The physics of barrel twist

[TXAZ]

I understand the basics of twist in a barrel, and that there are differences in caliber, bullet mass and other factors.

Can someone point me to a detailed technical reference or discussion, including the physics and equations involved of how to precisely calculate the optimum twist for a given circumstance? I'm less interested in the "rules of thumb", but would rather understand the details. Does such a reference exist? Most of the references I've seen make assumptions based on the 1879 Greenhill rule of thumb. Calculus is ok.
Thanks.

[mete]

First problem is your idea that bullet mass is important .Actually bullet LENGTH is more important . You'll find then that a long pointed bullet requires tighter twist than a shorter round nose.
After all the formulas you might find a certain bullet ,powder ,velocity is preferred by a specific rifle despite theory.

[TXAZ]

Thanks mete.

My understanding was that ideal twist rate was dependent upon mass, ie FMJ vs. DU rounds.

I'm really trying to understand all the factors involved, not just the first order factors covered in the rules of thumb.

[44 AMP]

Its not the mass (weight) directly, but the size of the bullet that makes the difference. Since the diameter is fixed (bore size) heavier bullets must be longer.

Longer bullets need a faster twist rate to stabilize than shorter ones. I don't know the formulas or the math details, but I know the principles, and this is a constant. The LONGER the bullet it, the faster it has to spin to be stable.

One clear example is a 150(ish) bullet.
In a .30 cal rifle, it needs a 1 in 10" twist (or so..)
In a .35 cal rifle, (or pistol) the twist rate is 1 in 14" or 1 in 16"

Same weight (mass) bullets, but different lengths, due to bore size.

[Theohazard]

Originally Posted by TXAZ

My understanding was that ideal twist rate was dependent upon mass

Just to clarify this for the OP, the reason why people usually say that heavier bullets need a faster twist is just like 44 AMP said: Heavier bullets are usually longer for any given caliber. And considering bullet weight is listed on the outside of a box of ammo (but bullet length rarely is), that's the main variable that people use to determine the ideal rifling twist.

However, when the bullet is made of a significant amount of a material different than lead, it changes the density and messes up the length-to-weight ratio. For example, the steel in 5.56 M855 penetrator rounds is less dense than lead, so a 62 gr. M855 5.56 bullet will be a little longer than a 62 gr. FMJ bullet. And the chemicals in tracer rounds are even less dense than that, so a tracer bullet is quite a bit longer than a normal bullet, which is one of the reasons that the military uses the fast 1:7 twist for the M4/M16.

[jtmckinney]

You might start at Wikipedia < http://en.wikipedia.org/wiki/Barrel_twist >.

The work by Alfred George Greenhill though very dated is still porbably relevant, also at Wikipedia < http://en.wikipedia.org/wiki/George_Greenhill >.

I used to have a reloading manual based on Mr. Greenhills work that gave a pretty good history and explination of the formulas he came up with but I cannot find it, probably gave it to a new reloader somewhere along the way.

Hope this helps.
James

[SSA]

There are dozens of instances where a lighter bullet is longer than a heavier bullet of the same caliber. Flat base or boat tail, spitzer or round nose, lead core or copper, plastic tips, all make a difference.

For 2 bullets the same caliber and weight, the longer bullet requires a faster twist.
For 2 bullets the same caliber and length, the lighter bullet requires a faster twist.
For 2 bullets the same weight and length, the smaller caliber requires a faster twist.

JBM Ballistics has a list of bullet lengths, and a stability calculator, on their website.

[Jim Watson]

I am not qualified to discuss, but Bryan Litz is.
One of his books looks useful
http://www.amazon.com/Modern-Advance...=1418173521352

The popular version of the Greenhill formula is simplistic, especially considering that George Greehill was a professional mathematician.

The Wiki on the Miller Stability Formula includes the long form of Greenhill.
http://en.wikipedia.org/wiki/Miller_twist_rule
It references some other approaches.

[Clark]

When I was a little kid in the 1950s, my father was chief engineer at Pac Car Renton, designing guns and vehicles for the military.
I saw him drawing and doing math.
I asked what he was doing and he said that he was calculating the forces from the bullet traveling in the rifled barrel.

He later told me that I he used Hayes Elements of Ordnance to get the formula for recoil that considers the velocity of the center of mass of the gas to be 4,700 fps.

I bought a copy of that 1939 book [expensive]. I asked the moderator here at TFL if I can post things from that book. I was told I could do a page if I gave a link to where it can be purchased.

just chapter 8, exterior ballistics [where I got this page], off ebay [for cheap]
http://www.ebay.com/itm/EXTERIOR-BAL...item3ce4694bd7

[TXAZ]

Thanks Clark. That's right inline of what I'm looking for.
(I hope you don't outbid me

[Clark]

I found the whole book for cheap, but it took years.

What he gleaned from that 1939 book in 1950 is still paying the bills in 2014, and Israel is still dragging out the M55 to shoot up Lebanon. The M107 and M110 are scrapped or in museums.

[Nathan]

Elements of Ordnance