Greehill Formula

[Halfcock]

In Paul Matthews book "Cast Bullets for the BPCR", he devotes a chapter to the Greenhill formula. Apparently the formula works well for .45 cal rounds with cast bullets which in the .45 X 2.1" with a 500+gr. bullet would be well below 1800fps. In smaller calibers such as the .38-55, the formula falls apart using a constant of 150. In the case of the .38-55, he used a constant of 125 and it worked well with a velocity of 1300 fps and a bullet length of 1.363". So it may be that the aspect ratio (dia / length)
has more than a little effect.

My ballistics book only gives the formula about one-half of a page and advises not to push it too far. The book does mention that Professor Greenhill was at the artillery college, Woolwich during the last two decades of the 19th century.

Using my own rifle, Shiloh of course, with a bullet length of 1.430" ; the bullet length in calibres is 1.430/.458 = 3.122 then 150 /3.122 =48.046 which is the twist in calibres. In inches the twist would be 48.046 X .458 or 22" so the bullet should easily be stabilized in a rifle with an 18" twist.

[Todd Birch]

Hey Halfcock

We'll give Paul Matthews the last word on the topic. His book has yet to be added to my library. It will be 'ere long.....

This business of re-discovering what was once common knowledge is akin to re-inventing the wheel.

The modern trend is to heavier bullets and faster twists to stabilize them.
What are we doing differently or what has changed since professor Greenhill's time?

Todd

[Jim Watson]

I have read that Greenhill was working with light artillery... which does not include even a .50-90. If you have to take a known case and work backwards to get a new constant for that one condition, the formula doesn't seem very useful to me. The shooters are learning how much twist it takes for a given length bullet in each caliber by experimentation; at the cost of some molds and barrels.

[RMulhern]

I cut and pasted this from Yahoo:

The number 150 is a constant used by Greenhill and works well at velocities in the vicinity of 1500 fps or greater. At 2800 fps the constant can be changed to 180 with good results.

Note that it is bullet LENGTH, not weight that is important. Greenhill works well with all lead/lead-alloys commonly used for bullets.

One must understand that Greenhill is derived from experience as well as from the calculated laws of physics. As such, it is a highly simplified, albeit useful, equation. Greenhill was worked out many years ago and is quoted in the British Textbook of Small Arms (1929). To the best of my knowledge, it was not used for the very low velocities that are representative of pistol bullets. The supposition that the constant decreases with veloc- ity is probably correct but only trials would prove that one way or the other.

There is no "ideal" bullet for any given barrel caliber and twist. Fortunately, many bullet type/velocities will work. Greenhill merely simplifies the starting point and gets one into the ball park. Once in the ballpark there are other factors affecting accuracy that become much more influential than small changes in bullet characteristics and velocities. Except for the extremely exacting requirements of bench rest shooters, and very long range shooters, an "over-stabilized" bullet (rifling twist faster than the minimum required for good stabilization) will shoot as well as a theoretically critically stabilized one.

Barrel twist is usually chosen for the longest bullet that will be fired in that gun. Accordingly, the military has fairly recently changed their .223 barrels to a 7 1/2" twist from a slower one for the newer, longer and heavier bullet that has become standard issue (68 grains, I believe).

For instance, Greenhill shows that the maximum .308 caliber bullet length for a 12" twist, using k=150, to be 1.2 inches. If a bullet longer than this is used, it is possible that it could become unstable. A k of 150 is not magic but has been empirical- ly demonstrated to be a reliable optimum.

Incidentally, groups at 100 yards are not necessarily indicative of long range accuracy, especially if your bullet length to twist relationship approach the critical. The gyroscopic (dynamic) stability can fall off at long range and what worked well at 100-200 yards can go wild at long range. I have (unintentionally) demonstrated this to myself on a number of occasions. It happens quite frequently with handguns because of the greater bullet length and velocity ratios that are commonly encountered.

I have been working with some ultra-light loads in a 7mm Remington Rolling block and loads that shoot about 1 inch at 25 yards go to about 8 FEET at 50 yards -- really enlightening! At these low velocities one can watch the bullet start out straight, then, as it's dynamic stability wanes, go into a dramatic curve. Kicking the velocity (therefore the rpm) up a couple of hundred feet a second increases the accurate range.


I presume that T is the minimal twist? So if my rifle has a twist of 10, and considering the bullet I'd be shooting, Green- hill's formula comes up with a T of 12, then every thing is ok.
Yes.

A T (twist) of 12 means 12" bore length per rifling revolution. In your rifle, the bullet will spin 360 degrees for each 12" of linear rifle barrel that it traverses. A twist of 10 is a faster twist; one revolution for each 10". Within reason, a twist that is faster than necessary will not appreciably effect stability (accuracy). This why the rifling is set up for the longest bullet that is likely to be fired in a particular gun.


What's meant by "how long a bullet will stabilize in a given twist"? You mean how long until it's stable, or how long till it's not stable? What unit is 'L'?
L= bullet length. It is the bullet length that is important - not its weight. A pure lead cylinder would be stabilized at a slower twist than a bullet formed of the same material and weight but with a pointed nose.

If one has a burning interest to pursue the understanding of this very complex subject, he can read the American Rifleman article by Col. E.H. Harrison, pg. 50, July 1962. For those who have the time, facilities and competence, Col. Harrison's article will give all necessary instructions to carry out meaningful experi- ments.

For those who would merely like to read a little more on the subject, the following Cast Bullet Association journal, The Fouling Shot, now called The Cast Bullet, articles are interesting and useful.

[Todd Birch]

Hey Sharpsman

That was a wonderful dissertation! I was able to follow the thread of your logic quite easily.

Lets open another can of worms.....ballistically speaking......bullet indexing.

At a Cowboy Action Shoot, the longest range open to us was 200 yards. Everyone was unlimbering their lever action and single shot .45-70s, etc., when a lady who uses a cane to walk asked if she could play.

When assured that she could indeed play with the men, she produced her Marlin .357 carbine and a box of factory round nosed 158 gr ammo, velocity 750 fps, maybe.
She sat down, feet over the bank, refusing the offered x-sticks as she had never used them before. She fired and the spotter told her that her round was low. She upped her rear sight the suggested number of notches and fired again - ding!
She had 8 more rounds to fire and made several more hits. The spotter was utterly amused and amazed that he was able to follow the flight of the bullet down range as it travelled in it's spiral. He was able to call her shots after a while, depending upon where he last saw her bullet in flight.

This suggested that had her bullets been indexed in some manner and loaded accordingly, she would not have had a circular group, but a more concentrated cluster.
It also suggested thatbher bullets were travelling in a 'cone' of flight, if you will.

Whatcha think?

Todd

[Omaha Poke]

Todd, while spotting for a number of people, I have watched the bullet as it flew in towards the target, or into the target. That is fun and is entirely dependent upon the existing lighting. Last year at the Quigley, I was able to follow the persons bullet that I was spotting for plus 3 other shooters during the same relay. The shooter directly to his left, and the two directly to his right. There were 4 other shooters on the line, and I was unable to watch their bullets' flight. Lighting is everything!

I doubt that indexing would have done much to improve this lady's group since she was shooting basically off-hand from a sitting position. I may be wrong, but I think the only way to tell whether it would have helped her or not would be for her to shoot off a bench rest. Off hand has too many variables. That is just my oppinion. It is good to hear stories like this, and I hope this lady keeps shooting, good on her. Randy

[Todd Birch]

Hey Omaha (or is that Poke?)

She was pretty steady resting her elbows on her knees in a most unlady-like position for a proper Victorian lady. Good thing she had on a long skirt.

My best shooting position is sitting, slung up with a GI leather sling, especially in rapid fire. My Garands really peform this way, far better than I can get from them bench shooting.

It is also my preferred position for a hunting shot. I shoot off hand only reluctantly and never beyond 50 yards. I like my game to drop in it's tracks, not leave me to follow them.

Todd

[RMulhern]

Todd Birch

<<bullet indexing. >>

My bullets are good! I just index the cases!!

[Todd Birch]

Tsk, tsk, tsk, ...."whatever would the Queen think?".....

All that trouble preparing cases - flash hole reaming, deburing, checking case wall concentricity, weighing cases, trimming.....and not marking bullets so that they can also be indexed.......

I'm shocked, shocked.....

Todd

[RMulhern]

Todd Birch

Yep! But.....look what they do:

http://f1.pg.photos.yahoo.com/ph/mulher ... m=8742.jpg

I'm a grinnin!

[Todd Birch]

Yeah, yeah, yeah....humble, too!

Your reloading room is entirely too tidy.

I want something done about it immediately.

Todd