Speed of chemical propellants

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I did a little more research (even touched my fluids and thermal text books {ewww...}) and I am fairly convinced we cannot treat these combustion gases as an ideal gas. Nearly all the products of combustion are supercritical fluids while in the gun bore and thus the ideal gas law no longer works. The ideal gas law assumes there is more space than particles and that the particle do not chemical react or are not attracted to each other, they simple act like perfectly elastic particles bumping into each other. CO2 at 20,000 psi and 800K is nearly the same density as water at room temperature. And there is no doubt that the particles in the gun barrel are interacting as more than simple elastic particles since a fair portion of them are combusting with each other.

I have found research paper measuring CO2 (a product of combustion in our discussion) above the critical point (7.39 Mpa/1071 psi and 31C/88F) and they have experimental measure the speed of sound in super critical CO2 at over 500 m/s at ~10MPA (1500 psi) only slightly elevated temperatures (~400K). Take that temperature up to 2500+ K and I think we would have a very high speed of sound.

In many ways supercritical fluids behave like liquids rather than gasses. The speed of sound in air at standard conditions is, as we all know, ~340 m/s in a liquid like water at room temperature is nearly 1500 m/s. As I stated in the first paragraph CO2 at only 20,000 psi has nearly the density of water. In that light I think a speed of sound in combustion gases approaching 2000 m/s seem plausible. That said I really wish I could find something more definitive.

-rambling
Limiting fluid flow to Mach 1 in a barrel would not only limit single stage guns to whatever the local sped of sound is it would make multiple stage guns pointless as their maximum velocity would be limited to that velocity.

A simple two stage gun, operated by the Navy was capable of launching 250 grams at 15,000 fps and a 60 gram projectile at 27,000 fps. The first stage was basically an old 12 inch gun breech, and used regular smokeless propellant, and second stage of this gun was auto-ignition of a pre-balanced hydrogen-oxygen atmosphere driving a 2 inch sabot carrying the payload.

Also, even a speed of sound of 2,000 m/s would be to low if you limit guns to sonic gas velocities. Project HARP manage to get muzzle velocities of 7,100 fps (2164 m/s) out of a single stage 16 inch gun.
 
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Limiting fluid flow to Mach 1 in a barrel would not only limit single stage guns to whatever the local sped of sound is it would make multiple stage guns pointless as their maximum velocity would be limited to that velocity.

A simple two stage gun, operated by the Navy was capable of launching 250 grams at 15,000 fps and a 60 gram projectile at 27,000 fps. The first stage was basically an old 12 inch gun breech, and used regular smokeless propellant, and second stage of this gun was auto-ignition of a pre-balanced hydrogen-oxygen atmosphere driving a 2 inch sabot carrying the payload.

Also, even a speed of sound of 2,000 m/s would be to low if you limit guns to sonic gas velocities. Project HARP manage to get muzzle velocities of 7,100 fps (2164 m/s) out of a single stage 16 inch gun.

Again it is not impossible to go faster than super sonic in your working fluid but it is very difficult since the shock wave in the tube makes it difficult to maintain base pressure on the round.

The two stage Navy gun you mention was create for just the reason I gave above. Neither stage in that gun had super sonic flow in the tubes. That is just another variation on the light gas gun I mentioned earlier in the thread. Instead of using helium in the second stage they are using the pre balance hydrogen-oxygen mix. Hydrogen-oxygen mix does not have as high of speed of sound as helium does (at similar temperatures) but when you compress it and ignite it gas temperatures get much higher than then compression along does for the helium. So due to this increased temperature you get similar performance as the helium second stage light gas guns. In either case the gases used in the second stage have much higher speeds of sound than the propellant gases of the first stage. This is the point of a two stage light gas gun.

Even the HARP gun did not have super sonic flow in the gun tube. They simply optimized the system very carefully to eek out every bit of velocity you can from a single stage gun getting very close to the theoretical limits for the propellants they where using. I have actually seen one of the, now abandon, HARP guns while doing my own testing at Yuma Proving Grounds with a previous job.
 
Okay, if the speed of sound in a 5.56mm very high and well above the velocity of the bullet in the barrel and is not choked, then how does one get choked flow in a high-low pressure chamber gun such as a 40mm grenade launcher?

These only work if there is a choked flow through the orifice, otherwise there wouldn't be much "high-low pressure". They also work on a much lower pressure differential, about 10,000 psi delta, with the same type gas and approximately the same temperatures in the high pressure chamber, the effective orifice size is about 0.0100 inch.
 
Okay, if the speed of sound in a 5.56mm very high and well above the velocity of the bullet in the barrel and is not choked, then how does one get choked flow in a high-low pressure chamber gun such as a 40mm grenade launcher?

These only work if there is a choked flow through the orifice, otherwise there wouldn't be much "high-low pressure". They also work on a much lower pressure differential, about 10,000 psi delta, with the same type gas and approximately the same temperatures in the high pressure chamber, the effective orifice size is about 0.0100 inch.


The flow through the orifices of the hi-low system of a 40mm is choked because its an orifice not because of a super sonic shock-wave. In that orifice you have velocities that are into the transonic speeds but not super sonic. As then exit the orifice they expand and slow down very rapidly. Which works good for 40mm as you maintain a high pressure in the combustion area to get a clean and efficient burn while keep pressure low behind the grenade so you don't blow up the aluminum barrel or break the soldier's shoulder. I have actually reloaded 40mm. In a pinch Bullseye will work if your supply of M9 propellant is unavailable. Bullseye is much easy to acquire on short notice than M9.
 
The flow through the orifices of the hi-low system of a 40mm is choked because its an orifice not because of a super sonic shock-wave. In that orifice you have velocities that are into the transonic speeds but not super sonic. As then exit the orifice they expand and slow down very rapidly. Which works good for 40mm as you maintain a high pressure in the combustion area to get a clean and efficient burn while keep pressure low behind the grenade so you don't blow up the aluminum barrel or break the soldier's shoulder. I have actually reloaded 40mm. In a pinch Bullseye will work if your supply of M9 propellant is unavailable. Bullseye is much easy to acquire on short notice than M9.
In an orifice, you have choked flow because there is a normal shockwave across the orifice and the velocity is limited to Mach 1.

mflchk.gif

Flow occurs between two different pressures, inside a gun barrel the only two pressures are the pressure in the chamber, and the pressure at the base of the bullet, which are not different by a whole bunch, for a 5.56mm it about 1,000 psi, that's not going to be enough to choke the flow . . .
 
Oh, and technically there isn't any "flow", it is a gas expansion problem, not a classic flow problem. At least until the bullet exits.

And you are probably right as I stated in my first post I am a solid-mechanics/dynamics focused mechanical engineer. In a previous job I worked with a lot of aerospace guys that did the god-awful fluid thermal stuff. I was just there to designed the mechanisms and they shot them down gun tubes. I have been pouring back through my undergrad fluid dynamics and thermal books and a lot of internet research to get this far in the discussion. I still want to see a good model for calculating the speed of sound in a supercritical fluid but am failing on that front badly. I would have thought someone would have published the properties of propellant gasses at high temperature and pressures and have failed to find it in both in publicly available professional publication (IEEE etc) or the publicly release research at dtic.mil. The later really surprised me. I am probably not searching for the right specific terms.
 
In an orifice, you have choked flow because there is a normal shockwave across the orifice and the velocity is limited to Mach 1.

View attachment 916890

Flow occurs between two different pressures, inside a gun barrel the two pressures are the pressure in the chamber, and the pressure at the base of the bullet, which is not a whole bunch, for a 5.56mm it about 1,000 psi, that's not going to be enough to choke the flow . . .

As I understand it you don't get a choked flow in a gun barrel since you never get going fast enough to form a shock-wave. As soon as you get close to super sonic in the gun tube a shock wave starts to form and this drops pressure on the base of the bullet and the bullet stops accelerating thus never allowing the gases to get to super sonic. The only way you can have super sonic flow in a tube is if it starts super sonic from a converging nozzle. You cannon transition from subsonic to super or the other way around in a uniform cross section tube (like a gun barrel) if my reading is correct.
 
And you are probably right as I stated in my first post I am a solid-mechanics/dynamics focused mechanical engineer. In a previous job I worked with a lot of aerospace guys that did the god-awful fluid thermal stuff. I was just there to designed the mechanisms and they shot them down gun tubes. I have been pouring back through my undergrad fluid dynamics and thermal books and a lot of internet research to get this far in the discussion. I still want to see a good model for calculating the speed of sound in a supercritical fluid but am failing on that front badly. I would have thought someone would have published the properties of propellant gasses at high temperature and pressures and have failed to find it in both in publicly available professional publication (IEEE etc) or the publicly release research at dtic.mil. The later really surprised me. I am probably not searching for the right specific terms.
If you look at models for interior ballistics, none of them worry about "flow", or "Mach number", or "shock waves", it's because they don't matter. They do worry about gamma and do treat the propellant gas as an ideal gas, so . . .

Flow does come up when modeling gas operated stuff, and that gets hairy quick.
 
As I understand it you don't get a choked flow in a gun barrel since you never get going fast enough to form a shock-wave. As soon as you get close to super sonic in the gun tube a shock wave starts to form and this drops pressure on the base of the bullet and the bullet stops accelerating thus never allowing the gases to get to super sonic. The only way you can have super sonic flow in a tube is if it starts super sonic from a converging nozzle. You cannon transition from subsonic to super or the other way around in a uniform cross section tube (like a gun barrel) if my reading is correct.
How fast will air move going from a pressure head of 1015 psi to ambient through a 1/4 inch tube? That is a good approximation of how fast the gas flows in a gun barrel, because that's the pressure differential and that's the approximate size of the hole.

Can gas expand faster that the speed of sound? Yes, that's the whole principle behind explosives. And, since the expanding gas in the barrel is not trying to push any other gas out of the way, there is no shock wave, behind the bullet.

(After the bullet exits you get a nice shock wave as the supersonic gas interacts the the ambient gas, and an increase in flow as the pressure head is now in the region of 10,000 psi to ambient.)
 
If you look at models for interior ballistics, none of them worry about "flow", or "Mach number", or "shock waves", it's because they don't matter. They do worry about gamma and do treat the propellant gas as an ideal gas, so . . .

Flow does come up when modeling gas operated stuff, and that gets hairy quick.

Right, because you can't create a shockwave in the tube so if your only worried about what you can do then why bother with the rest of this mess... But this idea that gases moving in the gun barrel can't easily transition to super sonic velocity while in the tube is what limits the maximum velocity of a combustion powered gun. That is the short answer to the OP's original question. The who, what, when, and why is what has led to this very messy thread.
 
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Right, because you can't create a shockwave in the tube so if your only worried about what you can do then why bother with the rest of this mess... But this idea that gases moving in the gun barrel can't easily transition to super sonic velocity while in the tube is what limits the maximum velocity of a combustion powered gun. That is the short answer to the OP's original question. The who, what, when, and why is what has led to this very messy thread.
You can create a shock wave in a tube, one forms in front of the bullet as soon as the velocity exceeds Mach 1. But, behind the bullet there is nothing for a shock wave to form in. A shock wave forms when something tries to push a gas out of the way faster than the gas can move. Behind the bullet, what is trying to push gas out of the way? Nothing, the gas is the one doing the pushing, and everything else is a solid.

What limits conventional gun technology?

The amount of energy available in the propellant, how much propellant you can realistically stuff into something - and how fast you can get gas to expand without exceeding the structural limits of the chamber. Practical limits with current technology: 6,000 fps
 
How fast will air move going from a pressure head of 1015 psi to ambient through a 1/4 inch tube? That is a good approximation of how fast the gas flows in a gun barrel, because that's the pressure differential and that's the approximate size of the hole.

Can gas expand faster that the speed of sound? Yes, that's the whole principle behind explosives. And, since the expanding gas in the barrel is not trying to push any other gas out of the way, there is no shock wave, behind the bullet.

(After the bullet exits you get a nice shock wave as the supersonic gas interacts the the ambient gas, and an increase in flow as the pressure head is now in the region of 10,000 psi to ambient.)

Find me a video of an open air explosion with a visible shockwave where the gases from the explosive that formed the shock wave are traveling ahead of the shock wave. You won't, it can't be done.
You can create a shock wave in a tube, one forms in front of the bullet as soon as the velocity exceeds Mach 1. But, behind the bullet there is nothing for a shock wave to form in. A shock wave forms when something tries to push a gas out of the way faster than the gas can move. Behind the bullet, what is trying to push gas out of the way? Nothing, the gas is the one doing the pushing, and everything else is a solid.

What limits conventional gun technology?

The amount of energy available in the propellant, how much propellant you can realistically stuff into something - and how fast you can get gas to expand without exceeding the structural limits of the chamber. Practical limits with current technology: 6,000 fps

Look up and study the reasons two-stage light gas guns exist and how they function. They exist because of this super sonic velocity in the working fluid limiting how fast you can push a projectile in a conventional gun. That is not my idea or guess. This super sonic velocity in the working fluid is the reasons given by the scientist and engineers that have invented and use these light gas guns to accelerate projectiles to hyper-sonic velocities.

I may have made a mess of the nitty-gritty details here and there in the explanation later is the thread but not my original post. It is spot on and it is not my guess but the reasons given by scientist and engineers better qualified than me. You cannot easily push a projectile down a barrel faster than the speed of sound in the working fluid pushing the projectile. This limits the velocity of airguns, conventional guns, and even single, two, and three stage light-gas-guns ultimately. We can argue the nuances all we want but the over arching idea is solid and well understood by those that use these systems and research in this area of hyper sonic projectiles and collisions.

If you don't believe me (and that is just fine as I am not a fluid thermal guy as stated previously) the best thing I can suggest is do some research on your own. There is plenty of good information in the public domain on air rifles, firearms and cannons, and various forms of light gas guns that support the idea that the speed of sound in the working fluid pushing the projectile is the critical factor limiting the maximum velocity of a fluid propelled projectile. I am sorry I cannot fully explain the details to everyone's satisfaction...:oops:
 
Some cleanup work performed. Let's see if we can continue with the discussion without turning it to a discussion about those involved in it instead of the original topic.
 
Find me a video of an open air explosion with a visible shockwave where the gases from the explosive that formed the shock wave are traveling ahead of the shock wave. You won't, it can't be done.
Find me some open air inside a gun barrel and we'll be even.

A shock wave forms when a high speed gas (or solid) runs into a low speed gas and the low speed gas cannot get out of the way fast enough. So, in open air the high speed gas from the burning explosive runs into the stationary gas of the ambient air and a shock wave forms.

Inside a gun barrel, where is the stationary gas the high speed gas runs into to form a shock wave? There isn't any. There is the tiny bit of ullage in the case but that gets compressed to chamber pressures before the bullet unseats from the cartridge case. After the bullet uncorks from the case all of the gas is moving in the same direction at more or less the same speed. No shockwave behind the bullet.

As to a light gas gun the shock wave that compresses the secondary charge is AHEAD of the "bullet", once the secondary charge ignites and starts to move the payload the shockwave disipates, as once again, all of the gas is moving in the same direction at more or less the same speed.

There is no shockwave behind the bullet in the propelling gas, therefore there is no limiting of the gas velocity due to shockwave formation.
 
Find me some open air inside a gun barrel and we'll be even.

A shock wave forms when a high speed gas (or solid) runs into a low speed gas and the low speed gas cannot get out of the way fast enough. So, in open air the high speed gas from the burning explosive runs into the stationary gas of the ambient air and a shock wave forms.

Inside a gun barrel, where is the stationary gas the high speed gas runs into to form a shock wave? There isn't any. There is the tiny bit of ullage in the case but that gets compressed to chamber pressures before the bullet unseats from the cartridge case. After the bullet uncorks from the case all of the gas is moving in the same direction at more or less the same speed. No shockwave behind the bullet.

As to a light gas gun the shock wave that compresses the secondary charge is AHEAD of the "bullet", once the secondary charge ignites and starts to move the payload the shockwave disipates, as once again, all of the gas is moving in the same direction at more or less the same speed.

There is no shockwave behind the bullet in the propelling gas, therefore there is no limiting of the gas velocity due to shockwave formation.

I unfortunately disagree with you. The speed of sound in the propelling gas is the primary factory limiting the velocity of a fluid propelled projectile. I stand by that assertion. There is plenty of literature out there to support that position if you're willing to look for it. Anything else I could say at this point in the thread would likely be repeating points I have already tried to make. If I find a really good explanation by someone reputable or some other new info I will add it to the thread.
 
I unfortunately disagree with you. The speed of sound in the propelling gas is the primary factory limiting the velocity of a fluid propelled projectile. I stand by that assertion. There is plenty of literature out there to support that position if you're willing to look for it. Anything else I could say at this point in the thread would likely be repeating points I have already tried to make. If I find a really good explanation by someone reputable or some other new info I will add it to the thread.
As long as you leave shockwaves out of it. The limiting factor is related to the speed of sound but has nothing to do with shockwaves as you asserted a bit back, and is not limited to Mach 1 in said gas.

It is very very difficult to push a bullet faster than the speed of sound in the propellant gases pushing the bullet. Going faster than the speed of sound (of the propellant gases) forms a shock-wave in the barrel choking the gas flow and significantly lowering the pressure on the base of the projectile limiting further acceleration.

The limit is as I state here:
. . . and how fast you can get gas to expand . . .
And, how fast you can expand a gas is governed by the equation:

Vexp = 2 a(o) /(gamma - 1)

Where:

Vexp = the maximum velocity an unrestrained expanding gas
a(o) = velocity of sound
gamma = gas constant for the working gas



As I stated in my very first post, you're estimation was good, the stated reason was incorrect. Might I suggest for you "Interior Ballistics of Guns" published by the Army Material Command.
 
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Wow, this definitely went Jedi vs. Sith for a while. A fascinating read that I can kind of follow. I do however, have one question.

Did Brady or someone else deflate the football's, or was it due to the temperature?

Damn! You gents know your stuff!
 
Wow, this definitely went Jedi vs. Sith for a while. A fascinating read that I can kind of follow. I do however, have one question.

Did Brady or someone else deflate the football's, or was it due to the temperature?

Damn! You gents know your stuff!
Someone did the math . . .

Did the weather play a role in all this Patriots-Colts Deflategate business? Very unlikely.

Here's why.

Every 10 degree drop in temperature (F) results in about .2 PSI loss in a football. Say the balls were inflated/checked at room temp prior to kickoff, which is around 70 degrees. Gametime temp was around 50 degrees. We're talking about .4 drop in pounds per square inch (PSI).

You may recall the footballs dropped from 13.5 PSI or so to 10.5 PSI.

https://www.cbssports.com/nfl/news/did-weather-play-a-role-in-patriots-colts-deflategate/
 
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