Bullet Hardness, Chamber Pressure And Accuracy

     Theories that bullet hardness and chamber pressure must be matched in some precise and scientific way to allow accurate and leading-free shooting have been presented by some authors and repeated by many others since 1984.

     To find out about these theories, I searched the literature back to the sources of the theories and tested the theories against pressure-hardness combinations used successfully.

     I concluded that these theories are contradicted by data. It is certainly true that higher velocities require harder alloys in rifles. But the notion that best accuracy is found at a specific pressure/hardness intersection and diminishes as hardness is increased or decreased from that junction is not borne out by the data.

     If it were true that this pressure-hardness relationship were important for accuracy, then a means of testing alloy for hardness and another means for estimating maximum chamber pressure would be necessary.

     Here is a table showing the results of hardness testing of bullets I cast out of one pot of wheel weights in a 2 cavity mold on 1/1/2006-one cavity with a dot and the other without. Six bullets were sent to each of the volunteer testers who tested for BHN on 1/11/2006.

     The variation from bullet to bullet, cavity to cavity and tester to tester suggests that precise estimation of BHN using reloader-type testers is not possible.

 ("Joe: My LBT BHN tool did indeed measure those numbers (above) even if they were grossly different from the others in the test. I annealed them and got the same averages of the group. I suspected that the bullets had been water dropped even if they had not been; they measured a typical wide range of hardness’s that many water droppers tend to get. That is why I no longer water drop them and rather choose to oven heat treat them for consistent BHNs. Bill McGraw )

     Then there is the question of pressure estimation.

     I think that I understand that velocity is a function of the area under the pressure curve-it's not intuitively obvious to me that the relationship is linear. I imagine acceleration varying during the travel of the bullet.

     "Quickload" is a computer program that estimates pressure and velocity upon entry of load data.

     Quickload seems to accurately predict velocity-we can easily measure velocity.

     It is not clear to me that the program accurately predicts maximum pressure, mainly because we don't have the equipment to measure pressure and check the Quickload predicted values.

     It does not provide for inclusion of primer type or brand in the calculations.

     Handloader, August 2005, "Velocity and Pressure" by John Barsness.

     The author cites "Any Shot You Want", the A-Square loading manual concerning variations in pressure with changes in primer. From that manual, on pg. 65 the table "Primer Experiment" shows: 7MM Remington Magnum, 160 grain Sierra boat-tail, 66.0 grains of Hodgdon H-4831 and Winchester cases.

     The author then performed a test on a ".300 Winchester Magnum with a 23-inch barrel, the load a 180-grain Nosler Partition with 75.0 grains of Hodgdon H-4831 in Winchester cases.

     This article suggests to me that Quickload maximum pressure data may be suspect in some cases.

     Without pressure-measuring equipment I think that estimating maximum pressure may be difficult, particularly for the novice.

     If the reloader cannot estimate alloy hardness precisely, and if pressure cannot be estimated precisely, then attempting to match hardness and pressure for maximum accuracy-even if the theories were true-is difficult to impossible. 

On to the data:

     This paper uses three sets of data to look at real-life pressures and BHN's, and test the theories with this data.

     The "Wosika" data is from Ed's article in The Fouling Shot (TFS) 170-12, with data in ksi = thousand psi.

     The "Bischoff" data is attached; the pressures were calculated by John Bischoff using Quickload. Pressures in psi, converted to ksi on the graph.

     The "13 Grains Red Dot" data is attached. The pressures were again calculated by John Bischoff using Quickload. Pressures in psi, are converted to ksi on the graph.

     While none of the members of the two sets of theories are borne out by experiment or data, they have achieved a life of their own, and are now embedded in the literature.

     All the theories use formulas including the Brinell Hardness Number (BHN) of the bullet.

     The BHN is the ratio of: the force applied to a ball in contact with the test specimen for a specific time, to: the area of the "dent" made in the test specimen by the ball. This dent is called, by geometers, a "spherical cap".

     The force is measured in kilograms and the spherical cap area is measured in millimeters squared.

     The earliest theory starts with converting the BHN from kg/mm^2 to pounds per square inch, psi. A bit of arithmetic leads to the fact that multiplying BHN by 1422 gives BHN in psi.

     Then the mistake is made, and this psi number is stated, incorrectly, to equal the compressive or tensile or ultimate compressive or yield strength of the material. None of these are true.

     So, for example, we might have a wheel weight bullet of BHN = 12. Multiplying 12 by 1422 gives us 17,064 psi, a precise and quite irrefutable number. Not, however, any measure of the strength of the alloy.

     Now, the theorists need to do something with that 17,064 number. Chamber pressure comes in thousands of psi, and looks like the (BHN X 1422) number.

     Enter "Obturation", the swelling or bumping-up of a bullet by the burning powder gasses on and shortly after ignition. The theorists now combine chamber pressure, obturation and the BHN psi number with one or more explanations of what is happening to the bullet on firing, and we're presented with these prescriptions.

• #1 Chamber pressure must equal or exceed (BHN X 1422) for obturation to occur, else leading and poor accuracy result.

• #2 Best accuracy occurs when chamber pressure = (BHN X 1422 X 90%), else leading and/or lesser accuracy result.

     The second set of theories is based on the relationship between BHN and tensile strength for lead alloys.

     For example, Table 5 in ASM Handbook, formerly 10th edition, Metals Handbook, Volume 2, 1998, "Nonferrous Alloys and Special-Purpose Materials".

     The theories make use of the fact that (BHN X 480) is an approximation of the tensile strength of the lead alloys in the table.

     (A regression analysis of the entries in this table for which there are both BHN and tensile strength entries yields: ksi = -.33 + .498 X BHN, with R^2 of .964. Some 96.4% of the variation in hardness is connected to the variation in BHN. The approximation using 480 is reasonable.)

     With this (480 X BHN) approximation for tensile strength we're not in the chamber pressure area. 

     For example, with a wheel weight bullet of BHN = 12, multiplying 12 by 480 gives us 5760, a not-very-like-chamber-pressure number.

     If a multiplier is introduced, such as "3", the expression is changed to (BHN X 480 X 3), and 12 X 480 X 3 = 17,280, a precise number in the chamber pressure area.

     Now, we have to do something with that 17,280 number. Get out "obturation", add chamber pressure and the BHN/480/multiplier formulas, and some explanations of what happens to the bullet on or just after firing can be imagined.

     These are the prescriptions for the "480" family of theories:

• #3 Chamber pressure must equal or exceed (BHN X 480 X 3) psi, else leading and diminished accuracy.

• #4 Chamber pressure must be between (BHN X 480 X 3) and (BHN X 480 X 4) else leading and diminished accuracy.

• #5 Chamber pressure must be between (BHN X 480 X 3) and (BHN X 480 X 3 + 10,500) psi else leading and diminished accuracy.

     The graph below shows all of these prescriptions, and all of the data points representing the "Wosika", "Bischoff" and "13 Grains of Red Dot" data. While some of the data points-loads are within the prescriptions, most are outside the prescriptions.

     It is somewhere between difficult and impossible to prove that theories such as these are absolutely incorrect, even though the foundations for these theories can be shown to be flawed or without data supporting them.

     However, the data-theory comparisons above show that there are a number of successful loads with BHN-Pressure intercepts outside the theory prescriptions. Then we are left with two possible statements:

• 1. The theories are not correct, or

• 2. One or more of the theories is correct, and many skilled shooters are not operating in the correct BHN/Pressure range. I favor 1.

     Ed Wosika suggests that since this data deals mostly with velocities under 2000 fps and associated low pressures, that we not make any statements about the BHN/Pressure relationship above 1900 fps and higher pressures. This is "extending the conclusions beyond the data". Ed is correct and I agree.

     Ed also suggests removing the few high pressure BHN/Pressure pairs. I refuse to remove data from a set for any reason. The reader is free to discount these data points. 

The "Bischoff" data

Another Opinion:

John Bischoff

     I have repeatedly found that the computer program "Quickload" is eerily accurate as to the velocity obtained with a particular powder, charge, bullet, barrel length etc. It frequently comes within 25 fps of the 5-shot average for a 2000 fps load, and sometimes it will only be a very few fps away from the 5-shot average fps for a given load.

     For instance, I shot some 22 caliber stuff last year or the year before.

     Here's a Quickload graph:

     Considering that velocity is a function of pressure (the whole area under the pressure curve) and time (the whole time taken to transit the barrel), if Quickload can come that close to predicting real world velocity results, it is a reasonably safe bet that Quickload's pressure and time calculations are equally valid. Wildly piling opinion on supposition atop estimation, it seems to follow then that Quickload's peak pressure 'results' are also decently accurate.

     In my rifles, all that stuff seems to hang together fairly well. "All that stuff" being: 

     Quickload, Lee's BHN vs. psi balance, Lee's alloy hardness measuring system, and so forth. Further, Lee's work has a beguiling reasonableness to it that seems to help validate his approach. It "makes sense" that (assuming reasonably proper bullet fit, etc.) a harder alloy will withstand a higher peak pressure and that it is possible to predict just how much pressure a given alloy hardness will handle, all else being equal. Lee steps aside from the BHN and moves directly to what he labels the Ultimate Compressive Strength (UCS) in Pounds per Square Inch (psi) which simplifies matching the alloy strength against the peak pressure in the same psi units. There is a rational relationship between UCS and BHN so that one can deal in either system with some confidence.

     There are load charts for cast bullets with different powders vs. chamber psi (proportional to BHN) printed in the 2nd edition of Lee's Modern Reloading, along with Lee's explanation of his approach to the question.

     That alone is worth the $12 that the book costs from Midway. Lee covers the 30-30, 308, and 30-06 with bullets from 125 to 200 grains and a bunch of Hodgdon powders, and pressures to match against BHN from 10 to 35 or from UCS 12000 to 46000 psi. He also describes how you can do your own calculations to come up with similar data for other calibers.

     It probably ought to be remembered that this approach is probably going to be most useful for those shooters who are neither neophytes nor masters in the art of shooting cast bullets. Neophytes should probably stick to the loads published in the Lyman Handbook until they have built up experience and confidence, and of course the masters of the art will not need to bother with this approach. I think that Lee's approach is as valuable in its way as are the chamber cast and bore slugging in their way.

Bullet Hardness-Strength-Pressure:

by John Alexander

     There is a natural inclination by serious cast bullet shooters to try to apply logic, mathematics and the results of experimentation to further the art of cast bullet shooting instead of simply going by ancient rules of thumb and old husband’s tales. The accuracy possible with cast bullets has improved dramatically since the Cast Bullet Association was founded 30 years ago. This has been achieved entirely by shooters using the scientific method. The rule followers contribute nothing to progress.

     However, the world is a complex place and applying the scientific method can be tricky. It sometimes leads to a procedure that looks very scientific but is based on an imperfect understanding of the factors involved and is really no more than a tarted up version of a good rule of thumb. These can sometimes lead us astray. I believe the technique sometimes advocated for selecting the right alloy hardness to use for use in cast bullet loads is an example where the proposed calculations are meaningless.

     Much has been written about the question of what hardness a cast bullet should be for a particular loading situation. It obviously makes a difference. If you are trying to duplicate full jacketed bullet velocities in a 308, a hard alloy is needed. For moderate velocity loads with less than perfectly fitted bullets a softer alloy that will upset to seal in the hot gases works much better than a harder alloy. Therefore, in developing a cast bullet load, it is reasonable to make some judgment about what hardness might work well based on the expected chamber pressure, bullet fit and type of firearm, and other factors.

     One approach that has been discussed at length involves measuring the hardness of the alloy, converting hardness to some measure of strength and then computing what chamber pressure this strength alloy could theoretically stand before the bullet would be deformed excessively.

     I believe this hardness - to strength - to chamber pressure (HSP) procedure makes things more complicated than we have the knowledge to do. It also ignores many factors affecting how hard the ideal bullet should be. It is not nearly as good, or honest, as a simple set of individual rules relating estimated chamber pressure, bullet fit, and type of gun, to the bullet hardness needed.

     Reality isn't as simple as we constantly try to make it. 

     The first step in the HSP procedure, converting hardness to strength is on shaky ground. There is a reliable straight line relationship between hardness as measured by the Brinell method and tensile strength of lead alloys as measured by a standard test. (Tensile Strength = 480 X BHN ). The problem is that 480 X BHN gives us the tensile strength when the alloy is strained slowly in the standard test. The strain rate applied by the burning powder is thousands of time faster and the strength at these higher rates will be significantly, and probably radically, different from the standard tensile strength.

     The second step, from tensile strength to chamber pressure, is on even shaker ground. The problem here is that even if we knew the tensile strength for the high strain rate imposed by burning powder it would be the wrong strength. We aren’t pulling the bullet apart in tension. The burning gas is trying to compress it and smush (scientific term equaling “upset”) it up to a larger diameter by shearing the lead alloy. So we need to know compressive or shearing strength. Even if we did know the right strength, doing the calculations is not a simple operation.

     Because of the above shortcomings, the strength numbers we use in the HSP method are really meaningless and imply a level of precision we don’t have. They amount to kidding ourselves.

     Individual rules to give general guidance are really all we are going to have until some extremely sophisticated testing and stress analysis is done. The rough rules relating loads to appropriate hardness, now used by some, may be helpful. These rules need to be refined based on careful experimental work.

     To be valid we need to know which rule to apply to loads for rifle, pistol, revolver or shotgun and take into consideration such things as  sectional density, burning rate of powder, lube, and is it gas checked or not.

     To be valid, they must be used along with an understanding of the loading situation in question, described by the answers to the following questions. Is it a rifle, pistol, revolver, or shotgun? Do the bullets fit the throat well? Additional significant factors may be; sectional density, burning rate of powder, lube, and whether gas checked or not.

Bullet Hardness Requirements

Bill McGraw, John Robinson, Ric Bowman,

     The bullet hardness required varies from firearm to firearm based on many factors that all contribute directly to pressure. Some of these factors are internal bore finish, rifling height, lubricant used, and in the case of revolvers, the relationship of the cylinder throat and bore dimensions. Even bullet weight and design play a part. Because all of these variables vary widely, there is no set rule for hardness that can't be broken. 

     Of all the variables that we adjust to compensate for these conditions, powder selection gives us the most control. Generally, the faster we bring up pressure, the lower the overall pressure level needs to be for a given bullet hardness. Or, stated another way, the faster pressure comes up before the bullet overcomes inertia, the harder the bullet needs to be to survive the process. As you advance in your knowledge of reloading cast bullets, you will learn techniques of how to control pressure and even adjust some of the conditions of your gun, so that you can achieve some very high velocities with softer lead hardness levels. Below are some hardness guidelines to get you started using cast bullets.

• A. For black powder muzzle loading rifles, where the bullet is to be loaded at bore size, or less, it must expand to groove size upon firing (obturate). The bullet should be made of lead only, with no or very little tin or antimony. BHN would be in the range of 4.2 - 5. Muzzle loading balls should be as close to 100% lead as possible.

     "I have always disagreed with the old adage that muzzle loader round balls have to be soft lead. Pure if you can get it. Well, I have shot hundreds of round balls as well as buffalo bullets made from wheel weights. So go figure. Good luck " John Pierce Jr. ASSRA

• B. For some black powder cartridge guns, where the chamber / cartridge / bullet dimensions are such that the largest bullet that can be loaded is smaller than throat or groove diameter, the bullet should be made of lead only, with very little tin and no antimony. The soft lead allows the bullet to bump up to groove diameter with black powder. BHN would be in the range of 4.2 - 6. These cartridges include, in some guns, 38 Colt, .41 Colt,  and some  transitional military rifles such as the Springfield 45/70, Werndl and Snider.

     "It's only in the cap and ball pistols that soft lead is a necessity, and that's to keep from bending the loading lever, not accuracy. Those few cases where the cartridge originally used a heel based bullet, e.g. .44 American, .38 S&W, .38 Colt, .41 Long and Short Colt, and .376 Eley and then switched to an internally loaded bullet without changing the bore diameter clearly need hollow based pure lead bullets in the smaller (internally loaded bullet) loadings. The 44-40 was never loaded heel based, so this does not apply to that cartridge." Wayne Smith

• C. Revolver bullets that are as large as the cylinder throat will shoot accurately and without leading, regardless of alloy, up to 850 f/s provided they are adequately lubricated. Revolver bullets that are as large as the cylinder throat will shoot accurately and without leading, if made from wheel weights, up to 1100 fps with proper lubrication. Generally, a harder alloy does NOT reduce leading or increase accuracy above 1100 fps. Excellent accuracy combined with no leading at velocities above 1100 fps requires a lot of experimentation with different powders of various burning rates and lubricants.

     "joe; I have driven many cylinder throat sized wheelweight bullets at full throttle from a .44 magnum with a slick fire-lapped bore with no leading. Incidentally, I have never hardness-tested any WW metal from clip-on type weights which tested as soft as the BHN listed by Lyman in their handbooks. All I have tested has been in the 12 - 13 BHN range on my LBT tester. Maybe they are using a far more sophisticated testing device, however my tester shows the same hardness for pure lead and linotype as shown in their tables so it must be reasonably accurate." Don Howe, ASSRA site

     "I have experienced many instances where powder burn rate is simply too fast for lead bullets other than soft bullseye target loads. This often leads to severe leading and a deterioration in accuracy after 15-20 shots. A simple change to slower powder can prove wonders, accuracy remains constant and virtually no leading occurs even after a longer practice session. Examples of this are often seen in the 9 mm Luger - the small case volume aggravates the situation and causes pressures to peak more severely than in the 38 Special for example.

     Lots of my customers have leading problems with .45 Auto - mostly semi-automatic pistols of course. They follow standard claimed loads ( 5.2 gr. N-320 and 200 gr. SWC) and many have leading issues. When I ask which bullet or hardness they use the answer is often BHN of 16-18. My usual advice is up the powder charge to 5.5 gr. which works in many cases, but is the maximum load recommended by VihtaVuori. Alternatively, I advise go to BHN 10 and use 4,8 to 5,0 gr. and this almost never fails. Many myths exist here in Germany that " the harder the better" this is simply not true!!! I have also other experiences which support this thinking. Cast loads for .32 S&W Long Wadcutter, purely bullseye target shooting. Very lights loads 1,8 gr. N-320 or 1,3 gr. N-310 just would not work with any bullets cast harder than BHN 10. Very severe leading and abysmal accuracy. Accuracy, returned with very soft alloys - almost pure lead, but still not quite as good as commercially swaged hollow-base wadcutters. Which is why I don't cast for .32 S&W Long or .38 Wadcutters.

For light loads and lighter weight bullets it is okay to use faster powders, but as bullet weight increases and/or velocity needs to be increased more reliable results are obtained with the slower powders. This is also borne out by the ever increasing popularity of the moderate burning pistol powders here in Germany like VithaVuori's N-340 or 3N37 in the pistol and revolver events demanding a certain power factor. This also follows the trend towards heavier bullets e.g. 180gr. in .357 Mag. class or 300 gr. in 44 Mag. I hope you find this helpful." Adrian Pitfield - Germany

     Gas-checked revolver bullet molds are available, and gas-checked revolver bullets are sworn by some shooters. Elmer Keith said that 10:1 properly sized and lubricated plain based revolver bullets can be shot at maximum velocities without leading. I have never shot a gas-checked revolver bullet, but I don't shoot anywhere near maximum velocity loads very often, because of the flinch I develop. After six maximum 44 Magnum loads I adopt the "close my eyes and yank that trigger" mode of shooting, and have noticed a slight decrease in accuracy.

     I just don't know about gas checks on revolver bullets.

• D. Some Schuetzen shooters contend that at velocities below 1500 fps, accuracy is better with lead and tin alloys, without any antimony or arsenic. Other shooters contend that wheel weight alloy works very well.

• E. For rifles at velocities up to about 1500 fps, properly fitted PLAIN BASED = WITHOUT GAS CHECK bullets of wheel weights with BHN of ~12 are accurate.

• F. For rifles at velocities up to about 1800 fps, properly fitted GAS CHECKED bullets of wheel weights with BHN of ~12 are accurate.

• G. For rifles at velocities up to 2100 f/s, GAS CHECKED bullets of linotype alloy with a BHN of ~21/22 will produce excellent accuracy, if the bullet is a very close fit to the throat. (This is outside of my experience.)