Parabolic taper
- Thread starter hoppefan
- Start date
Simple answer = a curved, or nonlinear taper.
A parabola is one of the conic sections. It is a curve, that can be expressed as
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Speaking geometricly, it is obtained by taking the union of a cone and a plane intersecting at a certain angle.
In terms of pool cues, it really only means a nonlinear or curved taper of a shaft. Typically, there is only part of a pool shaft that shows a great amount of curved taper, but a shaft can be cut the entire length to exactly match a particular segment of a parabolic equation. Often, a pool shaft is cut or sanded using a series of varying linear tapers. When sanding smooth, and when turned straight and sanding at the joint to match a butt, the end result takes on a smooth and curved look, but the individual portions most of the time would best be described using separate equations.
I personally think the term is used loosely when describing pool shafts because I doubt most shafts are cut to follow an actual parabolic equation. I have a degree in math, though, so the term parabolic has a classical meaning to me.
Kelly
Last edited:
It's what happens when someone uses a Coke bottle as a taper bar.
Ok, what Kelly said.
Ok, what Kelly said.
I agree with what Kelly_Guy said.
Here is a something to help you visualize it if you are still a little fuzzy. We don't all have math degrees
This is not a legit taper. Just an example! Also, the graph is squished horizontally. You'll have to use your imagination a little bit.
Link: http://www10.wolframalpha.com/input/?i=Plot[{%280.51+%2B+0.001+x+%2B+0.00002+x^3%29%2F2%2C+-1+*+%280.51+%2B+0.001+x+%2B+0.00002+x^3%29%2F2}%2C+{x%2C+-1%2C+30}]
See how that looks like a shaft taper? It's just a mathematical formula, in reality.
You might be surprised. Kersenbrock's book has the equations for two shaft tapers in the back. Both of them are parabolic. I would assume all of the shops he setup were at the very least started with a parabolic tapers as well. We use an actual parabolic taper too.
Last edited:
I agree with what Kelly_Guy said.
Here is a something to help you visualize it if you are still a little fuzzy. We don't all have math degrees
This is not a legit taper. Just an example! Also, the graph is squished horizontally. You'll have to use your imagination a little bit.
Link: http://www10.wolframalpha.com/input/?i=Plot[{%280.51+%2B+0.001+x+%2B+0.00002+x^3%29%2F2%2C+-1+*+%280.51+%2B+0.001+x+%2B+0.00002+x^3%29%2F2}%2C+{x%2C+-1%2C+30}]
See how that looks like a shaft taper? It's just a mathematical formula, in reality.
You might be surprised. Kersenbrock's book has the equations for two shaft tapers in the back. Both of them are parabolic. I would assume all of the shops he setup were at the very least started with a parabolic tapers as well. We use an actual parabolic taper too.
Thats cool information, thanks for letting me know. It may be more common than I suspect as you say. (I meant no disrespect ofcourse...)
Kelly
Some cuemakers use a parabolic taper on their butts, as well. Black Boar does, and Jeff Olney has been for quite some time.
An example would be...
A butt that is .840" at the joint - tapering smoothly up to 1.35" somewhere in the handle area - then tapering smoothly down to 1.24" at the bottom of the butt cap.
My custom Olney has a parabolic tapered butt, and it hits great - but I don't know how much the parabolic taper contributes in and of itself.
An example would be...
A butt that is .840" at the joint - tapering smoothly up to 1.35" somewhere in the handle area - then tapering smoothly down to 1.24" at the bottom of the butt cap.
My custom Olney has a parabolic tapered butt, and it hits great - but I don't know how much the parabolic taper contributes in and of itself.
Or make sure there is a cubic term so I can incorporate two inflection points in the shaft. :grin-square:
Kelly
That's not really parabolic.
Just dual-angle.
About .45 degrees for the forearm and less than .4 for the handle.
1.035 at the bottom of the handle you mean.
Mine is .855 at the joint and has two angles as well.
Zylr, Tad, Schon and a few more do a variance of dual or dompound taper butts.
That is an interesting taper! Are those real numbers, or just pulled from air?
Not bashing, just curious...
I run a straight taper from .850 to 1.300 over 29.5 inches (before I radius the butt cap- the measured diameter at the 'end' of the finished cue would be slightly less)
I had contemplated running a straight taper to the A joint, a straight (or less tapered/more straight) handle area, and then a straight taper to the end of the butt. Never tried it however.
Your idea to have the handle thicker (heavier) than the butt could work to move weight more forward, if that was the goal. However, if the wood in the handle area is different than the wood in the forearm and butt sleeve area (as is typical in 99% of cues), it would be (is) easier to control weight through wall thickness of the butt sleeve and wood selections. Conversely, if you had a house cue or other full splice it may be advantageous to control the weight this way.
Interesting...
He meant 1.035.
That would be about 30 thou thicker at the bottom of the forearm compared to a straight taper of aroud .0137 per inch.
I've never seen a cue whose middle is thicker than the bottom.
I haven't measured the high point in the middle - that was just illustrative. But the .840 joint & 1.24 at the bottom of the butt cap are real & confirmed.
Jeff Olney would be the one to know exactly what's in between, but what's there is a parabolic taper according to him.
Is there any commonality to the parabolic term for concave vs convex?
Let's be clear (as if it weren't already). I'm not a cue maker, just a very interested & enamored owner.
Jeff Olney would be the one to know exactly what's in between, but what's there is a parabolic taper according to him.
Is there any commonality to the parabolic term for concave vs convex?
Let's be clear (as if it weren't already). I'm not a cue maker, just a very interested & enamored owner.
I've seen a warped one that LOOKED that way when it was spun on the lathe, does that count???:grin:
Thanks for the clarification. It did get me thinking a bit! (you can still smell the ozone I think
)
It's also what happens when someone uses to much sandpaper and not enough forethought.
Alan
Last edited:
I agree with what Kelly_Guy said.
Here is a something to help you visualize it if you are still a little fuzzy. We don't all have math degrees
This is not a legit taper. Just an example! Also, the graph is squished horizontally. You'll have to use your imagination a little bit.
Link: http://www10.wolframalpha.com/input/?i=Plot[{%280.51+%2B+0.001+x+%2B+0.00002+x^3%29%2F2%2C+-1+*+%280.51+%2B+0.001+x+%2B+0.00002+x^3%29%2F2}%2C+{x%2C+-1%2C+30}]
See how that looks like a shaft taper? It's just a mathematical formula, in reality.
You might be surprised. Kersenbrock's book has the equations for two shaft tapers in the back. Both of them are parabolic. I would assume all of the shops he setup were at the very least started with a parabolic tapers as well. We use an actual parabolic taper too.
What I want to know is how you convert that equation into G-code. Or are we just picking some points along the line and then connecting the dot's or
a series of arcs.
macro
The best chance is to write a macro for the profile.
The macro can have the formula and it gives a x value at a constant z value and loops around for each z value.
It becomes a incremental repeat program.The z step or offset can be what ever you want, but as the x value increases you need to figure out the definition that you require.The larger the diameter of the cutter the more forgiving the step over can be.
Some controllers allow macro's to be writen with formula's and others don't.
Neil
The best chance is to write a macro for the profile.
The macro can have the formula and it gives a x value at a constant z value and loops around for each z value.
It becomes a incremental repeat program.The z step or offset can be what ever you want, but as the x value increases you need to figure out the definition that you require.The larger the diameter of the cutter the more forgiving the step over can be.
Some controllers allow macro's to be writen with formula's and others don't.
Neil
You missed the point of the question. We aren't really cutting a true parabolic curve. We would be cutting a whole lot of little lines or little arcs. Close to a true parabolic curve, but not really one.