Barlow's formula for tubes that use dissimilar metals???

[VA Rifleman]

At the risk of asking a stupid question.

What would be the proper use of Barlow's formula with a tube that uses dissimilar metals?
Would the idea be to prorate the tensile strength of the two materials for the combined thickness or somehow calculate each tube separately?   

Thinking cast tubes with liners or sleeved tubes using different materials.

Thanks

[dan610324]

barlows formula , whats that ??

[Double D]

Doesn't Barlow apply to pressure vessels and closed circuiit pipe? How would you apply it to a gun barrel.

N-SSA has given us a pressure standard to work to, what different pressure standard do you expect to achieve.

[GGaskill]

I'm not sure something that simple is appropriate.  Let me get home and dig out an engineering textbook.  This is a typical type of problem in a mechanical engineering text.  Unfortunately, I have forgotten the solution and can't find a textbook right now.

As I recall, you calculate the expansion of the inner tube and calculate the stress from the strain in the outer tube.  But don't hold me to this because it's been 40 years since I worked the problems and I haven't done one since.

It's not a simple application of Barlow's formula or the thick wall stress formula found here.

[seacoastartillery]

    Well here it is:    http://www.aerocomfittings.com/barlows.html     We don't know what you want to do with it, but we will give some good advice on what NOT to do with it.  You will put yourself between a Rock, (your assertion that less metal around the bore or chamber of any particular cannon than the one caliber rule states) and a Hard Place, ( this is place where the moderators rule from), if you make quasi-scientific assertions that less material thickness is OK in this or that situation based on Barlow's formula results or calculated data.  

     Keeping this in mind, the link we supplied should be used for the amusement of those who are curious, and NOT for cannon design purposes of any kind, and certainly NOT for argument purposes.  A word to the wise should be sufficient.

Mike and Tracy

[Double D]

N-SSA has given us a pressure standard to work to, what different pressure standard do you expect to achieve.

Why would you want to deviate from such a credible standard to start with?

[Cat Whisperer]

...What would be the proper use of Barlow's formula with a tube that uses dissimilar metals?
Would the idea be to prorate the tensile strength of the two materials ...

It's interesting to do in theory.  But to use it as an indication of 'safety' in the design of a cannon is too simple as what it leaves out is the effect of the repetitive hammering causing work-hardening (and hence cracking).  So you may well come up with a "number" that looks good (i.e.: is well under the strength of the material) but is not in fact a good design.

[Double D]

Just for the record.

We have been recommending the standards for cannon construction of the North South Skirmish Association as the basic standard. Here are the standards.

N-SSA National Rules for Cannons
Figure 10.1
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.

The liner must be closed at the breech end with a steel plug, sweat-fitted into the liner and welded. The breech plug must have a radius of at least 25 percent of the bore radius and be at least 1 inch thick at its thinnest point.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. (See figure 10.2 for example.) Liner may be affixed by casting barrel around the liner or by other approved methods such as bonding with high strength adhesives. The method of locking liner in barrel shall be approved by the Artillery Ordnance Officer.

The N-SSA is an established credible source whose standards are based historical design and modern engineering.  

I am aware that is is possible to build safely a cannon lighter than the standards established by N-SSA.  There are many variable involved to build cannons.

We have folks of widely varying background, experience and education here.

While one person may fully comprehend all the variables to be considered when building to lighter standards a lesser experienced person may not.

If you scale your cannon from an original design, with a few exceptions it will meet the dimensional standards of  N-SSA.   

There is no reason to engineer you own cannon, just follow the standards established by N-SSA.  It's safer for everyone that way.

[Cat Whisperer]

Let me echo that.

One must have the correct MATERIAL.
Use a good DESIGN, MACHINED-MANUFACTURED correctly AND
LOADED reasonably.

ALL must be done to be SAFE.

[VA Rifleman]

(your assertion that less metal around the bore or chamber of any particular cannon than the one caliber rule states) ??
Um, thank you for your advice but I haven't made any assertions along these lines nor do I intend to.

Fully support the 1 caliber rule. In fact my tube is at Beaufort naval armory for this very reason.  An ordnance Eng is milling a 8" billet of 1045 and shrinking it over the two existing 1026 tubes. The past owner found the wall thicknesses sufficient but after learning from you all, I did not. This is a success  (albeit minor) for the forum and moderators when it comes to safety.  Thank you and long live the 1 caliber rule!!

My use of Barlow's formula to calculate bursting pressures is academic. I found it interesting to plug in different materials, wall thicknesses and outside dia and see the resultant bursting pressure. Keep the same wall thickness, increase the diameter and the bursting pressure goes down. At a high level, it's like hydraulics, when you increase the surface area on a piston, the effective force goes up for a given pressure.  Barlow's fully supports increasing wall thickness. No conflict here with good design practices and the 1 caliber rule. When I tried different materials on the same tube, I ran into difficulties with the calc thus the question.  Mr GGaskill  has it 100% right.

It may be possible that math deepens our understanding of what we all enjoy without jeopardizing safety but I could be wrong.   

[gulfcoastblackpowder]

Like everyone has said, the 1 caliber rule is the best way to design a cannon.  Something to keep in mind though, such rules are devised to ensure a reasonable factor of safety in the design.  If you were to calculate the minimum necessary wall thickness to withstand a blast, you may be surprised at how thin it is (obviously, depending on material).  Math can certainly give us all the answers we want, but because of the many variables involved, it can be hard to account for everything.  Even then, you'd want to use a factor of safety that would give you a reason to believe that when you ignite a charge you don't get blown up, or worse...blow up someone else.  By sticking with tested and established rules for design, we don't have to "reengineer the wheel," just size it appropriately, using any number of safe materials according to that rule, and then we can have fun knowing we are doing it safely.

Wanting to run the numbers for academic research is great.  It will give you an idea of what the factor of safety on your design is, which is always nice to know.  On a cannon, I want it pretty high.

Math is a friend of an engineer, but established design rules can be even nicer, so long as you utilize them according to their conditions.

[Cat Whisperer]

VA rifleman --

The sleeve sounds like a good insurance policy and over building.     

I'd LOVE to see some pix of the process!

[RocklockI]

Barlow's formula ? That alone kept me from viewing this thread . BUT I was wrong ! this subject (when boiled beyond whatever Barlow said) is of great interest to me .

It's kinda funny with my casting of Bronze I was going to make the 1838 a 1 " bore and I could by the 1/3 rule ...... I went with .750 " just because . When your azcaillao is on the line ....you tend to cheat for saftey, at least I do .

Barlow smarlow ..... 1/4 wave plates and brewster windows is what I depend on ,depending on phasing and wavelength of couse . Sunspots ,Pollen counts ,Wiggle diggets , and One blue eyed no nosed nothing  , helps too .


YMMV Gary

[Double D]

My only concern with things like Barlow, and hoop strength formula's and a couple of other engineering formulas that pop up every once in a while is that folks might get take the wrong interpretation from the values and hurt themselves.

[little seacoast]

I'd like to throw my two bits in regarding this discussion.  Sometimes you want to know how and why something works just for it's own sake.  No ulterior motives or unstated agenda, just want to know.  Our collective desire to ensure safety in this hobby  seems to sometimes stifle this spirit of inquiry almost like a reflex action.  VA Rifleman seem committed to safe practice in his correspondence with the board and with me personally but as an enquiring mind... he just wants to know.  Respectfully, LS 

[dan610324]

knowledge is a very light burden to carry

[Double D]

Doesn't Barlow apply to pressure vessels and closed circuiit pipe? How would you apply it to a gun barrel.

 

Stifle!!!!  Call it what  you want.  I don't think the formula applies to gun barrels, how is that stifling.

I'll go back to my original question, what does Barlow's formula have to do with a cannon barrel.  Engineers?  Isn't Barlow's used for static pressures in fluid dynamics in closed vessels.  I don't recall it ever being used in discussion of gun barrel strength.

So someone just answer my question How does Barlow's formula apply to gun barrel. Show me the relevance Barlows formula  to gunbarrels and acceleratiing pressures of combustion gases.

If I am wrong, then I am wrong...been in that store before.   

 

[Cat Whisperer]

There are strong similarities in how pressure is/can be measured with a strain gauge in pipe or a rifle barrel.

The information (pressure, peak pressure) is in the same units.  It is the same measurment, which Barlow's formula estimates.

The issue, to me, is not that one gets X pressure from a given set of circumstances, but that X pressure is compared to Y strength.  That works well in STATIC situations like in pipes.

BUT, when you have dynamics, as in some high-pressure hydraulic systems and in cannons, the repition of those forces work-harden the metal and cause failures.  I've seen 1" bolts (a dozen of them holding the lid on a hydraulic tank) fail for this reason.  Even though they were WELL within 'design limits'.

[Cat Whisperer]

THEREFORE, USE the formula!  But understand it's limitations.  It is GOOD for making comparisons.

[little seacoast]

I knew better than to post that comment but couldn't help myself.  VA and DD seem to be asking the same question i.e. the relevance of Barlow's formula but from different points of view. Va seems to want to know how or if it could apply and DD seems to want to know why he'd want to know.

N-SSA has given us a pressure standard to work to, what different pressure standard do you expect to achieve.

Why would you want to deviate from such a credible standard to start with?

 No disrespect intended to ANY of the responders to this thread intended DD.  Still respectfully, LS

[Double D]

I knew better than to post that comment but couldn't help myself.  VA and DD seem to be asking the same question i.e. the relevance of Barlow's formula but from different points of view. Va seems to want to know how or if it could apply and DD seems to want to know why he'd want to know.  No disrespect intended to ANY of the responders to this thread intended DD.  Still respectfully, LS

No you don't have it quite right.

I am asking the same question, how does it apply?  I don't think it does apply.  Somebody prove me wrong....

[Cat Whisperer]

Pressure is pressure.

IF the pressure inside the vessle is causes greater stresses than the strength of material, something is going to break.

Barlow's formula transltes the pressure inside to the stresses laterally/circumferentially which should be well under the strength of the material (REGARDLESS of the source of the pressure).

In the simple case (static pressure) there is no other proof - it should be obvious.

Cannons and hydraulics and (...) are not the simple case.

The formula still applies in comparing materials - it gives one a basis for comparison.  It does not address the affects of flexing (albeit in very small increments) which is a function of the material's ability to resist cracking.  (See Charpy notch test.)

[Cat Whisperer]

The situation (hydraulic) where the 1" bolts broke, after the 2nd time (ok - the first breaking could have been from bad materials), we greatly increased the strength of the bolts (by changing the material and hardening them) AND redesigned the routing of the hydraulic hoses so that the valving didn't cause the repetitive pressure spikes back into the main tank.

Look at the strength of cast iron and bronze.  Are they not similar in tinsel strengths (a direct reference to the formula)?  (Yes, there is quite a RANGE of strengths.)  BUT comparing cast iron and bronze is not one MUCH more brittle?

Keep going.  Compare the strengths and the resistance to cracking to other common materials we consider for making cannons (limit it a little - everything I see gets considered).  1018 vs 1144sp vs 4140 vs (   ...   ).   Compare brass and bronze!

[Double D]

IF the pressure inside the vessel is causes greater stresses than the strength of material, something is going to break.

Perhaps the fundamental  basis for my lack of under standing the Barlow formula.

Here is the formula. http://www.engineeringtoolbox.com/barlow-d_1003.html

P = 2 s t / ((do - 2 t) SF)  

P = max. working pressure (psig)

s = material strength (psi)

t = wall thickness (in)

do = outside diameter (in)

SF = safety factor (in general 1.5 to 10)


Looking at the formula I think I see where I was going wrong.  I didn't see where the material used as the vessel or pipe was considered.  It is considered as s, the material strength.  I got it now.


 

[Zulu]

I thought Barlow was a knife?
Zulu

[Cat Whisperer]

I thought Barlow was a knife?
Zulu

BINGO!   I used to have one too!

But his knife sharpness formula is MUCH simpler!

[Victor3]

THEREFORE, USE the formula!  But understand it's limitations.  It is GOOD for making comparisons.

 "A man's got to know his [cannon's] limitations."

[Cat Whisperer]