Greenhill Formula

[Kenneth L. Walters]

Could someone explain this to me?

[calvon]

The purpose of the Greenhill formula is to assist you in determing the proper rate of barrel twist for a given bullet. Here's the formula:

(150*Bullet Diameter)/(Bullet Length/Bullet Diam)

(all measurements in inches)

In plain English, first multiply 150 times the bullet diameter. Then divide bullet length by bullet diameter. Divide the second result into the first. The resultant number is the recommended twist rate to stabilize a bullet of the dimensions used.

[Kenneth L. Walters]

Bare with me.  I'm still confused.

RCBS bullet 45-500-BPS cast from linotype has a diameter of 0.4601 inches and a length of 1.3521 inches.  Thus to compute it's Greenhill value you could use three numbers, namely 150*.4601 or 69.015, 1.3521/.4601 or 2.9387 and, finally, 69.015/2.9387 or 23.48.

My Ruger #1 45-70 has a rate of twist of 1 in 20 so, I guess, this bullets should be well stabilized.

But what about SAECO #015?  Cast from linotype it has a diameter of 0.4641 and a length of 0.8202.  Here that would yield 150*.4641 or 69.615, .8202/.4641 or 1.7673 and, finally, 69.615/1.7673 or 39.39.

So what would happen here?  The rate of twist in my Ruger is half as fast (or is it twice as fast) as it needs to be to stabilize this bullet??  Really?

So the Ruger rate of twist for this SAECO bullet is WAY off BUT the Ruger shoots this bullet quite accurately.  Doesn't that suggest that the Greenhill formula is, well, useless?

[Castaway]

Use the bore diameter on your calculations.   That's going to be the final diameter when the bullet leaves the barrel.

[calvon]

Go to Google:

http://www.google.com/

Then punch in "Greenhill Formula" and hit the Enter key.

You can read for hours. When you get all done you will have learned that the Greenhill formula, like other formulae, give you some estimates, food for conversation, and not much else. You probably already know that most high velocity rifles have twist rates that run from 1 turn in 8 or 9 inches to 1 turn in about 15 inches. Low velocity stuff will usually have twist rates of 1 in 20 and some muzzle loaders with twists of around 1 in 40. Most modern rifles in the .30-06 class have twist rates of 1 in 10 or 1 in 12. I had a .250 Savage that had a twist rate of 1 in 14.

[Naphtali]

Okay, Greenhill's Formula can solve for two variables: rate of twist; and bullet length. And while it is, in the last analysis, an estimated solution, I believe you will find the calculated solutions are acceptable solutions.

Sir Alfred Greenhill developed the formula in 1879 to calculate correct barrel twists for conical artillery projectiles that were being developed.
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The formula is T x L = 150, where T is rate of twist IN CALIBERS, not inches; and L is length of bullet IN CALIBERS, not inches. You must do a conversion to have these numbers be in inches.
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Example --

The optimum rate of twist for Sierra’s .30-caliber 200-gr MatchKing would be computed as T x L = 150 where:

T=rate of twist
L=bullet length in calibers (1.405”/.308) or 4.561688311688
T=150/4.56
T=32.89 calibers

To convert calibers to inches, multiply by the bullet diameter. In this example, (32.89)(.308)=10.1 inches.

According to Greenhill’s formula, then, the proper rate of twist for the Sierra .30-caliber, 200-gr MatchKing is 1:10”.
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Greenhill's Formula will not inform you that your bullet is being overstabilized. Probably a shotgun-like pattern on your target will be a giveaway.

Also, you cannot use excessive velocity to stabilize a too-long bullet. What is "too long?" Dunno. But if axial rotation is excessive, a yaw with a curving side-to-side curving bullet's path occurs. This Magnus Effect is also what causes a curve ball to break. Doesn't happen in a vacuum, though.

[calvon]

I stand corrected. Greenhill DOES use calibers, not inches, as I incorrectly stated.

Apologies.javascript:emoticon(':roll:')

[FAsmus]

Gentlemen,

The purpose of the Greenhill formula is to assist you in determing the proper rate of barrel twist for a given bullet. Here is the formula:

(150*Bullet Diameter)/(Bullet Length/Bullet Diam)

(all measurements in inches)

In plain English, first multiply 150 times the bullet diameter. Then divide bullet length by bullet diameter. Divide the second result into the first. The resultant number is the recommended twist rate to stabilize a bullet of the dimensions used.

Sure, this is a good formula and I've used it to determine what twist to use in custom cast bullet barrels. Such things as proper twist have to specified in advance to choosing the correct rate for a given shooting task.

The constant, that being 150, comes from the origin of the formula, which is artillery shells moving around 1500 ft/sec and thus it works well enough for the "normal" cast bullet velocities we shoot a lot of.

If a fellow shoots Hi-Velocity jacketed the constant should reflect the change. That is if you're planning on shooting in excess of 2700 ft/sec change the constant in Greenhill to 270.

Then, if you're going to shoot (like I do) slow, heavy cast bullets in Buffalo Rifles at 1250 ft/sec or less change the constant to 120.

Most recently I needed a new barrel in 50 caliber for a long range rifle. I figured out what weight bullet would be needed, how long it would probably be and worked these numbers through Greenhill using 120 as my constant. The result indicated that I would need at least a 22 twist to keep the bullets point-on. I ordered a barrel in 20:1 twist.

The project is now complete and shooting. Bullet stability is perfect all the way out to 1000 yards, just like the formula (as modified) indicated it would be. It is very handy to know these things in advance.

Good morning,
Forrest