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Barrel design calculations ?

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NoName0815

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Hi there,

I´d like to ask the experts here how they do their barrel designs.

I have books about this, but when compared to the reality they have nothing in common.

For example: A PPK Barrel fits after my calculations just the minimum amount of wall-thickness (Using 4140 Steel or eqal). Solid-Works / Cosmos Express says the same: Safety Factor of about 1, which means it would withstand the pressure, but barely.
Shouldn´t there be a safety factor of about 3 to 4 ?

A .22 design is even more confusing !! It is told / written that even a tube of a car antenna could withstand the pressure of a .22. When calculating the required wall thickness of a 22 barrel the results tell me that 2mm of high carbon steel (0,08 Inches) would burst at the average pressure of a .22lr.
And again: Cosmos Express came to the same results.
In reality I saw "The Mythbusters" blowing up some .22 rounds in a car fuse holder. Some of the shells didn´t burst, even if they were unsupported by a surrounding barrel/chamber.

So can someone please bring some light to my darkness ?
Are there some formulas which meet the reality ?
Do you have experiences on that issue ?
How do the manufacturers design and calculate their barrels ?
(They need to have some amount of safety unless they want to get sued)

Thanks for reading this ! And even more thanks for answearing !!!

NoName0815
 
Mythbusters

Quote:

>In reality I saw "The Mythbusters" blowing up some .22 rounds in a car fuse holder. Some of the shells didn´t burst, even if they were unsupported by a surrounding barrel/chamber.<
**********************

.22 rimfire rounds, when exploded in the open, don't usually burst the cases because the pressures developed by the powder charges are relatively low and because the case doesn't have a firm grip on the soft heel-based bullets.

Pull a bullet from one and you can see just how little the case grips the tapered heel. If the "experts" had detonated a few rounds of 9mm or .357 Magnum, they'd have seen some blown cases.
 
Hi,

finally some replies :)

@owen: I don´t calculate the peak pressure. The maximum pressure of every caliber is standardized by CIP.

@1911 Tuner:
Interesting Point. That could explain, why my calculations are wrong.
My calculations are "worst case scenarios" in which the whole maximum pressure
developed by the round effects only the chamber-walls. Since pressure effects all the surfaces including bullet and cartridge-base (indirectly the breech) it should be lower at the chamber walls. So I need to do some mor math on that one...

Anyway: The core of my thread isn´t answered yet:
How is the minimum amount of wall thickness in the chamber calulated as close to reality as possible.

Come on people ! There´s got to be someone who´s designed and built a gun
himself with the same problems !!!
 
I am not an engineer and I don't play one on TV, but most engineers will design to the optimum strength, which is usually the minimum size plus a safety factor. The reason is that any other approach would waste material and make the product too heavy. Why design say, a ladder, to hold people who weigh 2000 pounds, when no one weighs that much?

But guns are not necessarily designed that way. I suspect that if a bolt rifle, say, were made with the absolute minimum strength in the receiver, barrel and bolt, it would be very light. And it would kick the bejabbers out of the shooter!

So even if the designer and the manufacturer were willing to go with the minimum amount of metal, they can't because of other factors, including the expectations of the buyer. We are used to looking at the bolt of, say, a Mauser 98, with bolt lugs about 10mm long. Now we know from tests that the bolt lugs really have to be only half the length (shear strength) that they are to handle the standard pressure. But would anyone buy a rifle with locking lugs only 5mm long? Heck, no! It wouldn't look right and no one would believe it was strong enough.

The old designers rarely did those kind of calculations, plus they didn't have standardized steels or computer design software. So they played it by ear, often simply copying what they knew was good enough. And it almost always was.

And this doesn't even consider that the gun designer doesn't have control of the ammunition. Not only does factory ammo vary considerably in pressure, but the gun designer needs to consider reloading. The gun designer's life would be easier if he KNEW that no cartridge fired in his gun would ever exceed a certain pressure level. But he can't.

Jim
 
I apologize if I am getting to simple here. I have no idea what your experience level is.

1. Check your units.
2. Make a sanity check by modeling up a cylinder (no ends, so no axial stress) and doing the hoop stress calculation. Any time you use FEA, you need to run a sanity check like this.
3.if you are using Solid Works, and Cosmos, PM me. If I find the time, I'll take a look at it.
 
Hi Jim,

thanks for your answer.

I don´t think - as a designer - that you would have to worry about reloaders. There´s a maximum amount of pressure normed by CIP for each caliber.
And as a relaoder you are responsible not to overload your cartridges.

There are so many cases where guns did burst because of reloaded ammo. Somewhere you have to put a design limit.

Anyways, I would be interested in figures for

a) the mentioned minimum size
b) the mentioned safety factor

Well, the easiest way to find out - I guess - would be to bore a bar of steel to the correct Chamber-Diameter, add some kind of breech-block, fire it and turn the outer diameter down in a lathe. Then repeat until it bursts.

After that: Using 2-3 times of the wall thickness than the bursted one should be safe. What do you think ?
 
<psst...using a max pressure of 20ksi, a yield strenght of 30ksi, and a bore diameter of 9mm, I am coming up with a wall thickness of .118">
 
Hi, NoName,

Actually those tests have been done many times. Hatcher cut down locking lugs and turned down barrels. It is actually surprising how much extra strength is built into the average rifle. The main reason is that the early designers were not engineers and they were not working with the best possible steel; they didn't take the minimum and add a little, they added a lot. It is common knowledge that the weak point in a rifle is not the steel, but the brass cartridge case, which the gun designer cannot control.

But remember that strength is not the only criterion. The slide of an M1911 pistol is a lot heavier and thicker than it needs to be just for strength. But it MUST have the weight to keep the slide/barrel unit momentum at a certain level in recoil. Taping on a lump of lead is not practical, so the slide weight is balanced to achieve that goal. Again, remember that even if a 6 ounce .45 could be made, no one would want to shoot it, so weight is absolutely necessary whether it is needed for strength or not.

As to not worrying about reloaders, the lawyers would be taking numbers to sue any gun maker who didn't design to overstrength, and try telling a jury of women that you have no responsibility if Joe Klotz blew up his gun and left a widow and ten children. In fact, one of Remington's design goals with the 700 was to do everything possible to keep the idiot reloader from blowing up the gun.

Jim
 
I'm having to dredge from memory for 40+ years back, so cut me some slack:

ASTM, Section 8 (?), Pressure vessels.

It gives the formulas for cylinders containing pressure. Nuke reactor pressure vessels, propane tanks, suchlike.

But, any cylinder...

Art
 
I've kind of always wondered why my .22lr barrel thickness is about the same thickness as the bullet. Compared to other rounds/barrels (9mm comes to mind) thats very thick. I like the idea of just boring it out and then removing some tell you find the minimum thickness :D

A remote firing system and being behind some thing would be a very very good idea in that case.
 
@ Jim

Even if those tests have been done several times, I don´t have access to the results :(
I do know that any cartridge case will burst at some amount of pressure, but I didn´t know that it´s part of the pressure system. I thought of it as just a container, to keep all the ammo components together. I thought that the most amount of pressure is effecting the chamber walls. And the brass just bents to the maximum of the chamber dia. After that the elastic part of deformation would cause a slightly reduce of the shell dia, so it can be extracted....
Reloading and the Law: Well, in the U.S. Mc. Donalds got sued because someone got burnt by hot coffee. Now they do place warnings on the cups...
My opinion is: If you don´t know what you´re dealing with, whether it´s temperature or pressure, you should leave it so someone who does.
In Europe the Judges assume that you´re intelligent enough to know that hot water put through coffee powder will result in HOT coffee, so you might get burnt. And of course it is told when obtaining a reloading license, that YOU and nobody else is responsible if you overload a cardridge.
To say "It´s somebody elses fault" won´t bring you further in life... At least in Europe... :D


@Art

What is ASTM ?

@hcker2000

Of course this would have to be done remotely ;) But I would´t go so far to sacrifice a reliable Rifle. A simple steel bar or tube would do the job :neener:
Unfortunately in my Country such experiments are illegal :( At least for the average Joe.
 
Last edited:
I suspect that treating firearms as simple pressure vessels based on the maximum chamber pressure may yield some misleading results. A firearm only has to contain the pressure of a firing round for a tiny fraction of a second, and only a fraction of that is actually at peak pressure.

I doubt most rifles would respond to containing a constant 50,000+ psi the same way they respond to their normal couple of milliseconds at the same pressure.
 
Hi, NoName,

The cartridge case is an extremely important part of pressure containment. It wouldn't do much good to make the barrel and chamber of thick steel, and put heavy lugs on the bolt, if the case were to simply melt and let high pressure gas into the shooter's face. And melt is exactly what a brass case head does under very high pressure. Under normal pressure, an unsupported case will simply burst (case support is a major factor in gun design), but under very high pressure, the case will actually melt, almost dissolving.

A book I suggest you read is Hatcher's Notebook. It is available from Ray Riling for USD 40. See:
http://www.rayrilingarmsbooks.com/cgi-bin/rrb455.cgi/results.html

I think his many experiments will be of interest, even though his main "victim" was the U.S. Model 1903 rifle. Since he had access to all he wanted of those, he had no qualms about blowing up a few.

In design, a reasonable safety margin is often not enough. In a hotel a few years ago, a second story balcony-type walkway collapsed, killing a number of people. The design was more than adequate for normal use and someone was quoted as saying that it would be safe unless people were packed on it like sardines, a silly idea. But there was a show on the main floor and people did pack the walkway "like sardines" to watch, and were jumping with excitement to boot. The walkway collapsed, and the hotel, the architects and the builders had to pay a huge amount in damages.

Jim
 
@noname

Very sorry to hear that where you live your not allowed to experiment. To be honest I don't know what I would do if I were not allowed to do the things that I find interesting.

As they say knowledge is one of the most powerful things one person can have.
 
"...It is told / written that even a tube of a car antenna could withstand the pressure of a .22..." That's nonsense. Don't listen to anyone telling you stuff like that.
 
@sunray

This Information was from Truby´s "Zips, Pipes and Pens", Page 34 ;-)

NoName0815

@hcker2000
Well there are ways, but they usually cost lot of money and a lot of paper-work + background checks + knowledge test etc.
A lot of pain... for a little bit of experimenting....
 
That hotel, Jim, was the Hyatt-Regency and the walkway collapsed due to a construction change that didn't follow the original design. Sadly, a $10 piece of steel would have prevented it.

Construction issues led to a subtle but flawed design change that doubled the load on the connection between the fourth floor walkway support beams and the tie rods carrying the weight of the second floor walkway.
Click to expand...

http://en.wikipedia.org/wiki/Hyatt_Regency_walkway_collapse
 
Sorry, Sunray, but many "zip" guns were made from car antennas until government pressure forced the makers to change the diameter of their antenna tubing. How do I know? I refuse to answer on the grounds....

Jim
 
My dad told me he made a .22 zip gun out of a section of telescoping antenna. This would have been in the mid 50's.

The chamber section of a rifle barrel should be able to hold 50,000 psi easy.
 
I have the same education as my successful gun designer father, BSEE U of W 1978 vs BSEE U of W 1944.

I lack my father's genius, but he has explained to me how to calculate gun strength.

Thin wall hoop stress = [Pressure] [inside diameter]/ 2[wall thickness]

I asked my dad where he got that formula and he said, "By inspection".

OK, I can see it now, but I am not as smart as my dad.

On thick walled, he gave me two books,
"Machine Design" by Leutwiler 1917
"Mechanics of Materials" *by Laurson and Cox, 1938

Lame's formula:
Stress = [Pressure] [OD^2 +ID^2]/[OD^2 -ID^2]

The yield strength of steel changes with heat treat, and is proportional to hardness.

I have bought some partially hard 4140 round stock, and it comes at RC28.
This makes it still machinable, but yet stronger than annealed.
http://www.varmintal.com/arock.htm

This puts the yield strength at about 125ksi
That means that the steel will stretch more than it will go back when the tension in the steel reaches 125,000 psi tension.

Using the simple thin wall formula and the 20k psi SAAMI pressure for 22LR, and your safety factor of 1, then

125ksi/2 = [20,000 psi] [.223]/ [[2] [wall thickness]]

wall thickness = [20k/125k][.223] = .03568"

Barrel Outside diameter = inside diameter + 2 thickness = .223 + 2 [.03568] = .29436"

My guess is that if someone plugs those assumptions into Lame's formula, the barrel will grow to .3"

And I also guess that a 36 thou barrel wall will not blow up with a 40kpsi shot. Guns are harder to blow up than calculations suggest, ask me how I know.
 
@ clark

Seriously: Thanx a lot !!!

Actually this is the formula for hoop stress, written down in a gunsmithing book
I own. The thin walled one...

Even if the results are equal, where do you draw the line between thick and thin walls ?

And finally, I know that your last question is answered by experience, but I´d like to hear some more details... Just to feel a little more confident.

NoName0815
 
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