Bullet imbalance is one of the largest contributors to dispersion, and I knew about it for nearly 30 years. However, the problem was, that only in the last several years I have really understood exactly how it causes dispersion. Also, aside from making or buying perfect bullets, I couldn't fin a way to correct the situation. So, let's start out by understanding the problem.
right Figure 9-1 - Sketch showing how bullet imbalance causes a lateral drift velocity, which causes deflection of the bullet trajectory as it leaves the muzzle
Figure 9-1 demonstrates how bullet imbalance causes the bullet, when it leaves the muzzle, to be deflected. The sketch on the left Figure 9-1 side shows, how the Center of Gravity (CG), offset from the center line or geometric axis, is forced to rotate about the geometric axis. This is an unnatural condition. A spinning projectile will always spin about its principal axis and the principal axis always passes through the projectile CG, if free to spin so. Consequently, the instant it exits the muzzle, the bullet will start to spin about its principal axis and its CG. However, while the bullet is in the bore, the CG offset produces a tangential velocity component (Vt). When the bullet exits the bore, this tangential velocity component (Vt) will as a lateral drift velocity (Vd) be maintained. The lateral drift velocity direction will be perpendicular to the plane containing both the geometric and principal axes at the instant of muzzle exit, Obtained the distance, that the bullet will deflect, by multiplying the lateral drift velocity by the flight. time (FT). The equation that calculates the amount of bullet deflection at the target is
right Figure 9-2. Photograph of a .270" Bullet modified by drilling a hole to deliberately produce an exaggerated 0.00118 inch CG offset.
In the next section we will experimentally determine the dispersion radius for a 0.00118 inch CG offset. This exaggerates three to four times the maximum CG offset, to be expected in a production bullet. This CG offset value was determined by the diameter and length of the hole drilled in the side of the Bullet, used in the experiment that follows. Let's calculate the dispersion radius to be expected at 100 yards from this oversize CG offset.
s = 24*3.14159*(2900/10)*0.1*0.00118 = 2.58 inches
In 1909 Dr. Franklin Mann published a book (Reference 21) with an equation, that is equivalent to the here presented one. While his equation was correct and he tested it experimentally, his physical reasoning was flawed. However, this was a remarkable book for its time. Now we will experimentally evaluate the effect of CG offset.
Figure 9-3 - Plot of a target showing four 3-shot groups formed by indexing the bullets in 90 degree increments in roll angle. The bullets had a large CG offset c` 0.00118 inches. The experimentally determined radius of dispersion at 100 yards was approximately 2.5 inches.
We again turn to the "Olde Engineers Trick" to exaggerate an effect, to become measurable. This time we deliberately unbalance the 90 grain .270” bullets, by drilling a hole in the bullet side, that reaches exactly half way through. The hole is placed at the longitudinal CG position. Figure 9-2 chows a bullet picture, that has been modified to obtain a 0.00118 inch CG offset. Figure 9-3 plot shows the bullet holes from four 3-shot groups, fired with the hole-up, -right, -down, and -left at muzzle exit. The square symbols show each group’s center. The circular sketches near the group show the hole direction in the bullet sides, when they exit the muzzle. If you look at group l, you can see that the hole in the bullet points up at muzzle exit, which means that the bullet CG was below the geometric axis. With a clockwise rotation direction (right hand twist), the CG in group 1 translates to the left, that means the bullet will be deflected to the left, as it was. If you draw a 2.5 inch radius circle, you can see, it passes close to all four groups centers. In the previous section we calculated a 2.58 inches dispersion radius value. Roll angle is simply the rotation angle about the bullet geometrical axis (centerline). If you try this test, be sure to remove the extractor and the ejector and allow ample headspace between the bolt face and cartridge head. Otherwise you will rotate the cartridge in a random fashion to mess the results. Under ordinary conditions, the bullets deflect in completely random direction, only depending on the CG asymmetry roll angle orientation. This test confirms our problem diagnosis and determines the dispersion sensitivity to the CG offset amount. The question now becomes, how badly balanced are production bullets? Unfortunately, that requires a lot more work, but can be done.
| Figure 9-4 - Photograph of a device that
checks the static balance of bullets. The design is based on the
principle of the torsional pendulum. See Appendix C for complete
Two ways, to measure bullet imbalance, static and dynamic are. To measure static imbalance is the easiest, but least accurate and slowest method.
Figure 9-4 shows a static balance rig, based on the idea of a torsional pendulum, there two tightly stretched steel wires suspended the cradle, that holds the bullet. If there is a CG offset, the cradle will rotate, as the bullet is rotated and deflect a light beam, that shines alight spot on a screen. This light spot motion indicates the bullet CG offset amount. The nut on the screw on the cradle to, balances the device. The vane, hanging down between the two magnets, damps its rotational motion. Appendix C in detail describes to construct, calibrate and use such device. The results to measure the CG offset on box of one hundred 90 grain .270” HP bullets shows a bar graph in figure 9-5. Most bullets have a CG offset between 0.1 and 0.2 mils, while some of them are unbalanced by about 0.3 mil, can there be seen. This is for ordinary commercial bullets typical. Custom match bullets have about a third of this CG offset amount. Bear in mind, the 90 grain .270” HP is intended to shoot varmint and for that use certainly accurate enough.
|Figure 9-5 - Bar chart showing the results obtained in checking the static balance of a box of 100 caliber 270 bullets.||Figure 9-6 - Photograph of a dynamic balance device used to check the balance of bullets. It is based on the principle of the air bearing, where the unbalanced bullet spins inside the plastic cylinder producing an oscillating force on the two earphone diaphragms. This motion produces an oscillating electrical signal proportional to the imbalance. See Appendix C for complete description.|
Figure 9-6 shows a dynamic balance device. In this device, the bullet is run at 120 revolutions per second (rps) in an air bearing suspended between two magnetic microphones serve as electrical transducers. As the bullet spins, less touching the plastic cylinder inside surfaces, the air pressure between the spinning bullet and the cylindrical cavity walls force the cylindrical carrier to oscillate. This mechanical oscillation is transmitted to the two headphone diaphragms and converted to an electrical signal, that then on an oscilloscope can be observed. Appendix C also in detail describes to construct, calibrate and operate such dynamic balance device. The balance check results of the same previously staticly checked one hundred bullets shows Figure 9-7. The results are essentially the same, can there be seen. However, the dynamic balance data are smoother and probably accurater, than the data obtained from the static balance device. The dynamic device is much easier to use and more accurate, but much more difficult to make than the static balance device.
right, Figure 9-7 - Bar chart showing results of measuring the dynamic imbalance of the same 100 bullets used in the static balance measurement shown in Figure 9-5. Miss distance at 100 yards for a given imbalance is shown on the top scale.
The Figure 9-7 graph top shows the miss distance (dispersion radius) in inches for the corresponding CG offset. I developed a computer program that uses a random number generator to pick both the CG offset and roll angle orientation, and "fire" twenty 5-shot groups. Using this computer program with the same 100 bullets in Figure 9-7, with a 10 inch twist barrel, i found, the average group size would be around 0.7 inches. The maximum computed group size was 1.3 inches and the minimum group size 0.3 inches. This compares favorably with the last accuracy test fired in Chapter 8, so there is little doubt, bullet imbalance accounts for most remaining inaccuracy in the experimental rifle.
I hasten to point out, the measured imbalance on this particular bullet is typical for ordinary production bullets, that I tested. In fact, I found other manufacturers bullets worse. The most likely cause of bullet imbalance is the circumferential jacket wall thickness variation, that results from deep drawing a flat copper disk to form the jacket. In fact, I am amazed, bullets can in mass production be made as accurately, as they are. When you measure bullet jacket thickness run out at the same distance from the bullet base, you find circumferential variations consistent with measured CG offsets . The manufacturer states in their brochure, their hunt bullet jackets are held to 0.6 mil maximum and their match bullets to 0.3 mil” jacket concentricity. Since the jacket of these 90 grain hollow points is about 1/3 of the total weight, the CG offset is about 2/3 of the jacket concentricity. This means that the CG offset will be about 0.4 mil” for ordinary bullets and about 0.2 mils” for their match bullets. The 0.4 mil” imbalance agrees well with the measured data in Figure 9-7. The fact, lead to be much denser, (heavier per volume) than copper, of course, causes the CG offset. Some match bullets are held to less than 0.1 mil” CG offset. I tested 6mm 68 grain match bullets and got about 0.07 mils” maximum CG offset. If the bullets weren't balanced to 0.1 mil or better, even with a bench rest rifle, you would at 100 yards never be able to average 0.2 inch five shot groups. Match bullets are shorter than hunt bullets and made with thinner jackets, that, I guess, lets uniform thick jackets easier to draw. Unfortunately, the general purpose bullets jacket thickness must for reliable expansion characteristics on game animals be rather thick kept. Consequently, I doubt, any manufacturer may be able to produce ordinary hunt bullets significantly better, than they are now, unless somebody invents a better way to make bullet jackets. Before the bullet leaves the barrel, we need some way to compensate unavoidable, existing bullet imbalance.
The trick to solve the bullet imbalance problem would be, to allow the bullet before leaving the barrel to spin about its centroidal axis. The centroidal axis passes through the CG and is parallel to the geometric axis. If this could be done, the barrel would decrease the lateral drift velocity and the bullet imbalance effect. I tried three approaches to make a compensator. All three attempts failed.
The first approach for three inches distance to counterbore the muzzle. For this to work the radial clearance between the bullet and bore must be kept small (less than 3mils”). The reason for this small clearance is, the corrective effect depends on viscous interaction between bullet and barrel. I tried this, starting with a 1 mil” radial clearance, and the groups were enormous. I gradually increased the clearance. At about a 10 mil” radial clearance, the gun shot about as well, as it did before modification. After the muzzle blast shadowgraph tests, as we saw small partially burned powder granules traveling along with the bullet, I doub this method to ever work. After those tests I sectioned the barrel and found the counterbore to have been off bored center. So that may have doomed the test from the start. If anyone wants to try this, I suggest to grind piloted reamers in 1 mil” increments. According to computer calculations it should work, but I may have missed something in the physical model.
Another way to compensate the CG offset would be, to allow the barrel to move about the bullet CG, before the bullet exits the muzzle. I tried two different approaches. Neither one worked. One appeared to be work slightly, but as a result of thermal distortion drew straight lines of bullet holes. I tested the barrel on the bench and found, the muzzle warped with a modest temperature change enough to explain the drift.
While gave on this problem not up, I decided to go ahead and publish this book, because it is a difficult problem, that may not be solvable. Meanwhile all you can do, is to buy the best bullets to be found. Bullet manufacturers continually try to improve the quality of their bullets and, since this data were some time ago taken, the situation may by now have changed, also should be pointed out.
I would rather have a root canal operation on a tooth, than to make my own bullets. But on occasion I was forced to make some special bullets. Numberous articles appeared to make custom bullet. I take iissue with some recommendations. One of these procedures advises to lubricatie the slugs, before they are swaged into cores. Lead wire is cut into slightly heavier than swaged core slugs. The a mixture of vaseline and lanolin lubricates the slugs, although other lubricants were used . Lubrication is usually accomplished by rolling the slugs on a lubricant coated cotton cloth. Another way is to mix a known lubricant amount into a known solvent volume and then to dip the slugs into the solution. Drain the solution off and allow the solvent to evaporate. That leaves a thin uniform lubricant coat on the slugs. This seems to be the preferred method, because the coat should be thin and uniform. The core swage die then swages the lubricated slugs. There the excess lead bleeds off. Then a solvent degreases the swaged cores. Commonly use Methylene chloride, d since the EPA restricted trichlorethylene and l,1,1-trichloroethane use. The problem is, the solvent is usually over and over used. With repeated use, that procedure results the lubricant to increasingly concentrate in the in the solvent. This can result in a thin lubricant coat left on the cores.
To avoid this problem, some bullet makers degrease the cores by passing them through a series of three or four solvent containers, that are frequently replaced, so the last container remains relatively solubilized lubricant free. This technique requires a lot solvent, but is preferred over to repeatedly use the same solvent batch. To use lubricant, can cause potential problems. If lubricant is left on the cores, then during bullet spin-up cores may strip off the jacket, causing dispersion. Also, when the slugs are swaged into cores, could lubricant be trapped in the lead surface. This would in the finished bullet cause a gravity center offset. I never found to lubricate the slugs prior to swaging them into cores necessary. In fact, I first, by tumbling them in a water solution of detergent (Lemon Joy), clean and degrease the slugs, before I swage them into cores. Just to make sure the cores are clean, I also clean the swaged cores in the same manner. However, I made no custom bullets volume, that some bench rest shooters make, so for large volume situations may be a need to lubricate, that I'm not aware of.
In this business "Cleanliness is next to Godliness”. In fact, match bullets should be made in same type clean room that is used to produce electronic chips. All it takes, is a very small speck foreign matter either on the lead core or the jacket inside to cause the one flyer in one group, that causes you to loose a match.
At the moment jacket concentricity problem is a limiting factor. I
tried to correct jackets with machining less success. Maybe you could
use a boring tool in a super accurate lathe with essential zero (<
100 m inches) spindle runout to improve the
jackets, but I doubt that . Lathes this good exist in large shops, but
are expensive and difficult to keep adjusted. The best match jackets
come from a company called J-4 which apparently is connected with
Berger Bullets and are very good.
I think, I already mentioned the fact, that I accidentally found a small void in the lead core of a sectioned bullet, that would cause a large CG offset. A small piece slag, that was in the lead wire, probably caused that . Short of X-raying every core, I know not how one makes sure all cores are uniform. Of course, this would be prohibitively expensive production.
Another problem with hollow points is, during the point swaging operation, the core top surface may not stay flat and perpendicular. The coy may also bleed by the punch edge in the core swaging operation, causing a flash at the core to jacket junction. These problems offset the CG and principal misalign its axis. On commercial bullets that I sectioned I observed this problem. As you would expect, they shot very poorly. Reducing the amount of diameter reduction at the core front to leave a short (0.06") core projection, like to be seen in Figure 8-10, helps to alleviate this problem. Just don't make it too long. This problem lets you wonder, what in the throat during spin up happens to the into the rifling swaged core. Remains the core symmetrical? Nobody knows. You might be able to test this, when you proof the dynamic balance before and after fire, using a very soft recovery. I plan not to do it, because it would need enormous effort. Slender nose bullets perform well, may be, because less bullet length contacts the rifling. Some bench rest shooters seem to obtain superior performance from these slender nosed bullets, but I experienced that not.
Another problem with hollow point cores is, that extend too far forward into the ogive nose. To form the ogive nose, the jacket collapses in short segments and is usually not uniform thick. To swage the core into this forward jacket location could produce a CG asymmetry.
Some commercial bullet makers, as far as balance is concerned, turn pretty good match grade bullets out. In the last 30 years commercial bullets improved a lot. However, custom hand made bullet still win practically all bench rest matches. I guess the difference is jackets quality plus during swaging you discard a bullet "feels not right". An ordinary machine doesn't have such capability to feel.
If you decide to make your own bullets, be sure to use a slightly rounded heel at the bullet base. A sharp corner combined with the rifling lands can produce small fins, that the muzzle blast can break off. I have seen this in old spark shadowgraphs and recovered bullets. Such will cause an asymmetry. As far as I am concerned, unless you need to try a new idea or you want to do it for the "fun" of it, to make your own bullets, is a loosing proposition. It would help to be slightly crazy!
|Here comes the final accuracy test on the .270”
14" twist barrel experimental rifle. In the last test in Chapter 7
(Table 8), using 90 grain hollow point bullets with a 10" twist barrel,
we shot 0.804 inches average group size at 100 yards. With this
chapter’s theory we also estimated, if bullet imbalance was the only
error contributing to dispersion, the .270” should average about 0.7
inches at 100 yards. Consequently, with no other rifle errors
contributing to dispersion, with the 14" instead of a 10" twist barrel,
we should expect 0.7* 10/14 = 0.5 inches average group size. The 270
with a 14"twist barrel test results are shown in Table 11.
I think this test shows bullet imbalance dues most dispersion left in this experimental rifle. I also believe, with match grade bullets and a 14" twist barrel this gun would at 100 yards average around 0.2 inch groups. At this time unfortunately .270” match bullets are unavailable. This concludes our work on the .270” sporter.
Above was taken from the following Book, Rifle Accuracy Facts Written by Harold R. Vaughn . If ypu would like to improve your shooting, i strongly strongly advise to buy, read, understand Vaughn's Book, then act accordingly.
Rifle Accuracy Facts
Written by Harold R. Vaughn This book makes the
definitive study, made over a number of years, by a leading research
scientist, on the subject of why some rifles shoot very well… some
shoot fairly well… and others shoot poorly. C1278 (Wt. 2 lbs.)..$29.95
by Duncan MacPherson
Rifle Accuracy Facts>
Vaughn, Harold R.
Precision Shooting, Inc.
222 McKee St., Manchester, CT 06040soft cover $34.95, hard cover, $39.95 +$3.50 S&H 290 pages, many photos, figures, and graphs
A book review in V3#3 of the Wound Ballistics Review and a comment on this review in V3#4 brought up the issue of a good book describing exterior ballistics for the general reader. I said I didn’t know of one then, and Rifle Accuracy Facts is not devoted to this subject, but will fill this purpose for many readers. With this as an introduction, we will go back to a standard review format.
Harold R. Vaughn is an engineer whose distinguished technical career was spent at Sandia National Laboratories in flight dynamics and aerodynamics. He retired in 1986, and devoted his considerable technical skills to an orderly analysis and test program to understand and demonstrate what factors contribute to making rifles shoot more accurately. I called Mr. Vaughn to discuss some technical details not relevant here, and we had an interesting discussion about small arms and technology. We both deplore the fact that modern engineering capabilities and techniques are so little used by those interested in small arms. There is little hope that this situation will be rectified anytime soon by the firearms and ammunition manufacturers, who are forced to be very bottom line oriented in this very competitive market. The amount of money required to run a laboratory that could revolutionize understanding of a variety of small arms features is relatively modest, but there is little hope for anything like this anytime soon. The few government facilities that might fund this work do not have staff with the required technical skills, and there is no obvious other source for the money. As a result, the primary source of advances in understanding is talented individuals who are willing to devote their own resources and efforts to this end for the satisfaction of accomplishment. That is what Mr. Vaughn has done in the area of rifle accuracy, and fortunately, he has not only done this well, but has written it up well in Rifle Accuracy Facts.
Readers should be under no illusions; Rifle Accuracy Facts is not light reading, and not for anyone who thinks Guns and Ammo is a technical publication. Rifle Accuracy Facts is a superb book; most attentive readers will understand all or almost all the material in the main text. On the other hand, almost all readers will find that they have little or no interest in most of the appendix material (about 20% of the total) even though this will be invaluable to readers who wish to do sophisticated experimentation on their own or who are interested in detailed equations. The bulk of Rifle Accuracy Facts is a detailed description of Mr. Vaughn’s experimentation in making rifles shoot more accurately. This work is a true technical advance in understanding this issue, and the description of this work is interesting in its own right. Anyone seriously interested in rifle accuracy should own this book.
Anyone who wants a solid understanding of either interior or exterior ballistics should get this book even if they are not interested in rifle accuracy. The descriptions of interior and exterior ballistics (one chapter each) are both precise and understandable without forcing the reader to follow the details in a lot of equations. The important equations are there for readers who want them, but can be skipped without losing comprehension for readers not technically oriented. Each of these chapters could be “puffed up” to longer length and some readers might prefer this, but the information is efficiently imparted in the chapters as written and I personally prefer this approach.
Perhaps the best summary of the contents of Rifle Accuracy Facts is the chapter description given on the contents page of the book:
Appendices: Accelerometer design, barrel vibration computer equations, bullet balance device design, six degree of freedom computer equations, tunnel range construction, rail guns, shadowgraph testing.
As the chapter descriptions indicate, most of the material in Rifle Accuracy Facts is related to rifles, not handguns. However, those interested in handgun interior and exterior ballistics should not despair. The material in chapters 2 and 10 uses rifle bullets as examples, but the principles also apply to handgun bullets.
Reviews are supposed to describe the book’s shortcomings, but I found only two small faults, neither important to most readers for different reasons. There is a typographical error in the equations for F1 and F2 on page 187 (exponent ˝ on wrong bracket), but this will be recognized by most people attempting to use this equation and is of no importance to anyone else. The second topic is in the Chapter 11 discussion of “moly coated” bullets (the relatively recent technique of coating bullets with molybdenum disulfide and carnauba wax). Vaughn has done testing of some claims relative to the effects of moly coating bullets and has very interesting comments on several issues, but is essentially neutral on the effects of extended barrel life because he hasn’t proved this. This is a good example of how careful Vaughn is in making claims, a stance that many others in ballistics would do well to emulate. The careful distinction Vaughn makes throughout the book between what he has demonstrated and his speculations is laudable and very evident here. However, in this instance the advantages of properly moly coated bullets in extending barrel life have been established beyond reasonable dispute by many others, and Vaughn’s “could be true” is unnecessarily weak even though he hasn’t personally verified this. Again, readers who care will know this, and it doesn’t matter for the others.
Rifle Accuracy Facts is going to be recognized as a classic in years to come, you will be glad you got it.
Duncan Mc Pherson
From: "Sam Nichols" <firstname.lastname@example.org> To:
<email@example.com> Sent: Sunday, January 20, 2002
5:22 PM Subject: Re: [Fullbore] Bullet imbalance
Lutz and Larry, Have either of you or any listers used the Vern Juenke's International Concentricity Comparator (I. C. C.) According to the evaluation, that is quite capable of detecting bullet imbalance in bullets making trying to compensate for the imbalance unnecessary. I have never seen or used this device but you can see the evaluation in it's entirety at: http://www.shootingsoftware.com/reloading.htm Below is a copy of the text the evaluation of this device by the people at: Recreational Software (http://www.shootingsoftware.com/index.htm) A very interesting site with evaluation of reloading equipment and techniques and design of better devices for reloading.
It doesn't actually x-ray your bullets but Vern Juenke's Internal Concentricity Comparator (I. C. C.) seems to. This device uses sonic pulses to look "inside" bullets for concentricity problems
caused by voids and jacket irregularities. One past International Heavy Rifle Champion says, it is the secret to shoot 6 inch groups at 1000 yards. If you do everything else correctly, and still get an occasional flyer, it may be your bullets. Weighing bullets can not tell you if an entire box was made from jackets with walls that are thin on one side. But, if the lead core is not centered they can fly as bad as the worst out-of-round projectile. Top competitors with one of Vern's machine often use only 40% of the best hand swaged bullets for serious work. You may find only 10% of the less expensive or production bullets you have been using measure to "Golden BeeBee" standards, with as many as 1/4 or more actually measuring as "junk. Sam