to impact (that is momentum is equivalent).

This all sounds like conjecture, what's your source? What you're saying (that the silicon-dioxide in the chalk will actually break and thus lose grip if the tip is overly hard) sounds conceivable, but not likely, to me.
http://en.wikipedia.org/wiki/William_A._Spinks
See paragraph 2.
See also:
http://en.wikipedia.org/wiki/Corundum

The corumdum is often used as a grinding agent for gringing optical glass, especiall in the finer stages just before polishing. Since it is easily able to 'cut' glass, it will have little trouble cutting into leather or aramith. It rates as 9 on the mohs scale of hardness.

The only thing left undisclosed (from those links) is whether a sufficiently hard tip and a pool players stroke are sufficient to cause the crystals to shatter. I don't know where to find that info on these crystals.
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dr_dave said:
You can find info and experimental results related to these topics here:


Regards,
Dave
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Thanks Dave. I was not so concerned with endmass/squirt, since the concepts involved have been tested ad nauseum, with well-published results.

But you have answered at least one of my questions: from your first link a soft tip will remain in contact with the CB significantly longer than a hard tip. The measurements you cited indicated the difference may in fact be very large, with an extremely soft tip remaining in contact 4 times as long as a phenolic tip.

What about the transfer of momentum? For a given cue moving at a given speed with a center-ball hit, I'd really like to know how much the CB speed depends on tip hardness.

-Andrew
 
Andrew Manning said:
you have answered at least one of my questions: from your first link a soft tip will remain in contact with the CB significantly longer than a hard tip. The measurements you cited indicated the difference may in fact be very large, with an extremely soft tip remaining in contact 4 times as long as a phenolic tip. What about the transfer of momentum?
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I don't think this as important as it may sound. The contact time is still extremely small in both cases: close to a thousandth of a second (0.001 sec). Assuming the CB speed is the same in all comparisons: even though the peak force will be different (more with the shorter contact time), the amount of momentum (linear and angular) transferred to the CB will still be the same (because the sum of force over contact time is the same in both cases). The CB doesn't move much (translation or spin) during the extremely small contact time, so the only significant factor is the tip contact point at impact.

Andrew Manning said:
For a given cue moving at a given speed with a center-ball hit, I'd really like to know how much the CB speed depends on tip hardness.
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See:


However, for a given tip contact point, the spin-to-speed ratio (the "amount of English") will still be the same. Now, with slower-speed shots, the English will wear off a little faster (as the CB slides and rolls along the cloth), but that's probably not important in your comparisons.

I hope that helps,
Dave
 
dr_dave said:
Andrew Manning said:
you have answered at least one of my questions: from your first link a soft tip will remain in contact with the CB significantly longer than a hard tip. The measurements you cited indicated the difference may in fact be very large, with an extremely soft tip remaining in contact 4 times as long as a phenolic tip. What about the transfer of momentum?
Click to expand...
I don't think this as important as it may sound. The contact time is still extremely small in both cases: close to a thousandth of a second (0.001 sec). Assuming the CB speed is the same in all comparisons: even though the peak force will be different (more with the shorter contact time), the amount of momentum (linear and angular) transferred to the CB will still be the same (because the sum of force over contact time is the same in both cases). The CB doesn't move much (translation or spin) during the extremely small contact time, so the only significant factor is the tip contact point at impact.
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Also, you might be interested in the quote from Bob Jewett from here:

Bob_Jewett said:
One issue is which harness of tip will allow the farther-from-center hit. Some believe that a soft tip takes chalk better so it can hit the ball farther from center.

There is a counter theory, and that is because a softer tip will have a longer contact time than a hard tip. During contact, the tip rides around the side of the ball some, so the final eccentricity as the tip leaves the ball is larger than when the tip first hits the ball. A softer tip, with the longer contact time will be farther off center at the end than a harder tip with the same starting offset. If both tips can only hold to a certain point of offset, and you start your shot so the miscue point is barely reached at the end of contact, the average offset will be larger for the harder tip. This means that the harder tip can create more spin for a given ball speed.

Which dominates? Holding chalk better or starting farther off-center? I don't know of any experiment that has tested this.
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Regards,
Dave
 
Hi Dave and Bob,
Have you considered the effects of the frequency of the shaft during and after contact with the ball?
There is a frequency of shaft that will efectively hit the ball twice on alot of spin shots, making a seemed misscue, but still hitting the ball and sort of going where you intended the shot to go.The hit sounds like a long hit time is best way to describe it.
This may be part of why some cues play better with a hard tip.
I am trying to access a high speed camera for our new shaft analysis
Neil
 
Dr. Dave quotes Bob Jewett:
...the average offset will be larger for the harder tip. This means that the harder tip can create more spin for a given ball speed.
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I've heard it suggested before that the "average offset" of the tip while it's in contact with the CB determines the final spin-speed ratio. But I wonder why it wouldn't be the maximum tip offset (tip offset just before contact ceases) that determines final spin-speed ratio. Is there a specific reason?

pj
chgo
 
conetip said:
Hi Dave and Bob,
Have you considered the effects of the frequency of the shaft during and after contact with the ball?
There is a frequency of shaft that will efectively hit the ball twice on alot of spin shots, making a seemed misscue, but still hitting the ball and sort of going where you intended the shot to go.The hit sounds like a long hit time is best way to describe it.
This may be part of why some cues play better with a hard tip.
I am trying to access a high speed camera for our new shaft analysis
Neil
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I have not observed this effect with standard wood shafts (for a summary of some experimental results, see my October '05 article). But I can see how it might be an issue with much stiffer carbon-fiber shafts.

Also, I had forgotten about this, but I have filmed a wide range of maximum-English shots with various-hardness tips in the past. The clips are mentioned in the article. The clips are HSV A.98-A.106 here:


I didn't study these clips thoroughly, but I don't remember their being any obvious trends. My main purpose for the clips was to find the maximum English that could be applied, as described in the article.

Regards,
Dave
 
Patrick Johnson said:
I've heard it suggested before that the "average offset" of the tip while it's in contact with the CB determines the final spin-speed ratio. But I wonder why it wouldn't be the maximum tip offset (tip offset just before contact ceases) that determines final spin-speed ratio. Is there a specific reason?
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During contact, the force between the tip and ball increases and then decreases. The bulk of the impulse (sum of force over time) occurs near the middle of the contact interval.

Regards,
Dave
 
Patrick Johnson said:
I've heard it suggested before that the "average offset" of the tip while it's in contact with the CB determines the final spin-speed ratio. But I wonder why it wouldn't be the maximum tip offset (tip offset just before contact ceases) that determines final spin-speed ratio. Is there a specific reason?

pj
chgo
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Patrick, my two cents.

Take the simple case of a constant force applied through the center of mass of an object over a finite time T, (i.e., no spin involved). At time T the object will have moved a certain distance X. Its average distance (averaged over time), however, is exactly 1/3 of X (Xav = 1/3 X). It turns out that the range of of Xav is very small for a force which is symmetric about T/2 (which is the case for a constant force)...at least the ones I've looked at. Some examples:

Sawtooth: Xav=.292X
Sinusoidal: Xav=.297X
Thin spike at T/2: Xav=.25X

The symmetry about T/2 represents a perfectly elastic collision. The numbers don't change all that much with less than perfect elasticity, and fall into a similarly small range.

In the case of tip offset, things are more complicated, but the principle is the same. The average angle of rotation during impact, which is integral to figuring the average moment arm (offset) of the applied force, is a somewhat smallish fraction of the total rotation, as in the linear cases above. I was in the process of working this out a year or two ago, but was distracted (easily done!). From a few of the preliminary and incomplete results (sawtooth and sinusoidal - both elastic and inelastic) it appears that the numbers are very nearly the same within these cases, and as a guess, somewhere between 10% and 25% of the total rotation. This should be dependent on the initial offset itself. (I'm a bit fuzzy on this stuff now, so don't quote me :) ).

The moral is that the total amount of ball rotation is misleading since the force function, along with the moment arm (via ball rotation), and thus the torque (=force X moment arm), vary with time. You have to average the torque over the contact period, and then divide by the average force (also averaged over time) to isolate the average or effective offset. But from the linear cases, you get the intuitive sense that ball rotation doesn't add that much. And its effect is to just partially reclaim some (maybe all?) of the offset lost to squirt (i.e., the direction of the force is not straight ahead because of squirt, as I know you know).

Welcome back Dr. Dave!

Jim
 
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Neil,

When we filmed some of your carbon-fiber shafts in Colorado, did we observe any secondary tip contact on maximum-English shots? I don't remember, and I didn't keep the footage we shot.

Are you back in New Zealand now? I wish I could have visited the north island also; but as it turned out, we wish we had even more time on the south island. It's a beautiful place ... even with its lack of a large number of pool tables. :frown:

Regards,
Dave

dr_dave said:
conetip said:
Hi Dave and Bob,
Have you considered the effects of the frequency of the shaft during and after contact with the ball?
There is a frequency of shaft that will efectively hit the ball twice on alot of spin shots, making a seemed misscue, but still hitting the ball and sort of going where you intended the shot to go.The hit sounds like a long hit time is best way to describe it.
This may be part of why some cues play better with a hard tip.
I am trying to access a high speed camera for our new shaft analysis
Click to expand...
I have not observed this effect with standard wood shafts (for a summary of some experimental results, see my October '05 article). But I can see how it might be an issue with much stiffer carbon-fiber shafts.

Also, I had forgotten about this, but I have filmed a wide range of maximum-English shots with various-hardness tips in the past. The clips are mentioned in the article. The clips are HSV A.98-A.106 here:


I didn't study these clips thoroughly, but I don't remember their being any obvious trends. My main purpose for the clips was to find the maximum English that could be applied, as described in the article.

Regards,
Dave
Click to expand...
 
HI Dave, yes there are secondary tip contacts at the extreme edge of contact. With the wood cue,the result was a clear misscue,with the tip effectively skidding off the surface of the ball.
On the carbon shaft,for the same offset we saw the tip strike, move off and hit a second time with the edge of the shaft along aside of the ball.The carbon cue has a lower amplitude for the same frequency.
I will find the video and email it to you.
That is why I am trying to get another high speed camera. The new shaft is quite a lot better that what you used. I am still doing the development to get it all correct.
Frequency and responce seems to be a very important factor, not just light weight front end mass.
We have made very lightweight ridgid front ends and they are not as good as a heavier front end that has the right amount of flex.
Neil
 
i forgot, but when you tested, we changed tips from an elk, to a med moori to a super pro.In all cases,the cue ball came back and tapped the tripod leg.On the carbon cue with the set up, all 3 tips produced the same amount of spin on the cue ball,otherwise they would not have hit the tripod.
The wood cue you used , did not put as much spin on the cueball as the ball did not get to the tripod ,but hit bottom rail instead.
neil
 
conetip said:
i forgot, but when you tested, we changed tips from an elk, to a med moori to a super pro.In all cases,the cue ball came back and tapped the tripod leg.On the carbon cue with the set up, all 3 tips produced the same amount of spin on the cue ball,otherwise they would not have hit the tripod.
The wood cue you used , did not put as much spin on the cueball as the ball did not get to the tripod ,but hit bottom rail instead.
neil
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Sorry, but I don't remember any of the details. However, to compare English, you need to make sure the effective tip offset (accounting for squirt differences) is the same for each hit (i.e., each hit should be on the absolute verge of a miscue, for example). I don't think we did enough testing to guarantee this ... it would take a large number of hits.

Regards,
Dave
 
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