Muzzle Velocity In Psi?

[tewlman]

I was playing with a comp design and wanted to run an FEA program on my finished product to see how small i could make it and it still be safe. The program can apply a load in PSI so i wanted to know if anyone knew how to convert the muzzle velocity of x Ft/sec to a PSI value?

[Zak Smith]

QuickLoad can predict muzzle pressure.

[XRe]

Yeah, you need a program that can take a given load (powder, bullet, primer, OAL, etc) and muzzle velocity, and predict a pressure for you. There's no way to really say "I got 1400 fps, so that means I had 45,000 psi" in a simple fashion... And, you want pressure at the muzzle - peak pressure might be significantly different, depending on the powder....

[Zak Smith]

For a 16", it should be around 11-12,500 psi for M193 or Mk262.

Edited November 15, 2005 by Zak Smith

[wsimpso1]

Zak has a pretty good estimate of gas pressure at the muzzle. Trouble is that gas pressure at the muzzle is not what you have hitting the baffles on the compensator. And if it was, well, you would have 8000 pounds on the brake. OOF! What is hitting the baffles is gases that are moving and having their direction changed. You need to know what the forces look like. Momentum resolves into Force x time, and your hard part is figuring out what the time signature is.

As the muzzle is uncorked by the bullet, the gases leaving the bore will accelerate to their local speed of sound, which is way up there (over 4000 ft/s) compared to the nominal speed of sound in ambient air (1100 ft/s), pushing the air around the muzzle away as it does so. These now very fast gases are deflected away sideways by the baffle. So the energy still contained in a barrel full of powder gases at 11000 psi and say 1800 F (1250K) is converted into kinetic energy quite efficiently. The kinetic energy for any little parcel of gas is KE=1/2*sum of (mv^2).

One way to model this is to divide up the gas in the barrel into many small parcels, all at 77 MPA, and at their own velocities to have the front most one at muzzle velocity. Then you compute the mass of each one and then make a tiny time step and update the velocities and locations, then keep going. Include the ninety degree bend at the brake and the effect of expansion cooling on the temperature and temperature effect upon the local speed of sound, keep the local velocities at or below the local speed of sound, and you should have a pretty good estimate of the time-force profile on the brake baffle…

Another way is to make use of Conservation of Momentum. The momentum from this I=mv is largely converted from axial (downrange) to lateral (sideways) by the brake, with a commensurate pull forward that varies with time. Now we can estimate how much momentum is available in the expanding powder gases. What was the powder charge? Add 0.4 grains for the primer charge. Divide by 7000 to get pounds. Multiply by .454 to get it in kg. Average gas velocity leaving the barrel can be approximated at 4000 ft/sec, divide by 3.28 to get it in m/s. Multiply the kg by the m/s and you have momentum in N-s.

Now comes the hard part. How long does this event take and what does the flow look like? Hmmm. Now, if I had a rifle with a brake on it, and an oscilloscope and some strain gages, I could find out. I would place one strain gage circumferentially on the barrel near the muzzle, and another axially on the bottom of the brake. Run the wires so that powder gases would not blow them away. The one on the barrel would show some readings as vibrations from hammer fall, primer ignition and bullet engraving into the rifling occur, and then the big change would occur as the bullet passes this strain gage, and the barrel expands under the pressure of the powder gases. This would serve to trigger the scope to record data, both the one on the brake as well as the one on the barrel. Then we can watch the strains on the barrel and the brake as the barrel is uncorked and the brake works. And generate a curve for how the gases drain out, and how this brake applies load to the barrel.

As much fun as that stuff would be to run, I have not worked in a gun lab for 20 years, so does anybody else know what the pressure-time profile looks like during the gas drain?

Another way to do these calcs without knowing what the real curves are is to estimate the upper bounds and know that the real number is somewhat below the upper bound. One upper bound would be to assume that the gases expand adiabatically (no energy lost to the surroundings), in which case the pressure at the baffle decreases with the ratio of the areas (Pbrake = Pmuzzle*Abore/Abaffle). Reality will probably be lower than this…

Another estimate exists. We have gas at 11000 psi draining out of the barrel into a 15 psi area, and cooling as it does so from somewhere around 1250 K to say 400 K, so that is lessee, about 2200 times the volume it occupied in the barrel. If it all drains out at 4000 ft/s, you can calculate an approximate time for it to all blow out. Now it will actually take longer (as the barrel drains, things will slow down), and the peak velocity may actually be higher, but this might be a reasonable number.

Typical engineering consultation costs are way too high for you to have me or anybody else do this for you. I personally would just whittle some out and go shoot them. If the baffles bend over or parts fly off of it, the thing was too flimsy. Likewise, if you bend it in use. I suspect that handling is more stressful than shooting it, so build it to survive bumping around in the trunk and bumping barricades. Do that and the odds are pretty good it will survive shooting the thing.

Good luck.

Billski

[tewlman]

hey billski,

Thanks for the very detailed info. I understand where your thought process is and see where you cant just plug in a number like 11K psi and expect a realistic result.

I design using Solidworks and it includes FEAnalysis with software called Cosmosworks. it is the scaled down version of the full blown Cosmosworks that has quite a few more features. I tried plugging in the 11000 psi andof course the part failed miserably, but that value is considered a hydraulic constant load, not momuntery.

I am sure you can figure the moment and get a realsonable value to use, but I'm not sure the scaled version of this FEA program can compute the results according to how they should be applied. But i am just playing anyway and thought it would be neat to explore.

Steve

[wsimpso1]

Hey tewlman,

Cool stuff, that SolidWorks/COSMOSWorks, isn't it? I have the full suite available to me and I like using it. It has gotten good use on stuff for my job as well as for the airplane project, designing landing gear legs to absorb enough energy while stay below yield strength, designing hinges and doors for flight loads, roof for rollover protection. Then there are weld stresses, inpact loadings, etc.

One thing - Elastic strain (prior to yielding) occurs at the speed of sound in the material, and is about 26,000 ft/sec in steel, so , even though the load is on and off quickly, the load gets on and off way too slowly to not be fully felt by the brake components. Plastic deformation takes more time to develop. If the stresses do indicate that they would be above yield strength, they may not move appreciably on one firing, but a succession of firings will move it and eventually be visible.

For calculations around the brake... I do not want to discourage you. I am sure that you can find the fractions of gases from anaerobic combustion of nitrocellulose and nitrogylcerine, calculate the thermal capacity of those gases, look up the thermal energy released by anaerobic combuustion of nitro cellulose and nitroglycerin, compute the temperature/sonic velocity relationships, and then the temperature/pressure at the muzzle, and then go through the powder gas drainage modeling and find an estimate of the time-force curve for the brake. It just makes my head hurt faster than "I Am My Own Grampa".

Now if someone can get an oscilliscope and strain gauged barrel and brake out to the range, I would sure love to see the results. Maybe someone has some Stresscote that they can apply to a known brake, shoot it and get an estimate of stress from that. Both methods could validate the calculations.

[tewlman]

For calculations around the brake... I do not want to discourage you. I am sure that you can find the fractions of gases from anaerobic combustion of nitrocellulose and nitrogylcerine, calculate the thermal capacity of those gases, look up the thermal energy released by anaerobic combuustion of nitro cellulose and nitroglycerin, compute the temperature/sonic velocity relationships, and then the temperature/pressure at the muzzle, and then go through the powder gas drainage modeling and find an estimate of the time-force curve for the brake. It just makes my head hurt faster than "I Am My Own Grampa".

Yeah, i do calculations like that while sitting at the breakfast table sipping my morning coffee

Have you read that book: anaerobic combustion of nitrocellulose for fun and profit? Great reading! Your way over my head dude, but i really appreciate your input.

Do you fly? I've had my private for about 5 years and used to work on F16's in the AF.

Solidworks, hell yeah i love it! While I dont have the full blown CosmosWorks, I do have the full Camworks package including 3,4 and 5 axis programming and surfacing + wire EDM and lathe modules. Also have an add-on called GearTrax which makes drawing gears a piece of cake.

Steve