How accurate is the 'Greenhill' formula really?

[Grey Morel]

I was running some numbers for .22 caliber rimfire, as well as .22 caliber center fires, and the results of the 'Greenhill' formula just don't stack up:

Even when adjusted for the specific gravity of lead bullets, it computes a value of 1-14" for a standard velocity 40 grain rimfire - 2" faster than the majority of .22lr rifles. When you plug in the variables for a 29gr CB round, you get an even faster rate of 1-12" - 4" faster than average.

This seems odd to me, as my 1915 Favorite shoots single hole groups with both types, despite its 1-16" twist. None of my 3 Ruger 10-22s, with the same 1-16" twist, have eve had the slightest problem with these bullets either (I cycle CB longs manually).

Small bore center fires seem to suffer from the same inaccurat predictions to a less sever extent: My last .223 was a Ruger Hawkeye with a 1-12" twist whose favorite bullets were 62gr boat-tail hollow points; despite the 'Greenhill' prediction of instability, they shot MOA or better.

While recently researching the 22-250, nearly all those who shoot one in 1-14" twist say that 55gr, and sometimes even 60gr bullets will stabilize in there guns, despite the 'Greenhill' formula claiming that they wont.



Can someone clarify this for me? There are a LOT of "formulas" in the world of guns and ammo that are complete hogwash... Is this just another "ballpark figure" that doesn't really mean much in the real world, or does it just not work on smaller bore cartridges?

 

[rcmodel]

George Greenhill developed his formula in 1879 for use with field artillery.

There are possibly better methods to figure modern bullet designs with different velocity's then field artillery.

Check out this discussion:
http://kwk.us/twist.html

rc

 

[kragluver]

It works well for the velocity range it was intended for. Search the web and you'll find empirical corrections to the formula that apply to other velocities.

 

[Grey Morel]

Thanks guys.

rcmodel: That's actually the very same calculator that gave me these obviously erroneous results. Is there a better one?

When worked by hand, the 'updated' 1962 version of the formula produces a 1-13 twist for a 55gr bullet of .224 diameter as opposed to the 1-12 of the original. This splits the difference between the old calculations and the actual twist rate for most of the guns. It seems that the automatic calculator is set up to compute using the old version of the formula.

Am i correct in assuming that these numbers are the 'ideal' twist rate for a given bullet, not a minimum?

 

[rcmodel]

I didn't post it for the Greenhill calculator.

Scroll on down and read the article.
They discuss different takes on modifying it for better results.


BTW: It just occurred to me that pulling & measuring the exact length of an unfired .22 RF bullet is pretty hard to do. Without the exact length, the Greenhill Formula isn't going to work.

The heel-base soft lead bullet is crimped in the case, and no matter how you get it out, it is going to measure longer then it would if fired in a rifle chamber.

In that case, the pressure blows it out of the crimp and expands the hollow heel-base into the rifling.
A fired .22 bullet is shorter then it is after you pry it, kicking and screaming, out of a loaded round.

Further, the relatively slow rifling twist used in the .22 RF is a carry-over from when it was loaded with black powder. I think they used the slowest twist possible to stabilize the bullet in order to reduce black powder fouling in the rifling.
Apparently, it worked good enough that we are still using it.

rc

 

[Grey Morel]

I have several intact , un-deformed bullets of various calibers that I have recovered from various firings. I measured a recovered 40gr and a recovered 29gr with a micrometer to arrive at the values I used for input.

I did read the article.

 

[Clark]

The big problem for me is that bullets get less stable as they slow down.

75 gr Vmax, 1 in 14" twist, 33.5 gr W748, 6mmBR, 21.5" barrel, moly, 3051 ~ 3100 fps.

It shoots well at 50 yards, but sometimes key holes at 100 yards.

So if I have a bullet that shoots well at 100 yards [longest distance at my range], and then go hunting at 500 yards, I could be in trouble.