Dan, if there's not a booby trap somewhere in all those questions I'm Chinese!
There is an old saying about ballistics: "If all else is equal." Simple concept, but very difficult to put to practical use. More of a conceptual presentation than anything else actually and it says simply that if things are not the same your derived data is subject to question. EX: Same gun, different barrel...not the same. I'm sure you understand that variables are bountiful in this discussion. With the addition of each variable, the conclusions become less valid for broad application. The many comments made to this point about the necessity of heavy charges versus light charges needed to make a gun shoot is but one example.
To the issue of research on PRB ballistics. No, there isn't much out there and there probably won't be until the likes of Mr. Pletcher or like minded types set to and do it themselves. Ballistic research is geared in very much the opposite direction these days. The technology exists but the motive is absent.
Going back in time to Forsythe's day there is nothing but the highest regard for his work and that of others in the field. He was not pulling our legs and in fact it amazes me that the pragmatic approach to ballistic research and their intuition revealed so much to them. And there is the IQ thing at work. Forsythe was fairly brilliant in my opinion. I think his observation about 8-1/2' versus 12' twists are consistent. There is a practical minimum twist rate for a given caliber PRB. I don't know what it is but would think it caliber influenced to some degree. See my comment below about squares and cubes. On the other hand and this goes to the issue of variables, recall the success had by Mr. Crowley with his slow twist rate .50 caliber. Somewhere between the measures Forsythe commented on if I did my math correctly.
I would say that in very general terms, the exterior ballistics of PRB and conical bullets share but a few things. Gravity and drag are the big ones I'd say. Even though both are stabilized by rotation from rifled bores, there are distinctly different reasons for doing so and I think I touched on the primary issue early in this thread.
On the part of conical bullets, the CG and CP are not co-located and as a result gyroscopic stability is required to stabilize the bullet. CG and CP are co-located in round balls, thus there is no prevailing influence of overturning or pitching moments to influence its stability. Like conicals, PRBs are influenced by the magnus force to the extent that balls with random rotation typical of a smooth bore musket will disperse randomly. The slow spin of a RB rifle presents to consistent rotation on a single axis and does away with this adverse factor.
Conical bullets are affected by transition through the speed of sound when the CP shifts and a nutation or wobble is induced as it tries to stabilize from the influence of this upset. From my understanding of the circumstances, not all bullets experience this but in broad terms the CP shift is forward, or destabilizing. Since round balls do not have dislocated CG/CP, I have no reason to think this influences their flight path. I've certainly never seen such representation made in writing. Many folks seem to think the transition through the speed of sound is turbulent. It isn't. Regardless of twist rate or velocity from a PRB rifle, the spin rate is very low. I doubt it has anything to do with stability in the transonic range, either positive or negative. I say this simply because the reasons for spinning a round ball are different than for a conical and PRBs do not carry the same baggage in an aerodynamic sense. Gyroscopic stability in conical bullets presents a lot of penalties for the benefits gained...it is not a free lunch. If you peruse the Nennstiel web site linked below you'll begin to see that if you don't already.
Comment made about the ball orienting itself to the flight path: I don't think it would and such absence would, to very small degree, increase the influence of the magnus force. Understand that the magnus force is very small and not worthy of deep consideration in this discussion. It is present however.
http://www.nennstiel-ruprecht.de/bullfly/magnusf.htm#headerTo the question, the act of a bullet's spin axis conforming to the flight path is known as the tractability condition. It occurs because the bullet is 1) gyroscopically stabilized and 2) is pitched up relative to the flow field. This results in nutations of small order and if properly stabilized the bullet will precess to a new pitch axis which reduces the upsetting forces. Again, round balls have co-located CG/CP and there is no upsetting force which might cause the precession. Even if the ball is slightly oblate in shape due to obturation, there is no significant displacement of CP to promote the tractability condition.
http://www.nennstiel-ruprecht.de/bullfly/tractf.htm#headerRandom thoughts on variables which may have influence on the observations made by many of you.
1) Obturation is a variable influenced by charge, alloy and probably another half dozen things to small degree. A ball increases cross sectional area by the radius squared as caliber increases. It increases mass by the radius cubed. Raise the caliber, and you raise the BC, SD and a few other things.
2) Different rifles, each with a family tree of variables. Barrel pinning, breech, caliber, lock, patch...it's a long list I think. Each is its own animal.
I dunno that covered all the questions, but it's margarita time.
