doublegunshop.com - home Forums General Discussion DoubleGun BBS @ doublegunshop.com Damascus small bore upland guns

hoop stress is the radial force trying to pull the bbls apart at the seams divided by the lateral wall area...and in a small bore you have less area for the gas pressure to work on thus less hoop stress.

Found one of the references I was looking for so maybe this will help resolve the pressure issue - at least for 16ga: "Story Of European Proof Marks" by Englehardt Part II, Chapter II Proof In France.

St. Etienne Proof Loads between 1885 and 1923 (Chart inserted in the text) shows the Proof of finished barrel produced 893 Kg/sq CM. The extra strong proof was 1050 Kg/sq CM, Double Proof was 1472 Kg/sq CM, and the Triple was 1800 Kg/sq CM. The same chart also shows the normal load of 16ga shotgun cartridge in France during that time was 438 Kg/sq CM. There is always discussion about the absurdity of the pressures in the double and triple proofs, but in pursuing a realistic answer to the original question the 438 Kg/sq CM service loads might give us a reasonable response of approx 6230 psi. There will be problems in the conversion as we don't know exactly how these pressures were measured but quite probably by LUP so we can add about a 1800 psi to that for stress gage pressure reading equivalents as I recall. So an old 16ga prior to 1924 was probably intended to handle around 8000 psi as measured by strain gage. This seems consistent with other things I have read. Guess if I were reloading for such a gun I might choose to stay more toward the lower numbers around 6500 psi out of respect for age. However I routinely shoot CIP 2 1/2 inch 16ga shells in my gun from that period without trouble with pressures around the 8000psi end of the scale though.

If there is better guidance on my meager conversion knowledge please chime in.

That makes sense. It seems like it would be far more difficult to blow a .410 barrel with the same wall thickness of a 12 ga. barrel. Smaller diameter, lower hoop stress. This has been a great discussion.

There are several formulas for calculating hoop stresses. Without getting too deep over my head an illustrative example can I think be given by using one known as "Lamé's formula for cylinders subjected to high pressure. Using stress (S), presure (P), outside diameter (D), & inside diameter(d) we have the following formula; S = P times D²+d²/D²-d². Utilizing typical end of chamber dia for 12ga of .800" with .100" walls & a 7000K psi gives a figure of 31889psi as to what the bbl would be stressed to. (I realize the end of chamber is not actual high pressure point, but will still serve as a comparsion).
Switching formula around to work for P (P = S x D²-d²/D²+d²) using 31,889 for S and .685 for d for 20ga & maintaing .100" walls gives a figure of 7995psi for the 20ga pressure necessary to stress the steel to the same level as the 7K load in 12ga.
16ga would work out to 7,556psi (d=.732).

Jerry,
Exactly the type of reference info I was hoping someone would be able to provide.

Miller,
The info you have provided has been extremely helpful and I look forward to everything that you have to say related to the issue.

I think I understand the idea behind hoop stresses and how they are determined. The question I have is how do hoop stresses relate to the topic at hand. I am not trying to be difficult, only trying to put the bigger picture together. How does hoop stress relate to barrel strength? Is there a certain hoop stress that the industry shoots to come under in order to avoid significant problems ie barrel failure? Are there seperate hoop stress values over which damascus barrels and fluid steel barrels will fail. Based on Bells small sample size, if there is a difference it my not be much?? Obviously, if there are indeed values for the hoop stress at barrel failure, we can work backward to get the pressure developed.

Edit: I understand that there are going to be the normal variations in condition of barrels that is going to be a huge X-factor, but lets go on the assumption that barrels are in good condition and no flaws are found that would preclude it from being used.

Doc06;
The hoop stress, along with the strength of the steel, is what determines how much the bbl can contain without either bulging or bursting. Also to go even further there is also a certain limit which if exceed can lead to fatigue failure. Steel is normally rated for an "Ultimate" & Yield" strength. The yield point is where it will be permanetly elongated (bulged in case of bbl) while the ultimate is the point at which it will rupture. Below the yield point is the fatigue point above which constant motion will eventually lead to failure, as in bending a piece of wire. Understand as the charge goes down the bore, with the gas pressure behind it, the bbl actually swells slightly but as long as the yield point (also sometimes called the elastic point) is not exceeded it will return to normal. Thus if the ultimate point is exceeded the bbl will burst, if the yield is exceeded it will bulge, while continiously exceeding the fatigue point will eventually tresult in a break, often a crack which doesn't show signs of high pressure failure etc.
The only "Fly in the Ointment" is for older steels & particularly composite bbls we simply don't know with accuracy just what all those points are. For modern steels these are all worked out in metalurgical labs. During my career as a machinist I was on some occasions relegated the job of preparing some of these test specimens for the "Met Lab" to test. We had several types we made & tolerances were vere close.

I went back through Bell's work after this topic got started and hoped to find any hints about where to go to find more definitive info. In the article where Bell compares smokeless and black powders, Summer 2002, he lists that he had read several articles realted to the topic before doing the tests. The technical data was dated between 1896 and 1933, and appeared to have some comparison of pressures. The only article he specifically lists is titled "Smokeless Shotgun Powders" by Wallace Coxe of Du Pont. I have searched for this article on the web and a limited search on a University Library I have access to with no luck. The refrence is for sale on Amazon for $40, but didn't want to spend the money without knowing what type of info it held. If anyone has this refrence or access to it, or the others Bell refers to, I would love to look them over or the info shared.

Doc06;
I do not have that article, however the American Rifleman ran an article on shotgun powders, back in the 50's I believe, which was also printed in a handloaders guide they once put out (Copyright 1969). In this article they ran the pressure curves for the first 10" of travel for 4 of the tested powders of this data. These were 3fg black, DuPont bulk Smokeless, DuPont Oval & DuPont MX, both dense smokeless. I believe that Coxe also included DuPont Ballistite in his test but it was not included in the Rifleman article. I have scanned in these 4 curves & e-mailed them to someone here on the board sometime ago & they have been posted. Perhaps whoever it was still has them & will see this & put them up again. If not see if you can PM me your e-mail address & I will send them to you. I am not currently set up to post pictures. All loads were in 12ga for a 3 dram or equivelent powder charge with 1¼oz shot.

Here you go: