Author Topic: Twist rate required to stabilize a bullet? (Read 1558 times)

PaulS · « **on:** February 14, 2003, 02:08:33 PM »

Donna,
I am a bit confused. The twist rate required to stabilize a bullet has nothing to do with it's center of gravity or its weight. It is the diameter and length that determines twist rate required so how does changing it's density or center of gravity solve the problem?

I understand the characteristic of high density at the nose being more stable (shuttle-cocking) but it has never been shown to work well in bullet technology.

PaulS

Donna · « **Reply #1 on:** February 15, 2003, 02:30:21 PM »

Hello Paul S,

I am sorry to say, and I say this with kindness, that you are wrong. Bullet stability, as you have stated, is related to its diameter and length but it is also related to the bullet’s density and balance or its center of gravity along its length.

The bullet’s weight only applies because as a bullet’s length increases, for a given diameter or caliber and material it is made from, it’s weight must also increase and vice versa.

Sir Alfred George Greenhill (1847-1927) in 1879 worked out a formula that bares his name, the Greenhill formula, simply put: Bullet Caliber (K ÷ (bullet length in inches ÷ bullet caliber)) = 1 twist in so many inches (round down to next whole number). There are a lot of things going on in this formula that are not readily apparent. The bullet length and caliber are apparent but the constant K is not. The constant K is the factor of bullet velocity but the entire formula was figured out with a bullet made of a copper jacketed lead core that has a general specific gravity of 10.9 and assuming a bullet is balanced along its length.

It has been shown that the bullet’s diameter is inversely proportional to the stability of the bullet’s spin. That means that as the diameter of the bullet increases the amount of spin required to stabilize the bullet decreases, provided all else being equal. And the bullet’s length is proportional to the amount of spin required to stabilize the bullet.

Changing the material that the bullet is made from, it is the change in density that one must look at in calculating the changes in the ballistic characteristics. By increasing the mass of the bullet that changes the moment of inertia of the bullet's axis, effectively making the bullet look like it is larger in diameter there by requiring less spin to stabilize the bullet.

It has also been shown mathematically and experimentally in the laboratory and in the field that as the point of balance moves to the rear of the bullet it becomes unstable requiring more spin to over come this instability. Likewise, the point of balance moves to the front of the bullet to the point of being over stabilized. An over stable bullet might sound good to have but it is not. As a bullet is shot from any firearm it is in an upward direction to the target, if it were not the bullet could never be zeroed or even hit the target along level ground do to gravity. An over stable bullet will keep this inclination angle of fire throughout its flight path and as the tangent of the flight path veers away from the inclination angle of fire more of the bullet’s profile will be exposed to the drag forces of air making the bullet fall short of its intended target or capability. Like all things in life there needs to be a small amount of instability for things to work right. The trick is to decrease this amount of instability to the lowest possible figure and still keep things working.

Further reading on this subject, I would suggest looking at my web site, “The Bullet’s Flight From Powder to Target” by F.W. Mann, “Hatcher’s Notebook” by J.S Hatcher, and others listed in my BIBLIOGRAPHY page.

I hope this helps.

Donna

Cat Whisperer · « **Reply #2 on:** February 15, 2003, 03:36:45 PM »

This raises a nagging question about the Greenhill formula. If I'm not mistaken the formula used a flat based bullet with an ogive of (something) coming to a point. Has any one done any serious tuning of the formula (like bullet manufacturers) so as to accomodate such features as different points (flat, hollow etc.) and different ogives (2, 3, 4, 5, 6, 7 caliber radii and so forth) and 'boat tails'?

I would assume that these would be the basis for the trajectory calculation programs out there.

Donna · « **Reply #3 on:** February 15, 2003, 11:18:25 PM »

Hello Cat Whisperer,

The flat base to boattail and the different caliber radii of the ogive merely shifts the point of balance and increases or decreases the bullet’s length for the same sectional density. The Greenhill formula just let's you know if your rifle twist rate is in the ball park for a certain length of bullet or vice versa. The Greenhill formula has nothing else to do with the trajectory of a bullet or it’s construction.

I don’t think that the bullet manufacturers are doing any more work with the Greenhill or any other rifle twist rate formulas as far as the construction of the bullet is concerned.

donna

talon · « **Reply #4 on:** February 16, 2003, 04:03:27 AM »

I have seen advertisements that show cutaway views of bullets. Some have a nylon tip, some have different thicknesses of jacket at the tip, the waist, and at the base, and some have a void or steel rod in the nose area. While these elements are advertised to benefit the striking power of the bullet, I suspect they have some effect on the accuracy (sectional density, spin rate perfection, CG, etc.) Can anyone clarify this for me?

Donna · « **Reply #5 on:** February 16, 2003, 08:42:34 AM »

I’m sorry Talon; I must be in an extra dense mod right now. What exactly is your question or possibly rephrase it? :?

Donna

talon · « **Reply #6 on:** February 16, 2003, 09:43:10 AM »

OK. Isn't all of this talk about accuracy? Isn't the formula you mentioned to bring sundry varitables into harmony? If so, isn't the sectional density factor currently based upon homogeneousness, in this case a simple (ie, plain) jacket, and a core of all like material? Doesn't a multithickness jacket and /or a core of 2 or more different densities require refactoring of the Greenhill formula? I don't think bullet weight and length are necessarly in a tradeoff condition if you can munipulate homogeneousness. With this thought in mind (and I could be wrong) and my observation that there are several bullet companies making bullets with different jacket and core constructs, I asked for someone to tell me if these products aren't achieving the same ends as would be in making a powdered tungsten bullet (for instance). Also, I have heard that "some bullets don't shoot well in some rifles. Then, if the hunter experiments with different manufacturer's bullets of the same weight and outward appearance, he is very likely to find one that is perfect for his rifle." Could it be that this mistery is explained by the way different bullets are put together?(here, the Greenhill concept rather than the stated formula comes into play). If this is correct, then there are same weight-length bullets available, by different manufacturers, having different in-flight characterics though this may not have been the intended purpose, one of which may just be perfect for the twist rate you are stuck with! So, Donna, what I was asking for is someone who has been studying this subject for some time comment on these observations and assumptions.

Donna · « **Reply #7 on:** February 17, 2003, 10:05:45 PM »

Hello all,

Talon, you are correct in that if one makes a bullet of different construction; partitions, extra thick base and/or wall thickness, multi-jacketed/multi-cores, mixing core materials, or stacking different multi-core material in a bullet, then one would need to recalculate the density of the bullet and use that figure to recalculate the end result of the Greenhill formula. That’s one of the beautiful aspects of ballistics; it can be very math intensive.

Make the bullet with whatever construction design that you want. Than measure the length of your bullet and calculate the twist rate using the Greenhill formula. The formula is already calculated for an over all bullet density of 10.9. Then calculate the bullet density that you just made. Than if the density is other than 10.9 recalculate the results of the Greenhill formula with the new average density of the new bullet.

Let’s say you just made a bullet with the construction designs you wanted and the bullet is a .308 and measures 1.183 inches long and its average density of 9.5.

In short a .308 bullet that is 1.183 inches long having a 1:12 inch twist according to the formula for a bullet with an average density of 10.9 and yours is 9.5. We would correct for the density by taking 10.9 dividing it by 9.5, which equals about 1.147368421. Then taking the square root we find is 1.071152847 and taking the inverse (1/1.071152847) is 0.933573582. This number is now multiplied to the 12 (of the 1:12) to get the new twist rate of 11 or a 1:11. It is more like 11.2 but we round down. But your rifle has a 1:12 twist. So, you replace some of the lead with a denser material to bring the average density of the bullet back up, then you recalculate. This might make change the bullet from a lead tip to an open tip bullet or it might stay the same.

One word of caution, do not take these formulas to heart. They are just approximations to get you in the ballpark. The formulas can be a good guide, if you match up the right formula to the correct situation.

Bullet construction is to produce a desired result usually at the target, with better expansion at high velocity, better expansion at low velocity, no expansion at all, a bullet that hold together, or a total disintegration on a semi-hard target. But I would suspect that no one gives much thought to the balance or the amount of spin it takes past a certain point. Making a bullet say with a plastic tip vice a lead tip would change the whole characteristics of the bullet’s dynamics. In this case it would through the balance more to the rear, lightening the sectional density without changing the length of the bullet causing the bullet to require more spin to stabilize and lowering the BC. The increase in spin could cause any imperfection in the bullet to be magnified that much greater.

Donna

talon · « **Reply #8 on:** February 18, 2003, 04:42:53 AM »

Donna.... You hurt my head!!! It'll take me a week to recover from all those numbers!!! Thanks for the guidance, though. Now, I'll study the subject a bit. Might as well: there's 14" of drifting snow keeping me indoors!

PaulS · « **Reply #9 on:** February 20, 2003, 12:56:37 PM »

Donna,
I hate to be a pest, and your math is easy for me to grasp so don't worry about teaching me something - I may be ignorant but I can learn.

Most bullets made today are designed with the center of mass toward the rear of the projectile - given

Most bullets are made of lead - exceptions being Barnes and Bitterroot

Do the copper bullets need more or less twist than the lead?
They are longer for a given weight and less dense

On a side note and purely as information only I shoot a 158 grain JHC Sierra pistol bullet out of my .358 Winchester (1:10) at just over 2500 FPS that groups to .33" at 100 yards - by all accounts this bullet should be way over-stabilized to be this accurate - Is there an explaination for this?

PaulS

Donna · « **Reply #10 on:** February 20, 2003, 03:37:26 PM »

Hello PaulS,

This is provided the caliber is the same. A solid copper bullet will need a faster twist rate than a copper-jacketed lead bullet of the same length. Now, if your asking, does a solid copper bullet of one weight need more or less rate twist than a copper-jacketed lead bullet of the same weight? Well, it takes more twist rate for a longer bullet and compound this with a lower average density bullet of the latter, yes, the solid copper bullet will require a much faster twist rate than the same weight of a denser material bullet like a copper-jacketed lead or even faster for a pure solid lead. :roll:

Pistol bullets are shorter than rifle bullets, in general. And it takes less twist rate to get a shorter bullet to stabilize. So, yes they probably are being over stabilized. But I never said an over stabilized bullet could not be accurate. It just means that you’ll need a bit more elevation to hit the target than normal and they do tend to be less accurate particularly at long ranges. If they were that accurate, just imagine how accurate those same bullets would have been if they were properly stabilized. :wink:

Donna

PaulS · « **Reply #11 on:** February 21, 2003, 12:01:11 PM »

Donna,
I really enjoy the numbers but you bring up an interesting point. Some bullets - ammo - guns are accurate in spite of all the "wrong" numbers. I guess there are rules of thumb that usually apply but as in all things there are exceptions.
It is interesting to me (that engineer thing) that I might be able to use a lighter compound to make longer bullets fire accurately in my single shot weapons. It would reduce recoil (to which I am sensitive) and increase range (higher ballistic co-efficients) with those weapons.
So, without investing a small fortune, how do I go about getting started in swaging lighter compounds into good bullets?

PaulS

Donna · « **Reply #12 on:** February 21, 2003, 04:18:28 PM »

Well, first off a lighter compound will decrease your sectional density and that means the BC will decrease, if all else being equal.

Now, for your question, “How do I go about getting started in swaging lighter compounds into good bullets?” After the swaging press and bullet die set, you can have a tube made that fits, the same thickness of, the jacket you are using and another punch needs to be made for the whole works. Dave Corbin gave me a price of just under $200.00 to add the needed tooling to do powder metal. Than you need to contact Metal Powder Supply houses for the powder metal you wish to use. But yes, you could make essentially a solid copper bullet on a regular swaging press with your present dies and very economically too. That would be a great way to save one’s shoulders.

So far, I have been able to cut my cost of lead wire in half, jackets by almost 60%, and powder tungsten by 50% just by shopping around.

A special note: Dave Corbin is of course not the only one that can make any of the swaging equipment I have or will have. I just have a very comfortable working relationship not just with Dave but the whole crew at Corbin mfg.

Donna