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

#### JC

##### Coos Cues
Gold Member
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.
There is no hump when spun on a lathe because it's still equal distance from center to od at all points when measured perpendicular to center. But there is a hump when you run your hand up and down it on the long axis.

If you cut it as you describe it's not a curve it's just a taper that decreases in a non linear fashion. But it's always decreasing.

This is a curve ) Here is another one ( Tell me how you put this in a stick of wood without it being smaller at some point than previously and reach the end of the stick?

#### MVPCues

##### AzB Gold Member
Gold Member
Silver Member
There is no hump when spun on a lathe because it's still equal distance from center to od at all points when measured perpendicular to center. But there is a hump when you run your hand up and down it on the long axis.

If you cut it as you describe it's not a curve it's just a taper that decreases in a non linear fashion. But it's always decreasing.

This is a curve ) Here is another one ( Tell me how you put this in a stick of wood without it being smaller at some point than previously and reach the end of the stick?

Wow.

A curve doesn't have to have a relative maximum or relative minimum to be a curve.

#### BarenbruggeCues

##### Unregistered User
Silver Member
My eyes are bleeding...my eyes are bleeding!

#### JoeyInCali

##### AzB Silver Member
Silver Member
My eyes are bleeding...my eyes are bleeding!
my taper is professional parabolic symmetric compound

#### Hits 'em Hard

##### AzB Silver Member
Silver Member
This is a curve ) Here is another one ( Tell me how you put this in a stick of wood without it being smaller at some point than previously and reach the end of the stick?
Wow. I cannot believe this. Your )( example is flawed as hell. At no point does the taper of the cue get smaller. It’s always increasing. It’s the rate of increase that you’re having issues with.

#### Thunder Thighs

##### learning daily...
Silver Member
my taper is professional parabolic symmetric compound
Can I get cheese with that please?

Silver Member

#### JC

##### Coos Cues
Gold Member
Wow. I cannot believe this. Your )( example is flawed as hell. At no point does the taper of the cue get smaller. It’s always increasing. It’s the rate of increase that you’re having issues with.
I'm not a quick study can you please take a moment and sketch out your taper with curves that is always on the increase? It's a simple 2d drawing should only take a few minutes. Thank you.

#### billsey

##### Registered
A parabolic, hyperbolic or dang near any conic section curve on a cue will start narrow at the tip and gradually get wider toward the butt. In order to get 'bumps' the curve has to change to be shallower or more acute at various places on the cue. That's no longer going to be a single curve, it's going to be complex curves. I expect most cues that use a curve at all use curves in some sections and straight tapers in others. A pro taper for the shaft starts out pretty close to no taper at all, then uses a slight curve to move in to a straight taper to the joint. That curve is only there to keep the player from feeling any sort of abrupt change. If you were to use a parabolic taper on the shaft you would either end up with the first portion after the tip getting ever so slightly narrower (not likely) before widening to match the correct joint size if the parabola had the center point included along the length, or it would gradually increase in width all the way from the tip to the joint, with the parabola center either at the tip or further past the tip. I'm assuming the latter is what the original poster was asking about. It is possible to define a parabola with any three points, and the tip, joint and butt could fit that. I would expect the handle would feel a little weird, but it might not be too weird since the parabola is going to be fairly close to a flat line... 0.5", 0.85", 1.20" only has 0.10" more width added in the second half of the curve, so it's close to a European taper.

#### JoeyInCali

##### AzB Silver Member
Silver Member
A parabolic, hyperbolic or dang near any conic section curve on a cue will start narrow at the tip and gradually get wider toward the butt. In order to get 'bumps' the curve has to change to be shallower or more acute at various places on the cue. That's no longer going to be a single curve, it's going to be complex curves. I expect most cues that use a curve at all use curves in some sections and straight tapers in others. A pro taper for the shaft starts out pretty close to no taper at all, then uses a slight curve to move in to a straight taper to the joint. That curve is only there to keep the player from feeling any sort of abrupt change. If you were to use a parabolic taper on the shaft you would either end up with the first portion after the tip getting ever so slightly narrower (not likely) before widening to match the correct joint size if the parabola had the center point included along the length, or it would gradually increase in width all the way from the tip to the joint, with the parabola center either at the tip or further past the tip. I'm assuming the latter is what the original poster was asking about. It is possible to define a parabola with any three points, and the tip, joint and butt could fit that. I would expect the handle would feel a little weird, but it might not be too weird since the parabola is going to be fairly close to a flat line... 0.5", 0.85", 1.20" only has 0.10" more width added in the second half of the curve, so it's close to a European taper.
A shaft cannot fully have a curved taper from joint to tip.
The stroking section will eventually have to have a linear angle .

#### MVPCues

##### AzB Gold Member
Gold Member
Silver Member
A shaft cannot fully have a curved taper from joint to tip.
The stroking section will eventually have to have a linear angle .
No. Curves can have asymptotes. The boundary of an asymptote is linear but the line that approaches it is still a curve. It has to be a curve since it never reaches it. The shaft would gradually increase in diameter from the tip but slowly enough that it would look like a "pro taper" or very shallow linear taper, but it is still a curve as defined on paper. Place the point of the curve where it starts to deviate from the boundary significantly around the 11-13" mark. Set the parameters so the scale is appropriate for tip and joint diameter. Logarithmic functions are good for this, which is what CueCut uses to generate a shaft taper from scratch rather than copying from an existing one.

And different curves can be pieced together at the vertices (diameter points along the length) or splines can be fit to the data points along the entire length. And no there won't necessarily be huge humps at the vertices like some have suggested. What some fail to grasp is the scale these curves are applied to in a shaft. What small blips you see in a data graph that is very not to scale and what is seen or felt in an actual 29" long shaft with the other axis ranging between 13mm and .840" is very different. Models are models. Finished products are finished products.

Does anybody do all of this? Initially as a baseline model, maybe. Well, I should say sometimes since I did with CueCut. But taper models defined by equations should be a starting point not an end result, and these ideas aren't always easy to implement. If a parabolic taper bar is machined, it isn't adjustable. If a GCode program includes the curves that define a parabolic taper, that isn't the easiest to modify either. This is why I designed CueCut to implement shaft tapers as multiple linear tapers with a 1" resolution between points. That resolution is fine enough to approximate curves in the hand. The initial data points can be generated by any equation(s) one wants to try, but the idea that there exists one magical equation that is perfect for shaft tapers for all bridge lengths, all tip diameters, all players, all wood choices, and all shaft types is as preposterous as saying a parentheses is the only shape of a curve.

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#### HawaiianEye

##### AzB Silver Member
Silver Member
Somehow , Kao Kao , who has a really fancy factory has not copied the taper .
SW's assembly is actually fairly simple .
I don't know if they've copied that .
But, if you are making cues in China, they better be cored .
SW's are not .
So, when you see a SW with ebony nose, it is ebony nose .
Jackpot ebony forearms are not cored.

#### JoeyInCali

##### AzB Silver Member
Silver Member
Jackpot ebony forearms are not cored.
Shcmelke doesn't.
Their ebony front full-splice blanks are not cored either .
Judd did not core his cues at all . My first custom from him was ebony nose with maple points.
SW and Searing do not core their ebony cues either .
Old Adam ebony cues were not cored either .
Today, most makers won't do ebony forearm or handle uncored .

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#### Ssonerai

##### AzB Silver Member
Silver Member
Today, most makers won't do ebony forearm or handle uncored

Probably because most people are not working from old stock dry lumber.
"turning squares" in ebony (& other hard woods) can take a decade to dry and may still keep moving.
Coring helps 2 ways - get the moisture out of the center & prevent cracking while it rests. Plus a little bit more stability as a construction.
A lot of it is branch wood.
I remain unconvinced the coring is not partially a crutch. Even if the wood is dry, coring allows the use of "iffy" material in terms of grain run-out, figure, and other inherent stability issues. A person can no longer afford to throw out 2/3 of a lumber pile to use only the best stuff, even for a presumably high \$\$ cue.

I'm more or less in favor of coring, but lazy.

#### Hungarian

##### AzB Silver Member
Silver Member
I believe the turbo encabulator was built on the parabolic curve principal. You need special sperving bearings to make it play right though,
Yes, you are correct. This will prevent side fumbling very effectively.

#### JoeyInCali

##### AzB Silver Member
Silver Member
Probably because most people are not working from old stock dry lumber.
"turning squares" in ebony (& other hard woods) can take a decade to dry and may still keep moving.
Coring helps 2 ways - get the moisture out of the center & prevent cracking while it rests. Plus a little bit more stability as a construction.
A lot of it is branch wood.
I remain unconvinced the coring is not partially a crutch. Even if the wood is dry, coring allows the use of "iffy" material in terms of grain run-out, figure, and other inherent stability issues. A person can no longer afford to throw out 2/3 of a lumber pile to use only the best stuff, even for a presumably high \$\$ cue.

I'm more or less in favor of coring, but lazy.
I got ebonies that were bought in the mid-90's. They are dry .
I've seen ebony butt sleeve crack in a finished cue by a big named maker.
I was at a friend's home and I pointed it to him b/c he did not notice . The cue was standing on his setup for years .
That's a butt sleeve even .
Coring ebony has way too many advantages to mention .
Moisture is just one of them. But, there are plenty of ebony out there by makers who have been in storage for ages .
Gabon ebony is one wood that can betray you anytime during the build and after the build . Coring reduces that chance.
Reduction of weight is a great motivation too . A cored gabon with select maple dowel makes for a great hitting cue .
Better than pure gabon imo .

#### scdiveteam

##### Rick Geschrey
Silver Member
what dimensions are used to make the cone?

cue tip and end of butt diameter? joint? cue length? all of the above?

I'm trying to design a cue, and am wondering how variable these dimensions can be/
what dimensions "fix" the cone shape

thanks for any info.-
Hi,

I am the biggest fan of DPK. He is the Tiger Woods of Cuemakers.

On my Esoteric Cue Design the first 12 inches of the butt from the joint to the A Joint is conical .850 to .1004. From 12" to 29 I have a slight constant parabolic curve to the end. If you put a straight edge against my profile you see an air gap.

Also IMO, the best shaft taper has three major segments.

1. From 0 to ten inches
2. From 10 inches to 15"
3. From 15" to 29".

If you have the good playable geometry, the cue will flex at 6 to 8" from the tip when you bend it while you hold two fingers on top of the shaft and your thumb underneath on the very ends of the shaft.

Why is this important?

The flex point needs to be in the area of your bridge hand which acts as a steady rest. Why? Because when the tip contacts the stationary cue ball the shaft wants to deflect behind the bridge at the moment of inertia if the taper does not have a strong climb at the #2 segment of the total profile geometry 35 to 40 thou from 10 to 15".

If you shaft bends closer the the middle it negates the steady rest effect of a closed bridge and just a slight deflection toward the center of the shaft will cause the tip to move on the cue ball during what Newton refers to the elastic collision. Depending on the velocity it can squirt and apply unintended english on the ball. And the player does not even understand what happened when the object ball misses the pocket. Bad equipment will not make you get better no matter how many L drills you perform.

From 15" to the joint, the geometry can be anything you want as long as you land on the number of the joint dia. Here is where the shaft can incorporate a parabolic taper or as some refer the the coke bottle.

Again, these observations are based on physics. The interpretation I have just stated are only my approach to this subject. If the reader does not agree, please just agree to disagree with me because I will not get into any pissing matches.

Of coarse this steady rest effect is not as effective with an open bridge but the described geometry above will still out perform any shaft that flexes closer to the center.

BTW, the next time you have a Cog or Gina shaft at hand, try the test and observe with your own eyes.

So my advise to new cuemakers is if your shafts bend toward the center, go back to the drawing board.

I will not share my geometry numbers but a good place to start your investigation is to mic a Predatator Z Shaft as your start point.

Rick

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#### JoeyInCali

##### AzB Silver Member
Silver Member
If you shaft bends closer the the middle it negates the steady rest effect of a closed bridge and just a slight deflection toward the center of the shaft will cause the tip to move on the cue ball during what Newton refers to the elastic collision. Depending on the velocity it can squirt and apply unintended english on the ball. And the player does not even understand what happened when the object ball misses the pocket. Bad equipment will not make you get better no matter how many L drills you perform.
That's unfounded Physics.
When the tip hits the cue ball and it has bounced off the tip, the shaft cannot buckle fast enough to hit again unless it's a miscue .
Or buckle and apply unintended English .
The original 314 shaft, barely had diameter increase to the middle of the shaft .

A great number of the Taiwanese pros who use SW shafts, sand the crap out of them in the middle .
Some of them look like twigs after a while and they still use them .

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#### scdiveteam

##### Rick Geschrey
Silver Member
That's unfounded Physics.
When the tip hits the cue ball and it has bounced off the tip, the shaft cannot buckle fast enough to hit again unless it's a miscue .
Or buckle and apply unintended English .
The original 314 shaft, barely had diameter increase to the middle of the shaft .

A great number of the Taiwanese pros who use SW shafts, sand the crap out of them in the middle .
Some of them look like twigs after a while and still use them .

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#### scdiveteam

##### Rick Geschrey
Silver Member
In the elastic collision, the ball does not bounce Joe or foul by hitting twice as you described. It stays on the cue ball for a period of time based on the shaft velocity and hardness or softness of the tip. Like a golf ball staying on the club face and compressing only to a lesser extent.
If there is any deflection in the shaft as a rod the tip will move laterally randomly causing squirt if any left or right hand english was part of the aim point by the player.

– An elastic collision is one in which no energy is lost. – A partially inelastic collision is one in which some energy is lost, but the objects do not stick together

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