Sonic Choke? Maybe not. 2162 FPS

[Bill G]

If at any point a person has decided that they are the smartest guy in the room, they would be well advised to find another room.  multiple smart minds are greatly better than one smart mind.   Uhhhhh, that's why we all started coming to forums....... remember?  I do. 

I think this has officially moved from trying to disprove that a limit exists to where is the limit?(on HPA of course)

Bill

[MichaelM]

I remember a few years ago watching some college kids launching ping pong balls through several pop cans using a setup that that placed the barrel in vacuum and then using relatively low pressure filling the pressure chamber with air till a thin layer of plastic ( like garbage bag thin) burst sending a ping pong ball with enough velocity to blow right through soda cans ....... theory being the vacuum pulled the projectile while the pressure pushed it to reach speeds......

at the sake of sounding ignorant(which I mostly AM when it comes to this type of maths) could something like this be happening to help with the velocities? wouldn't the atmospheric pressure in the barrel be at a relative vacuum to the pressure chamber making for a lot more force being applied to the projectile both pulling and pushing?


sorry if thats been covered.... I will admit I glossed over a few pages in this thread as the maths was making my eyes go a bit crossed at a few points LOL!!

Hi Michael,
The vacuum on the ping pong ball keeps coming up but I never did the math on it to see what was going on.     If you pull a vacuum in front of the ping pong ball you really are just applying a pressure of about 14.5 psi (atmospheric pressure) behind it.  The PP ball weighs 2.7grams = 41.7 grains.  The caliber is 1.575.   If you use a 24" long tube/barrel you have the equivalent of a 766cc tank in front of the PP ball.
Doing the math with my spreadsheet, because the PP ball is so light compared to its caliber, at the end of the  24" barrel, it should be going about 460 fps.  You better be about 20 feet back from the table because that is a 313 mph serve! 
Basically, it is 1.575 cal, 41.7 gn, 766 cc dumptank at 14.5 psi, using a reasonable 60% system efficiency, gives you 460 fps.  Unfortunately, adding that extra 14.5 psi on top of 3,000 or 4,000 psi in a regular pcp, wouldn't be noticeable.
Lloyd

yea I have seen the ones where they basically just apply a vacuum to the tube and pop one side using just the atmo pressure of 14.5 psi... this is the video I am referring to.... where they add a converging
/diverging nozzle (venturie?) and a presurrized air chamber behind it and achieve supersonic speeds... *(&^ even if its not applicable it sure is impressive lol


dunno.. lol its obvious that extreme velocities are possible seems everyone is just trying to understand HOW it works lol... frankly my vote is magic.......

[Scotchmo]

Don't have a formula or graph, but I'd guess that exceeding the threshold is accomplished by changing the environment through a higher pressure than which the threshold was originally theorized.
Just as we have a so called constant speed of gravity on earth, if the mass of the gravitational force were increased so would be the speed of gravity.

That was my first intuition, and it's very close. But this is what it is:

"...exceeding the threshold is accomplished by changing the environment through a higher pressure temperature than which the threshold was originally theorized."

[Scotchmo]

If at any point a person has decided that they are the smartest guy in the room, they would be well advised to find another room.  multiple smart minds are greatly better than one smart mind.   Uhhhhh, that's why we all started coming to forums....... remember?  I do. 

I think this has officially moved from trying to disprove that a limit exists to where is the limit?(on HPA of course)

Bill

Smart is good, but being the smartest doesn't always get you there.

Be open minded and use impeccable logic. You either come up with the right answer or can admit that it is beyond your current knowledge base. Use logic, increase your knowledge base, and - AHA!

[rsterne]

OK, here is the back of the napkin calculation for the temperature rise of the air in Lloyd's 2031 fps shot (but with infinite reservoir, and therefore constant pressure), assuming the 30% loss in efficiency all changes to heat.... I would appreciate it if someone will double check my method and calculations.... First, the shot criteria used in Lloyd's J4 Spreadsheet....

Pressure = 4000 psi, 9.1 gr. bullet, bore = 0.278", barrel length = 47.5", 1 lb. bore drag, 70% efficiency, air mass included, Isothermal expansion (because of dump shot and infinite reservoir).... Predicted velocity 2049 fps, energy = 84.85 FPE....

Change bore drag to 0, and efficiency to 100%, no other changes.... Predicted velocity 2459 fps, energy = 122.16 FPE.... Energy lost to heat = 122.16 - 84.85 = 37.31 FPE....

Using the calculator at Peacesoft for the properties of air at 4000 psi and 20*C.... http://www.peacesoftware.de/einigewerte/calc_luft.php5

Air density = 302.45 kg/m^3
Specific Heat Capacity = 1.343 kJ/kg.K
Multiplying those together gives 302.45 x 1.343 = 406.2 kJ/m^3.K .... ie it would take that much energy to raise the temperature of 1 m^3 of air at 4000 psi by 1 deg. K....

Barrel volume is 0.278^2 x PI/4 x 47.5 = 2.883 in^3 x 16.39 = 47.25 cc = 0.00004725 m^3
Multiply that by the energy per degree above, and we get 406.2 x 0.00004725 = 0.0192 kJ/*K, or 19.2 joules.... which is 14.2 FPE....
We have 37.31 FPE available, so dividing 37.31 / 14.2 = 2.63*K, which is 4.7*F.... The energy available in the 30% loss of efficiency would raise the temperature of the air in the barrel by less than 5*F.... It would appear that is nowhere near enough to account for any significant increase in the molecular velocity.... As I said, someone please double check my numbers....

It is interesting to note that if we calculate the theoretical maximum FPE for Lloyd's test gun at 4000 psi, neglecting the mass of the air, we get 961 FPE, as follows....

Bore area = 0.278^2 x PI/4 = 0.0607 in^2 x 4000 psi = 242.8 lbs x 47.5 / 12 ft = 961 FPE....

Bob

[Scotchmo]

.... The energy available in the 30% loss of efficiency would raise the temperature of the air in the barrel by less than 5*F.... It would appear that is nowhere near enough to account for any significant increase in the molecular velocity.... As I said, someone please double check my numbers....

It is interesting to note that if we calculate the theoretical maximum FPE for Lloyd's test gun at 4000 psi, neglecting the mass of the air, we get 961 FPE, as follows....

Bore area = 0.278^2 x PI/4 = 0.0607 in^2 x 4000 psi = 242.8 lbs x 47.5 / 12 ft = 961 FPE....

Bob

I made the same error at first. You used just the pellet. The air must also be included. So it's 30% of total energy.

The heat gain is 30% of 961fpe (0.37btu). And the highest concentration of that gain is directly behind the pellet.

The following picture is an attempt to visually show what is happening. The actual temperature rises will be different. But you get the picture:

[rsterne]

I wondered about that (why I mentioned the theoretical maximum).... but in fact a very large portion of that 961 FPE ends up being the KE of the air being blasted out the muzzle, right?.... Even if that was correct, we would have 30% of 961 FPE = 288 FPE / 14.2 FPE/*K = 20.3*K, which is less than 37*F increase.... The molecular velocity of air at 40.3*C is still only 1703 fps.... To reach 2000 fps, you need an air temperature of 160*C, way above the boiling point of water.... I still think that simple "focusing" of the faster molecules by the velocity gradient is the reason, or some/most of it.... Can we really explain more than a 140*C rise in temperature?....

Bob

[Scotchmo]

I wondered about that (why I mentioned the theoretical maximum).... but in fact a very large portion of that 961 FPE ends up being the KE of the air being blasted out the muzzle, right?.... Even if that was correct, we would have 30% of 961 FPE = 288 FPE / 14.2 FPE/*K = 20.3*K, which is less than 37*F increase.... The molecular velocity of air at 40.3*C is still only 1703 fps.... To reach 2000 fps, you need an air temperature of 160*C, way above the boiling point of water.... I still think that simple "focusing" of the faster molecules by the velocity gradient is the reason, or some/most of it.... Can we really explain more than a 140*C rise in temperature?....

Bob

Yes. We can't determine the exact peak temperature within the column of air without an exact model of the viscous shear. But we can easily speculate that it will be higher than the average temperature rise. And it will occur at the base of the pellet.

Imagine a 1 grain-mole (mole=chemical term for amount) cylinder of air that will travel down the barrel. It gains entropy in the first inch of travel down the barrel. It moves into the second inch of the barrel, gaining more entropy. It makes room for another grain-mole to enter the barrel and gain entropy. At this point in time, the first grain-mole to enter the barrel has gained twice as much as the second grain-mole. 2/3 of the heat gain is in the first grain-mole. The first grain-mole is right behind the pellet.

It’s not that simple as the air is accelerating, heating, and expanding faster than the air that comes later. The grain-mole cylinder of air immediately behind the pellet will be longer than the grain-mole of air just entering the barrel. I'm not sure yet how that will affect my numerical integration which models the process as small fixed length segments of barrel.

I think we have an integral within an integral.

I did not check your math, so I can’t say if the 37F rise is correct. But I say that the temperature rise of the air behind the pellet will be at least twice that of the average temperature rise.

Note: We will never be able to actually measure the peak temperature since it happens in the last microsecond before the pellet exits. And then it's gone.

[lloyd-ss]

This is a very interesting puzzle.  I can see both possibilities:  heating the air to increase the molecular speed, and the focusing of the molecular movement toward the path of least resistance: the muzzle of the barrel. 
Scott, I see the hot leading edge of the air, basically in contact with the projectile.  The way heat energy manifests itself is very varied.  I normally think of something getting hot as a fairly slow and deliberate process, with solid evidence that an object got hot.  I don't tink of heat as being instantaneous in its happening and dispersing.  I watched a youtube experiment where they smacked two 1-1/2" ball bearings together.  One bearing in each hand, smacked together, and they came to a more or less dead stop.  The question was: Where did the kinetic energy go?"  The answer was: heat.   They smacked the balls together again but this time with a piece of paper between them.  afterwards, looking at the paper, it had a tiny hole at the collision point, with an almost invisible charred edge, and a burnt smell.  There was really no sensation of heat being produced in a conventional sense, but obviously all of that energy was converted to heat.

If there is heating of the air directly behind the pellet, maybe it is something similar: very quick, and then gone.  It requires a paradigm shift in my thinking if that is indeed the case.

[Scotchmo]

This is a very interesting puzzle.  I can see both possibilities:  heating the air to increase the molecular speed, and the focusing of the molecular movement toward the path of least resistance: the muzzle of the barrel. 
Scott, I see the hot leading edge of the air, basically in contact with the projectile.  The way heat energy manifests itself is very varied.  I normally think of something getting hot as a fairly slow and deliberate process, with solid evidence that an object got hot.  I don't tink of heat as being instantaneous in its happening and dispersing.  I watched a youtube experiment where they smacked two 1-1/2" ball bearings together.  One bearing in each hand, smacked together, and they came to a more or less dead stop.  The question was: Where did the kinetic energy go?"  The answer was: heat.   They smacked the balls together again but this time with a piece of paper between them.  afterwards, looking at the paper, it had a tiny hole at the collision point, with an almost invisible charred edge, and a burnt smell.  There was really no sensation of heat being produced in a conventional sense, but obviously all of that energy was converted to heat.

If there is heating of the air directly behind the pellet, maybe it is something similar: very quick, and then gone.  It requires a paradigm shift in my thinking if that is indeed the case.

Right on.

The heating is happening at the molecular level inside of the air. It is not flowing into the air. It is an instant heat increase. Some of that heat may flow back toward the start of the barrel, or into the barrel wall. But the shot cycle is fairly brief so not much time for that to happen. I would assume that virtually all of the heat stays in the air, exactly at the point where the entropy gain takes place.

[rsterne]

Scott, you made reference on the Yellow to the importance of integrating the addition of air to the system, instead of just using half the mass of the filled barrel.... To illustrate this, I used Steve's formula (modified to include the omitted PI/4 term, with the corrected constant), and compared it to the output of Lloyd's J4 Spreadsheet.... I used the criteria for Lloyd's 2031 fps shot (.278 cal, 9.1 gr. pellet, 4000 psi), and varied the barrel length.... For Lloyd's spreadsheet, that would provide a prediction of the MV if you progressively shortened the barrel (only)....  Here are the results....



Steve's equation, when corrected as above, predicts a maximum velocity of 1854 fps at zero projectile weight (instead of 1643).... You can see that without the integration being performed at intervals, my (Steve's) equation predicts too low a maximum velocity at longer barrel lengths, just as you suggested.... the proof being that Lloyd was able to exceed them.... In other words, you can't simply use half the total amount of air in the barrel to calculate the mass, and the error increases with barrel length.... in agreement with your statement that his equation may only be useful at zero barrel length.... Even so, when corrected, it would predict 1854 fps, not 1643, with zero projectile weight....

Bob

[Scotchmo]

I have some new theories of my own.

1) The 1640 1854fps 70F limit is correct for freely expanding air. efficiency = 100%

2) In a barrel, there are losses. efficiency < 100%

3) The entropy gain raises the limit to >1640 1854fps

4) When further entropy_gain = kinetice_energy_gain. efficiency = 50%

5) At 50% efficiency, the pellet is no longer accelerating.

6) 1640 1854fps/50% = 3280 3708fps

7) That happens at a barrel length of infinity.

Lloyd, If you attempt to prove that wrong, you've got your work cut out for you. 

[rsterne]

Gee, I think I heard that idea of a maximum of 3300 fps somewhere before.... *grin*.... both in my "thought experiments", and in the trend in the graphs in post #326....

Lloyd, If you attempt to prove that wrong, you've got your work cut out for you

and that's no joke.... sonic or otherwise.... 

Bob

[Scotchmo]

Bob, Lloyd, et al,

My new theory is the result of a "thought experiment" that has been running through my head.

The missing piece of the experiment was entropy. No one seemed to be seriously considering it. The only way to ignore it is to let the air expand freely, without entropy production. Without the barrel, the 1640 1854fps works. If we are talking about airguns, you need a barrel. As a barrel gets longer and longer, the entropy production raises the limit, but also reduces the efficiency. The falling efficiency makes it that much harder to accelerate the pellet. Longer and longer barrels give diminishing returns. At some point it should stop accelerating. The efficiency keeps falling but will never quite reach a low of 50%. So you keep extending the barrel. Eventually you reach infinity and finally 50% efficiency.

I'm talking about overall efficiency that includes kinetic energy of the gas. Actually, the pellet mass can drop out for this thought experiment.

70% efficiency is still a ways away from 50%. How far are we willing to venture down an infinite path?

47.5" is far enough to satisfy my curiosity. Plenty of length to explore and keep us occupied.

[rsterne]

I can understand your argument about the 50% efficiency being a reasonable limit.... equal parts heat and kinetic energy.... Connecting the dots from there to doubling the velocity I'm having a little more trouble with.... Energy is proportional to velocity squared, half the energy (efficiency?) would be 0.707 of the velocity.... That might yield 1647 / 0.707 = 2330 fps.... and I'm not sure that can't be surpassed.... starting with air at 70*F, given enough pressure, reservoir, and barrel length, and a light enough bullet....

I'm not sure there is any way to prove this, one way of the other.... even on a theoretical basis.... For sure it is above my pay grade.... 

All we know for sure, is that 1647 fps isn't the limit.... nor is 2000 fps.... If we can get a light enough bullet, at 6000 psi, I think we will put Mach 2 behind us as well, with Lloyd's current setup.... Doubling the barrel length again might give us another 10%.... or not, depending on if/when we start losing efficiency as you are predicting.... Realistically, if we put Mach 2 behind us, I think it's time to quit.... at least for now....

Bob

[lloyd-ss]

I am very confused. 
Lloyd

[rsterne]

Just a short PS.... For the molecular velocity to reach 3280 fps requires a temperature of about 900*C.... Aluminum melts at 660*C.... the equivalent velocity of air molecules is 2940 fps....

I'm afraid I am too, Lloyd....

Bob

[Scotchmo]

I can understand your argument about the 50% efficiency being a reasonable limit.... equal parts heat and kinetic energy.... Connecting the dots from there to doubling the velocity I'm having a little more trouble with.... Energy is proportional to velocity squared, half the energy (efficiency?) would be 0.707 of the velocity.... That might yield 1647 / 0.707 = 2330 fps.... and I'm not sure that can't be surpassed.... starting with air at 70*F, given enough pressure, reservoir, and barrel length, and a light enough bullet....

I'm not sure there is any way to prove this, one way of the other.... even on a theoretical basis.... For sure it is above my pay grade.... 

All we know for sure, is that 1647 fps isn't the limit.... nor is 2000 fps.... If we can get a light enough bullet, at 6000 psi, I think we will put Mach 2 behind us as well, with Lloyd's current setup.... Doubling the barrel length again might give us another 10%.... or not, depending on if/when we start losing efficiency as you are predicting.... Realistically, if we put Mach 2 behind us, I think it's time to quit.... at least for now....

Bob

Bob,

You could be right about the actual velocity limit. We won't have enough energy remaining to even get close to the 3280fps molecule velocity.  The main point is that if you drive it to the point of 50% efficiency, you can't drive it any faster. And that speed will always be less than the molecule velocity, whatever it may be. 2330fps sounds almost too slow. I wanted a molecule velocity that was unreachable, but sounded plausible.

It's just a starting point for discussion. You threw the first curve-ball.

Your 2330fps gives Lloyd a difficult, though maybe attainable goal. If we can't reach it while pushing hard enough to get 50% efficiency, I'll go with your improved version of the new theory.

I'll avoid "Mach", and stick with fps. Isn't the fps value of Mach changing directly with the molecule velocity?

[rsterne]

I think it will be very difficult to reach 2330 at 70% efficiency.... at 50% I don't think we have a hope.... According to Lloyd's present J4 Spreadsheet, that would take 10,000 psi in an 8 ft. barrel, with a 3.5 gr. bullet in his existing gun.... The temperature of the air would have to be 310*C, if molecular velocity is really what matters....

Bob

[Scotchmo]

I think it will be very difficult to reach 2330 at 70% efficiency.... at 50% I don't think we have a hope.... According to Lloyd's present J4 Spreadsheet, that would take 10,000 psi in an 8 ft. barrel, with a 3.5 gr. bullet in his existing gun....

Bob

8 ft. is much less than infinity. I think it will still be around 60-70% efficient. Just guessing.

There is plenty of data still to be gained from a 4 ft. barrel.