Cannon math

[Thorn]

In another thread Artilleryman posted a good question, that i think needs its own thread.

Do any of you BRAINS know anything about the math it takes to determine the minimum safe wall thickness of a steel barrel?
You would probably have to factor in thing like bore diam., type of powder, weight of the projectile, friction(rifling), ect.......

What was the pressure the original guns were rated for / produced?

Personally i would like to know the working P.S.I. for a 3 inch diam 6 foot long rifled bore BP barrel. Knowing that I could then figgure out the type of steel and wall thickness.

Of course, the barrel would be over built anyway, but i think its important to determine a minimum standards for people that build guns that are not poured & bored.

[Rickk]

For simplistic answer, I suspect that all that could be arrived at would be some rule of thumb based on historical experience and some limited test data.

Material stress and fatigue is a heavy duty subject. The effect of stress would be a very non-linear equation... things would be fine up to a certain pressure level and then they would deteriorate quicky. Temperature is a big factor as well, and tghat is also non-linear... there will be a certain tempepature at which each type of material deteriorates very quickly.

Most materials are tested and rated under conditions of a constant pressure at a certain temperature over a period of many days. That would not extrapolate at all to a short duration "impulse".

Most likely, given the task of designing a cannon barrel to someone with considerable engineering experience but not in cannon design, an engineer would do tests in a pressure test barrel to determine peak pressure, double the expected peak pressure (a very common practice) consult the material strength tables, add in a bit of a safety factor to cover his butt (engineers hate being embarased, I know, I am one), round up to the nearest standard size, bring it to a peer review where it would get bigger still to make everyone happy, and the result would be a 12 inch diameter tube with a 1 inch bore in it.

[jeeper1]

Personally i would like to know the working P.S.I. for a 3 inch diam 6 foot long rifled bore BP barrel. Knowing that I could then figure out the type of steel and wall thickness.

If you are wanting to build a cannon you could call
 http://www.bigskysurplus.com/
and ask them what the OD is on the rifled barrels they sell. Those were made for smokeless powder and would be more than adequate for BP.

[Smokin Joe]

Thorn, I saw this on an engineer's web site:

P=(2t x S) / O

Where:

P is burst pressure in PSI
t is wall thickness in inches
S is tensile strength of material in PSI
O is outside diameter in inches

Working pressure is usually 1/4 of this

[Double D]

Oh no here we go again. Last time this subject came up I had to spank some hands. Fair warning.  Be polite, don't troll or bait.  Present facts to support your position, name calling and being rude just denigrates you position. If I see rudness or meaness, I am going delete your rude and mean remarks with some of those explanations that CW  has parked up in the Board rules so every one can see. Fair warning.



The engineers are going roll out their hoop strength formulas, stress charts and metal specifications.

No one however last time this came up presented anything on pressure values of muzzleloading artillery, but everyone had the right answer on what the right steel was.

Personally for me the discussion is not needed.  I simply accept that the technical committee of the N-SSA has done the engineering and testing and have a established safe guidlines based on their research.  I let their ruiles about cannons construction and maximum loads be my guidline when building a gun.


So Thorn I think what  your asking how much chamber pressure does a 3 inch rifled gun using black powder generate? Is that correct?




 

[Cat Whisperer]

Thorn, I saw this on an engineer's web site:

P=(2t x S) / O

Where:
....

Nice formula, BUT...


This isn't simple pipe under constant pressure.

The pressure is obviously dynamic, the products of combustion are corrosive AND the DESIGN (the shape of the interior) and the materials used all come into play.

The simple answer IS this:

Take a proven design (materials and form), with proven materials, and use prudent proven loading procedures.

Even a design engineer (and I have done tooling design and design in other areas) will take best GUESS from applying all known factors and formulas and make a PROTOTYPE and TEST it. 

IF you want to be successful on the one and only tube you design/build, copy a successful one.

[Smokin Joe]

This was never intended to be the Definative answer to all  pressure values of muzzleloading artillery. It was an reply to a posted question.

[Double D]

The Red warning is a Generic warning and not directed at anyone. It's just a reminder for everyone.

[Double D]

This was never intended to be the Definative answer to all  pressure values of muzzleloading artillery. It was an reply to a posted question.

I don't think CW  or anyone else thought you were giving a definitive answer, just a possible answer.  CW  is trying point how it may not apply.

 

[GGaskill]

Personally I would like to know the working P.S.I. for a 3 inch diam 6 foot long rifled bore BP barrel.

Barrel length doesn't really matter as the peak pressure (especially with black powder) is reached very early, probably within the first foot.  You do have to specify both shot weight and charge weight (we are assuming you would be using cannon grade powder as anything smaller is inappropriate for 3" bore) in relation to a specific chamber pressure.

This is a subject that constantly bothers us as cannon makers, especially if we want to make something freelance instead of a copy of an existing design.  The much referenced Matt Switlik ran a couple of sets of cannon pressure tests which are summarized here (the grains they are referring to, such as "240,000 grains per pound," are physical particles of powder, not grains weight.  The "almost 40% more pressure" does not compute from the numbers given; either Fg is 87% higher than Cannon or Cannon is 46% lower than Fg.)  They were run in a 3" wrought iron rifle which is pretty close to what you are asking about.  The most recent one was about 20 years ago.

If you take designs of successful guns of the past and do stress calculations on their dimensions, you will see that they are designed for maximum stresses far less than the maximum strength of the material used.  That is a good practice.

[moose53]

Here are pressure tables for smokeless powder, for comparison to blackpowder from ELEMENTS OF ORDNANCE  A Textbook for Use of Cadets of the United States Military Academy                                                                                                                                                                                                                                 

[Thorn]

My primary consern is about people building cannons on their own, without any refrence to the chamber pressues involved. Ive seen a couple of them that are more than questionable.

While the cannon associations have guidlines, i believe they are for the liners in a cast gun and not for standalone tubes.

I think it would be of great help, especially to people new to cannon making if there were minimum standalone material and thickness standards.

Personally, I do need to know more on the subject. My intention is to build several guns eventually, and the difficulty im experiancing finding an inexpensive barrel, leads me to conclude that i may have to delve into making my own.

Im glad we have engineers here this math stuff makes my head hurt !!

Moose, that chart certanly helps, thank you.

Oh, thanks to the rest of you too.

[Double D]

Well actually you do have some minimum standards you can go by..  The N-SSA guidlines are the minimun standards.

All reproduction barrels must be made of iron, steel or bronze.

All reproduction barrels and those original barrels failing inspection must be lined with a bore liner of extruded seamless steel tubing of a minimum ANSI standard and of a minimum 3/8-inch wall thickness.

No reproduction barrel shall be approved after March 1, 1986, which does not have one caliber's thickness of metal surrounding the bore at the breech.

Now there are some other guidlines about cannon breechplugs and locking liners in.  Mortars have there own set of rules for breech plugs

They don't mention specifically solid machine steel tubes, but if you build a your gun from solid steel to exceed the dimensions in these guidelines you are building in an extra margin of safety. Solid steel would exceed sweated and welded steel. 

 N-SSA does allow solid steel machined tubes.  A good number of the mortar tubes used in N-SSA is the Confederate pattern made by the Long Bros from solid steel.

[moose53]

Here are the black powder pressure tables by Matt Switlik as found in his article in the Fall 1988 issue of The Artilleryman. The gun was a 3in Ordnance Rifle modified and reinforced for the pressure tests.                                                                                                                                                                                                                                                                                                                                                                                                             

[PaulS]

If we are talking about Black Powder cannons I would think that chamber pressures would be below 30000 psi.
Since I am not an engineer I tend to be conservative in my designs. So we double the maximum to 60000 psi.
Standard 3" schedule 40 pipe can take an internal pressure of 800 psi; schedule 80 2400. It would be safe to assume that the wall thickness could be used to determine the strength so long as similar materials were used.
I schedule 80 pipe has a wall thickness of 3/16" the we can multiply it by the maximum pressure of 60000 divided by the rated pressure of 2400 to get the wall thickness required for our cannon.
60000 / 2400 = 25
We now multiply the existing wall thickness by that number.
25 x 3/16" =4.6875
so, we have a bore of 3" with a wall thickness of 4.6875" so we have an outside diameter of 12.375" using mild steel as the material.
Specifications for chrome moly tubing are considerably higher and would therefore require less wall thickness to perform at the same level.

I personally doubt that most black powder cannons have pressures which exceed 15000 psi and if wadding is the only projectile the pressure is probably half that. still, it would look impressive to wheel out your 12 inch diameter, four foot long cannon on the fourth of July to display to the neighbors. Light the fuse and fire it off and then wheel it back into the basment.

[Cat Whisperer]

My primary consern is about people building cannons on their own, without any refrence to the chamber pressues involved.
....

I think we're headed in the right direction, gaining knowledge to be more infomred.

My fear is that unless serious attention is paid to not only the strength of the material, but the NATURE of the material (hardness/brittleness etc etc) AND to the DESIGN (sharp/rounded internal corners etc) AND to the proper loading, that someone will think they have something safe and will make the national news when they find otherwise.

That is why I take the prespective of using proven existing designs and procedures, AND study everything I can get a hold of to learn more about it.

Understand that my perspective is flavored by having seen a cannon (1" bore) explode from the perspective of standing behind it some 15' or less.  A commercially built one too.  (some 35 years ago, so there's not a whole lot I remember about it)

When you light the fuse you MUST KNOW that it's a cannon and not a bomb.

[Squire Robin]

30,000 psi?

The pressure drops off very quickly as the ball moves up the barrel, so lets assume a 3" diameter, 4 lb ball accelerating over a distance of 1 calibre, ie: 3"

I make it 923 ft/s at the muzzle

I suppose that doesn't sound too far fetched despite the ultra short barrel, especially when you consider how high you can toss an anvil using no barrel at all 

best regards

Squire Robin (whose maths is notoriously unreliable)

[Double D]

Look at Switlik's pressure chart he used 16 oz of Cannon grade for 16,400 PSI in a 3 inch barrel. 

Remember the safety guidlines from AAA  and N-SSA. Maximum charge is no more than 3 oz of Cannon per inch of bore.  Maximum charge is 9 oz. That's 5 oz folks less than the hot load Switlik tested

With 8 oz charge of Cannon grade he got  10,500 psi.



 

[Squire Robin]

16,400 psi = 682 fps
10,500 psi = 546 fps