Since I already have the barrel, I solved to find the optimum bullet length for my rifle which is .730.

What shape bullet does the Greenhill formula assume?

Does anyone know of a resource that lists the overall length of various bullets?

The Greenhill formula was originally developed for field artillery. Would anticipate this would be be spitzer shaped artillery round.

Just found this nifty little calculator... http://www.uslink.net/~tom1/twistrate.htm

As kdub said, the Greenhill formula applies to artillery, not small arms. The critical factor is projectile aspect ratio, not profile. It makes no difference if the shape would correspond to a round nose, spitzer or wadcutter. Aspect ratio is the length divided by diameter, but I assume you already know that. It also was developed in the 19th century and applies generally to projectile lengths of no more than about 2-3 calibers.

It is my understanding that although the Greenhill formula was orginally applied to artillery, it is at least somewhat useful for calculating twist rates for small arms barrels. Do you disagree with this?

It is the aspect ratio I'm having trouble with. It seems like the shape of the bullet would have to make a difference if you were trying to come up with an optimum bullet for a given twist. I know things are not always as they "seem".

For example, my computed bullet length is .730. The bullets I'm trying to shoot are .490 long. They shoot great at 50 yards, at 100 yards they shoot a very occasional good group but mostly patterns.

What caliber and twist are you shooting? Also what bullet weight and configuration are you trying?

32-20 with 1-20 twist. Bullets are 85 and 100 grain Hornady XTPs and 100 grain Speer JHP, pistol bullets in other words. Very limited selection of jacketed .312 bullets.

Since I already have the barrel, I solved to find the optimum bullet length for my rifle which is .730.

What shape bullet does the Greenhill formula assume?

Does anyone know of a resource that lists the overall length of various bullets?


Lot of people have lost some faith in the greenhill formula, but it does predict a bullet length that is useable. Based on a round nose bullet and flat base...shuld be just fine with the flatish nosed bullets the 32-20 seems to be most useful with. It predicts bullet stability...that's to say bullets that cut round holes in paper...doesn't predict accuracy.

Yep...the detractors ae right...most barrels will also work with bullets a bit longer than what the formul predicts. that's really not the point of Greenhill, it's to predict the best bet for your first try...after that, if you've the urge to try one a bit loner, feel free.

And while I'm at it, length does seem to be the key. Sharp onts will be LIGHTER for the length...boat tails will be lighter for the length...flat noses will be a bit heavier for the same length, and wad cuttters would be about as heavy as possible for the same length....but in general, if it's .730" long, it will spin and fly point forward (accuracy is a whole 'nuther ball game, that's got a lot more variables than just being stable).

As far as cast bullets...Beartooth does list the length of it's bullets (but few other cast bullet suppliers seem to bother).

Looks like your caliber and rate of twist are way out of spec. Not even close in my book. I see you say you have a custom barrel. First my book shows the 32-20 in a .308 bullet diameter. And with a 1-10 twist using anywhere from 110 grain to 135 grain bullets. According to this you should be shooting 200 grain bullets. At least 200 grainers. I am curious where the .312 bullet diameter came from in your rifle since the norm is .308? Just looks like your bullet weight is way too light for a 1-20 twist barrel.

Looks like your caliber and rate of twist are way out of spec. Not even close in my book. I see you say you have a custom barrel. First my book shows the 32-20 in a .308 bullet diameter. And with a 1-10 twist using anywhere from 110 grain to 135 grain bullets. According to this you should be shooting 200 grain bullets. At least 200 grainers. I am curious where the .312 bullet diameter came from in your rifle since the norm is .308? Just looks like your bullet weight is way too light for a 1-20 twist barrel.


The norm is not .308"...and the twist is normally not 1:10. Think those numbers come from the MODERN .30T/C barrels...the older T/C Contender barrels were either 1:20 or 1:22 twist. The old "stadard" twsit was 1:22 and most 32-20's will be in the .311 to .313" range.

(BTW..T/C also made some modern 1:12 .30carbine barrels. Their old original T/C Contender barrels came with 1:20, which is the same as the military rifles).

So the normal for a 32-20 Rifle is 1:20 and somthing close to .311" (pistols are eiher 1:18.75 (S&W) or 1:14 (Colt).

Something is going on, consistent 1 1/2 moa at 50 yards should not become 10 moa at 100 yards. The bullets are not keyholing.

If your bullets are shorter than Greenhill calculates, you should be OK. If they're longer, you'll need faster twist. If they're shorter, the extra twist should not be a problem. Only time you get a problem is when you get very high velocity & very high twist that generates too much centrifugal force in the bullets so they self-destruct upon leaving the barrel. You sure won't get that in a 32-20!

Check your muzzle crown for damage. It may be upsetting the bullet as it exits the barrel, which can be a cumulative effect over distance.

There is no question that Greenhill is at least marginally applicable to small arms. The problem is that it predicts twist rates that are very close to the absolute minimum required, not the optimum. That is why the .44 M and .444 Marlin had a 38" twist, and frequently will not shot bullets heavier (longer) than the 265 gr. Hornady. I have a Marlin .45 Cowboy Limited with the 38" twist that will shoot 325 gr. WLN's, so there aren'y any absolutes.

The .32-20 originally was loaded with bullets from 100-120 grains. 100 & 115 became the standards until the 115 was dropped. Nominal bullet diameter is.311, with the normal range of barrels from .310-.314. S&W tends to the .314. Twist rates range from 16" (Colt), 18 3/4" (S&W) to 20" (Winchester). If you are having stability problems with bullets in this range, and a twist rate in the indicated range, then there is something else causing it rather than just the bullet/twist relationship.

Alk8944

Got me...that Colt 1:14 was probably for the .32CNP...was running on memory rather than a reference book. A Marlin 27 of mine had a 1:22 twist by measure, not sure what it was supose to have, but that's what was on her. that's enough for at least 115gr. FN bullets...anything heavier takes up too much case volume (if seated to an OAL that will cycle through the rifle).

Know that 147gr. FMJ military bullets won't spin in a 1:20 (a .30carbine in this case)...makes a very odd sound as the bullets tumble though the air...hard to describe the noise, but it's kind of spooky.

I need to actually slug my barrel and measure the twist.

Marlin's website says it has a 1-20 twist, it also says micro-groove barrel which is absolutely not true.

Greg Mushial's site lists a 1-16 twist for his 1894CL

Never believe what you read and only half of what you see.

Rifle doesn't have the 1-20 twist Marlin says, it is 1-24

Here is a link to a good write-up on the Greenhill formula:

Load From a Disk Discussion of Twist Rate and the Greenhill forumula (http://www.loadammo.com/Topics/July01.htm)

Kenk,

Darn your hide anyhow. You sir are a trouble maker getting this started! For years I have one of the first batch of 1894CL .32-20 rifles since it was new. One thing I never have worried about is the twist rate in a production gun, since there is nothing, short of re-barrelling, that can be done about it. I don't even know what the claimed rate was in those guns made in the 1980's, but probably just what they are claiming now. Well, the bottom line is you got me curious enough to check mine. With the length of the barrel it is necessary to visually estimate 1/2 turn, since the rifled portion is too short for even one turn in a 20" twist. The average of three tries comes close to 25 1/2"! That is why the convention when describing a twist rate, bore diameter, length, etc. is to use the term "nominal". That's quite a difference. Since anything to 32" or so should work just fine for the short bullets used in the .32-20 cartridge I am certainly not going to worry about it.

Something is going on, consistent 1 1/2 moa at 50 yards should not become 10 moa at 100 yards. The bullets are not keyholing.


Had the same problem with mine when shooting higher velocity loads with 115gr lead casts. When I dropped the velocity down, the groups tightened right up at 100yds.
The lighter bullets worked okay for me at all velocities. Might be too slow of a twist for the heavyweights at higher velocities??? :confused:
Light Trailboss loads were the best for me.

Good Luck,
whizzum

Guess I'm lazy.

That old Marlin 27 had a rough bore..still shot well, but tended to foul from it's long past, black powder, corrosive primers, etc..

So fire lapping came to mind as a way to reduce fouling and increase the time between must-do cleaning sessions.

thinking about it, decided to use tome 150gr. .312" bullets aleady on hand...didn't want to psh them fast, I already had them cast and ready, and didn't give ahoot about accuracy, just wanted to run a few dozen though with some lapping compound.

But being a gun-nut, had to fire some of them on paper. Keyholed and scattered to the four corners of the target paper. No way that 1:22 twsit was going to spin even a stumpy 150gr. bullet well....but it did the job in getting fouling under control (can't cure pits..but can at least knock the sharp edges off them and allow a resonable number of shots).

SOOO...

Got bored on day...have a lathe...had some 150gr. .311" Spitzers....decided to see how short i had to make them in order for them to not key-hole and shoot nice round holes.

Sorry...those notebooks are lost, and i don't remember the length. Do remembe the odd looking flat nosed jacketed bullets were 122gr. by the time they started forming groups and not patterns.

Check out: A New Rule For Estimating Rifling Twist, by Don Miller, Precision Shooting Magazine, March, 2005, PP 43-48. Miller had a separate article on Sir George Greenhill in the July, 2004 issue. From his introduction to the article:

“Greenhill’s old simple rule is tl=150, where t is the twist in calibers/turn and l is bullet length in calibers. Derived in 1879 for a football-shaped bullet at subsonic velocities, it estimates a “safe” twist in terms of bullet length alone and assumes a density of 10.9 g/cm³. It works much better than expected at modern velocities, with actual stability factors of 1.5-2 at 2800 ft/sec. However, it is not as good for Black Powder velocities.

There are also modern “fast design” programs that either estimate twist directly or are based on estimating twist from the “overturning moment” CMα. Public domain examples are Bob McCoy’s McGyro and Intlift. However, besides the length, they typically require detailed and hard-to-get knowledge of bullet shape, moments of inertia, and the center of gravity. Unfortunately they give conflicting results, and the conflicts are worse below about 1500 ft/sec.

Miller goes on to demonstrate a new estimating rule that, like Greenhill, considers length and not shape, but adds the inclusion of mass into the equation. It is based upon a 2800 ft/s projectile, and he shows that it is within 7% of meticulous calculations of a projectile, erring on the fast side for twist. He then gives a correction factors for velocities other than 2800 fps and for temperature and air pressure. He explains the military practice of designing the stability factor to fall between 1.5-2.0 under Army Standard Metro conditions so that then firing under different air density conditions, such as extreme cold, don’t make the bullet unstable.

A worthwhile read.

I have created a zipped Excel file that performs Miller’s estimate. You can get it here: Miller_twist_estimator2.Xls.Zip on Bigupload.Com (http://www.bigupload.com/d=BEB4C3CC) When you go to this site you have to wait 30 seconds and enter a scrambled key to download the file.

You may also see a red message that warns you are using an anonymous proxy server and that the site won't work with that. Not true. It works fine. It is just their advertising that doesn't work.

Nick

Thanks for the calculator, unclenick. What do you make of the "s" factors? I have read that best accuracy is often obtained with the minimum twist needed to stabilize a given bullet.

I tried some .800 long bullets this afternoon. With the starting load they keyholed nicely at ten yards. With a maximum charge they almost hit point on. The calculator computed an s factor of .80. I would need to get nearly 3,000 fps for a factor of 1.00.

Ken,

Keep in mind the calculator is, like the Greenhill formula, an estimator for choosing a barrel. The author admits it errs 7% on the high side for twist in its basic form, which is for 2800 fps. The formulas used to compensate for other velocities and for temperature and pressure are, in the author's own words "crude". So I am not surprised you have the error in s you do.

Actual s can be measured, however. Harold Vaughn (Rifle Accuracy Facts, Precision Shooting Publications, 2000 (http://www.precisionshooting.com/books.html)) points out that as s increases (Vaughn calls it GS, for gyroscopic stability factor), vertical displacement of point of impact due to side wind will also increase. He shoots a group in shifting wind with the sights fixed and gets a diagonal line of bullet holes. The horizontal displacement due to wind is the greater of the two. If you measure the angle off the horizontal line, he has a chart for converting that angle to the real s factor. For example, a 17° diagonal corresponds to an s of 1.6. I have put another Excel file here (http://www.savefile.com/files/3173770) based on Vaughn’s table.

Vaughn points out that reducing s slightly reduces the adverse influence of axially asymmetric flaws in the bullet. Getting it too low, however, costs you in how quickly damping of coning motion occurs. This damping is what recovers the bullet from initial exit angle error, whether caused by the bullet being tipped in the bore or by gas jetting unevenly around a poor muzzle crown.

Vaughn also demonstrates that in bullets accelerated too quickly into rotation, core stripping occurs (the jacket is de-bonded from the core and spins faster than the core). Running some bullets up in the 3200 fps range, he was able to get 25% or more of some bullet makes to strip. Since this is caused by rotational acceleration (actually, angular acceleration with respect to the bore axis), too fast a twist at a lower muzzle velocity could still cause it. It caused his groups to open up from 0.2” to 1.0”. I suspect a lot of people who think their bullets are “over-stabilized” are actually seeing this phenomenon. It suggest that for very fast bullets, particularly as bullet diameter increases in chamberings with with large powder charges, like the Lazzeroni’s or the Baer Magnum, you really want to use bullets with bonded jackets or you will have to go to a minimum twist.

Vaughn concludes that from the standpoint of stability and avoiding too much vertical dispersion from side wind and too much coning from an axial tilt, it would be about ideal to keep a bullet at an s of 1.4 from muzzle to target. This also limits the likelihood of bullet core stripping. Since rotation slows more gradually than frontal velocity as a bullet goes down range, a fixed s is seldom possible to maintain. Don Miller’s point that many people under-stabilize bullets intended for hunting in multiple weather and altitude conditions should also be born in mind. For a gun to be fired under multiple conditions, I think it would be better to aim for s=2 under normal conditions (the high end of the military range). Maybe higher if you know you’ll be in extreme cold at low altitude?

If you use the second Excel file to determine your real s from firing in wind, you can get a multiplier of difference between that and what Miller’s estimation says. Adjust your other condition inputs for this bullet by that factor. Just be sure that in your absolute worst conditions you stay above 1.0.

Nick

Interesting stuff, Nick.

If I'm understanding correctly an S factor of 1 is the minimum for stabilization. So in my case above, it's not an error. The formula gives an S of .80 and the bullet does in fact keyhole.

I'm going to have to study this second formula and wind deflection. I often have weird (to me anyway) groupings where I go from horizontal to vertical to diagonal stringing.

Ken,

OK. I misunderstood. I thought you were getting .80 and still were stabilized.

You are correct. s=1 is the breaking point by definition. In flight, if the bullet leaves the muzzle blast zone slightly tipped (Vaughn used 0.2 degrees in his example, as something not out of line with common reality) the bullet goes into a coning motion in which the tip is describing a circle whose radius is set by that initial angle and the spin rate. If s>1, then the circle gets progressively smaller as the bullet goes downrange. This is called damping of the coning motion, and Vaughn thinks it happens too slowly for best accuracy below s=1.4. When s=1 exactly, the coning never damps out. The circle just stays exactly the same size. When s<1, the coning motion actually grows as the bullet goes downrange, with the circle described by the tip getting bigger and bigger, and eventually it is big enough that the bullet catches the slipstream too hard to correct and is abruptly flipped sideways which initiates its tumbling end over end. It is not spinning fast enough to recover a stable attitude.

If you have group stinging that changes direction during firing in still air conditions, then is likely to be a heat related problem. The two most common ones are stock pressure shifting due to heat expansion, or you asymmetric barrel stress either in the barrel itself or due to the barrel shoulder contact with the receiver (ar barrel lug in a Remington, for example) being not perfectly even. In the former case, bed the rifle and cut away enough of the barrel channel in the stock so it doesn't touch the barrel anywhere, even when hot or when resting it on bags. For asymmetric barrel stress, cryo stress relief can clear it up. If you have a contact unevennes, then you need the action and barrel shoulder "blueprinted" to be sure they are true.

The only other type of trouble commonly causing stringing issues are in the gas systems of some semi-automatic rifles. In that case, send it to the factory with a complaint about the problem. In fact, sending to the factory can often get all these problems addressed. The gun companies typically respond positively to people who care about accuracy, though they can be slow getting the work done. I've had two guns reworked by the factory and they both came back shooting much better with no effort required on my part.

Nick