REAL pressure within a chamber...

[Land_Owner]

Hypothetical speaking...

Has anyone really[/b] determined the upper limit of pressure of the expanding gas in a rifle or pistol chamber?  We frequently discuss 20,000+  and 50,000+ CUP (psi?) pressures as relative maximums, but do we really know the upper pressure limit?

How would you test for that?  PV=nRT (Boyle's Law of Compressible Gas)?

What I am trying to say is how much "barrel/breech" strength (i.e. bore thickness) would be necessary to fully control (say) a bullet touching the lands that gets stuck immediatly upon firing?  How large would that pressure spike be?

Food for thought...

Land Owner
If it was easy, anybody could do it!

[victorcharlie]

Those might be a question for varmit al at:  http://www.varmintal.com/

If he can't answer them I don't know anyone that can.

[Reed1911]

I don't know that you could REALLY do it for any barrel, at least not in the specific sense that you are asking the question. We do know that in a confined space what certain powders will produce, as that is not hard to measure; We can safely calculate the burst pressure of a given chamber by way of the steel and heat treatment used.  PVnRT is not really easy to use to figure out pressure in a chamber since it is a totally dynamic process and you can only calculate for a given set of variables and at a given point in time. When a load is tested the newer (and more accurate) way is to measure the strech of the metal and calculate the pressure spike from there. With a bullet that sticks and no longer moves, we than have a sealed pressure chamber and yes we can calculate what the burst pressure would be and duplicate it.  Obviously there are problems in "real world" sense that apply here, but I think this is more an excersie of the mind.

Maybe I misunderstood the question?

[PaulS]

Hypothetical speaking...

Has anyone really[/b] determined the upper limit of pressure of the expanding gas in a rifle or pistol chamber?  We frequently discuss 20,000+  and 50,000+ CUP (psi?) pressures as relative maximums, but do we really know the upper pressure limit?

How would you test for that?  PV=nRT (Boyle's Law of Compressible Gas)?

What I am trying to say is how much "barrel/breech" strength (i.e. bore thickness) would be necessary to fully control (say) a bullet touching the lands that gets stuck immediatly upon firing?  How large would that pressure spike be?

Food for thought...

Land Owner
If it was easy, anybody could do it!

Land_Owner,
What you are describing is a closed pressure bomb. It is a device that is used to test the burn rate of a given powder under these conditions:
A certain amount of a smokeless powder is placed into a container with a measured internal volume and is sealed in place with a pressure cap. The case contains a piezoelectric heat sender, a piezoelectric pressure transducer, an ignition device suitable for igniting the powder in use and a device to release the pressure.
The chamber is a bit different because it hase less volume and more powder used per cubic inch. It is ignited with the use of an explosive and it is vented to external space. There is no rifle chamber that could withstand the pressure generated in such a way as you describe. The cartridge would fail releasing gasses to the atmosphere through the bolt (assuming a bolt action is used). If the gun could be made to contain the pressure the rifle would fail catastrophically. The only reason that guns don't fail is that the bullet is allowed to move down the barrel releasing pressure as it is building. Peak pressure for the volume of the powder and the volume of the chamber would require inches of wall thickness to contain the pressure and heat build up.

[Land_Owner]

Oops...double posted

[Land_Owner]

this is more an excersie of the mind

YES and

a device to release the pressure

not what I had in mind.  

If the gun could be made to contain the pressure the rifle would fail catastrophically.

A rhetorical question: If it was purposley made to contain the pressure, why would it fail?  No answer required.

If we disregard the concept of projectile and precision machined parts, go back to a basics metal block or sphere with

A certain amount of a smokeless powder is placed into a container with a measured internal volume and is sealed in place with a pressure cap.

 and don't release the pressure, how much metal thickness is required for a mid-range powder charge?  How high is the pressure spike (250K, 500K, millions?)?

It is just a "mental itch" that I am trying to scratch...

Land Owner
If it was easy, anybody could do it!

[Reed1911]

Good deal, I was hoping I understood what you meant.

Metal thickness? Well it depends on the burning speed and amount of powder to be burned. I can't remember the name of the book, but there are several good ones out there that run through the history of explosives, and most will answer you questions that this whole topic will bring up. Most powder companies test the lots of powder in this manner, point of fact this is one of the way that shaping explosive charges came to be. I don't remember the exact story, but to the effect of when the blocks were tested many had the lotnumber stamped into it. It was noticed that the interior of the chamber was negitivly impressed with this shape.

From there BP charges were made, and of course later in history, PETN, RDX, HMX, PNY, and PYX were used with greater sucess. Get to the book store or Amazon and do a bit of reading on high energy explosives
I think this will answer most of your questions. In the meanwhile I'll see if I can't find the book I'm thinking of.

[PaulS]

The actual calculations will take some real work and time to perform - unless someone has software that will make these calculations it will have to wait until I have some time to do this.

[Land_Owner]

PaulS, as it was an "academic" post, I wouldn't go to any trouble to figure it out.  I thought this topic may have been discussed before and an "answer" would be relatively easy to post.  I was just looking for the Order of Magnitude, nothing more.  I will check out the high energy and history of explosives references cited.

I don't fully understand "fast" versus "slow" burning powders other than the relative speed with which one burns as compared to a datum (mid-range burning powder?) but that increasing/decreasing "rate of burn" can be a factor in improving accuracy.  How one decides the "right" powder to use is, IMO to be left to the bullet manufacturer's recommendations through their extensive testing.  

I am NOT going to subject one of my rifles or pistols to experimentation, other than making my own bullets within the tolerances and specifications as publlished by bullet and powder manufacturers, starting low and working up.  Reloading within their published ranges and components, I have found all of the suitibility and accuracy that I need to put bullets on target or into game where I expect them to go.

Land Owner
If it was easy, anybody could do it!

[PaulS]

PaulS, as it was an "academic" post, I wouldn't go to any trouble to figure it out.  I thought this topic may have been discussed before and an "answer" would be relatively easy to post.  I was just looking for the Order of Magnitude, nothing more.  I will check out the high energy and history of explosives references cited.

I don't fully understand "fast" versus "slow" burning powders other than the relative speed with which one burns as compared to a datum (mid-range burning powder?) but that increasing/decreasing "rate of burn" can be a factor in improving accuracy.  How one decides the "right" powder to use is, IMO to be left to the bullet manufacturer's recommendations through their extensive testing.  

Land Owner
If it was easy, anybody could do it!

Fast versus slow powders is how the powders react in a closed presure bomb. You will find that some powders that are slow in one application will be "faster" in anoth load or with another bullet. The problem is that smokeless powders are sensitive to pressure - more pressure = faster burn rate. In testing for faster and slower burn rates pressure is whatever maximum the powder produces in its burn under the conditions of the test. Our rifles and pistols are a completely different environment than the testing environment. Playing with different powders of varying burn rates can find you a more accurate or a more tollerant load (same accuracy over a wider range of conditions) so long as you always use the information provided in manuals and are aware of differences in the data between manuals. I did some quick calculations and have listed them here:
=============
A surface area of 175.4 inches is required to contain the 36,487,436.5 PSI generated by the 176.7 grains of WW 748 fired in a 1 cu inch spherical chamber completely sealed. The outside diameter of the "bomb" is 7.5 inches with a one cubic inch spherical chamber at it's center.
This is a simplified calulation based on an equal weight of gas from a given weight of powder and an expansion coefficient of 1.3% per 100 degrees with a maximum heat rise of 1847 degrees.(an approximation that includes heat loss from the vessel to an abient temperature of 68 degrees F. (which is also the beginning temperature of ALL components)
I did NOT take into account the weakening of the 4140 steel as it's temperature rose so it may be necessary to add wall thickness to compensate for the heat retained in the case as the powder burns.
=============

I should put all kinds of warnings like don't do this at home - you must be licensed to use and detonate explosives to make and test this data. Attempting to make and use such a device can cause serious injury and death.
But I doubt that anyone here has the machinery needed to make such a device and if they have it and know how to use it they could easily make the calculations themselves.

[Land_Owner]

PaulS, I am not sure I undertand your 175+ inches [sic] of surface area.  Area should be in units of square inches.  Correct me if I am wrong, but a 7.5" diameter sphere provides just over 44 square inches of total exterior surface area, which is 25% of the quoted surface area [Area of a sphere = pi *  d^2 * (1/4)].  

I am amazed at the pressure spike [>35 Mpsi] and IMHO correcting for steel weakening is akin to integral calculus where the sum from i to n (as i approaches n) of f(x) = y is equal to smaller and smaller or more and more negligible change...but let us not go there.  Thermodynamics was not a favorite collegiate subject of mine.

Land Owner
If it was easy, anybody could do it!

[DWTim]

If you knew the peak pressure (in a practical sense, not with the theoretical iso-chamber), you can work backwards to get a chamber wall thickness, using Barlow's Formula and a stress limit for the steel in question. The burn rate increases under pressure for smokeless powder, but there has to be an upper limit for that. Wouldn't the nature of the molecules have changed long before the pressure reached 2.4 million atmospheres? Nitrogen and Carbon do all kinds of whacky stuff at extreme pressures.

Also: I didn't know that a fast rate of burn directly leads to better accuracy. My understanding is repeatability is the goal. A faster powder will be more consistent in a mostly-empty case, because it reaches working pressure before the bullet moves too much, i.e. the chamber volume changes. However, a good crimp over a charge of slower burning powder can be just as consistent. Right?

[PaulS]

PaulS, I am not sure I undertand your 175+ inches [sic] of surface area.  Area should be in units of square inches.  Correct me if I am wrong, but a 7.5" diameter sphere provides just over 44 square inches of total exterior surface area, which is 25% of the quoted surface area [Area of a sphere = pi *  d^2 * (1/4)].  

I am amazed at the pressure spike [>35 Mpsi] and IMHO correcting for steel weakening is akin to integral calculus where the sum from i to n (as i approaches n) of f(x) = y is equal to smaller and smaller or more and more negligible change...but let us not go there.  Thermodynamics was not a favorite collegiate subject of mine.

Land Owner
If it was easy, anybody could do it!

Land_Owner,

The 175.4 is area(as I stated) and is in square inches (understood as a unit of area) - sometimes I take things like notation for granted.
I think if you look up the formula for the surface area of a sphere you will find it listed as diameter squared times Pi or as 4 times Pi times radius squared. They are different ways to state the same thing. It looks to me like you have changed the 4 into 1/4 - I double checked and now I think you should.

[PaulS]

If you knew the peak pressure (in a practical sense, not with the theoretical iso-chamber), you can work backwards to get a chamber wall thickness, using Barlow's Formula and a stress limit for the steel in question. The burn rate increases under pressure for smokeless powder, but there has to be an upper limit for that. Wouldn't the nature of the molecules have changed long before the pressure reached 2.4 million atmospheres? Nitrogen and Carbon do all kinds of whacky stuff at extreme pressures.

Tim, if you are looking for actual chamber pressure just look at the SAAMI specs - we know that those are the expected standard maximums. As for what happens to molecules under pressure - you need either a lot more than 2 or 3million PSI or a lot more than 1800 degrees of heat. Molecules will break down into atoms of individual elements and then recombine as pressure and tempurature normalize

Also: I didn't know that a fast rate of burn directly leads to better accuracy. My understanding is repeatability is the goal. A faster powder will be more consistent in a mostly-empty case, because it reaches working pressure before the bullet moves too much, i.e. the chamber volume changes. However, a good crimp over a charge of slower burning powder can be just as consistent. Right?

I never said that a fast burning powder would be more accurate. I said that by playing with different burn rates you might find one that was more accurate or more consistant. I never specified that it would be a faster or slower burning powder. Crimping is used only to keep a bullet from moving under recoil or spring pressure. I seriously doubt that a crimp will provide for better ignition. The only crimping I do is for my revolver - even my 358 doesn't need crimpingfor accuracy.

[DWTim]

Just to clarify, I was talking about 2.4M atmospheres, just another way of notating the aforementioned 36M PSI figure.

As for my point about Barlow's Formula, I was just trying to be helpful re: the poster's original question. If he picked an arbitrary limit, like say 160,000 PSI, the formula can be used to determine how thick the chamber would need to be.