Twist rates and the Greenhill formula

Pumpkinslinger

I really wasn't sure whether to put this here or under "Gun and Firearms Discussions" but I figured that handloaders would be more likely to use the information.

I'm sure we've covered this before on this website but I've noticed some recent discussions on twist rates so I thought I'd add a refresher on the Greenhill formula. The formula was developed sometime in the late 1800s by Sir Alfred Greenhill, was a professor of mathmatics at the Woolrich Military Academy for British artillery officers.

This formula isn't a hard and fast rule because of differences in bullet shapes and velocities. However, it will get you into an acceptable range for twist. For velocities over 2000 ft/sec you can use a little slower twist and again for over 3000 ft/sec a little slower yet.

The formula is >> Twist = (150 * bullet-diamter) / (bullet-length / bullet-diameter)

As an example, I grabbed a Sierra 0.224" diameter, 63 grain Semi-pointed bullet off the shelf. The length of this bullet is 0.767".

Twist = (150 * 0.224) / (0.767 / 0.224)
= (33.6) / (3.424)
= 9.813

By the way, this bullet has given me my best group yet from my DPMS "Lo Pro Classic" AR-15 with a 1-in-9" twist.

There is a fuller explanation, along with more on bullet stability, in "Understanding Firearm Ballistics" by Robert Rinker.

Vince

Thanks Punkin...an interesting and useful addition to my knowledgebase on shooting info.

Cheers, Vince

SingleShotLover

Another interesting formula to assist in determining optimum twist rate is as follows:

180 divided by the length of the bullet in calibers multiplied by the bullet diameter.

Example: If a Hornady 55 grain 22-caliber SP (.224 caliber) bullet is .701" long

.701 (length) / .224 (diameter) = 3.129 (length of bullet in calibers)
180 / 3.129 = 57.53
57.53 X .224 = 12.89" (1 turn in 12.9 inches)

For anticipated velocities under 3,000 fps, the factor of 150 is usually more accurate than the factor of 180.

Not sure who the original author of this one was, but it's another way of getting to the same point. It's fun just playing with the numbers.

chambered221

SSL, This is a variation of the Greenhill formula.

It’s been determined that substituting 180 in place of 150 in the equation.
Thus taking into account modern day velocities.

PaulS

Rather than saying these formulas find the optimum twist rate it should be the "Minimum" twist rate. More twist is always better than less.

SingleShotLover

chambered221 wrote:

SSL, This is a variation of the Greenhill formula.

It’s been determined that substituting 180 in place of 150 in the equation.
Thus taking into account modern day velocities.

In my defense, when you are as mathematically impaired as I, if the numbers don't look identical and in the same order I don[t recognize it! Confused

jeh7mmmag · Member Joined: Dec 24, 2006 Posts: 223 Location: DFW, TX.

Pumpkin slinger
Thanks, Alway have a problem findin g the lenght of bullets.
Do you have any more source for bullet lenght.
James

Pumpkinslinger

James, some websites for bullet manufacturers list the length but not many. I just measured what I had onhand. It sure would be nice if more listed it! In fact, maybe an email campaign is in order.

jeh7mmmag · Member Joined: Dec 24, 2006 Posts: 223 Location: DFW, TX.

Good deal. I will see what I can get out of Sierra regarding length

jeh7mmmag · Member Joined: Dec 24, 2006 Posts: 223 Location: DFW, TX.

Look what I found. Looks like a pretty good listing.

www.shootforum.com/for...letdb.html

Pumpkinslinger

Thanks James! Great resource!