shakes said:
This brings up a question for me... Do you guys consider the whole of the shaft when you talk about the taper, or are you just speaking of the shape the taper bar (for example)? I've always just considered the shape of the taper bar, thus ruling out the ability to call it hyperbolic. I've always called them parabolic or reverse parabolic. (Parabolic being the curve going in making it thinner, reverse parabolic being the curve going AWAY from the center making it a fatter taper). If you consider the whole of the shaft instead of just the actual taper itself, I don't see how you can consider anything Parabolic. I don't have a degree in math, so please don't think I'm making fun, I'm just attempting to clarify. Thanks for the excellent discussion, Fred.
No harm here regarding making fun...its all good...I hope my post didn't come off the wrong way.
Regarding: "I've always just considered the shape of the taper bar, thus ruling out the ability to call it hyperbolic."
Hyperbolic is not describing the concavity or inflection, it is a curve that may look parabolic, but is created by a different equation.
Regarding: "I've always called them parabolic or reverse parabolic. (Parabolic being the curve going in making it thinner, reverse parabolic being the curve going AWAY from the center making it a fatter taper)."
I don't think there really is a thing called "reverse parabolic". Some taper bars have the curves on both sides, making the width of the bar the same dimension its entire length. Both sides have the same taper and can be described by the same set of equations. Also, there will be inflection points in a shaft, creating both concave and convex areas.
Curves can be Circular, elliptical, parabolic, hyperbolic, etc. They are all described by different specific equations that are not linear. It isn't really plausible for a cuemaker to say...the first 6 inches of my shaft I have a very very small linear taper...the next 4 inches the taper picks up every so slightly even more but is still linear...then 10 inches to 18 inches it changes to a parabolic taper yielded by such and such equation, then the next 6 inches the taper is back to linear...then the last 5 inches is another parabolic curve yield by such and such equation.... Instead, the cuemaker looks at the curves that defines his taper from others, knows the rate of change is not linear (may or may not truly be defined by a parabola...may be several pieces of a parabola fitted together), and states he uses a parabolic taper.
I think for the most part when people talk about the taper, it is describing the point of the shaft where the change in diameter is largest, that area that varies more than other areas from cue to cue. Personally, if I talk about taper, I'm talking about both the curves of the taper bar, and the curves of the shaft equally, and the location of where they start and stop. Though the final product is changed somewhat due to final sanding, the curves of the taper bar dictate the
curves of the shaft. The locations where the curves start and stop is important as well, which is what I think Dale was pointing out about the pro taper.
