Simple Squirt Test

[Patrick Johnson]

I also think there's a great danger or temptation to succumb to paralysis by analysis. Too much techie stuff can produce that.

Nonsense. Give me one example of a player who was "paralyzed by too much techie stuff". How do you define "paralyzed" and "techie stuff" anyway?

I'm not waiting on the techie stuff to actually produce a system.

A system that accounts for all the factors you listed? With our without the "techie stuff", you're in for a long wait.

pj
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[Flex]

Nonsense. Give me one example of a player who was "paralyzed by too much techie stuff". How do you define "paralyzed" and "techie stuff" anyway?



"Techie stuff" is all that stuff that is rather useful to know but not get lost in. When I use the phrase "techie stuff" I'm referring to the kind of explanations that one needs to give to someone who has some idea how to shoot and play and so on but who wants to know the "why" of how things happen on a pool table. Explaining the "why" can get very, very complicated, and raise oodles of other questions and discussions. Maybe that's why I'm more interested in outcomes and not only the explanations of how things work.

I know too many guys who are paralyzed by the techie stuff. I'm not going to mention his name, but a very strong player in northern Virginia told me once "There are times when I look at the ball and my mind is muddled and I can't execute. I don't know what to do about it." He defined execute to mean the mental effort to shoot the ball properly, that is in the way to achieve his goal, and get shape, or figure out what he wanted to do. That is what I mean by "paralysis by analysis." FWIW, this young gun plays very close to Mike Davis's speed; I've seen him take Davis down on more than one occasion.



A system that accounts for all the factors you listed? With our without the "techie stuff", you're in for a long wait.

As for such a system, I think I have a good part of it pretty much figured out in my head. Putting it into practice with any sort of consistency and with the desired results is quite a different thing. I'm certainly nowhere near that yet.

Pat, I really do appreciate this back and forth. Thanks!

Flex

 

[Patrick Johnson]

Jim:
A better way is to aim the center of the shaft at the (1/2)R offset (instead of making this the actual contact point as per your first diagram), with the object ball still displaced (1/2)R from a line going through the center of the cueball in the aim direction (as you had it).

You may be right but I think this would be too complicated for a "simple" technique. I think the distance correction you suggest takes care of the problem by itself - if you adjust the distance as I describe below.

...upon a successful pot, take the pivot point distance as the distance between the ball's edges (as you had it, more or less), but add R to this.

I think you're right that something has to be added to the measurement, but by my estimate it should be 1 radius + 1 diameter (to = the distance between the tip and the edge of the OB). With that I think the method is correct to within a forgivable margin of error for all but very small pivot lengths (a few inches). Do you agree?

pj
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[Patrick Johnson]

FYI, I've corrected and simplified the original post based on a couple of suggestions made by JAL.

Thanks, Jim.

pj
chgo

 

[Jal]

I think you're right that something has to be added to the measurement, but by my estimate it should be 1 radius + 1 diameter (to = the distance between the tip and the edge of the OB). With that I think the method is correct to within a forgivable margin of error for all but very small pivot lengths (a few inches). Do you agree?

Pat, I'm afraid that won't quite do it, but the fix is very simple. If the true pivot was 12", say, the method shown in the current diagram would yield a distance between the edges of the balls of 5.5" with a nickel radius tip (I'm using 13/32" for a nickel's radius, which isn't exact but easy to remember). The first version of the diagram would yield 7.4". If the true pivot point was 18", the first and current diagams would yield 11.8" and 9.9", respectively. (I mentioned above that the current version overestimates the pivot point distance, but I was, in effect, using a differnt tip offset than the one shown.)

All that needs to be done is the following. Rotate the striped "cueball" slightly so that the edge of the stripe points at the edge of the OB, as per your first diagram. Second, align the center of the shaft, as opposed to the contact point, with the edge of the stripe. (Aligning at the actual contact point generates most of the discrepancy.) Finally, the pivot point distance is the distance between edges (as shown in the diagram) plus a ball's radius.

Excluding normal tester error, this yields the exact pivot point. If you want justification, I will supply it. While I'm pretty certain that this is right, it never hurts to have someone else look at it.

Hmmm, I just noticed a recent post that indicates you've made some changes. I haven't looked at them yet (it's getting late), will do so tomorrow.

Jim

P.S. Here is the reasoning. P is the pivot point distance from the tip. The two similar right triangles yield the proportions shown.

You want the offset of the center of the shaft to be (1/2)R. That's why the edge of the stripe needs to be aligned with the edge of the object ball.

 

[Patrick Johnson]

Jim, I think we're both off by 1 radius (the correct answer is midway between our calculations). I don't have the ability to do a drawing here at work, so I'll try to describe my reasoning verbally:

First, to define terms:

Aim Line = a line extended from the tip/CB contact point to the edge of the object ball. [With the CB's stripe oriented along the Aim Line as you suggest, Tip Offset also = the apparent distance from the CB's "surface center" to the edge of the stripe, viewed from the perspective of a shooter facing along the Aim Line, so the tip/CB contact point should be on the edge of the CB's stripe.]

Tip Offset = the distance from the CB's center-of-mass ("peach pit center") to the Aim Line measured along a line perpendicular to the Aim Line.

CB Path = the line-of-centers between CB and OB when the Aim Line is correctly adjusted for squirt (the CB's intended path).

Pivot Length = the distance the cue ball travels along the CB Path before diverging from the Aim Line by the amount of the Tip Offset.

Now my reasoning:

With the CB's stripe oriented so its edge points at the OB's edge, we know that the CB starts with its center-of-mass 1/2 radius from the Aim Line, and that this = the Tip Offset.

We know that the Aim Line is 1 radius away from the OB's center-of-mass because that's where we point it for this test. This is an increase of 1/2 radius (= Tip Offset) over the CB center-of-mass initial distance from the Aim Line, and the amount of divergence from the Aim Line needed to correctly measure the Pivot Length.

Therefore, if the CB's center-of-mass travels the necessary distance to reach the position of the OB's center-of-mass, that distance = the Pivot Length. [The CB probably will not travel that actual distance during the test, but that doesn't change the reasoning.]

To reach the position of the OB's center-of-mass, the CB's center-of-mass would have to travel 1 radius + the distance between the CB and OB + 1 more radius. Therefore the Pivot Length = the distance between the CB and OB + 1 ball diameter (2.25").

I've actually suspected this outcome intuitively all along, but couldn't pin down the reasoning before.

Please let me know if you understand and agree with this, or if you don't please tell me why (hopefully without resorting to formulas, which give me a headache).

Thanks,

pj
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[Jal]

Patrick,

Thanks for defining the terms. That does show where our differences come about. The logic that leads to the addition of one ball diameter to the edge-edge distance, as opposed to one radius or three radii is impeccable, if I may judge, given the definitions you presented. But I think we have to look at those definitions.

Aim Line = a line extended from the tip/CB contact point to the edge of the object ball. [With the CB's stripe oriented along the Aim Line as you suggest, Tip Offset also = the apparent distance from the CB's "surface center" to the edge of the stripe, viewed from the perspective of a shooter facing along the Aim Line, so the tip/CB contact point should be on the edge of the CB's stripe.]

I'm not sure what "Tip Offset also = ...." means here, but I don't think it's important.

Tip Offset = the distance from the CB's center-of-mass ("peach pit center") to the Aim Line measured along a line perpendicular to the Aim Line.

Agreed. We might distinguish between the apparent tip offset, b, which is the offset of the center of the shaft, and the offset of the actual contact point, b'. Note: in your current diagram, the offset b' is a little bit larger than (1/2)R since the stripe's edge is not pointing at the OB's edge.

CB Path = the line-of-centers between CB and OB when the Aim Line is correctly adjusted for squirt (the CB's intended path).

Agreed.

Pivot Length = the distance the cue ball travels along the CB Path before diverging from the Aim Line by the amount of the Tip Offset.

This is the crux of the issue. I've used this definition at times, but it is incompatible with the standard definition.

Let me repeat the aim-and-pivot defintion, used by Bob Jewett, Ron Shepard, and Dr. Dave Alciatore, amongst others. This is the most natural one as it goes directly to how you use it. To wit: line up for center ball and then pivot about the PP. After shooting in the new direction, the cueball will travel in the same direction as when lined up for centerball. I'm pretty certain you completely agree with this, but I just wanted to put it out there.

Given that, in order for the cueball to diverge from the aim line direction by an amount equal to the tip offset, it must travel a distance along the line of centers which depends on which offset we're talking about, b or b'. In the case of b (offset of center of shaft), this will be the pivot length P plus one ball radius. In the case of b' (offset of contact point), this will be the same distance (P + R) multiplied by a factor which depends on the tip's radius of curvature. (If you can abide it, the factor is R/(R +r), where r is the tip's radius. Using 13/32" for an approx. nickel radius, and R =1.125", the factor is .7347.)

So, you get significanlty different results depending on which offset you use.

Using the center of the shaft at a (1/2)R offset, and pointing it toward the edge of object ball, the cueball travels (P + R) - 2R before colliding withe OB. The -2R comes from the necessary separation at collision, as per your argument. Since P + R - 2R = P - R, we must add R, and only R, to the edge to edge travel distance to get P.

Using the actual contact point offset at (1/2)R, the cueball travels .7347(P + R) - 2R before colliding. There's no way to extract P from this by adding any integral multiple of R to it. You'd have to add (2 - .7347)R, then multiply by 1/.7347, assuming of course that the tip's radius is 13/32".

How does any of this sound? (Could be I've gone completely nuts somewhere along the way.)

Jim

 

[Patrick Johnson]

Me:
Pivot Length = the distance the cue ball travels along the CB Path before diverging from the Aim Line by the amount of the Tip Offset.

Jim:
This is the crux of the issue. I've used this definition at times, but it is incompatible with the standard definition.

Let me repeat the aim-and-pivot defintion, used by Bob Jewett, Ron Shepard, and Dr. Dave Alciatore, amongst others. This is the most natural one as it goes directly to how you use it. To wit: line up for center ball and then pivot about the PP.

No need to appeal to authority, Jim , I agree this is the common definition of how to use a Pivot Length. But using the shaft's centerline to determine Tip Offset makes measuring the Pivot Length complicated and non-universal because it introduces tip curvature as a variable. This leaves only the aim-and-pivot method to measure "Common" Pivot Length, which I think is prone to operator error (if not outright unworkable for most players), and produces a Pivot Point that's only strictly accurate for one Tip Offset (the one used when measuring the Pivot Point).

I think it's valuable to have a simple, universal and accurate way to measure the "Contact Point" Pivot Length, even if it means slightly changing the way it's used - by pivoting the tip's center to the desired offset and then shifting the stick parallel a small amount to actually hit that point with the tip.

So I'll leave my method as-is (with the distance corrected - thanks for making me think that through) for those who want an easy way to measure a "Contact Point" Pivot Length instead of an error-prone way to measure a "Common" Pivot Length.

Unless, of course, I've gone completely nuts along the way.

pj
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