Sonic Choke? Maybe not. 2162 FPS

[Buldawg76]

I will just say this very short and direct statement in that those of us who have been following this thread from its beginning until now know who the true unbiased and totally objective people are and what has been accomplished for the sole purpose of finding the truth and limits if there is actually one to be found.

There will always be those that believe theirs is the only way and to mock it or rebel against it is either hierarchy or lunacy since it just cannot be any other way but theirs. If that were the case our technology would have been stagnated centuries ago and we would still be in the dark ages.

Since we all know for a fact that is not the case then how can one person knowingly in good conscious and faith be so ignorant as to continue to keep his head buried in the sand in an attempt to force the discovered facts to be seen as impossible or inaccurate due to faulty or skewed testing of which has been as far above scrutiny or inconsistencies as humanely possible.

It is truly a sad day in this country when such thinking takes place and only tries to divide us instead of unite us for the common good not unlike the direction this country is headed as well.

 "To infinity and beyond "

Mike   

[lloyd-ss]

Mike, some good thoughts there.
Lloyd

[lloyd-ss]

Version 3, and barrel length of Version 2.
Progress on Version 3 is moving slowly as preparing for the Funshoot in a week and a half is taking priority. But I will be bringing Version 2 there.
Just thinking out loud, but it would not be too difficult to swap out the .278 bore barrel for a nominal .334 smooth bore barrel with a length up to 71". Still 4500 psi and 55 cc dump.  There is a slim chance of getting the projectile to less than 8 grains. Personally, I think it is worth doing, and it could be done quickly and at little expense.  Any thoughts?
Thanks, Lloyd

[MichaelM]

I know there would be slimmer chance of getting the projectile down to the weights your looking for.. but it seems to me the larger bore diameter would allow for better efficiency and more force acting on the base of the projectile.... ALSO seem to me that it would be a heck of a lot easier to machine a larger projectile then a small one lol...  maybe even opening up some possibilities of a less draggy sealing method like maybe a reversed "parachute: type of seal like whats used on springer pistons???   though thta sounds like a pain in the butt to machine lol..... either way maybe something like a sleeved aluminum projectile with delrin to help cut back on weight...

[lloyd-ss]

Michael, Yes, with the larger dia, it might be easier to stretch a Teflon seal over the aluminum center part, and cut both the weight and friction. 
Lloyd

[rsterne]

You know you're going to do it, Lloyd!.... and good on ya' for that....

buldawg.... Amen to that !

Bob

[rsterne]

My Grandfather once told me that if you cannot say something nice about someone, it is better to say nothing at all.... My Dad added that sometimes it is better to keep your mouth shut and be thought a fool, than open it and prove that fact.... I will endeavour in future to reflect on their advice, tempered by the caveat that I will always try and defend the truth....

Bob

[rsterne]

Yet another possibility exists for a way to calculate the maximum velocity of an airgun.... Let's start with the equation for the KE of a moving column of air in a tube.... from the Hyperphysics website.... http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html



We have another, very basic equation, for the maximum Kinetic Energy (ft.lb) that can be developed by a PCP, which is the force F (lb) times the distance (ft), as follows.... The force F, is the pressure P (psi) times the bore area A (in^2), and the bore area is the caliber (in) squared times PI/4.... The distance (ft) is the barrel length L (in) divided by 12 (in/ft).... so the absolute maximum KE for a given pressure and barrel can be found from the equation....

KE = P x (cal^2 x PI/4) x (L / 12) .... Note Lloyd and I use this in his maximum velocity thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0

It should be noted that the barrel volume V (in^3) is the bore area A (in^2) times the barrel length L (in), so substituting V in the equation above, we get....

KE = P x V / 12 .... the units are (lb/in^2) x (in^3) / (in/ft).... which reduces to ft.lb, exactly as it should....

If we rearrange the first equation to solve for the maximum velocity in the middle of the air column Vm (fps), we get....

(D/2) x ( Vm^2 / 3 ) = KE / V .... where D (which I use instead of rho) is the air Density (slug/in^3), and then....

Vm^2 = KE x 2 x 3 / V / D .... take the square root of both sides, and we have....

Vm = sqrt ( 6 x KE / V / D ) .... However, from the equation for the maximum KE above, we can substitute ( P x V / 12 ) for the KE, which gives us....

Vm = sqrt ( 6 x ( P x V / 12 ) / V / D ) .... The volume V cancels out, leaving us with....

Vm = sqrt ( P / D / 2 ) .... the units are (lb/in^2) / (slug/in^3) / (in/ft).... with the unit for slugs being (lb.sec^2/ft).... so we end up with ft/sec, exactly the way it should be.... 

Air density D is usually quoted (in the Imperial system) in lb/in^3, and to convert to slugs, we must divide by 32.174, so the equation then becomes....

Vm - sqrt ( P / ( D / 32.174) / 2 ) = sqrt. ( 16.087 x P / D ) = Vm = 4.011 sqrt ( P / D ) .... with Pressure P in psi and Density D in lb/in^3....

This is exactly the same equation I came up with in posts # 517 & 523 by a completely different method.... If nothing else, that proves I am consistent....  .... Here is a graph of the predictions using this formula.... Note this is for zero pellet mass and constant pressure, it represents the maximum velocity of the center of the air stream in the barrel.... At least in theory, the pellet should not be able to exceed that velocity unless there are some unknown temperature effects taking place....



It is worth noting that for an Ideal Gas, where the Density is directly proportional to the Pressure, the predicted velocity would be a constant.... Using NTP conditions (20*C, 14.7 psi and 1.204 kg/m^3 = 0.0000435 lb/in^3) that value would be 2332 fps.... However, air is not an Ideal Gas, with the pressure increasing significantly faster than the density at over 2000 psi.... This means that the gas itself is less dense, and therefore easier to push along the barrel, compared to the pressure pushing it.... resulting in an increase in the maximum velocity at high pressures.... Please note that the above is only one theory among many, and is only valid until somebody exceeds these numbers, at which point it must be discarded....

Bob

[lloyd-ss]

Bob, I am having a problem with one substitution you are making in the above post. 

in this section, quoted from your post,==========
Vm^2 = KE x 2 x 3 / V / D .... take the square root of both sides, and we have....

Vm = sqrt ( 6 x KE / V / D ) .... However, from the equation for the maximum KE above, we can substitute ( P x V / 12 ) for the KE, which gives us....

Vm = sqrt ( 6 x ( P x V / 12 ) / V / D ) .... The volume V cancels out, leaving us with....
===============
Referencing the 3 lines above, in the first  line, the KE is "average KE".   In the first part of the second line, the KE is "average KE."  But in the second part of the line, the KE that you want to substitute for the average KE, is actually the maximum KE, which is different.  Am I missing something?

Thanks,
Lloyd



Lloyd

[rsterne]

Lloyd, as I understand it, the term "Average KE" from the Hyperphysics post means the average kinetic energy of the column of air per unit of length (volume).... The air in the center of the column is moving twice as fast as the air at the outside edge, so the KE of the center of the stream would be four times as great.... So in a "packet" of air of, say, 1" long, the average KE of that packet would be given by the equation, and that is where the 1/3 factor comes from (and they show the derivation of that).... I simply chose the unit of length (volume) to equal the length (volume) of the barrel, so they cancel out....

The maximum KE for any give PCP is the Force times Distance, which distills down to ( P x V / 12 ) in FPE.... If we substitute that for the KE in the original (Hyperphysics) equation we can calculate the maximum velocity Vm of the airstream.... ie the velocity in the center of the moving column of air....

Sound OK now?....

Bob

[Scotchmo]

As I understand it, the term "Average KE" from the Hyperphysics post means the average kinetic energy of the column of air per unit of length (volume).... The air in the center of the column is moving twice as fast as the air at the outside edge, so the KE of the center of the stream would be four times as great.... So in a "packet" of air of, say, 1" long, the average KE of that packet would be given by the equation, and that is where the 1/3 factor comes from (and they show the derivation of that).... I simply chose the unit of length (volume) to equal the length (volume) of the barrel, so they cancel out....

The maximum KE for any give PCP is the Force times Distance, which distills down to ( P x V / 12 ) in FPE.... If we substitute that for the KE in the original (Hyperphysics) equation we can calculate the maximum velocity Vm of the airstream.... ie the velocity in the center of the moving column of air....

Sound OK now?....

Bob

Should be OK for subsonic.

Some things that I found in my research and believe to be true:

The mass flux is at a maximum once the inlet reaches Mach 1.

Go any further downstream, and there is a reduction in average air density. So that packet of air that was originally 1" long may grow to longer than 1".

Or you could say that, for supersonic velocities, the mass of air in a 1" section of barrel is less near the muzzle, than it is close to the breech.

For Fanno flow, the density ratio is the inverse of the velocity ratio. That makes sense, because it would result in a constant momentum density (momentum per unit volume).

I think the density at maximum velocity will be:

Density_muzzle = Density_inlet/sqrt((2/(k-1))+1)

[rsterne]

Scott, I'm strictly working with F=ma here, not trying to incorporate any temperature change.... I know you are working with Fanno Flow, but I don't understand it, so I'm just plodding along the best I know how.... The assumption above is that the pressure and density are constant throughout the barrel.... I know that is not realistic, but it should produce the maximum velocity with zero pellet mass.... This model, of course, does not work incrementally, it looks at the barrel full of air as one chunk, all moving at the same (average) velocity (center faster, of course).... but since it is based on the maximum KE that the gun can produce, I feel it at least bears investigating.... Like any other theory, it's only valid until it's broken.... 

It is entirely probable that the mass flow limit at the inlet is the actual governing factor, and Lloyd has worked that into his new L4 spreadsheet, using the correct SoS for the incremental reservoir pressure, along with the VanDerWaals correction for density.... In Lloyd's new spreadsheet, the velocity curve is highlighted where the flow chokes, and it's a pretty interesting visualization.... However, in the models of his actual shots, the choking is not very severe, so it's effect on the results is rather small.... His new spreadsheet only has about 3% greater losses than the previous one, using Boyle's Law and no choking.... ie if you increase the efficiency factor by 3% the model again matches the experimental results.... I think that is because the VanDerWaals density effect works in the opposite direction to choking.... by increasing the velocity calculation, while choking decreases it....

One comment I will make is that if the density of a set length "packet" of air decreases, ie it's mass is less, then so is the pressure.... The ratio will be according to VanDerWaals corrections.... If indeed the density is inversely proportional to the velocity, then eventually the pressure loss will decrease the available acceleration.... Of course if that only occurs near the muzzle, it won't matter much.... but most of the velocity gain occurs early, so the effect on the pressure available to produce acceleration could be significant.... If you apply your equation incrementally, you may find you have a lot less pressure available for your F=ma acceleration calculations....

Bob

[Scotchmo]

...
One comment I will make is that if the density of a set length "packet" of air decreases, ie it's mass is less, then so is the pressure.... The ratio will be according to VanDerWaals corrections.... If indeed the density is inversely proportional to the velocity, then eventually the pressure loss will decrease the available acceleration.... Of course if that only occurs near the muzzle, it won't matter much.... but most of the velocity gain occurs early, so the effect on the pressure available to produce acceleration could be significant.... If you apply your equation incrementally, you may find you have a lot less pressure available for your F=ma acceleration calculations....

Bob

True. Apparent pressure will fall. The Fanno pressure ratio is the same as the density ratio.

The falling pressure means that it will take a longer barrel to reach the higher velocities allowed by Fanno flow. But, at the same time, the total air mass being accelerated will be lower.

From Wikipedia:


pressure ratio, density ratio, temperature ratio, velocity ratio, stagnation pressure ratio.

Those equations are ratios. They don't predict conditions for different barrel lengths. Just for different Mach numbers. We are interested in M=1.

The difference will end up being, that your supersonic inlet will predict a higher velocity with shorter barrels. But the max velocity attainable will be higher with the Fanno model, even though the Fanno inlet will be limited to sonic.

Those Fanno equations would be for an ideal gas. So they are only approximations for our case which is not ideal.

[Buldawg76]

My Grandfather once told me that if you cannot say something nice about someone, it is better to say nothing at all.... My Dad added that sometimes it is better to keep your mouth shut and be thought a fool, than open it and prove that fact.... I will endeavour in future to reflect on their advice, tempered by the caveat that I will always try and defend the truth....

Bob

Bob
I believe our grandparents and parent were cut from some of the same molds as I have heard the same phrases all my life as well and try to live as close to them as possible. It is truly difficult to do so at times when you know that the facts are glaringly evident and well proven yet to defend them only serves to fuel the fire, not that it is bad to fuel a fire.

If feeding the fire does make unwilling minds see the flames even if only briefly then it has served its purpose and that is to some extent I believe the case here.  The facts are compiled and presented here so that to deny it has been accomplished only serves to make the joker even more of a fool.

In an age where universal deceit is considered normal, telling the truth is considered an act of rebellion.

Mike

[rsterne]

"The progress of science is that of a focused rebellion in the search for truth"....

rsterne, 2016

[Buldawg76]

Bob
Agreed 100%

Mike

[lloyd-ss]

You know you're going to do it, Lloyd!.... and good on ya' for that....

buldawg.... Amen to that !

Bob

I got the 6' lengths of 1/2" O.D. x .083 wall DOM tubing today.  They do indeed check out at .334 I.D.  Since this is strictly a lab set-up for the Version 3 valve, it can use Teflon or Delrin for very light weight projectiles, or possibly lead slugs, too.  The Version 3 valve does not use the projectile as a structural element, so that means that it will be much easier to make lots of shots. After the version 3 valve is proven to be effective (fingers crossed  ) a .30 cal TJ's/Bob's airgun barrel can be used to see how lead projectiles will do at high velocities. John Cripe is preparing some swaged lightweight lead bullets for testing.  His concern is that the twist rate might be too high for the hi vel, light weight bullets.  We might be in uncharted territory, but I would be surprised if someone else hasn't already been there. 
The version 3 valve is designed for a max 6000 psi, so Scott, the high pressure nitrogen is in the not-too-distant future.   
Lloyd

[rsterne]

Good news on the Version 3 progress, Lloyd.... A Delrin cylinder of that caliber and 3/8" long would only weigh 12 gn.... less if you use a center drill to create a hollow skirted base....

The TJ's barrel is only a 26" twist, which will certainly help.... I don't think there is a slower twist .30 cal barrel available anywhere....

PS, I answered your question about the KE above.... hopefully to your satisfaction....

Bob

[lloyd-ss]

Bob,
Yes, I saw the response Bob, and thank you for the explanation, but I forgot to reply.  I hear what you are saying and I think I am ok with it, but still not 100% sure. I just need to think about it some more.

Part of it has to do with my interpretation of the KE avg equation. If you rearrange that equation to make it
KE avg = 1/2 x density x volume x Vel max squared x 1/3
Basically, that equation is the old standard KE = mass x velocity squared, but also multiplied  1/2 and 1/3.  I see the 1/2 as the multiplier for the average, and 1/3 as the multiplier for the volume of a cone, which is the higher velocity center portion of the moving mass of air.
That means that the average KE of the moving column of air is 1/6 th of the maximum velocity portion.
Does that get us back to the old formula of :  Output energy = Input energy - system losses?  Probably not, because that would mean the 5/6 of the energy is not delivered to the projectile.

I hope that in the end we might be able to come up with an empirically "augmented" equation to predict the output of a PCP.  All of the various methods of calculation that take into account pressure and density and velocity and temperature get us closer and closer, but in the end, I am sure that some sort of fudge factor(s), the "empirical" part of the equation, will still be needed to correct for those unknowns.    I applaud the efforts of everyone to track down all the actual calculations for the internal ballistics, because, I am certainly not up to the task, LOL.  I will continue to build and test and hopefully provide useful empirical data to be used in conjunction with all of the physical formulas.

This is quite a process!
Lloyd

[rsterne]

Well, KE = 1/2 Mv^2, and in this case M is the air volume in the barrel times the air density in the barrel.... The only factor in addition to that equation is the 1/3, and that takes into account the velocity profile across the moving column of air where the center is moving the fastest (about twice the average) and the outside hardly at all.... Since the velocity used in the formula is the velocity at the center of the stream (ie the maximum velocity), but the KE is the total (averaged across the stream).... and the total cannot exceed the input KE.... I think it makes perfect sense....

Don't forget that the "average KE" of the moving column of air is the integral of all the layers added together, divided by the volume.... If you use 1" increments, each 1" packet of air will have a total KE equal to that of all the layers, across the diameter (area) of the tube, times the 1" of length.... That's what makes it the "average KE", but for that 1" packet of air, it is also the total KE (of that packet).... If you follow through the integration on the Hyperphysics website, that factor of 1/3 is the result of the integration, relative to what the KE of the packet of air would be if it were all moving at the same velocity of the center of the stream (the maximum velocity).... You state that the KE is 1/6th that of the center portion, but in fact it is only 1/3, right?....

All of the KE is delivered to the air (in the case where the projectile mass is zero).... but more of it shows up in the center of the stream....

Bob