Rifle Twist Rates and Optimum Bullet Weight Question????

[cslinger]

Ok I understand that different twist rates favor different bullet weights.

Could someone explain to me why this is exactly. I mean I think I have a basic understanding but want some clarification.

That being said what would be the optimal bullet weight for a .308 barrel with a 1 in 10 twist rate. Optimal as far as accuracy is concerned, not lethality as I am thinking target shooting at this point not hunting.

Barrel length is 24 inches and while we are on the subject with modern barrels does length really play that big of a factor? I would think that as long as the barrel is long enough to stabilize the projectile that the shorter barrel would be stiffer and therefore more accurate. Is there really any need for 26+inch barrels.

Thanks
Chris

 

[Hkmp5sd]

HERE is an excellent article on twist rates by Clint McKee.

 

[Steve Smith]

That formula was NOT written by CM

It was written by Sir Alfred George Greenhill. Here is an article by Mark Brooks ( http://www.mamut.com/homepages/Norway/3/15/MarkBrooks/newsdet35.htm ) about the Greenhill formula. It is interesting that the largest name on Hkmp5sd's linked article is CM's while Sir Greenhill deserves the credit.



The Greenhill Formula is a simplified method for determining mathematically the amount of spin necessary to stabilize a bullet. It was worked out in 1879 by Sir Alfred George Greenhill who was a Professor of Mathematics at Woolwich and teaching the Advanced British Artillery Officers Class. It was considered satisfactory for bullets having a density of .392 lbs/cubic inch or greater. (Lead has a density of .409 lbs/ cubic inch, and copper has a density of from .318-.325 lbs/cubic inch, depending on the alloy) The formula is Twist required (in calibers) = 150 divided by the length of the bullet (in calibers). It makes no allowance for nose shape, considering round noses and all spitzers and spire points as the same. It does not work for bullets having a density below .392 lb/ cubic inch. All copper or brass solids and most heavy jacketed bullets have average densities below .392 lbs./cubic inch. Notice I said average, as the formula makes no allowance for bullets of variable construction, linearly. The formula was a shortcut and was useful at the time, as most bullets were roundnoses and were lightly jacketed, if jacketed at all. Because the math is simple, the Greenhill Formula has remained in use to this day. Just a few years ago I had an engineer at a major ammunition manufacturing firm quote me the Greenhill Formula as a method for calculating the spin required to stabilize a long, 10 caliber spitzer, 7mm 175 gr. , variable density, hunting bullet. Needless to say, he was not even close. The Greenhill Formula is accurate when used in the context for which it was intended, but many folks who use it today have forgotten, or never learned that context.

The actual formula is much more complicated It is Gyroscopic Stability (GS) = the spin rate (in radians per second, squared) times the polar moment of inertia, squared, divided by the pitching moment coefficient derivative per sine of the angle of attack times the transverse moment of inertia times the air density times the velocity squared. (My keyboard does not have all the correct symbols and that is why I wrote it out). For the bullet to be stable, GS > 1.0. This is actually a short version as the pitching moment coefficient component is a complicated calculation that derives the center of gravity and the center of reverse air pressure. The equation is basically calculating the linear difference between the center of gravity and the center of reverse air pressure on the nose of the bullet. The greater the difference, the greater the spin required to keep the bullet pointed nose forward. It used to take me about three days to calculate one new design by hand. My computer does it in about 20 seconds, now.

 

[Hkmp5sd]

That formula was NOT written by CM

No it wasn't. The article explaining it in relation to the AR-15 was. Stephen Hawking didn't write the E=MC^2 formula, but he's written several books explaining it.

 

[Steve Smith]

Hkmp5sd, please do not misread my clarification as being mean spirited to you. Such a retort was not really necessary.

CM is not to Sir Greenhill as Stephen Hawking is to Einstein.