Sonic Choke? Maybe not. 2162 FPS

[rsterne]

I agree, that was just one set of numbers that came out to get 2330 fps @ 50%.... If the efficiency is 60-70% (which I would expect) it would be a lot easier.... At 70%, it should take "only" 6000 psi with a 5 gr. bullet with the existing 47.5" barrel.... *LOL*....

Bob

[phoebeisis]

2030 fps-pretty fast-congrats.Still following this-
Curious if you get a bit more with N2-?
I wonder what sort of FPS FPE a 270  (.277 of 130 grains or so) would do-?
The below is a cut from the yellow forum-this seems to be their(his take anyway) WHY of why you can't get over 1640 fps.
They seemed to have treated the air column as a solid rod-or a liquid column-not as tiny tiny particles with LOTS of empty space.




Nope. No matter how high the pressure, ~1640fps remains an absolute limit for cold air.   November 12 2008, 4:24 PM

This simply because as pressure rises, so does the mass of the air filling the bore behind the pellet. Since this air has to be accelerated along with the pellet, as pressure rises without limit, eventually all of the available energy goes to accelerate air and not lead.

The velocity at that limit is 1640fps.

To go any faster requires, not more pressure, but a propellant with a lower molecular density.

Steve

Bulldawg-Mike-in 362 below- I-charlie phoebeisis(our first greyhounds were phoebe isis)  was unclear-the above is a cut from the yellow forum-with STEVE's EXPLANATION-from Nov 12 2008-of what 1640 is the upper limit-I should have been more clear-
charlie

[Buldawg76]

2030 fps-pretty fast-congrats.Still following this-
Curious if you get a bit more with N2-?
I wonder what sort of FPS FPE a 270  (.277 of 130 grains or so) would do-?
The below is a cut from the yellow forum-this seems to be their(his take anyway) WHY of why you can't get over 1640 fps.
They seemed to have treated the air column as a solid rod-or a liquid column-not as tiny tiny particles with LOTS of empty space.




Nope. No matter how high the pressure, ~1640fps remains an absolute limit for cold air.   November 12 2008, 4:24 PM

This simply because as pressure rises, so does the mass of the air filling the bore behind the pellet. Since this air has to be accelerated along with the pellet, as pressure rises without limit, eventually all of the available energy goes to accelerate air and not lead.

The velocity at that limit is 1640fps.

To go any faster requires, not more pressure, but a propellant with a lower molecular density.

Steve

Steve

Lloyd has already disproved that theory/fact with his 1745 fps shot in the .22 cal test gun and further disproved it with the 2030 fps shot in the .278 test gun as well.

I have all the faith he will break Mach 2 as well in the very near future.

Mike

[rsterne]

Steve, you have pretty much found the point of this thread.... to disprove that theory that has been around for nearly a decade now.... which has now been done successfully, several times....

Bob

[I_like_Irons]

How about measuring the pressure in the barrel at two points with respect to time?  The first point near the breach, and the second near the muzzle.

How does one do this?, you may be asking yourself while thinking it is a good idea.

The simple answer is to use strain gauges, Wheatstone bridges, a computer sound card with stereo microphone inputs, and Audacity sound analyzing software.  If you have a sound card that has four microphone inputs, then you can measure the pressure in four places.

In case you are not familiar with strain gauges, they work on the principle that when you stretch a wire it gets longer and skinnier and thus its resistance goes up.  Likewise if you compress the wire the resistance goes down.  The typical strain gauge is a flat serpentine wire laid onto a plastic backer.  The serpentine shape makes for more stretch in the wire for a given strain.   The gauges are glued to the item you want to measure the strain in. 

The Wheatstone bridge is a four resister device that amplifies the change in resistance in one of the resistors.  It consists of four "equal" resistors in a series loop.  The signal voltage is applied at two opposite nodes, while the voltage is read across the other two nodes.   Typically the strain gauge is one of the resistors while an "equal" value potentiometer (rheostat) is placed opposite.  The other two resistors are standard with a nominal value equal to the strain gauge at rest.

The bridge is balanced by adjusting the potentiometer so that the volt meter reads zero volts when the system is at rest.  If you are familiar with an analog multimeter you probably have balanced the bridge when you have used the ohm adjustment.

As far as the signal voltage, that is something which needs a bit more research, and may be dependent on the sound card, and perhaps the software.  But, the output signal will be fairly linear with respect to pressure since the strain and resistance response of the gauge will be linear as well.

I do know that Audacity has been used to make chronographs, and to measure time from one channel to the other along with frequency and amplitude.  Here, we would be interested in the amplitude with respect to time.  The other question I'm not too sure about is can Audacity deal with a direct current source and measure the voltage like a storage oscilloscope, or does it need an alternating source?  If the alternating source is required then it would have to be a pretty high frequency. 

The problem for the signal source, I think, would only be for calibration.  Here you have a static pressure for a period of time while you adjust the signals to get an equal and easy to read value.  The calibration procedure would go as follows:

Bridges are first balanced.  Then the muzzle is plugged (I suggest a "Champagne" cork).  The pressure inside the system is brought to the working pressure (4000 psi).  The output signals are adjusted to some equal value and reasonable value by adjusting the input voltages.  Note that the bridges will remain balanced regardless of the input voltage. 

Then the pressure is lowered  incrementally by some value like 500 psi, and notes made to the software output.  It should be linear, but, the software being designed for audio it may be logarithmic.  Too, there may be slight differences due to the sound card response.

The hardware (for a DC device) would be easy to make on a breadboard or a project board.  The things to get are strain gauges.  Make sure you get the type that only measure in one direction.  You will need two (or four) potentiometers that have an adjustment range the same as the nominal resistance of the gauges.  Two resistors for each bridge that have the same nominal value of the gauges. 

For the adjustable signal supply, you need to determine what your output voltages are likely to be.  Then you need to choose a battery, or battery bank/holder to get the desired input voltage.  A couple of voltage dividers with potentiometers might make for easily adjustable output signals.

[rsterne]

This idea could be used not only to confirm the accuracy of Lloyd's Spreadsheet (because it can predict the pressure drop vs. distance along the barrel).... but also to determine whether the expansion is Adiabatic, Isothermal, or in fact is increasing because of heating.... Calibration would be the key....

Bob

[I_like_Irons]

More than just that.  The strain gauges may be sensitive enough to get at least a feel for the pressure ahead of the bullet.  Also of interest is the time it takes for the bullet to get from point A to B (to C and D).  That coupled with the muzzle velocity, one may surmise as to the true rate of acceleration in the barrel.

Another thing it could measure is the after exit cooling affect due to adiabatic expansion and the internal stress relief of the barrel itself.

[lloyd-ss]

More than just that.  The strain gauges may be sensitive enough to get at least a feel for the pressure ahead of the bullet.  Also of interest is the time it takes for the bullet to get from point A to B (to C and D).  That coupled with the muzzle velocity, one may surmise as to the true rate of acceleration in the barrel.

Another thing it could measure is the after exit cooling affect due to adiabatic expansion and the internal stress relief of the barrel itself.

David,
Great ideas, all you need now is someone with the time and money and perseverance to implement them.   
Lloyd
P.S.
Incrementally sawing the barrel off will will provide us with the acceleration information.

[Scotchmo]

I agree, that was just one set of numbers that came out to get 2330 fps @ 50%.... If the efficiency is 60-70% (which I would expect) it would be a lot easier.... At 70%, it should take "only" 6000 psi with a 5 gr. bullet with the existing 47.5" barrel.... *LOL*....

Bob

Bob,

As soon as Lloyd attains 2330fps, it blows your limit theory. It will likely happen in the 70% efficiency range (according to my theory). 70% efficiency is doable. 50% is not. 50% is the limit that can never be reached.

My theory says 16401854/0.5

Your theory says 16401854/(sqrt 0.5)

Here is something to think about:

At 100% efficiency, all of the energy gains result in a velocity increase.

At 50% efficiency, none of the energy gains result in a velocity increase.

[rsterne]

Actually, my theory says 3,300 is the absolute limit with 70*F air, based on the idea of a supersonic jet firing a cannon, as Lloyd's analogy goes.... In fact, there is an equation kicking around (also proposed by Steve, in connection with his "Sonic Horizon" theory.... that if modified to use 1650 fps I think predicts a limit of 3300.... I'll do up a post about that.... I was just saying that if your idea works, I would think that since the KE is proportional to the square of the velocity, and the limit you suggested was when KE = Entropy, perhaps 0.707 would be the appropriate divisor in that case.... I also stated I didn't think that was a high enough limit, because I thought it might be attainable.... and of course limits should never be reached, or they wouldn't be limits....

Incidently, a gun like a Disco is only about 58% efficient in stock form.... Lower efficiency is often not associated with high performance, but something else restricting/affecting what could be happening.... the most common thing being hammer bounce, of course.... Your idea could really only be applied to dump shots with wide open barrels, I would think....

Bob

[Scotchmo]

Actually, my theory says 3,300 is the absolute limit with 70*F air, based on the idea of a supersonic jet firing a cannon, as Lloyd's analogy goes.... In fact, there is an equation kicking around (also proposed by Steve, in connection with his "Sonic Horizon" theory.... that if modified to use 1650 fps I think predicts a limit of 3300.... I'll do up a post about that.... I was just saying that if your idea works, I would think that since the KE is proportional to the square of the velocity, and the limit you suggested was when KE = Entropy, perhaps 0.707 would be the appropriate divisor in that case.... I also stated I didn't think that was a high enough limit, because I thought it might be attainable.... and of course limits should never be reached, or they wouldn't be limits....

Incidently, a gun like a Disco is only about 58% efficient in stock form.... Lower efficiency is often not associated with high performance, but something else restricting/affecting what could be happening.... the most common thing being hammer bounce, of course.... Your idea could really only be applied to dump shots with wide open barrels, I would think....

Bob

1640fps vs 1650fps is just a minor temperature difference in air. They relate to my 3280fps and your 3300fps. So we are really talking the same thing here. That jet/cannon analogy is starting to make a lot of sense. A gas(jet) at 1640fps with 1640fps booster molecules (cannon) pushing the pellet.

It would be nice to show it with math. That's partly why I dwell on it.
--------------------------------------
Edit: substitute 1854 for 1640.

Thought experiment:

At 100% efficiency, all energy is converted to acceleration. 1854/(sqrt 1) = 1854

At 50% efficiency, no energy converted to acceleration. 1854/(sqrt 0) =

What about in between 100% and 50%?

What about at 70.71% efficiency? Is 50% of the energy converted to acceleration? 1854/(sqrt 0.5) = 2622fps

Looks about right, but I'm not sure if continuing gets us there either.

---------------------------------------

We could try to work backwards from 3708 as well.

1854/(sqrt ??) =3708

?? = 0.25, or 25% converted to acceleration? But, according to my pseudo-theory, it was supposed to be none or 0%. Is it still accelerating at 3708fps? That makes me question whether a velocity limit even exists.

I think we need to integrate the denominator. We can't simply use sqrt.

What if we integrate between barrel_length = 0 (100% efficiency), and barrel_length = infinity (50% efficiency)?

I struggled through calculus and differential equations. Numerical methods (my forte) fall short - literally.

I'm not really equipped to handle that problem mathematically. But I still like to think about it.

----------------------------------------

Lloyd can certainly test the 2330fps theory. Not sure about the rest.

----------------------------------------

As far as the 58% in the Disco:

In a actual physical system, efficiency will almost always be a little (or a lot) lower than theory.

It can also be higher if unaccounted for energy (heat) "leaked" into the system.

That's why well monitored tests are a necessity when testing limits of a theory. Lloyd runs a tight ship, with few "leaks" to worry about.

[rsterne]

Here is one of Steve's original posts about the "Sonic Horizon Theory".... He explains it in detail in that thread, no reason for me to rehash it....

http://www.network54.com/Forum/275684/message/1139726675/Friday+I+posted+a+sketch+showing+how+an+air-conserving+valve+can+save+1-3rd+of+the+air----

I discussed this with Steve at length a few years ago, from the point of view that many PCPs can create shots well past what his theory predicted.... I presented evidence, but he remained unimpressed.... I asked him for the equation he used to plot the graph, and he gave me the following....

Position of Valve Ineffectiveness P = ( 1 - MV / ( 2 x SoS ) ) ^2

I am quite certain he showed me how he derived that, but I didn't record it, I just used it verbatim.... I then suggested that IF the equation made sense (to me) that we should use the molecular velocity of 1650 fps instead of the speed of sound.... I supplied him with this graph, comparing the two, using the different velocities....



He remained unimpressed, and we agreed to disagree.... A couple of days ago, I revisted my spreadsheet which I used to plot that graph, wondering what would happen if I carried it on to higher velocities.... To my surprise, it goes to zero at 3300 fps, like this....



The basic idea is that as molecules are released from the valve/chamber, (go back to the "packets of air" in my thought experiment) they push on the packet in front, and so on up the line, with eventually the front packet pushing on the bullet.... As the bullet goes faster and faster, eventually it will get to the muzzle before air being released from the valve can have any effect.... This happens in any dump shot, of course, eventually.... but the idea is that based on the velocity of the air entering the barrel there could be a limit.... Steve's equation, when modified to use the molecular velocity of 1650 fps, confirms the proposal in my "thought experiment" that limit may well be 3300 fps.... Note that at 2000 fps, only the air released when the pellet is in the first 15% of the barrel would be having any effect on the result.... This is consistent with the increasing insensitivity to reservoir volume (but not pressure) that we are seeing as the MV increases.... the size of the reservoir, once reasonable, means little at extreme velocities.... I think that is what the graph is saying.... At the limit, only the pressure would matter.... something to think about?....

Bob

[Scotchmo]

For practical applications, the real problem is figuring out what happens between those two boundaries. Especially with a pellet along for the ride.

Edit: changed drawing. Replaced 172 with 194. Use D instead of Z. Constant ended up as 274.

[rsterne]

The constant is 194.... sqrt(450,436/12).... and Z may or may not be density/2....

Bob

[Scotchmo]

The constant is 194.... sqrt(450,436/12).... and Z may or may not be density/2....

Bob

Bob,

I looked a little closer at a derivation of the formula that someone posted on the yellow forum. It shows 172. I found the extra "piece of pie". No explanation of it.

194 sqrt(pi/4) = 172

I'm not sure at this point which to use.

I keep hearing that the number should net the rms of air. The rms calculator that I use for air confirms that 172 is the better number. 

I may look at it again later. As I would have cared more early on. I'll use 172 194 for now. It does not matter too much to me at this point, as that prediction appears to be the minimum velocity to expect for freely escaping air. It will climb as soon as the air enters the barrel. So it's never a limit for real airguns. 2x that number may be a limit. If we ever pass 3300fps, then 194 it is.

I changed the drawing to show the formula further decomposed. I got rid of Z and used density.

[rsterne]

If you follow through Herb1836's thread I posted above, he shows the deriviation of the constant.... The value of 172 is indeed different from 194 by the sqrt(Pi/4).... It is supposed to represent the collection of all the constants in the equation, and if the mass used is only the mass of the pellet, that would be correct.... However, when you add the mass of the gas in the denominator of the equation, you must use the volume of the barrel, multiplied by Z, the density factor, for which Steve used Density/2.... The problem is, that he forgot the PI/4 in the denominator of the equation.... The proper way to resolve this, is to change the constant to 194, and add the PI/4 back into BOTH the numerator and denominator of the equation in the barrel volume calculation.... Herb mentions this, and suggests that the proper value should be 2088 fps, but Steve blows him off by reminding him that it "can't be faster than the molecular velocity", and Herb basically gives up.... What Herb didn't realize, is that when he corrected the constant to 194, he forgot to put the PI/4 back in the numerator of the equation himself, when he got the 2088 result.... ie he corrected one error, and made another.... Had he done it properly, he would have got the answer I do, which is 1854 fps....

This is a combination of errors and comedy.... The original equation, by Steve, is incorrect, but worked out to a value that just happened to look like the molecular velocity.... Because of that, nobody has bothered to fix the error.... If you read through Herb's thread, and follow the derivation of the equation, and how he arrived at the constant, and then take the extra step to start from scratch, with the PI/4 term in BOTH places, where it should be.... you will arrive at the same answer I got, of 1854 fps.... The value of "Q" needs to have the PI/4 term in BOTH places.... Just because the equation Steve wrote happens to give a number that "looks right".... doesn't mean the equation is right....

Bob

[Scotchmo]

If you follow through Herb1836's thread I posted above, he shows the deriviation of the constant.... The value of 172 is indeed different from 194 by the sqrt(Pi/4).... It is supposed to represent the collection of all the constants in the equation, and if the mass used is only the mass of the pellet, that would be correct.... However, when you add the mass of the gas in the denominator of the equation, you must use the volume of the barrel, multiplied by Z, the density factor, for which Steve used Density/2.... The problem is, that he forgot the PI/4 in the denominator of the equation.... The proper way to resolve this, is to change the constant to 194, and add the PI/4 back into BOTH the numerator and denominator of the equation in the barrel volume calculation.... Herb mentions this, and suggests that the proper value should be 2088 fps, but Steve blows him off by reminding him that it "can't be faster than the molecular velocity", and Herb basically gives up.... What Herb didn't realize, is that when he corrected the constant to 194, he forgot to put the PI/4 back in the numerator of the equation himself, when he got the 2088 result.... ie he corrected one error, and made another.... Had he done it properly, he would have got the answer I do, which is 1854 fps....

This is a combination of errors and comedy.... The original equation, by Steve, is incorrect, but worked out to a value that just happened to look like the molecular velocity.... Because of that, nobody has bothered to fix the error.... If you read through Herb's thread, and follow the derivation of the equation, and how he arrived at the constant, and then take the extra step to start from scratch, with the PI/4 term in BOTH places, where it should be.... you will arrive at the same answer I got, of 1854 fps.... The value of "Q" needs to have the PI/4 term in BOTH places.... Just because the equation Steve wrote happens to give a number that "looks right".... doesn't mean the equation is right....

Bob

Sheesh!

I'll need to look at that all over again. I dropped out all of the pi, barrel_length, and mass terms. I probably should have used 194 then.

1854fps or 1650fps, they only represent a starting point. Lloyd broke 1854fps 3x.

1) At supersonic velocity, there will be significant entropy gain.
2) The air will heat up.
3) The temperature corrected density will decrease.
4) The lower mass will allow additional acceleration.
5) So, either one is not an upper limit!

I could be wrong about the infinity barrel length. But I think not, as long as the dump is infinite. It will keep accelerating.

Edit: I did take up the molecule velocity thing to explain why it was not a limit. I prefer the f=ma solution. I'll fix some posts.

[39M]

Turbocharging seems the next logical step.

[rsterne]

Scott, after sleeping on it overnight, I have decided to go through the whole equation, step by step, and lay it all out here, to make sure of everything.... You can only collect the constants if they apply to EVERY term in the equation.... The 172 was fine when there was only the pellet mass in the denominator, but when the air mass got added in everything got messed up.... I'll work on that after breakfast....

Bob

[Scotchmo]

Scott, after sleeping on it overnight, I have decided to go through the whole equation, step by step, and lay it all out here, to make sure of everything.... You can only collect the constants if they apply to EVERY term in the equation.... The 172 was fine when there was only the pellet mass in the denominator, but when the air mass got added in everything got messed up.... I'll work on that after breakfast....

Bob

Thanks Bob,

I knew I should do that but did not want to take it on with so many other things to look at.

It was sure comforting to think that the 1650fps rms molecular speed matched the f=ma speed limit.

If it doesn't, either:

1st choice) The formula had an error that coincidentally caused the match up.
2nd choice) We are missing something.
3rd choice) or, it was fudged to cause the match?

I'm going with 1st choice until I hear otherwise from you. And I'm going with f=ma, rather than the rms

I ended up factoring out the pellet completely for now, and the barrel dimensions. I guess that leaves a single string of air molecules. I still get 1854fps.