BHN and Pressure

[joeb33050]

BHN and Pressure
A quick internet search shows dozens of sites where success in shooting cast bullets is equated with some relationship between the hardness of a bullet (BHN) and the chamber pressure in the gun.
One relationship is that BHN * 1422 should equal pressure.
Another is that pressure should be between BHN * 480 * 3 and BHN * 480 * 4.
The word "obturation" is often mentioned.
BHN is the ratio of: force applied to a ball in contact with the test material for a given time; to the area of the semi-spherical indentation in the test material made by the ball. Units are kilograms and mm squared. Converting to pound-feet units, we find that BHN * 1422 expresses the ratio in pounds and inches squared.
Now 1422 looks like the 1422 in the first relationship above, and like the 480 * 3 in the second relationship. (480 * 3 = 1440)
The BHN testing dimple/crater/indentation area in the test material and the force applied for a given time have nothing that I can imagine to do with peak or average or initial chamber pressure.
So the contention is that for a given pressure, if BHN is too low, something bad happens, (I can't find out what), and if BHN is too high the bullet won't obturate-gas leaks by and the gun leads.
Does anyone out there have any information or data supporting this?
Is it nonsense science?
Thanks;
joe b.

[Maven]

joeb, Have you asked these questions of Steve Hurst (CBA)? I've read his articles, e.g., FS 131-10, and assumed (not necessarily a good idea) they were empircally based.

[MikeP]

Lee's second-edition reloading manual, the current one, has a great discussion of all this, including a chart showning pressure limits vs BHN factors.

[Bass Ackward]

So the contention is that for a given pressure, if BHN is too low, something bad happens, (I can't find out what), and if BHN is too high the bullet won't obturate-gas leaks by and the gun leads.
Does anyone out there have any information or data supporting this?
Is it nonsense science?
Thanks;
joe b.


Joeb,

Is it nonsense? No. But it is just a guide. A lot depends on the case capacity you are shooting in relation to the bore size. There are many other factors too. Like how much above bore diameter you are shooting to fit your throat. I have had 14 BHN up to 62,000 psi and got leading but held 2" groups. The failure at that point was in the lube quality or lube quantity, not the hardness of the mix.

I am still working on this after a year or two, but my best accuracy seems to occur with lead hardness between 10 and 18 BHN across all caliber lines. If I need a harder bullet, then the bullet I am using isn't carrying enough lube for that pressure range and barrel length. Whether my bullet is 14 BHN or 35, all lead begins to vaporize, that can be seen with the naked eye, at about 3500 fps on clear days. Sometimes you can see the vapor trails around 3200 fps under dark conditions of high humidity. Of coarse meplat size plays a big part in exactly where this occurs.

[joeb33050]

Ed Wosika wrote an article in the July-August Fouling Shot (170-13) "The Accuracy Kpsi/BHN ratio. Using estimates of pressure and BHN for successful loads reported in TFS, he concludes that 1200-1600 fps loads are successful with Kpsi/BHN ratios of .4-1.9, and that 1800-2200 fps loads are successful with Kpsi/BHN ratios of 1.5-2.5.
To express BHN in foot-pound-second units, BHN must be multiplied by 1422, and if the pressure/hardness ratio should be 1, then pressure/BHN * 1422 should equal 1, and Kpsi/BHN = 1.422.
{P/BHN * 1422 = 1, P * 1422/BHN * 1422 = 1422, P/BHN = 1422, (P/1000=Kpsi)/BHN = 1.422.}
The range of Kpsi/BHN for Ed's examples of successful loads is .4 to 2.5.
Then the multipliers, 1422 or 3 * 480 = 1440 or 4 * 480 = 1920 can't be correct, since the multipliers for Ed's examples of successful loads range from 400 to 2500.
Actual data seems to contradict the rule, suggesting that.......
Ed says that the pressure must be great enough to squish the lube out of the grooves and keep a film of lube between the bullet and the barrel.


Assume that cast bullet BHN ranges from 5 to 30, and chamber pressures range from 10000 to 50000 psi. The Pressure/BHN ratios range from 333 (BHN 30 bullet at 10,000 fps) to 10,000 (BHN 5 bullet at 50,000 psi.). These numbers, 333 to 10,000, compare to the popular 1422.
Now narrow the BHN limits, from 9 = wheelweights to 21 = linotype, and the ratios range from 1111 (BHN 9 bullet at 10,000 psi) to 2381 (BHN 21 bullet at 50,000 psi) and we're closer to the real world. The ratio is never 7 and never a million. For reasonable BHNs and pressures the ratio is going to clump in the low thousands.
I'm starting to think that the 1422 or 1440 numbers are merely convoluted expressions of what's happening now. Kind of like "the rule of 72", which we watched fall apart in the 80's.
I'm still looking for DATA, which is damn sparse in the CB world.
I can't find any way to equate BHN to Yield or Tensile or Compressive strength.
Tom, Bill and John suggest that the "bump up" is necessary when the bullet doesn't fit.
Certainly true, I've always found that bigger is better.

I've been referred to Lee's book-could somebody send me to pertinent pages?, and TFS article by Steve Hurst, 131-10 is the location. I'll ask Glenn for a copy of the article.

Still looking for references or data.
Thanks;
joe b.

[MikeP]

Modern Reloading, Second Edition, by Richard Lee, contains Chapter 10 entitled "Matching Bullet Metal to Chamber Pressures." This is the chapter in which Lee discusses the issue, on pages 129 - 139.

[scrapcan]

The following is already known by many, but I thought it would be a good rehash for others that are not so well read. By the way I have looked for data also and have not found much. I just took Mechanics of Materials last fall and asked everyone I got close to about helping find the data. You might call your state univeristy and talk to a mechanics of materials instructor, they might actually be a shooter. I was very surprised at who I found to be avid shooters.

You might also ask the owner, Donna, of www.aeroballisticsonline.com. She has alot of info on her site and she may have references. I just read her review of an article about Secondary Explosion effect of using slow powders and getting chamber rings or spontaneous dissambly of firearms. at http://www.aeroballisticsonline.com/articles/mystery_solved.html and foun dlots of things referenced.

This whole relationship centers around the elastic limit for the allowy you are using and what the elastic limit is. the elastic limit is the point at which stresses can occur to an object and it will return to it's relative shape. Once you have reached the deformation stage it no longer returns to relative shape. this is a very simplified version of this topic as it pertains to engineering mechanics of materials.

This is meant to be a guide and to keep you within safe/acceptable limits for pressure and alloy for your purposes. Obturated bullets do not mean that the shape has went through plastic deformation, just that it has expanded and stayed within the elastic limits of the alloy.

The formula does not take into account other factors that aide in reducing friction and thus combined forces on the cast slug. As stated above, one member is getting very good accuracy with soft (by most peoples standards) alloys in high velocity loads (for cast anyway).

Another factor not talked aobut is the pressure curve of the powder/cartridge combination. Does it spike quickly (fast pistol powder in rifle size case) or is it a gradual increase (full case of slower powder). Protection of the bullet base can also be a factor, we routinely do this by gas-checking, using lube wads, or fillers.

Internal ballistics is complex and then couple it to a bullet made of an unknown alloy and that spells FUN (Further Understanding Necessary) that is only had by actually shooting.

The use of this technique is explained pretty well in Lee's Modern reloading 2nd edition.