Greenhill Formula for Rifling twist

Note that experience (not only mine) has shown that this formula produces a rate proper for an initial velocity of 1,000fps. i Experience has shown, from competition use, that if 1" is subracted from the above twist rate, the result will be the minimum rate of twist for an initial velocity of 1,200fps. Rates faster than this take care of velocity and length increases. Higher velocities require slightly faster twists as well. This formula was taken from the SPG loading manual by Steve Garbe and Mike Venturino. BTW - SPG is an excellent bullet lube for BP loads, muzzleloading or ctg. & will allow many shots between cleanings, provided the bullet is a black powdeer design, with deep, wide grease grooves. Examples are the #515141 Lyman, or 450gr. .50 Cal Lee which duplicates it. Others are the .457125 Lyman bullet for examples of proper BP lube grooves.
:1/. Bullet Length DIVIDED by it's dia.-(both in hundredths inch)
:2/. 150 DIVIDED by the result of step #1.
:3/. Result step #2 SUBTRACT bullet dia in hundredths inch.
:4/. Result step #2 - 1" = twist for 1,200fps velocity.
: Test- 1" bullet- grooved for grease, approximate weight 450gr. .50 cal.- .005" deep rifling, .500 bore..510 groove dia.
1/. 1.0" DIVIDED by .510" = 1.96
2/. 150 DIVIDED by 1.96 = 76.53
3/. 76.53 X .510 = 39"
4/. 39" - 1" = 38" twist for 1,200fps MINIMUM rate - Initial speeds of 1,400fps will require a twist rate of 36" for respectable accuracy to 200yds. Extended ranges will require faster rates of twist. Faster rates, up to approximately 24" will give increased accuracy & stabilize much heavier & longer bullets as well.
: Many shooters, involved with long range target shooting with BP ctg. and muzleloaders use the constant of 100 isntead of 150. Other's use figures in between these two constants such as 125. This increases the twist rate considerably, which is helpfull for very long range accuracy. Try it and you will see above length of bullet's rate of suggested twist increases remarkably. Because all of these constants actually work in practise, it is plain to see there is considerable leeway in FASTER twist rates, especially with low velocity, BP loads. Rates slower than given by the formulae will result in poor accuracy and instability to the point of tumbling in flight. Bullets 'on the ragged edge' of stability, require very little to cause tumbling or veering off course. They are also much more prone to wind drift, which can be considerable, even at ranges of only 100yds.
: I hope this explains how to figure required twist rates. Other formulae are available, which include the initial velocity, like the Artillery formula but are generally more difficult to work with than this one. There are some short forms, but the important criteria of diameter, length and velocity needs to be addressed.

 

It should be "Result step #2" multiplied by bullet dia. - as in the expample below the test.

 

[musketman]

OOPs- screwed up step #3.in text - It should be "Result step #2" multiplied by bullet dia. - as in the expample below the test.

Well now, that makes a difference... :haha:

Thanks for the correction...

 

[JKVirginia]

As a former math geek, can't resist simplifying that to an algebraic equation. (Math haters are warned to close your eyes now....

RR = BD^2/BL * 150(CV)

Where RR = Rifling Rate, BD = Bullet Diameter, and BL = Bullet length. (CV denotes 150 as a constant value, though as stated above some might alter their constant) So, to get your rifling rate, multiply 150 times the square of your bullet diameter, and divide by bullet length

Interestingly, in this format, it can be fairly easily reversed to calculate the ideal bullet length for a given rifling rate. IE

Since another fellow mentioned a 1:28 rifled barrel for a .50 Hawken, let's calculate his ideal bullet length

28 = .5^2/BL * 150
28 = .25/BL * 150
28 = 37.5/BL

Now, to get the unknown variable on the other side of the equation, we multiply both sides by BL and get...

28 * BL = 37.5
BL, therefore equals 37.5/28 or 1.33" which strikes me as a darned long conical or else a sabot.

To simplify that ideal-bullet-length formula, you could write it as...

BL = 150*BD^2/RR

:sorry: for the geekery, I have a soft spot for simple, elegant math.

Jon.

 

[Donny]

Once again, this formula is for bullets. How does it compare with round ball?? ::

 

[HardBall]

Once again, this formula is for bullets. How does it compare with round ball?? ::

You work the formula the same way. Since a round ball is, well, round You use the same number for diameter as you do length.

Remember to watch your decimal places.

 

[JKVirginia]

Donny,

In the case of a roundball, the diameter and length are identical, thus canceling each other out.

So your equation will look like... RR = 150 * BD

Ie, a .45 PRB (.440 caliber) will shoot ideally in a 1:66 twist barrel.

 

[Rat]

O.K. I'm a total math retard.

What is the ideal twist for a .580" bullet that is .7735" long??

Rat

 

[HardBall]

Assuming a bullet dia. of .58 and not .575 or some such, the twist would be 1 in 65" (rounded)

A round ball .58 would be around 1 in 86" rate of twist

Cool how the larger the caliber the slower the twist need be.

 

[JKVirginia]

Rat,

for your .580 bullet at .7735 long, the math would look like this:

RR = .580^2/.7735 * 150

So that's approximately a 1:65 twist at 1000fps or 1:64 at 1200.

Note that most of us shoot at somewhat higher velocities than this, so your barrel twist can be significantly faster without causing you any trouble.

 

[Rat]

Hey thanks guys. I really do have a math "deficit".

That's interesting because:

The twist of my 1861 is 1:66. The bullet is a 456 grain REAL, and is indeed .580".

It shoots that bullet really good, but so far, with longer bullets/slugs/minnies accuracy deteriorates. Yep it all makes sense. The math works out.

Don't know what my velocity is, but I use 90 grains of T7 under it. From eariler (sp?) discussions it's probably around 1200-1250fps, realistically speaking, although wishful thinking would put it around 1350fps or more. !!! I know, need to actually shoot it over the clock.

rat

 

[Keith]

I am not up to this math what is the ideal length for a 1:48 twist .50?
And how does that equate to bullet weight?
Now that I think about does the bullet design i.e. bearing surface of the bullet on the rifling affect the accuracy of this formula? (Does anyone understand that question?)

 

[Zonie]

JKVirginia: I'm probably wrong, but I believe the original formula gives the slowest twist which will stabilize a given bullet length at 1200 FPS.
Reversing the formula as you have, says the 1:28 twist will stabilize a .50 caliber bullet up to the 1.33 length if it is traveling at 1200 FPS muzzle velocity.

This does not preclude the successful use of shorter bullets with that twist rate. ::

geek can be good! ::

 

[JKVirginia]

Think you're right, Zonie... Also that if you're shooting at significantly higher velocity, a faster twist will do you no harm and probably some good.

I'm curious if there's a formula to calculate the maximum twist rate for a given projectile and velocity, since this calculates the slowest rate of twist that will stabilize at a given velocity

I've seen a lot of anecdotal evidence that roundballs in particular can be "overspun" to the detriment of accuracy (ie, firing them out of a 1:28 twist barrel or such)

 

Generally what happens with RB's when spun too fast, is that they strip in the rifling or "they cannot climb that steep a hill and therefore trip over the rifle" as Forsythe would have said. No wonder I had to read it three times to understand the English.
: If patched tightly enough to remain in the rifing grooves, they may osilate or gyrate around their axis until they've slowed enough as to become stable. The close range innacuracy may, however, have them so far off course, they are useless by the time they are properly stabilized.
: Fast twists do shoot round balls well, at reduced pistol-type velocities. They will shoot very accurately indeed, to perhaps 50/60yds.or evne more, given light wind.

 

JK,.... It'll take me a second ta "double check" yore figger'n, but I think yore "close"!! :crackup: :crackup:

YMHS
rollingb

 

JK- you're absolutely right about formulae and they are generally preferred by me as well.
: No, I hate math, except when it deals with my hobbies. I find I forget the various symbals if I'm away from them for a while.
: I do hope everone understands that the formula is for 1,200fps. Increasing the velocity, will increase the demand for a faster twist.
: There is some leeway here, of course - in quicker numbers, but the slower ones result in severe problems at longer ranges.
: Commercial .50 cal. barrels can be purchased up to 15" for the fastest rate, while Military BMG barrels have 1 in 10" twists. These two twsits are for high velocity rounds in the 2,00ps range and above.
: Barrels specifically for the BP ctg. rifles run 24" to 26" of twist and 28" to 32" for the Muzzleloading crowd. Note that Shilo uses 36" in their .50 Cal Sharps. Note also that these Sharps are not noted for their amazing accuracy, but will shoot in the 3" to 4" range at 100yds. Exceptional accuracy comes from the faster twists, including 24, 26 & 28".
: There is a learning curve to shooting BP and bullets. Experimentation is the rule here, not the exception. Paul Mathews hit the nail on the head with his experiments. His type of loads work exceptionally well in BP Ctg. guns and muzzleloaders alike, as he developed them for both. Not only does he shoot a muzzleloader, but also loads his Ctg. gun as a muzzleloader for increased performance.
: Given the same quality of barrel and bedding, a muzzleloader has the potential to be more accurate than a cartridge gun, as it doesn't have a loose fitting case holding powder and bullet, but has everything inline with the axis of the bore, and is using the most accurate of all propellents. No smokeless powder will give as low SD's as will normal black powder.