I accidentally dropped in here, I came to the Forum to ask a new question. Back to the top, the original question of parabola vs. ellipse. And I confess I've pontificated on this in another thread.
Bill B. answered it in his first response. "They're so close at the size we're talking about that it is meaningless to get mired down in the minutiae of difference between the two. Besides, once the flute has been polished to remove the machine marks, the flute will be neither parabolic nor elliptical. There is not just a single shape for either a parabola or an ellipse, but a whole family of curves for each".
I'll do my usual Murph Says pontification. A V is a V, and a U is a U - and both have straight sides. A true V gouge would have a point at the bottom, the actual V gouges have a curve at the bottom (else they would be useless for our work) then the sides "straighten out" as they diverge. A true U gouge would have a larger diameter curve at the bottom and the sides would be verticle, the actual U gouges have the sides straighten out to near verticle, but they still diverge.
In both cases the sides, extended to infinity, would never meet. The V and the U are not in a family of curves.
By contrast, the ellipse and the parabola are both in families of curves. The ellipse family never meets as it goes off into infinity, but the curves are continuous. The parabola family will eventually close and make an orbit, but it might take billions of miles to finish its cycle. Our earth's orbit is parabolic, luckily. The comet coming in from deep space is also parabolic - but a lot longer parabola. Whether there is a natural object following an ellipse is a matter for the particle physicists and astronomers.
Let's come back to a practical level. I repeat Bill Boehme's comment - "They're so close at the size we're talking about that it is meaningless to get mired down in the minutiae of difference between the two. Besides, once the flute has been polished to remove the machine marks, the flute will be neither parabolic nor elliptical. There is not just a single shape for either a parabola or an ellipse, but a whole family of curves for each.". The advantage to the turner in sharpening, and using, the gouge is not the specific parameters of the curve - it is that the curve is consistent through its length. The side bevel of a long winged gouge changes gradually and consistently. The V and the U don't do that (although some called Vs do). The same applies to spindle gouges, but they are normally a steady curve.
This thread digressed, something I've been accused of in other threads <grin>. I happen to have a set of CBN wheels (D-Way), and you don't need a Baldor grinder. As an old man on Social Security I am not rich, but the CBNs have already saved me money (had the fine wheel with the rounded edges, a la Ellsworth cutting tools I make myself) for three years, and the course for two years. My old 1750 "low speed" grinder died a year ago. I bought a Delta VS at Lowe's for under $100 and it works fine. I was concerned that the bottom range was 2250, but the CBN wheels grind so "cool" and gentle that I can touch up my tools with a single pass - and I can regrind at 3400 without overheating. What I spent on the wheels I save on the tool steel.
One more thing from this thread - the tool steel itself. A while back my old Ellsworth Signature 5/8" (US) from Crown was getting short. I invested in a Pro-PM, as it was the only one I was sure was "parabolic" and a better steel. Since then I've done a bit of research and discovered that the PM is said to not take as sharp an edge as the M2, but that it holds it better than the M2. The research shows M42 is best at both. My solution is to use my PM for shaping the bowl then my M2 for the final cuts.
I took note of some comments on scrapers, and the steel. I buy my scrapers from PSI, they are rated M2 (by an outside agency) and they are cheap. I reshape them often for particular work pieces. I'm not a great fan of scrapers, I prefer to cut, but they have many uses. I grind to about 70 dgs. and use the Veritas device to make the burr. That makes a "forward burr" rather than the "back burr" done with a hand honer, but it is consistent and easy to do. I think spending money on the best steel for scraper is a waste - better to regrind and re-burr the square end "el cheapos" (as long as they are M2 or better). Why spend money for the grinding by the vendor when you can grind the shape you want yourself?
In summary, the ellipse and the parabola are the same thing, each is a continuous curve. The shape of the curve varies, but the key for our use is that it is continuous.Some steels take a better edge, some hold the edge longer (but don't take as good an edge). M42 is expensive and does both, but do you really need it. In ten years you may want M442 <grin>. Perfection is in the hands of the turner.
I take the liberty of quoting Bill Boehme again - It's a lot like golf clubs and fishing rods. We can get lost in the details and forget that it's the person holding the tool that makes the difference.
To each his own, and each will find his favorite. But it is easier to find a favorite when the curve is consistent.
Best, Jon
