To answer that question----- no specific scientific tests that I know.
My 14 bore has .012" rifling with a 66" rate of twist. I tested that rifle off sand bags to 200gr. 2F on target and achieved the same accuracy at 100 meters as when using only 140gr. ie: 1" to 1 1/2" accuracy at 100 meters or 3" at 200 which is the last time I benched it, last summer.
Any less than 140gr.2F and the accuracy degrades. More powder merely shoots the same, but with a flatter trajectory. Due to the deeper rifling and faster twist than the Forsyth principal, I am using a .684" ball along with a minimum of .030" patch. Like I've said before, you have to WANT to seat it flush. Once there, it loads what I call easily with the rifle's tapered Hickory rod, 7/16" to 3/8". Although I'm getting long in the tooth, I'm still far from weak, I guess.
With the lighter powder charges like 82gr. of 2F, this rifle will allow a thinner patch, but not with the heavy ones - they hole and burn. Thus, I want the slower twist and shallower rifling of Forsyth's principal - but in a 16 bore. Even the slightly undersized 14 bore ball kicks a bit much for me now- or will in a year or two.
I had to increase patch thickness with heavier charges as my barrel was burning normal the .0225" patches (with normal combination .005" under ball with 10 ounce denim patch) with the heavier charges of powder. Lighter charges, although accurate to 40yards and not too bad to 60yards, did not give me the accuracy nor the trajectory I demanded for heavy game and longer ranges.
For some reason this particular barrel demands to be fed larger than normal powder charges to achieve it's BEST & repeatable accuracy. I would have expected a 66" twist to shoot well with a mere 110gr. to 120gr. 2F. Perhaps this is because it is has a far from smooth interior - it has radial marks caused by the poorly done original reaming - looking more like drilling marks. It never picks up fouling, but does not load as slickly as any other barrel I have & they all shoot the heavier charges with the standard "combination".
There might be other causes - Forsyth addressed one.
Perhaps the demand for heavier powder charges is due, as Forsyth indicated, to the damage caused to the sides of the ball in impressing it into the lands with a heavy patch which causes more atmospheric disturbance which causes loss of stability and therefore accuracy. The heavy patch was necessary due to the depth of rifling. The depth of rifling was necessary due to the quickness of the twist. The twist rate demanded a tighter load be used so the ball wouldn't strip in the rifling. The required tighter load demanded thicker patching which caused damage to the ball - ie: - Forsyth's vicious circle of demands. Each 'fix' caused more problems. He found that 'hunting accuracy' could be obtained with such a slow twist and shallow rifling, that merely humored the ball out the barrel, rather than forcing it into radical spinning in faster twists which did strip with healthy loads.
His written word also stated that twists could be one turn in 10feet or even as slow as one turn in 12feet if one only required hunting accuracy to a mere 150yards. If accuracy to 200yards was desired, then the 1/4 turn was his favourite.
A moose and I suppose the side of a water buffalo as well, has about a 30" kill zone on it's side - that's a big X ring. I demand better accuracy and am cautious about going too far in slow twisting, due to the powder charges they might demand. Afterall, my 66" twist demanded at least 140gr. I want a twist that will shoot accurately enough for me, yet have shallow easily loading rifling that will hold the ball "without tripping over the rifle".(his words to describe stipping)
I was not be happy with 3" to 4" groups at 100 yards and rainbow trajectories which is what a mere 82gr. (3drams) of powder provided in the .69. I did not like those groups, nor the arching trajectory, therefore I tested with more powder until I achieved my demands - firstly to achieve the accuracy as in 140gr.2F and secondly to obtain the desired trajectory, which required even more powder, ie: 165gr.2f- GOEX. I now have a 6" point blank range where the ball is neither more than 3" above nor below the line of sight all the way to 125yards. Not bad for a 480gr. round ball. Trouble is, it is difficult to load with WW alloy balls due to the depth of rifling.
The trouble with a slow twist, shallow rifling in a .72 cal. barrel is, it's going to kick with a load that will accuracy shoot it's 545gr. ball in a slow twist? If I were to build one, it would be 10 pounds or more and of English design of the 1850's - no other is suitable.
72" is faster than Forsyth's 1/4 turn principal said, should be used in rifles. But then, so is 80" or 90". His principal called for a 1/4 turn in the length of the barrels - normally 26" bl. therefore 104" twist. He also called for very shallow rifling and very narrow lands - almost 'knife' edged or knife-like were his words, to use a ball that barely passed down the bore. The patch alone was to 'take' the rifling. No particulars were given as to actual width or depth. If use to seeing .030" rifling as on the continent in some rifles, perhaps .010" seemed shallow. It looks shallow in my 14 bore barrel, especially compared to the rounded rifling in other large bore barrels I've seen. A friend has one in .75 cal. - too deep to fill with with normal patching of up to .030".
Since the patch must also be pressed between the ball and the tops of the lands, yet allow easy loading, we surmise/guess that the ball used was probably 1 bore size smaller - ie: a 13 bore ball in a .12 bore rifle, 15 in a 14, etc. and something on the order of heavy linen was used - maybe around .016" to .018".
A 14 bore, ie: .693" bore with .008" rifling would be .709" groove to groove. (.709 is actually 13 bore, groove to groove - that makes sense in more ways than one) A .677" ball with .016" patch, would measure out at .677 + .016 + .016 = .709" - same as the groove depth. The .018" patchwould load, in narrow lands, almost as easily and the rod would almost push the ball down by it's own weight - any hardness of ball could be used - the other MAJOR factor and reason for rifling shallow and slow.
The most important aspect of Forsyth's principal is that the rifling must be shallow enough to allow any hardness balls to be used.
Hard or hardened balls were necessary to penetration sufficiently on dangerous game. At that time, muzzleloading bullets were cast of soft lead to allow easy loading and had to be soft to allow obturation/expansion by the powder charge to 'take' the rifling - The problem in using soft bullets was that soft bullets gave dangerously shallow penetration on heavy game, especially when they struck heavy bone. They simply stopped or deflected into the 'soft parts of the body, causing little or no damage", more like the thrust of a sword, rather than the smashing blow of a hammer, which the spherical ball provided.
Samuel Baker spoke of that more than once. The conical "Led me into such scrapes that I eventually gave the conical us as useless for killing dangerous game".
In short
The twist must be slow enough, that a 'weak' ball and patch combination that loaded easily with a hardened ball, still held onto the grooves with heavy charges, gave game killing accuracy and was easily reloaded. A tall order, but filled by his design - if you can handle the recoil in the larger sizes.
This is my opinion on the why's and wherefores.
