Sonic Choke? Maybe not. 2162 FPS



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Offline Scotchmo

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #480 on: April 12, 2016, 02:52:32 PM »
Scott, how are you calculating the maximum mass flow rate?.... During a discussion in another thread we multiplied the air density at the pressure (kg/m^3) used by the orifice area (m^2) times the speed of sound at that pressure (m/s) to get the maximum mass flow rate (in kg/s).... This was then derated about 5-10% to allow for losses.... You can use the calculator I linked to above for the speed of sound and air density.... http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8/

For example, at 4000 psi and 20*C, we get Mach 1 of 451.1 m/s and a density of 302.7 kg/m^3.... for an orifice of 1 cm, we get....

451.1 x 302.7 x 1 x  PI/4 / 100 / 100 = 10.72 kg/sec.... which is 10.72 grams/mSec.... or 165.4 grains/mSec.... less a derating factor of course.... 150 gr/mSec seems about right....

The only way to increase the mass flow at that temperature is to increase the inlet pressure, it is completely independent of outlet pressure.... In addition one of the conditions for choked flow is a pressure drop of 47% across the choke.... Here is the discussion, if you haven't gone through it yet.... Jim_Hbar's Post #69 is particularly revealing.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.60

How does that compare to what you are doing?....

Bob


Bob,
I'm calculating the mass flux that same way.  The problem is in determining what Mach 1 for all conditions and every point in time at the inlet.

I'm not pushing "sonic choke" as a limit on pellet speed. But as a means to estimate how much friction to apply.

The mass flux at the inlet is limited by pressure. Pressure is not a limit. It is just a another variable.
The mass flux at the inlet is limited by Mach1. Mach1 is not a limit. It is just another variable. Where to go from there?
 
I have not yet figured out how to get an exact Mach 1 velocity yet. But I'm closer. Except for that last test graph I posted for you, I have never entered the value of Mach1 into my program.  The program determines and uses it to as a point where and how much friction to apply. Some interesting things though:

It appears that the same variables that are needed to calculate the Mach1 speed, are the same variables that control the compress-ability (expand-ability). One of those variables being the specific heat ratio Cp/Cv. And that changes with pressure (high pressure). I never really considered those changes to Cp/Cv in pipe flow work since I only dealt with low pressures up till now. I have always used 1.4, but more research shows that to be way off for 1000-6000psi air. It gets up into the 1.7 range. When I use the correct value of Cp/Cv, the Mach1 speed gets closer to what that WolframAlpha program predicts (though still not enough). But that change also changes the expand-ability of the gas in the program, which I have also been taking into account. They almost cancel out. I change Cp/Cv, increasing expand-ability, and Mach1 value changes as well. The main affect of the change is to push the point where I start applying friction farther down the tube. only minor changes in the result. If I were to pick a fixed Mach1 value (that is not the right way to do it), and change Cp/Cv, there are bigger changes in the results. If I set Cp/Cv, and vary Mach1, there are also bigger changes in the results. When changed in concert, the maximum velocity down a long barrel does not change much.

All of the spreadsheet models are using f=ma. Mine included. That part is easy enough. But we also consider the expand-ability (compress-ability) of air. Cp/Cv. And then we need to consider friction factors as that is an opposing force. That gets complicated. We can use a fudge factor or efficiency coefficient. I'm just trying to get a more precise model.

For this latest spreadsheet model, I don't start using any friction until the inlet hits Mach1. So my model is not valid for predicting subsonic projectiles. In my model, friction appears to spike from zero at velocities over Mach1, The base friction is ignored and I still get accurate results at supersonic velocities. Eventually, I want to include all friction. This exercise gives me better insight into how that can be accomplished.

Mach1 determines the maximum mass flux. Mass flux does not determine the expansion velocity downstream. Increasing pressure increases value of Mach1. We can increase the mass flux with higher pressures. We can increase the downstream velocity with longer barrels. That only real limit is that imposed by the resulting fluid friction. And I know that is the most difficult part to figure out. At this point, it looks like there will always be a way to increase the velocity a little more.

The Mach1 "choke" is just a design parameter, not a constraint.

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Offline Scotchmo

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #481 on: April 12, 2016, 05:10:02 PM »
Here is a little more about what I'm trying for in a better simulation. I avoided any math as I'm just trying to convey the concept.

------------------------------
Vehicle A (current model):

The PSI x area is the throttle. No limit. More throttle, more pressure = more speed.

Mach1 is used as feedback to apply the automatic brakes (friction). Only two settings. Zero, or all.

Jerky ride as the brakes finally pulse on and off while the speed is increased.


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

A little research shows that viscosity is a function of molecular speed. Friction is a function of viscosity. It makes me want try a slightly different approach to friction.

------------------------------
Vehicle B (my next vehicle):

The PSI x area is the throttle. No limit. More throttle, more pressure = more speed.

RMS is used as feedback to apply the automatic brakes (friction). Variable brake settings. Zero up to sqrt2 x RMS.

The ride is smooth as the brakes are gradually applied while the speed is increased.


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

I'm not even sure I can implement this in a spreadsheet. But if so, I think it will get a me a better simulation. An abstract image of the concept. Hatched area is the braking force:



If these shortcuts to friction don't work out, I'll take a couple steps back on the evolution of my model, and figure out the actual friction. Once we start getting down close to 50% efficiency, modeling the friction accurately becomes very important. There is a lot of good info out there. But not sure if anything covers 4000psi and 2000fps:

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Viscosity.pdf
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #482 on: April 12, 2016, 05:12:57 PM »
Scott, what I have done is to put the density and speed of sound, from the online calculators, into a spreadsheet, using pressures up to 6000 psi, and then used Excel to generate a trendline for each.... This equation is then used to calculate the density and Mach 1 from the pressure for ANY pressure <= 6000 psi.... It is what Lloyd is using for his new spreadsheet with the VanDerWaals corrections.... In the spreadsheet I have the trendline equations for air, Helium, and Nitrogen, and I will send you a copy of the same one I sent to Lloyd.... All the data is at 20*C.... Lloyd hasn't added a column for maximum Mass Flow yet, but once you have the Density and Mach 1 for each Pressure increment it's just one more column.... If there are no restrictions, the orifice ends up being the bore diameter....

Bob
« Last Edit: April 12, 2016, 05:24:09 PM by rsterne »
  • Coalmont, BC, Canada
Dominion Marksman Silver Shield - 5890 x 6000 in 1976, and downhill ever since!
Airsonal:
1750 CO2 Carbine, .177 Uber-Pumper, .22 Uber-Carbine, .25 Discovery, 2260 PCP 8-shot Carbine, 2260 HPA (37 FPE), 2560 HPA (52 FPE), .22 QB79 HPA, Disco Doubles in .22, .25 & .30 cal, "Hayabusa" Custom PCP Project (Mk.I is .22 & .25 cal regulated; Mk.II is .224, .257, 7mm, .308 & .357; Mk.III is .410 shotgun and .458 cal), .257 "Monocoque" Bench PCP, 6mm Regulated PCP and .257 Unregulated, Two BRods.

Offline Scotchmo

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #483 on: April 12, 2016, 06:13:10 PM »
Scott, what I have done is to put the density and speed of sound, from the online calculators, into a spreadsheet, using pressures up to 6000 psi, and then used Excel to generate a trendline for each.... This equation is then used to calculate the density and Mach 1 from the pressure for ANY pressure <= 6000 psi.... It is what Lloyd is using for his new spreadsheet with the VanDerWaals corrections.... In the spreadsheet I have the trendline equations for air, Helium, and Nitrogen, and I will send you a copy of the same one I sent to Lloyd.... All the data is at 20*C.... Lloyd hasn't added a column for maximum Mass Flow yet, but once you have the Density and Mach 1 for each Pressure increment it's just one more column.... If there are no restrictions, the orifice ends up being the bore diameter....

Bob

Yes. I would appreciate that equation. I could not get it figured out so I was going to make a lookup table to retrieve values. Last night I used that WolframAlpha to get every Cp/Cv from 100 psi up to 6000psi in 100psi increments, and plotted it but had not yet worked it into the spreadsheet. The equation will make it much easier.

Thank you,
scott hull at scott hull . us

PS: remember that when you add the limit for mass flux, the air will keep expanding and accelerating the pellet. You could model it as a pressure drop behind the pellet. That's what us M.E.s normally do but we are usually more concerned about flow rate. I modeled the airgun with a temperature increase. OK - now I have to think about that. Yeah - there will be heat from the entropy gain. Now we are back to how much. Any that is not available for work. So I'll use all of it. Too much ends up back as work anyway.
« Last Edit: April 12, 2016, 06:22:47 PM by Scotchmo »
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Offline phoebeisis

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #484 on: April 13, 2016, 11:04:29 AM »
Scott
Thanks for the quick reply.
So Steve or SteveNC did some calculations back in 2008-they indicated -to him-that 1640 fps was maximum velocity with air room temperature-that about it-
now data says he is wrong-
he doesn't agree

« Last Edit: April 14, 2016, 07:06:11 AM by phoebeisis »
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #485 on: April 15, 2016, 02:16:28 PM »
Interesting little tid-bit here for you.... Prompted by a calculation done by Steve about how rapidly a .25 cal Delrin ball travelling supersonic slows down (he claimed 5% each foot), I decided to work through a couple of examples to see what the actual muzzle velocity might be, when corrected for the distance to the Chrony.... First I used a .25 cal Delrin ball weighing 2.75 gr. as used by NickN in his UNI to achieve 1882 fps on 3000 psi, with the Chrony 3-4 ft. from the muzzle.... Then I did Lloyd's 2162 fps shot on 4600 psi with a 7.7 gr. aluminum pellet, same Chrony distance.... I assumed ICAO atmospheric conditions, and adjusted the MV to obtain the recorded velocity at 3.5 ft. (average) from the muzzle.... For the sphere, I used the Cd for a roundball travelling at the observed velocity, taken from the GS profile, which is 1.009.... and without having a drag profile for Lloyd's pellet, I assumed the same Cd, because I have found that our pellets typically have about the same drag as a roundball when supersonic....

2.75 gr. Delrin sphere, .250 cal.... SD = 0.0063.... MV = 2116 fps
7.7 gr. Aluminum pellet, .278 cal.... SD = 0.0142.... MV = 2277 fps (over Mach 2)

Acccording to my calculations, Lloyd's shot had already slowed over 100 fps by the time the velocity was measured, and Nick's well over 200 fps.... The curious thing is that Steve should bring this up, because is makes his arguments for a 1640 fps limit even harder to justify.... Incidently, several years ago, on the Yellow, one of the non-believers in the limit used similar calculations on the Quackenbush and Dean high velocity shots using Delrin bullets to question the 1640 limit.... They recorded 1474 fps, with the Chrony's about 10 feet or more from the muzzle, and when he calculated the MV, it was over 1700 fps....

Bob
« Last Edit: April 15, 2016, 02:29:01 PM by rsterne »
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Offline Bill G

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #486 on: April 16, 2016, 12:39:12 AM »
Yes!  Mass flux.  that is a great way to see it.  through the orifice it is limited to mach1 but the expansion has no limit (?)....keep the orifice as exactly that and the amount or air at any psi will be greater than through a port, of any length, that is equal to the bore diameter.  >< (this shape)  reservoir at the left and bore at the right.  Compared to what we typically use in valve and transfer porting, I imagine there are serious gains.  that being said and with some reflection on thought,  to use full bore orifice is still going to be superior I think.  The inlet side being converging would seem to promote sonic flow early and in concert with next to no dead volume, result in superior velocity.  Now the benefit here would be to apply this idea to the calibers that are large enough to cause poppet material to become compromised.  With this orifice idea,  the mass flow could be high enough to allow a smaller diameter yet attain the high mass flow.  Helps make for an easier opening valve and a lot lighter hammer and spring to achieve a high order of energy.  The balance valve would reduce that even more.     

 You guys have left me in the dust and contributing by me has come to an end.  I hear school bells and I'm in the seat early when I can make it to class. LOL 

Good call on leaving all the "smartest guy in the room by himself"  Let us dumb guys lead the way to discovering the whys and hows by way of not being "the smartest guy in the room".  I've said it before.   If you find your self being the smartest guy in the room, you probably need to find another room.  Why?  because your not going to learn anything in the current room.


Great work guys!
Bill
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #487 on: April 16, 2016, 12:59:35 AM »
Bill, using a restriction (ie CD nozzle between the reservoir and barrel less than bore-size) WILL reduce the velocity and energy of the pellet, because the mass flow is limited by the orifice area, and upstream pressure.... While you might be able to increase the downstream air velocity past Mach 1, the mass of air pushing the pellet, and hence the pressure, will be less....

Bob
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Airsonal:
1750 CO2 Carbine, .177 Uber-Pumper, .22 Uber-Carbine, .25 Discovery, 2260 PCP 8-shot Carbine, 2260 HPA (37 FPE), 2560 HPA (52 FPE), .22 QB79 HPA, Disco Doubles in .22, .25 & .30 cal, "Hayabusa" Custom PCP Project (Mk.I is .22 & .25 cal regulated; Mk.II is .224, .257, 7mm, .308 & .357; Mk.III is .410 shotgun and .458 cal), .257 "Monocoque" Bench PCP, 6mm Regulated PCP and .257 Unregulated, Two BRods.

Offline I_like_Irons

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #488 on: April 16, 2016, 02:34:54 PM »
Yes, the pressure will be a lot less which reduces expansion with a convergent/divergent port.  In an ideal convergent/divergent rocket nozzle, for instance, you want the  exiting high velocity gas to be at atmospheric when it leaves the nozzle opening.  In this ideal case there is no room for expansion afterwards.  You get thrust from the acceleration of the air mass to that velocity. 


On another note, I've been working on trying to find an inexpensive ADC (analog to digital converter) to instrument a barrel.  I still think it would be instructive, to know what the air pressure is doing at various points in the barrel.  The problem I'm having is finding a fast enough ADC with sufficient channels without a whole lot of extra stuff, and is affordable. 

On the analog side of the system with strain gauges and signal conditioning, I have a good handle on those design principles.  It is with the ADC and type of input to the computer (serial, or parallel)  that I'm having trouble.  Software will depend on how data is delivered to the computer, which is yet another hurdle. 
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #489 on: April 16, 2016, 06:47:11 PM »
Great way of summing up the divergent portion of the nozzle, David.... I hadn't thought of that before, but since velocity increases and pressure (and density) drops to keep the mass flow constant, for maximum efficiency in a rocket nozzle, the pressure at the outlet should be ambient (hence generating the greatest velocity, and hence thrust....  Any excess pressure at the exit is wasted energy because the gas can still expand.... Not really applicable to a PCP, but makes perfect sense.... and is in complete agreement with the fact that the lower the residual muzzle pressure the more efficient (and quieter) the shot....

Bob
  • Coalmont, BC, Canada
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #490 on: April 17, 2016, 11:08:04 PM »
Here is a little more confirmation that 1650 fps is not the limit.... The rifle is my .25 cal Discovery, with a 24" TJ's barrel, running tethered at 2900 psi.... The gun is tuned to shoot 50.6 gr. cast bullets in a 3 shot string at 960, 966, and 956 fps (104 FPE) starting from that pressure, and was not retuned for this test.... I did, however, shoot a couple of JSB pellets over the Chrony to confirm the performance.... The 34.2 gr. Heavy shot at 1152 fps (101 FPE), and the 25.4 gr. King reached 1254 fps (89 FPE).... Here is the setup I use, and have used for the last 7 years, to Chrony all my guns.... The muzzle is 2 feet from the first sensor and 3 feet from the second, and this setup is rock solid and reliable from under 500 fps to over 550 FPE, the velocity readings are steady, reliable, and consistent with what I get outside.... The lighting kit is a factory Chrony setup, running two long 40W incandescent bulbs.... Without a pellet in the gun, it NEVER registers anything, so muzzle blast is having no effect.... The Chrony is on an angle to be parallel to the path of the pellet, because my target is on the floor, 20' away.... When shooting, the butt of the gun is slightly higher than in the photo, and I am shooting right through the center of the triangle formed by the rods and diffusers....



This gun holds air perfectly, and when I took it down off the rack, where it has been stored for over a month, the gauge still said 2900 psi.... Likewise, the Great White tank it was tethered to, was filled at the same time, about a month ago, and both were at room temperature, 68*F.... I hooked it up to the regulated tether, ran the shots with the JSBs to confirm it was performing normally, and then proceeded with the testing.... The first test was a pellet made from a 1/4" piece of Delrin rod that was 3/8" long, rounded at the front, and counterdrilled at the back to resemble a cylindrical skirted pellet.... It weighed 6.9 gr, and crossed the Chrony at 1595 fps.... I then changed over to something much lighter, based on a 6mm Airsoft BB, as shown in the photos below....



The BB, which weighed 1.8 gr., was too small for the .25 cal barrel, and rolled out the muzzle, although a quick test firing (muzzle raised, lowered just before firing) produced a velocity of 1740 fps.... I assume the Airsoft BB was already rolling down the barrel, so didn't get the benefit of the entire 24" for acceleration.... In order to make the BB stay in place until fired, and fit the bore a bit better, I wrapped it in tinfoil, as shown in the photo above.... The piece of tinfoil was a bit over 1" square, folded over the front and twisted 1/2 turn at the back while stretching it as tight as possible.... I then cut the back of the foil off with scissors, to produce the pellet shown.... As you can see in the photo below, it weighs 2.2 gr....



The pellet was loaded normally, with the twisted part of the foil at the back, and slid into firing position with the bolt.... I fired a total of 10 of these pellets, and the velocities varied from 1722 to 1752 fps except for one shot at 1706 fps, where I noticed the tinfoil following the pellet to the target (I assume it dislodged in the barrel).... I made up each pellet between shots, so the gun had a couple of minutes to stabilze in temperature, although all that was happening between shots was for the regulator to top up the gun about 200 psi after each shot.... There was NO observable change in temperature of any part of the system during the tests.... The average over the 10 shots was 1734 fps (14.7 FPE).... I had two shots at 1750 fps, and one at 1752 fps, as shown in the photo below....



All 10 shots hit my target backstop, 20' away, producing a group size of about 3".... As you can imagine these shots were extremely loud, since the high velocity meant the pellet was exiting while the valve was still open, even though the gun was not retuned.... The calculated residual muzzle pressure was nearly 2500 psi.... I cannot stress enough that there were NO changes made to the gun, it was shot as tuned to deliver 104 FPE with 50.6 gr. cast bullets.... It didn't have any special firing chamber or valve, the barrel was only 24" long, and the pellet was a lousy fit, shimmed up with tin foil....

I would suggest that anyone having a .25 cal PCP that is capable of hitting 100 FPE should be able to duplicate this experiment and prove to yourself that the long-proposed 1650 fps velocity limit for PCP running room temperature air is a flawed theory.... I have no doubt that a smoothbore barrel of the proper diameter for airsoft BBs, that was 36" long or more, and running higher pressures, could achieve much higher velocities, up to 2000 fps or more....

Bob
« Last Edit: April 17, 2016, 11:22:51 PM by rsterne »
  • Coalmont, BC, Canada
Dominion Marksman Silver Shield - 5890 x 6000 in 1976, and downhill ever since!
Airsonal:
1750 CO2 Carbine, .177 Uber-Pumper, .22 Uber-Carbine, .25 Discovery, 2260 PCP 8-shot Carbine, 2260 HPA (37 FPE), 2560 HPA (52 FPE), .22 QB79 HPA, Disco Doubles in .22, .25 & .30 cal, "Hayabusa" Custom PCP Project (Mk.I is .22 & .25 cal regulated; Mk.II is .224, .257, 7mm, .308 & .357; Mk.III is .410 shotgun and .458 cal), .257 "Monocoque" Bench PCP, 6mm Regulated PCP and .257 Unregulated, Two BRods.

Offline buldawg76

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #491 on: April 18, 2016, 02:52:49 AM »
Bob
You got my seal of approval on a very well presented and accurate test structure to insure the are no hiccups that could skew the results IMO.

That's some impressive FPE out of a airsoft BB covered in tin foil as well.

Mike
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Offline MichaelM

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #492 on: April 18, 2016, 03:40:27 AM »
there has been and idea buzzing around and around in my poor noggin....  Been  thinking about convergent/divergent nozzles and talk of laminar flow and i think they had a date night and some poor child was born from it....

ANYWAYS I dont have the smarts to figure out the maths and models ...its more of a picture in my head.. and its also probably completely dumb...

from what I understand a converging/diverging nozzle is basically eating up the energy to accelerate the flow of gas.... ideally the gas leaving it is at atmospheric pressure turning its energy into high velocity movement.....

Now Laminar flow down a tube describes how the gas would be denser and slower on the outside layers while faster and less dense down the middle in dumb speak.... forming its OWN restrictions in the barrel

the picture I have in my head is this laminar flow of gas forming a continuously evolving convergent/divergent nozzle as it travels down the barrel and helping form a stream that is constantly accelerating its self as its converting its stored energy into supersonic and even hypersonic velocities????



to kinda even further back this up as silly as it seems..... you ever see the parlor trick of blowing up a really long cylindrical plastic bag with a puff of air from your lungs??? if its a REALLY long bag ( I have done it with 15 and 20 foot bags...) that little puff starts out slow but by the time it reaches the end of the bag its traveling quiet fast  and if your not holding onto the bag it can take it from your hands and have a nice POP as the pressure wave an fast moving air hits the end... (as an aside I understand the inflation of the bag is due to the bernoulli effect drawing in air... I am thinking more about the pressure was created from that first hard puff of air and watching it accelerate down the tube...)

 
« Last Edit: April 18, 2016, 03:59:38 AM by MichaelM »
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Offline madeInLV

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #493 on: April 19, 2016, 05:49:27 PM »
Loyd,

The exhausting of the air from the rear piston chamber drops the closing force so that the opening force on the front margin of the valve  forces the valve rearward and cracks the valve open at the barrel breech. As soon as the valve is cracked, the pressure imbalance doubles and the valve slams open and fires the pellet.  Lag time is virtually nil.

Please reread my earlyer post about the acceleration of the projectile and the plunger. According to your description the pilot stage creates an imbalance which merely "cracks" the valve open creating further pressure imbalance. "Time lag is virtually nil" True. I CASE OF A HEAVY PROJECTILE THIS IS THE CASE. In case of a LIGHT projectile the smallest (slow moving valve) crack will push the pellet way down the barrel before the main valve has reached full steam. TESTED EXPERIMENTALLY.

Imbalance needs to be designed such that the pilot stage is enough to accelerate the valve sufficient for ACCEPTIBLE speeds. As you can see this is a dead end-the lighter the projectile the larger the imbalance needs to be. Start by figuring out what the weight of the pellet will be.

"Easy to open..... difficult to close
" Man ....you have no idea:)

Also, you mentioned that paintball marker have similar valves. Would you mind pointing me in that direction? Or is there a name for it that i can google?
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Offline madeInLV

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #494 on: April 19, 2016, 06:19:11 PM »
Scott, Bob,

thank you for the passion for the subject and the unquenched desire to get to the bottom of this. I recognize fellow engineers when i see them:)

Loads of usefull information and thought provoking analysis.
I once was doing exactly that until i realized my BS in ME was not enough. My conclusion was that i understood the energy transfer during the firing cycle well enough and sort of understood the key variables that are at play and realized what i can actually influence within the framework of a reasonably sized PCP gun. Shortly put-least Resistance (in line valve, no choke points), no dead space (proved to be false for real valves), max pressure (limited to 4500psi for now) Limited to about 325m/s due to the transsonic region and the associated inefficiencies.

From what I see, you are trying to find a closed loop algebraic equation that will give you a "digital PCP" so to speak. IMHO it is not possible. At best we can come up with general equations that fit Loyd's empirical data and shows general trends.

I hope I'm wrong though.

Have you looked at the "Theory of High Speed Guns" Seigel, 1965 (NASA) that i posted a ling to in my very first post? I believe it addressed everything you are talking about here. 

BTW Scott, where did you find the info of gamma (Cp/Cv) being close to 1.7 for air at high pressures?

Also, as Loyd is working on the next valve model (the pif-paf aka pilot-plunger) at some point it will become obvious that we are dealing with a converging nozzle here as well as an annular transfer port (the area between the plunger valve and the cone/valve seat that increases while the plunger moves rearward) Both of these areas will need optimization. So....are any of you good at CFD?:):):)
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #495 on: April 20, 2016, 12:15:43 AM »
Alex.... There is a chart in the very first post a thread in this Gate.... http://www.gatewaytoairguns.org/GTA/index.php?topic=105696.0 .... that shows a chart of gamma vs. pressure at various temperatures.... If you look at the one for 70*F, a value of 1.7 would be the one to use from 2000-6000 psi.... bang on at 3000 psi and within about 0.05 (3%) over that range....

PS, I am definitely NOT an Engineer, I want my solutions simple, if at all possible.... *grin*.... I do wish I had paid more attention in Math and Physics while getting my BSc (Chem), though....

Bob
« Last Edit: April 20, 2016, 10:57:11 PM by rsterne »
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Airsonal:
1750 CO2 Carbine, .177 Uber-Pumper, .22 Uber-Carbine, .25 Discovery, 2260 PCP 8-shot Carbine, 2260 HPA (37 FPE), 2560 HPA (52 FPE), .22 QB79 HPA, Disco Doubles in .22, .25 & .30 cal, "Hayabusa" Custom PCP Project (Mk.I is .22 & .25 cal regulated; Mk.II is .224, .257, 7mm, .308 & .357; Mk.III is .410 shotgun and .458 cal), .257 "Monocoque" Bench PCP, 6mm Regulated PCP and .257 Unregulated, Two BRods.

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #496 on: April 20, 2016, 11:10:35 PM »
Bob,
Nice work on getting the high velocity out of your high powered .25 Disco.   Even though the math explains it, it is still surprising how much lighter the projectile has to be to get only incremental increases in velocity.
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #497 on: April 20, 2016, 11:23:44 PM »
Loyd,
.................................................
Imbalance needs to be designed such that the pilot stage is enough to accelerate the valve sufficient for ACCEPTIBLE speeds. As you can see this is a dead end-the lighter the projectile the larger the imbalance needs to be. Start by figuring out what the weight of the pellet will be.

"Easy to open..... difficult to close
" Man ....you have no idea:)

Also, you mentioned that paintball marker have similar valves. Would you mind pointing me in that direction? Or is there a name for it that i can google?

LV,
"Easy to open..... difficult to close" Man ....you have no idea:)

Believe me, I DO know how difficult it is, LOL!

For the paint ball marker info, look at the animations on this site (markers and regulators, too).  Some of the best that I have found.  Even though they might not provide exactly the information you are looking for, they will definitely stimulate the thought processes. Some very sophisticated equipment.

http://www.zdspb.com/tech/misc/animations.html

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My YouTube channel is    Airgun Lab

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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #498 on: April 21, 2016, 12:14:28 AM »
I have been working on my internal ballistics spreadsheet to see if the predictions can be made more accurate.  It is quite a daunting task.  The VanDerWaals corrections are in place and now the mass flow/mass flux limits are underway.  I am having trouble figuring what the air velocity at the breech end of the barrel is.  If I understand correctly, the mass flow limit is reached when the velocity of the air entering the barrel is at the speed of sound for the pressure of the air entering the barrel.  But the speed of the air entering the breech of the barrel is not necesarily the same as the speed of the projectile in the barrel. Correct?

Look at this example as part of what is puzzling me.
This is one of the fastest shots I have taken so far.  .278 cal, 7.7 gn, 4500 psi, 55cc air, MV = 2162fps.
If you look at what I will call the maximum INPUT FPE (machines have input BTUs and OUTPUT BTUs, and never are they over 100%.
So, even though it is impossible, lets say the INPUT fpe equals :  bore area x psi x barrel length(feet). 
Max INPUT FPE = .0607sqin x 4500psi x 3.833 feet = 1047 FPE
The final air mass in the barrel (based on the expanding 55ccs of original air) is 127.4 grains. (a full barrel of 4500 psi air would be 234gns).  If you back figure the velocity from the air mass + the pellet mass,  Velocity in FPS=sgrt [( 1047fpe x 450240)/(127.4gn + 7.7gn)] = 1880 FPS. But the actual FPS was 2162.  So, the actual velocity is much higher than calculated, even though the 1047 fpe is also too high.  One explanation is that a much smaller mass of air is being accelerated in the barrel behind the pellet.  Baffling.  There is a lot of thermal activity (Scott's entropy?)  or something happening that is not easily identified or quantified.

No response necessary, I am just rambling.
Thanks,
Lloyd
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Re: Sonic Choke? Maybe not. 2162 FPS
« Reply #499 on: April 21, 2016, 02:12:40 AM »
I would agree that the logical explanation is that the mass of air being accelerated behind the pellet must be less for the pellet to reach the velocity it does.... Perhaps the velocity profile of the air moving down the bore, as Scott often draws, and as typically shown for laminar flow, where the air against the barrel is basically stationary and each layer slides over the next until the air in the center is moving at twice the average velocity, is the key?.... The volume of a parabola is half the volume of a cylinder of the same size.... sooooooooooooo....

Using Lloyd's 2162 fps shot as the inputs to his new L4 spreadsheet, and using 0.5 of the air mass in the calculations, requires dropping the efficiency number down to 48% to bring the MV to 2162 fps.... When you do that, the air mass used for the shot drops from 127.4 gn to 64.7 gn, and the maximum velocity ends up being 2580 fps.... That is certainly far enough above the 2162 MV measured to allow for losses, I would think....

I did find one reference about the KE in a fluid moving through a tube here.... http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html .... complete with a formula for calculating it.... I haven't worked through it at all, but the variables are the maximum flow velocity (which is likely the pellet velocity) and the density of the fluid.... both of which we have for each time increment.... The result being the avg. KE per unit of volume.... Anything there we can use?....

Bob
« Last Edit: April 21, 2016, 02:21:33 AM by rsterne »
  • Coalmont, BC, Canada
Dominion Marksman Silver Shield - 5890 x 6000 in 1976, and downhill ever since!
Airsonal:
1750 CO2 Carbine, .177 Uber-Pumper, .22 Uber-Carbine, .25 Discovery, 2260 PCP 8-shot Carbine, 2260 HPA (37 FPE), 2560 HPA (52 FPE), .22 QB79 HPA, Disco Doubles in .22, .25 & .30 cal, "Hayabusa" Custom PCP Project (Mk.I is .22 & .25 cal regulated; Mk.II is .224, .257, 7mm, .308 & .357; Mk.III is .410 shotgun and .458 cal), .257 "Monocoque" Bench PCP, 6mm Regulated PCP and .257 Unregulated, Two BRods.

How do you word it... "Air Guns" or "AirGuns"?