Let me start with a firm “I don’t know”.  But want to.

This rule of thumb gets thrown out every time there is a discussion on bullet length and when questioned answers are either silence, I don’t know, but it seems to work, or it’s a secret.

The Greenhill formula is tossed out there and it matches for some cartridges and bullets, but not others. Part of that is because the Greenhill formula does not take into account bullet shape or velocity, more correctly, spin rate which is determined by the combination of velocity and twist.

For most shooters velocity changes of a few hundred FPS, will not change spin rate enough to warrant a change in twist rate, but the Greenhill formula is basically accepted for velocities under 2800 fps. That is more of a 2000 fps spread.

The best way to compare the Greenhill formula and the rule of thumb 3 bore diameter length, no twist mentioned idea, is to lay out a table, or two.

Montana bullet works has done that for us. Link is here, screen shots attached below.
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Looking at the tables it’s easy to see many popular combinations seem to fit the “rule of thumb” pretty closely. 25 caliber, 86 grain bullet, .710”, 14 twist, aligns with a Lyman 85 grain bullet and early 25 caliber rifles.

But that cartridge was developed after the Greenhill formula was published in 1879. What about cartridges predating the formula?

One example would be the 38-50 Ballard. According to Grant in “Single Shot Rifles” it used a 255 grain bullet and a 1/20 twist. That also aligns well with the Greenhill formula. Apparently the “rule of thumb” also predates the formula.

Enter Sir Joseph Whitworth. 

In 1854, Whitworth was charged with creating a better rifle for the British army. The bullet needed to weigh 530 grains, charged with 70 grains of powder. He was provided a test facility of 500 yards where he hung tissue paper the track stability and trajectory of the bullet. He created what at the time was considered the first small bore rifle of 45 caliber.

To make weight, the bullet ended up at roughly 1.350”, or 3X the bore. For best accuracy through mostly trial and error, the twist rate, 1/20.

The Whitworth rifle, the most accurate in its day, prized by the Confederate Sharpshooters, who routinely shot the Union Army sharpshooters and officers at longer distances. The story of the rifle here.
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there are lots of general guidelines but not all work out.I've played alot with 30 caliber plainbase in 1-10 and 1-12 Twist and the above data is optimistic of bullet length for.stability.i find 1.25" at plainbase velocity is about it for not getting tippers.
While the x3 guideline is a bit conservative of what I've been able to shoot well.

David Minshall helped me date a Parker Hale 2 band years back.He's a wonderful fellow full of information.

marlinguy wrote on Jul 4^th, 2023 at 11:10pm:


exactly!

Dellet wrote on Jul 4^th, 2023 at 2:31pm:


the Greenhill formula is for 1" diameter x(some) length artillery shell with a 1R ogive.  For what it was derived it WORKS.  Applying it blindly to bullet "A" or bullet "B" will come CLOSE, but obviously not optimal.