figuring out a barrel's minimum safe thickness ?

[RobSmith]

How do modern gunsmiths/gun designers/barrel makers figure out the minimum thickness a barrel needs to have ? Just one of those questions that's always been in the back of my mind but never bothered to ask.... How did they used to do it in the old days, before the days of modern alloys, advanced metallurgy etc... ? Was it simply a matter of loading up a charge, attach a long string to the trigger, go hide behind a tree or other solid object, pull string, if the gun doesn't blow up you're good to go ?

Seems that anything from brass to cast iron to damascus steel to stainless steel to carbon fiber to whatever is/has been used to make a barrel at one point or another... There must be <some> manner of crunching the numbers out there to figure out what a *safe minimum" is.

 

[cosmic]

Designers perform a stress analysis to esablish a design. These methods were available in the old days, but were not as sophisticated as today. With computers, very detailed analyses can be done. Stresses are limited to values that are known to be safe for a given material, such as 4140 chrome moly. This work is complex, and is traditionally left to mechanical engineers who specialize in this field. (I'm a mech eng'g, but this is not my area of specialization....)
Surprisingly, modern actions/barrels are more highly stressed than their predecessors from 80 years ago. The reasons being:
- Designers can more accurately analyse the stresses
- Stronger materials are available
- Material quality has improved - methods are available today that can ensure the material is free of imperfections that could cause premature failure.
So its safe to say that modern firearm components are more heavily engineered. This allows the prospect of savings in materials and manufacturing costs, while (hopefully) retaining a high degree of reliability.
In the old days, "factors of safety" were relied upon to ensure safe designs, along with destructive tests, including a proof test for each rifle (just in case there is a flaw in a crucial part)
If you want a good example, compare a P-14 to a modern sporting rifle.

 

[Anvil]

Was it simply a matter of loading up a charge, attach a long string to the trigger, go hide behind a tree or other solid object, pull string, if the gun doesn't blow up you're good to go ?

QUOTE]

This is where the term proof testing came from. Guns in Britain are still tested this way, albiet in a slightly more sophisticated form.
Calculating stresses is an extremely complicated thing to do, with many many variables.
I have a shotgun that has been proof tested about 100 years ago at the Birmingham Proof House. Is it still in proof and functions perfectly. The left barrel is 0.015" thick on the thin side and the right barrel is 0.017". I'm pretty sure no modern manufacturers would consider building barrels this thin but they have worked perfectly since the gun was built.
I would venture a guess that most firearms in use today were designed without much number crunching. In the past bad designs were weeded out by actual failure in a much less litigious era.
As an aside, in Hatcher's Notebook, he describes an experiment where he progressively turned rifle barrel thinner. At each step he tried to make the barrel failure with extreme overpressure loads. When he reached 1/16 of an inch barrel thickness he still couldn't make the barrel fail until he plugged the bore with a bullet driven into the muzzle.

 

[Rapt]

As an aside, in Hatcher's Notebook, he describes an experiment where he progressively turned rifle barrel thinner. At each step he tried to make the barrel failure with extreme overpressure loads. When he reached 1/16 of an inch barrel thickness he still couldn't make the barrel fail until he plugged the bore with a bullet driven into the muzzle.

This is where the real concerns come in, how thick does the barrel have to be to fail in a SAFE manner when something like this occurs. I.E. Bulge instead of peel or split or throw shrapnel. The in "normal" operation there is a pressure release available (the moving bullet), its the extenuating circumstances that need to be designed for.

Also the other consideration is of course accuracy, thats tied to rigidity which is tied to barrel thickness. Thick barrels are stiffer, less flex means less variation/harmonic motion when firing. This means greater accuracy. Not a safety issue per se, but still a vital part of the engineering process.

 

[thecollector]

How do modern gunsmiths/gun designers/barrel makers figure out the minimum thickness a barrel needs to have ?

Primarly from Lame's equation for thick walled cylinders (I'm too lazzy to key it in and define all the terms here). It can be found in any text book of mechanical engineering. Normally saftey factors significantly greater than 2 are applied to the results of the calculated value.

 

[cosmic]

Well - I suspect that in the plugged barrel scenario,the principal cause of failure is the shock of the moving bullet hitting an obstruction, and releasing a lot of energy quickly, resulting in extremely high local pressures - the same thing happens when shooting at a steel plate. Complete containment of this would be hard to do - the barrel would be too thick for normal use, and would still deform internally.
However, use of more ductile metals could limit crack propagation. I suspect many catastrophic barrel failures, where the barrel fractures over its entire length, are due to metallurgical shortcomings - ie too brittle to resist the additional strain energy caused from hot loads, barrel obstructions, etc.

 

[Clark]

I have been doing experiments on guns for a decade.
My father was a great gun designer.
He has helped me learn the math.

The hoop stress [burst like a banana peel] in a thin walled barrel is:

S=Pr/t

Where S is the stress in psi of tension

P is the chamber pressure in psi

r is radius of the chamber or bore in inches

t is the thickness or the metal in inches

The longitudinal or axial stress [break off like a lizard's tail] is:

S=Pr/[2t]

Because the longitudinal stress is 1/2 of the hoop stress, one can cut

threads on a barrel 1/2 way through the barrel if the receiver supports

the barrel right where the treads start. This is how Republic Arms

Patriots are made.

Hoop stress for barrels with thick walls and high accuracy we need

Lame's formula for maximum stress in a thick walled cylinder subject to

internal pressure:

S=P(r2 squared +r1 squared)/(r2 squared - r1 squared)

Where S is the stress in psi of tension

P is the chamber pressure in psi

r1 is radius of the chamber or bore in inches

r2 is radius of the barrel [center to outside] in inches

http://www.riflebarrels.com/articles/custom_actions/bolt_lug_strength.htm

This book by Muller is great for stress calcultions on guns:
http://www.amazon.com/gp/product/0941653544