Dennis, it seems meandering is generic to the Forum - I'll try to come back to your original question. I haven't seen Glenn's DVD, nor Grant's comments, but it seems to me that the continuously changing curve of the parabolic (or partial ellipse) flute shape is a match for the continuously changing grind angle when using a jig and making "long" wings. As I picture the process it seems that the wings on a V would change angle more rapidly that on a parabolic when using a jig. A hand grinder could compensate for that, but that is beyond my skills.
Oops, just saw John Lucas' post in this thread - what he describes is what I was guessing at. I guess the answer is that if you can compensate for the straight sides of the V then keep on using it, but if you haven't learned how to do that yet go with the parabolic.
I do have a couple of Thompson U gouges that I grind as "bottom feeders" - a tip bevel of about 80 dgs. and very short wings - but they are "specialty" tools for me.
I "tugs me forelock, respectful" to Odie. Adapt on the go, learn to use your tools in different woods. But it is a lot easier to do that if the curve of the grind changes consistently along the wings, and I think the parabolic makes it easier to maintain that with a jig.
The meandering has started with the mention of Don Geiger's vertical system, so I'll add to it. I had bought his original about six months before he came out with the improved one (the one with a pin to set four different fixed distances given the same setting of the main arm). Don was kind enough to sell me parts to make the conversion, and I made a few of my own modifications. It is a gem - I can duplicate my grinds in two passes (more if I've done a lot of honing). I've looked at the instructions on the Evolution and it appears it performs the same function for a lot less money - at least for most turners.
I'm sorry Don has dropped the VS, and seems also to have dropped his "centering solution". I agree with Hockenberry, he is a genius in devising devices for sharpening - but also for other things. The Centering Solution is a drill guide that screws into the threading of your chuck or face plate so you can drill a hole (I think about 3/8 or so) into the tenon of a bowl. With it is a plug that fits into the hole, and rides in a revolving tail stock center. Actually only tapered one's like Oneway, but I got a discount from Don to not take his plug and made my own out of aluminum stock. Using the plug shoved about 7/16' deep into the tenon I can recenter a bowl on a jam chuck that isn't a close fit in about two minutes, and sometimes it is perfect the first try. It used to take me a half hour using a pin center. And I no longer have wish I had space and money for a vacuum chuck.
OK, digression - but I wanted to support Hockenberry's compliments to Don Geiger, whose devices save money and time and actually work.
Best, Jon