Formula for optimum rate of twist?

[WadePatton]

Without the caliber, and what the gun will be used for, answering your question is kind of like the old joke question” what’s the difference between a duck”.

 It all depends on those two things. Big calibers can shoot well with a fast twist at close range with light charges. And, small calibers can shoot well at close and moderate range with slow twists and heavier charges. But, you have to decide what use the gun will be put to. The 1 in 48” twist was considered a universal twist because it did pretty well out to a hundred yards with most calibers.

  Hungry Horse

RightO.  Once you understand all the trade-offs, you have to decide which ones are acceptable for your purposes. There's no un-plowed ground here, and no lack of folks who might argue that their set of tradeoffs is best.  Well, their set should be best-for them and their purposes. And it loops back to my first response. 

[Hungry Horse]

Just to illustrate that almost any twist/caliber combo can be made to work if you understand the principles, I have a perfect illustration. A kid bought a muzzleloader from a yard sale, and brought it to me to find out what it would take to shoot it. It was a cheap plastic stocked sidelock .50 cal. with a 1in 28” twist barrel. I explained to him that it was designed to shoot bullets, not balls. He was disappointed to say the least. I told him that it might shoot pretty well with pistol sized charges at relatively short range. He shot with some of us a couple of weeks later, and did very well on all targets at 100 yards and less. You could literally see the flight of the balls when he shot those new cast balls out to the 100 yard target, and they had a hard time knocking down big steel targets out there. But, he was deadly on the paper targets.

  Hungry Horse

[Dphariss]

I have for some time wanted to make a 66 cal (.660 bore shooting a .645-.650 ball ) and often wondered if a 1-85 twist would work with a 4 dram load. Hoping to keep recoil down some with that light of charge.

DPhar could answer that, however he is on the road at this time.  His English gun has a 16 bore Dave Rayle barrel. I think it has an 85" twist, shallow grooves (I think) and he uses just over 5 drams for best accuracy, IIRC.





Also - if I remember correctly, Dave makes his 16 bore barrels (any twist you want) with a .665" bore, so you can use a full 16 bore ball, ie: .662" Lyman mould.

Its an 80". Shoots great with 140 g of FF Swiss .662 ball. 1600 fps. Hard or soft lead. Even paper cartridges all shoot to the same point of aim at 50 yards. Hard lead needs a thinner patch since they cast larger from the same mould since the alloy shrinks less than lead.
Bores under 58 should work fine with a 48" twist. I think most modern makers use too slow a twist for the typical Kentucky Rifle calibers. When I get the  chance I will shoot a 48" twist 62 I have to see if it blows patches. Then cut it into pistol barrels.

Dan

[bgf]

Just thinking out loud, but the problem with Greenhill formula for round ball is that round balls do not need to be spin-stabilized in the same way as conicals.  They are inherently stable in theory, but spin does seem to help empirically.  My guess is that all the spin does is level out any irregularities in the ball, which if true would lead to the conclusion that it would be best to err on the slow side as far as twist goes, since spinning too fast would cause more problems than it solves.  To support this conjecture, I could point to the tradition that larger calibers intended for higher velocities typically have slower twists, perhaps because the larger radius amplifies negative effects of too much spin?  On the other hand, too slow might require excessive velocity...

As pointed out above by HH, fast twists often do fine with lower velocities, so obviously there is a sweet spot, but it would seem to depend on caliber and velocity, as well as perhaps uniformity of the round ball?  And as DPhariss points out, faster twist can rip off patches at higher charges, which muddies the waters.

[Daryl]

Actually, Forsyth quite well explained this, in his VISCIOUS circle of events.  The more spin, (faster twist), the tighter must be the hold, which might deform the ball, which reacting with the atmosphere, required more twist to stabilize, which then required a tighter fit, etc, etc.

As to round balls needed less twist, that is shown quite well in the slower twist barrels available today.  They do not, however embody completely Forsyth'sa principle of slow twist and really shallow grooves with very narrow lands - like the photograph I posted, shows.

I have proven, at least to my satisfaction, in my .69's 66" twist, that a tight fitting ball with produce 2" to 2 1/2" groups at 100 meters off the bags with a mere 82gr. 2F, but that 82gr. 3F produced 4" groups- go figure.  I recently (last summer) discovered that the 2f load produced exactly the same velocity as-had the earlier (1986 0-GOEX) 3f produced & that 2f was more accurate than the previous 3F gave me.  I then found that increasing the charge to 165gr., of 2F produced groups from 1" to 1 1/2" at the same range, of 100 meters.  I suspect a 48" twist would not produce such groups at 1,550fps, as-did the 165gr. charge.

 I do not know that as fact as I do not know from experience, what a 48" twist will produce in that calibre.  I would, however, very much like to test an 85" to 104" twist in that calibre, if bored to Forsyth specifications. The barrel would need to be straight or minor taper, 1 1/8" at the breech. I know a guy who can re-barrel my rifle, for me.

[David R. Pennington]

Without the caliber, and what the gun will be used for, answering your question is kind of like the old joke question” what’s the difference between a duck”.

 This kind of misses the point of my original question. I was wondering if anyone had ever tried to come up with a mathematical equasion (where you could plug in all the variables, such as caliber, average rb velocity etc.,.) and come up with a formula to calculate, at least in theory, what the optimum rate of twist should be.

[Daryl]

Nothing I am aware of for round ball guns. The Greenhill Formula is for conicals. 
This formula has been modernized  slightly to give more realistic #'s for today's higher
velocity rifles.
Note that this formula produced the 'slowest' twist that would work for that length of
projectile, not the optimum twist. 
The problem with having the slowest, barely stabilizing
twist for elongated projectiles, was that at extended ranges, accuracy fell off as the projectile
slowed.
This is also shown in Lt. James Forsyth's book, as he noted if one was shooting fairly close
ranges, a 12' twist was enough, but if wanting to range to 150 or 200yards, that an 8'8" twist
was the best. He was talking of "bore" rifles, not .45's through .58's which he though of as toys,
as they were totally useless in the pursuit of the game he chose to pursue.

[Dphariss]

The Greenhill formula is only a guide, it was intended for use for bulleted ARTILLERY according my reading. In bulleted small arms, shooting 3 caliber + long bullets, its about 2" slower than it could be. IE if Greenhill gives a 20" twist then use an 18. For round balls? They are so forgiving that I would not worry. As I stated above 48" is very good for most calibers in use today.  Remembering that this would be about one turn in the barrel of most "4 foot" (+-) barreled Kentuckys. I have never been able to figure out why modern ML barrels are twisted so slow. I would prefer 48" for everything I own other than the 16 bore rifle. Heavy balls have more rotational inertia and are more likely the "blow" the patch as they start to rotate. At 1600 fps a 48 in twist  barrel gives the ball 24000 RPM.  In an 80" twist its only 14400 rpm so the heavier ball is less likely to "blow" or "strip" the patch. Remembering how fast the ball goes from 0 to many thousands of RPM in the length of the barrel.

See  http://bulletin.accurateshooter.com/2008/06/calculating-bullet-rpm-spin-rates-and-stability/
Another formula is MV/twist in feet * 60 it was my solution before finding this site it gave the same answer.

Dan