how to design a true parabolic/conical tapered cue- ?

Hits 'em Hard

AzB Silver Member
Silver Member
None of that matters. If you add a curve to a cue shaft or butt it will have to get smaller in ID than it was previously upstream. This is fine if the smaller section falls at the end of the butt but anywhere else and you have yourself a funky odd looking POS with a lump in it.

Nothing complex about that. It's 2D conception, not the frigging universe big bang. You may fancy yourself a mathematician but this is not calculus.

You are vastly misunderstanding how curves work, and are massively misunderstanding how important calculus is to the understanding of this subject. Your perspective as to where the curve is, is the problem. And it’s not a hump. It’s the peak of the curve, and it’s relation to the start and end of it. Think of a sine wave that transitions to an exponential curve. That’s an extreme level, but draw it out long enough and due to the offset of the taper. It creates a ‘hump’ when rolled. But it’s due to how the curve isn’t parallel to a centerline.

JoeyInCali

AzB Silver Member
Silver Member
Is this the secret sauce recipe for a Southwest?
Mostly, yes.
SW does have a great history.
Like it or not, that funky taper is loved by many.
Even if the cue rolls funny on the table .

HawaiianEye

AzB Silver Member
Silver Member
FWIW, I have a shaft by a custom cue maker that he defined as a “modified Predator parabolic pro taper”.

I can’t explain it, but it is different. I don’t think you can see anything different, but it feels different than my other cues that mostly have pro tapers

I use a tight closed bridge and can feel even the slightest rises and this shaft is definitely not like a normal shaft taper of any kind I have used.

JoeyInCali

AzB Silver Member
Silver Member
None of that matters. If you add a curve to a cue shaft or butt it will have to get smaller in ID than it was previously upstream. This is fine if the smaller section falls at the end of the butt but anywhere else and you have yourself a funky odd looking POS with a lump in it.

Nothing complex about that. It's 2D conception, not the frigging universe big bang. You may fancy yourself a mathematician but this is not calculus.
OD, you mean.
Yeah, the DPK numbers have funky numbers . Numbers do not consistently go down from joint to the tip.
SW's butt is some .830 at the joint, some 1.060 at the bottom of the forearm and only some 1.250" at the very bottom. And it has that noticeable hump in the middle .
Their saw tapering machine has got to have a curved template . Not linear.

HawaiianEye

AzB Silver Member
Silver Member
OD, you mean.
Yeah, the DPK numbers have funky numbers . Numbers do not consistently go down from joint to the tip.
SW's butt is some .830 at the joint, some 1.060 at the bottom of the forearm and only some 1.250" at the very bottom. And it has that noticeable hump in the middle .
Their saw tapering machine has got to have a curved template . Not linear.

Are the same dimensions used on every cue, no matter the weight or wood combination desired?

I know some woods are heavier than others.

How do they control the weight and balances if they keep the same dimensions?

Ssonerai

AzB Silver Member
Silver Member
about the joint- I've heard of cuemakers that value joint thickness as a cue aspect that really affects the hit of a cue. do you agree?

I do.

I think the idea might be that a thick/strong joint helps energy remain in the cue, but I'm not sure.

As Mr. Barrenbrugge notes there's a lot more at play in a cue than meets the eye.
My theory and practice agree with you. Seemingly so does that paper by all the physicists and engineers in the Argonne National labs billiards club (by implication; the focus of the paper is squirt). Actually, another question is, "what is a strong joint depending on the mating components?"

My cues are "lumpy" but they don't look it standing there.
The handle section is almost straight, then sweeps down in the forearm to an .870 joint (I've actually made some as small as .860 )
The joint area is straight-ish for a couple inches, then the shaft takes a curved taper down to the last 12", which gradually reduces about .005" to the tip. I like 12.75 for the ferule/tip.

Thought i was going to get more into making cues & get more of them out there for feedback after (semi) retiring, but there seems to be a range of other interests that consume all my time, as long as i can stay healthy. Can't even get near the planer (shaft machine) - it's covered with metal, tools, chips, and a pile of plywood in front.

smt

JoeyInCali

AzB Silver Member
Silver Member
Are the same dimensions used on every cue, no matter the weight or wood combination desired?

I know some woods are heavier than others.

How do they control the weight and balances if they keep the same dimensions?
Same.
You don't find too many SW less than 19 oz.

thoffen

AzB Silver Member
Silver Member
If anyone wants some scientific calculation, I found this as a starting point: https://www.mdpi.com/2076-3417/8/1/94/pdf

But actually trying to calculate how a particular cue taper might perform? Seems totally silly to me. Just use experimentation and bear in mind that there is a lot of variability inherent in the materials and process that you can't control for.

Parabolic is a bad word IMO. Any taper following the shape of a parabola makes no sense for a cue. Sigmoidal would be the best description of the kind of shape of the taper if you had to pick a single word, but I doubt a cue maker would choose a true sigmoidal curve for the taper. Likely a compound taper with continuously tapered sections (following a curve). This could be simulated with very small linear steps, and once you add hand-sanding you are completely changing whatever you might model, but you could probably end up with a result which is a reasonable approximation of some specifically calculated curve.

JoeyInCali

AzB Silver Member
Silver Member
If anyone wants some scientific calculation, I found this as a starting point: https://www.mdpi.com/2076-3417/8/1/94/pdf

But actually trying to calculate how a particular cue taper might perform? Seems totally silly to me. Just use experimentation and bear in mind that there is a lot of variability inherent in the materials and process that you can't control for.

Parabolic is a bad word IMO. Any taper following the shape of a parabola makes no sense for a cue. Sigmoidal would be the best description of the kind of shape of the taper if you had to pick a single word, but I doubt a cue maker would choose a true sigmoidal curve for the taper. Likely a compound taper with continuously tapered sections (following a curve). This could be simulated with very small linear steps, and once you add hand-sanding you are completely changing whatever you might model, but you could probably end up with a result which is a reasonable approximation of some specifically calculated curve.
I wonder how big a circle DPK and SW used as basis for the curve/arc.

Hits 'em Hard

AzB Silver Member
Silver Member
I wonder how big a circle DPK and SW used as basis for the curve/arc.

Why can’t it be a smaller sound wave that has been altered? That was always my impression of the notion of parabolic taper was it was meant to jive with a sound wave.

JoeyInCali

AzB Silver Member
Silver Member
Why can’t it be a smaller sound wave that has been altered? That was always my impression of the notion of parabolic taper was it was meant to jive with a sound wave.
I have no clue

DaveK

Still crazy after all these years
Silver Member
Parabolic is a bad word IMO. Any taper following the shape of a parabola makes no sense for a cue.
In my mind it depends on what portion of a parabola the taper is based on. Anything near the focus makes no sense as you say, but at larger values of X the parabola is pretty "straight" and could be used ... IMO as a hack-pool-player small-time-cue-collector non-cuemaker engineer.

Dave

thoffen

AzB Silver Member
Silver Member
In my mind it depends on what portion of a parabola the taper is based on. Anything near the focus makes no sense as you say, but at larger values of X the parabola is pretty "straight" and could be used ... IMO as a hack-pool-player small-time-cue-collector non-cuemaker engineer.

Dave

It really isn't. It kind of looks that way, but the function of a parabola is quadratic f(x) = a*x^2 + b*x + c. A hyperbola is going to asymptotically approach a linear function. That being said, yes you can have a parabola that is almost linear across the range you are looking at it, but that's sort of cheating. There wouldn't be any practical benefit to the non-linearity. The rate of growth of the taper across its length regardless of what section of the parabola you are choosing would be the first derivative, f'(x) = 1/2ax + b.

The math is probably taking us in the weeds, but the basic point is that no matter what section of the parabola you use, the cue would be getting fatter at a faster rate wherever you end the taper than at any place before. That just isn't the shape of a cue. It gets fatter to a point and then would slow down the taper. No parabola slows down its growth as you move along it. The natural taper of a cue is closer to an "S" which is mathematically a sigmoid function.

Edit: the above is sort of true, but I'm not sure why I didn't realize what would happen if the term "a" is negative. I still think that this wouldn't be a practical cue taper, but when I gave time I'll graph some to see how it looks. I still think the point where the taper starts in that case is destined to be ridiculous instead of where it ends, but it doesn't hurt to try it.

Last edited:

Hits 'em Hard

AzB Silver Member
Silver Member
Parabolic means shape derived from a parabola. Terms and definitions seems to be lost around here.

JC

Coos Cues
Gold Member
You are vastly misunderstanding how curves work, and are massively misunderstanding how important calculus is to the understanding of this subject. Your perspective as to where the curve is, is the problem. And it’s not a hump. It’s the peak of the curve, and it’s relation to the start and end of it. Think of a sine wave that transitions to an exponential curve. That’s an extreme level, but draw it out long enough and due to the offset of the taper. It creates a ‘hump’ when rolled. But it’s due to how the curve isn’t parallel to a centerline.
It's a stick with a taper. A piece of wood. Curves make lumps in wooden sticks. Calculus doesn't change this one iota.

I'm not a mathematician, just an astute observer of my world.

I fail to see your point other than trying to sound intellectual. You're doing ok at that but your lectures are not remotely relevant to the shape of a well designed pool cue.

What happened to your steel toed jack boot avatar? I think I liked that hits 'em hard better than the doctoral version.

CuesDirectly

AzB Silver Member
Silver Member
It's a stick with a taper. A piece of wood. Curves make lumps in wooden sticks. Calculus doesn't change this one iota.

I'm not a mathematician, just an astute observer of my world.

I fail to see your point other than trying to sound intellectual. You're doing ok at that but your lectures are not remotely relevant to the shape of a well designed pool cue.

What happened to your steel toed jack boot avatar? I think I liked that hits 'em hard better than the doctoral version.

Math.

Thank the Man for his explanation.

JC

Coos Cues
Gold Member

Math.

Thank the Man for his explanation.
For this?

"And it’s not a hump. It’s the peak of the curve, and it’s relation to the start and end of it. Think of a sine wave that transitions to an exponential curve. That’s an extreme level, but draw it out long enough and due to the offset of the taper. It creates a ‘hump’ when rolled. But it’s due to how the curve isn’t parallel to a centerline."

A curve isn't parallel to the center line? Who would have thought?

Sounds like a fancy way of describing a hump in a wooden stick to me.

When I said math is the most important thing in the shop I was talking about the stuff we learned in Junior High School not abstract theory.

BarenbruggeCues

Unregistered User
Silver Member
stuff we learned in Junior High School

Still trying to figure out what they meant by 1 plus 1 = 3 back then?

Silver Member
deleted

Last edited:

Hits 'em Hard

AzB Silver Member
Silver Member
For this?

"And it’s not a hump. It’s the peak of the curve, and it’s relation to the start and end of it. Think of a sine wave that transitions to an exponential curve. That’s an extreme level, but draw it out long enough and due to the offset of the taper. It creates a ‘hump’ when rolled. But it’s due to how the curve isn’t parallel to a centerline."

A curve isn't parallel to the center line? Who would have thought?

Sounds like a fancy way of describing a hump in a wooden stick to me.

When I said math is the most important thing in the shop I was talking about the stuff we learned in Junior High School not abstract theory.

Like I said, this concept must be to advanced for you to grasp. This isn’t some abstract theory like you claim. A cone has a standard rate of increase. What happens when you vary that rate of increase? Up or down. You'll never get a smaller section of the butt. It never becomes smaller like you claim. Its always increasing. But because it no longer matches the rate of increase of the straight line, you’ve taken it completely out of context. It’s not smaller diameter for fucks sake. Nothing tapers back down. It’s just no longer doing what you think it should be doing. Again, it’s all due to the rate of increase going down below what it was. That’s what creates a ‘hump’ when rolled. But when spun on a lathe, there is no hump.