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The Firing Line

Greenhill Formula

Uploaded on August 06, 2009

The Greenhill Formula is commonly used to calculate rifling twist. Bullet weight does not directly enter into the equation. It assumes for a given caliber the heavier the bullet the longer it will be. The formula also assumes a specific gravity of a jacketed lead core bullet of 10.9. A series of equations may fine tune this equation, but generally:
twist for velocities under 1800 fps = 150 times D squared divided by length = twist
twist for velocities 1800 - 4000 = 180 times D squared divided by length = twist

My question is, do modern bullets that are not lead core(10.9 specific gravity) require a change in the formula?

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from Reid Jones wrote 4 years 36 weeks ago

uhmmm....uhhh...ehhh...what?

+2 Good Comment? | | Report
from Happy Myles wrote 4 years 36 weeks ago

Reid, A perfect answer! One for you.

+1 Good Comment? | | Report
from 2Poppa wrote 4 years 36 weeks ago

It depends on what it is made of ...

Check out this link,as it has different types of metal that is part of the equation.

http://kwk.us/twist.html

+2 Good Comment? | | Report
from Jim in Mo wrote 4 years 36 weeks ago

I believe it does, can't tell you the formula, but it's proven lead core flies better than solid copper. JMO

0 Good Comment? | | Report
from Jeff Bowers wrote 4 years 36 weeks ago

I agree with Reid. How in the absolute heck does that affect anyone who isn't actually making their own rifled barrels?

How about a much cheaper and more universal method of dealing with different weight bullets... Fire a couple and see where they hit.

Like I'm going to trade my 1-in-16" twist for a 1-16.2" twist barrel.

0 Good Comment? | | Report
from Happy Myles wrote 4 years 36 weeks ago

2Poppa,
Thank you. The link you provided seems to answer the queation

0 Good Comment? | | Report
from shane wrote 4 years 36 weeks ago

Overstabilization is something I never considered. It's bad news if the bullet doesn't change angle as the trajectory does.

In other words, as the trajectory arcs, the bullet doesn't, it maintains the angle of the barrel.

I wonder how often this happens. Probably not very, but I could see those 45-50 grain bullets doing this out of a 1-7 barrel, that is if they don't get ripped apart right after the muzzle.

0 Good Comment? | | Report
from shane wrote 4 years 36 weeks ago

I think the specific gravity of the bullet is somewhat significant, but twist rates have more to do with bullet length than anything else.

0 Good Comment? | | Report
from MLH wrote 4 years 36 weeks ago

Thanks, Happy. Good link 2poppa. Always something more to learn. Will wake up in the middle of the night wondering about this. Would be nice to have the resources and time to test these things out.

0 Good Comment? | | Report
from ken.mcloud wrote 4 years 33 weeks ago

Jeff is mostly right, this stuff only really applies to people designing their own firearms.

Here's where I disagree with Jeff, I guess that the formula could come into play if you wanted to determine the ideal round for your particular gun. Jeff suggests that buying a bunch of rounds is "a much cheaper and more universal method of dealing with different weight bullets". In reality punching a few numbers into a calculator is free and buying a bunch of high end rifle rounds can be VERY expensive.

There are a lot of equations like this floating around in the engineering world. They hail from a time decades ago when math was done on slide rules the philosophy was "get it in the ballpark with math and then test it to get it right".

Since the equations were only intended to get "in the ball park" they are wildly oversimplified, don't accurately represent the factors they account for, and ignore many factors that have significant impacts. They were fine for what they were intended to do, but they don't have much place in a modern world of $5 calculators and lightning fast computers.

for just a couple of examples of how inacurate the greenhill formula is:

1) The mass of the bullet obviously does not scale well with bullet length. One need only hold a 200 grain .45 ACP round next to a 75 grain .223 round to see how ridiculous that idea is.

2) The issue of bullet composition is a BIG deal too. Not just in terms of specific gravity (analogous to density), but also in terms of the moment of inertia. The moment of inertia describes how hard it is to change the rotational speed of an object. A bullet with a high moment of inertia will "want" to keep spinning longer than one with a low moment of inertia, it will therefore be more stable.

3) think about how crazy it is that there are two different formulas for two different speed ranges. Obviously, bullets at 1799 fps don't behave entirely differently from bullets at 1801 fps. This is an artifact of oversimplifying two pages of calculations into something that can be done by punching a few numbers into a calculator.

+1 Good Comment? | | Report

Post a Reply

from Reid Jones wrote 4 years 36 weeks ago

uhmmm....uhhh...ehhh...what?

+2 Good Comment? | | Report
from 2Poppa wrote 4 years 36 weeks ago

It depends on what it is made of ...

Check out this link,as it has different types of metal that is part of the equation.

http://kwk.us/twist.html

+2 Good Comment? | | Report
from Happy Myles wrote 4 years 36 weeks ago

Reid, A perfect answer! One for you.

+1 Good Comment? | | Report
from ken.mcloud wrote 4 years 33 weeks ago

Jeff is mostly right, this stuff only really applies to people designing their own firearms.

Here's where I disagree with Jeff, I guess that the formula could come into play if you wanted to determine the ideal round for your particular gun. Jeff suggests that buying a bunch of rounds is "a much cheaper and more universal method of dealing with different weight bullets". In reality punching a few numbers into a calculator is free and buying a bunch of high end rifle rounds can be VERY expensive.

There are a lot of equations like this floating around in the engineering world. They hail from a time decades ago when math was done on slide rules the philosophy was "get it in the ballpark with math and then test it to get it right".

Since the equations were only intended to get "in the ball park" they are wildly oversimplified, don't accurately represent the factors they account for, and ignore many factors that have significant impacts. They were fine for what they were intended to do, but they don't have much place in a modern world of $5 calculators and lightning fast computers.

for just a couple of examples of how inacurate the greenhill formula is:

1) The mass of the bullet obviously does not scale well with bullet length. One need only hold a 200 grain .45 ACP round next to a 75 grain .223 round to see how ridiculous that idea is.

2) The issue of bullet composition is a BIG deal too. Not just in terms of specific gravity (analogous to density), but also in terms of the moment of inertia. The moment of inertia describes how hard it is to change the rotational speed of an object. A bullet with a high moment of inertia will "want" to keep spinning longer than one with a low moment of inertia, it will therefore be more stable.

3) think about how crazy it is that there are two different formulas for two different speed ranges. Obviously, bullets at 1799 fps don't behave entirely differently from bullets at 1801 fps. This is an artifact of oversimplifying two pages of calculations into something that can be done by punching a few numbers into a calculator.

+1 Good Comment? | | Report
from Jim in Mo wrote 4 years 36 weeks ago

I believe it does, can't tell you the formula, but it's proven lead core flies better than solid copper. JMO

0 Good Comment? | | Report
from Jeff Bowers wrote 4 years 36 weeks ago

I agree with Reid. How in the absolute heck does that affect anyone who isn't actually making their own rifled barrels?

How about a much cheaper and more universal method of dealing with different weight bullets... Fire a couple and see where they hit.

Like I'm going to trade my 1-in-16" twist for a 1-16.2" twist barrel.

0 Good Comment? | | Report
from Happy Myles wrote 4 years 36 weeks ago

2Poppa,
Thank you. The link you provided seems to answer the queation

0 Good Comment? | | Report
from shane wrote 4 years 36 weeks ago

Overstabilization is something I never considered. It's bad news if the bullet doesn't change angle as the trajectory does.

In other words, as the trajectory arcs, the bullet doesn't, it maintains the angle of the barrel.

I wonder how often this happens. Probably not very, but I could see those 45-50 grain bullets doing this out of a 1-7 barrel, that is if they don't get ripped apart right after the muzzle.

0 Good Comment? | | Report
from shane wrote 4 years 36 weeks ago

I think the specific gravity of the bullet is somewhat significant, but twist rates have more to do with bullet length than anything else.

0 Good Comment? | | Report
from MLH wrote 4 years 36 weeks ago

Thanks, Happy. Good link 2poppa. Always something more to learn. Will wake up in the middle of the night wondering about this. Would be nice to have the resources and time to test these things out.

0 Good Comment? | | Report

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