Sonic Choke? Maybe not. 2162 FPS

[sixshootertexan]

Scott, That is very interesting and certainly gives hope to achieving much higher velocities. 

There is something funny in the Wiki article, though:
"As always when a diaphragm ruptures, a shock wave propagates into the low-pressure region (here the dump tank) and an expansion wave propagates into the high-pressure region (here the nozzle and the long tube). "
Quoted from : https://en.wikipedia.org/wiki/Ludwieg_tube

They are calling the dump tank the low pressure region.  Isn't that backwards?  For there to be flow, the air has to move from a high pressure area to a lower pressure area, hence, from the tank to  the nozzles/exit.  It can still be from a low velocity area to a high velocity area, but the pressures have to go from high to low.  Am I missing something?
Lloyd

Great reading as usual guys. Here's a video of a supersonic ping pong ball.  Hope it helps.

[Bill G]

After working on another copy of my sheet based on an older version, I reproduced what I left at my desk, at work.  first off, this is based on a dump valve setup.  It appears that there is an applicable set of polynomials that are required.  One of them will pertain to the PSI and the other will pertain to the port area.  My calculus if far too weak to try and derive a combination so brute force math will have to do.  I have a gut feeling that the port calculations will be really close to linear and that the pressure calculations will be much more curved.  I'm currently working on developing the best regression model for the two and then find a way to employ them at the same time.   I gotta find my Ti-83.  Kids were using it and they never put thing back where they find them.   Just based on Lloyd's data, It appears that there is an optimal flow for a 14.5cc plenum at 1750psi.  As the psi increases the velocity increases but not at a velocity that would be expected.  The predicted velocity, with my sheet, is much greater than what Lloyd has achieved with his test rig.  for the sake of simplicity, I will depict the flow efficiency as a percentage.  What I have done is take the 14.5cc at an established psi and calculated the velocity. At 1800 psi, I had to use 97% of the plenum to achieve a velocity that matches the actual velocity.  if I modeled it to use 100% of plenum, the psi used would be 1746. 
For lack of a better way of expressing this it goes as follows.

psi               Flow efficiency     Lolyd's published velocity     my predicted velocity
1746                  100%                       N/A                                      1241.7
1800                    97%                     1254                                      1257
2500                 57.2%                     1373                                      1375
3300                   38%                      1465                                      1466.3
3750                 33.3%                     1521                                      1524
4500                 27.4%                     1605                                      1602
just for hmmmm factor.
17503                     1%                     N/A                                        850

This is based on 100% bore area. 

Once I find my Ti-83, I'll work on the regression for both psi and port area. 

The flow efficiency % is simply a percentage of the plenum.  But if it is a dump valve, then the whole volume is used at what ever psi is applied. This got me to thinking about what Bob says about improving efficiency by closing the valve before the projectile leaves the bore. Perhaps as the psi increases, the flow of air molecules just cant fit in the valve/ bore quickly enough.  But the force from the psi is obviously high enough to improve the velocity, just not linear.  The fudge factor could be what I am dubbing flow efficiency.  My gut tells me that the velocity change from porting will be nearly linear(at least on a dump valve with orifice TP).  The flow efficiency plays well into Bob's lessons of closing the valve before the Elvis is gone.  It also makes since from the stand point of Boyl's law too.  At 4500 psi is requires a much smaller dump plenum to attain the same velocity.  According to what I've presented, 14.5cc at 1746 gets 1241fps and  ~4cc at 4500psi will get 1602fps.     

[lloyd-ss]

.......... Sorry, Lloyd, but what seemed to work pretty well for your "wide open" dump shot test gun doesn't work very well for a typical (low pressure) PCP........

Bob

Gee Bob, I hope you don't feet tooooo bad about making me jump thru hoops on all the dead end revisions, ha ha.   
I've been thinking about it too, and one thing that happens early in each time iteration of the bullets progress in the barrel, is the actual amount of air that is used for that iteration.  The actual amount of force that that amount of air applies to the bullet might be adjusted, but still, the air volume consumed must be correct.  If it isn't, then the total amount of air used for the shot will be wrong, and then the actual efficiency of the shot (FPE/std-cuin) won't be right, and the ability to predict follow-on shots will be futile.  I think I will try and draw a flow chart of the spreadsheet to help locate where the "force" losses, and air flow reductions are most likely occurring.

Does anybody know if there is an easy flowchart application in Excel or Word?  I think Visio was pretty good, but I don't have that.  I can write the flow chart  out by hand but an interactive app would  be nice because of the multiple layers of conditional statements in the spreadsheet.

Lloyd

[Bill G]

Found my Ti-84..  Looks like the best fitting regression model is a cubic regression.  y=ax^3+bx^2+cx+d

R^2 =.9999.  Of course this fit is based on the pressures and velocities published by Lloyd

a= -5.0332^-11
b= 5.8976 E-7
c= -.002349
d= 3.46759

Now, I have no idea how to integrate that into my sheet . 

[rsterne]

I understand that the correct amount of air needs to be used in each iteration, or the total air consumption will be in error.... However, if you restrict the transfer port, you WILL use less air, in fact generally the FPE/CI goes up, not down.... When you included ALL the air in the shot with the smaller transfer port, not only was the air consumption the same as if the TP was bore size.... but that massive amount of air reduced the velocity of the shot even more than the J7 version.... and as you can see, it is too slow....

I really thought I was onto something, because the system worked well for your dump shots, and I have used is successfully to predict the MAXIMUM FPE in quite a few PCPs before they were built.... It generally overestimates the power by about 10% compared to what mere mortals can get.... but at least it gives a "lofty goal".... When applied to the data I had for the Disco, the predictions were quite a bit below what I measured....

and, yes, I feel TERRIBLE about all the work I caused you, especially when you were trying to duck company to do it....

Bob

[lloyd-ss]

I took another diversion from all the math stuff, and wanted to try shooting  something faster than my previous best of 16.5fps. Since bigger cal and lighter weight seemed the best approach, I slightly modified the test bed to use a 30 cal air barrel from Mike Sayers (Bob's design, BTW).  It barely fit in, using the 7/16-20 barrel retention  thread in the breech.  Increased the dump tank to 26.1cc. Made a couple of 30 cal o-ring bullets out of aluminum and necked them down to reduce the weight.  One is 17.1 gn, the other 14.7.

30 cal O-ring bullets 17.1 gn and 14.7 gn


I was expecting great things. Based on the 1605fps I got with the 10.2gn 22 cal at 4500, the 17.1 gn 30 cal had the potential to do better than 1700fps.  So, I set the video cam up, got the gun all loaded and ready to shoot, filled to 4500psi, pulled the trip cord to fire, and darn, it was totally jammed.  I guess my effort to reduce the bullet weight weakened it too much and it bent under the pressure and wedged tight between the release cam and the barrel.  I hadn't done the math and now realize the aluminum bullet had 318 pounds of force on it. So anyway, when it totally jammed,  I stopped the recording and had to get a hammer to tap the trip lever hard several times (including replacing a bent screw) to fire the gun.  The bullet went over the chrony at a disappointing 1655fps.  Plus, the bullet ended up going thru the grocery bag soft trap and went into the heavy steel trap where I can't retrieve it to see what really happened.  I might try the 14.7 gn bullet at a lower pressure in hopes that it won't bend and jam. I need to figure out a light weight bullet that is still sturdy, plus, a more robust rotating mechanism for the cam.
Still, I guess 1655fps from a failed attempt isn't too bad.
Lloyd

[rsterne]

Pretty funny when the mechanical strength of the bullet becomes a limiting factor instead of the RMS velocity of the air molecules.... *grin*.... but even with a "failed attempt" it looks like you surpassed that number (1650 fps @ 70*F)....

Looks to me like you can eliminate almost all of the O-ring land on the back side of the groove (just enough for loading)?.... no force in that direction, as the O-ring "pulls" the bullet through the barrel.... use that material to replace that where the bullet is so thin on the bottom (which is where I'm guessing it bent)....

Bob

[lloyd-ss]

Bob, I have a small rod of Grade 5 TiAlloy. About 60% heavier than the aluminum, but 3 times the yield strength. Might try a more robust aluminum bullet first and save the Ti as a fall back position.
1700 is in sight.  BTW, my shop is attached to the house and I always warn my wife when a big boomer is coming.  She said the 30 cal was way louder than the .22 stuff.  The residual muzzle pressure was similar, but the volume of air was a lot greater I guess.
Lloyd

[rsterne]

Yeah, I started doing that with my wife as well.... My garage/shop isn't attached, but as soon as I go supersonic she can easily hear it in the house.... Can't you get an aluminum bullet in .22 cal down under 8 gr?....

Bob

[Scotchmo]

Bob, I have a small rod of Grade 5 TiAlloy. About 60% heavier than the aluminum, but 3 times the yield strength. Might try a more robust aluminum bullet first and save the Ti as a fall back position.
1700 is in sight.  BTW, my shop is attached to the house and I always warn my wife when a big boomer is coming.  She said the 30 cal was way louder than the .22 stuff.  The residual muzzle pressure was similar, but the volume of air was a lot greater I guess.
Lloyd

Lloyd,

You did not give the barrel length, so I put the info in my spreadsheet and went down the FPS column until I reached 1655fps. That
was at 15.3".

The 14.7gr shows 1714fps at the same 15.3" length.

What is the actual length of the .308 caliber barrel?

Edit: I used the wrong PSI initially. At 3300psi, it shows about the same velocities with a 23.8" barrel.

[lloyd-ss]

Scott,
Here is my data:
Previous highest vel shot was .22 cal, 10.2 gn, 4500 psi, 14.5cc tank, 23.3" barrel, dump shot, full bore port, 1605fps actual velocity.

Based on that actual data, for the .300 cal, 17.1 gn, 4500 psi, 26.1cc tank, 27.3" barrel, dump shot, full bore port, I estimated an actual of 1735fps.  But after the bullet got all hung up in the release cam, it probably dragged all the way down the barrel and only got 1655fps.

Lloyd

[lloyd-ss]

...................... Can't you get an aluminum bullet in .22 cal down under 8 gr?....

Bob

Bob, you are right, I think I can.  This is from my reply #59 in this thread. 
"So then I made a new aluminum one and managed to get it down to 8.0 grains. Predicted vel = 1693 fps.  It was getting too late and I turned the gland that the o-ring fits into at .120, instead of .115 like all the previous projectiles had been.  It was off the lathe before I really discovered the mistake so I thought I'd try it anyway (one of those bad decisions you make when too tired.). I FORCED it into the barrel. How much difference can a tight o-ring make, anyway.  Well, instead of 1693, I got 1576. Double darn.  I didn't think the .005 difference in the gland depth would have made that big a difference, but doing the math, that is a 23% difference in the o-ring compression.  Very significant."

I found the 8gn one in my tin full of dead soldiers and it is in rough shape but I think I can do a better job at it this time.
Lloyd

[Bill G]

Lloyd, not to bother you but I was wondering what your course of data collection is going to be? 

multiple calibers
multiple dump volumes
various barrel lengths

It would be interesting to see the data on various plenum volumes as % of bore volume.  Kinda like you did with the port sizes.

Thanks
Bill

[lloyd-ss]

Lloyd, not to bother you but I was wondering what your course of data collection is going to be? 

multiple calibers
multiple dump volumes
various barrel lengths

It would be interesting to see the data on various plenum volumes as % of bore volume.  Kinda like you did with the port sizes.

Thanks
Bill

Hi Bill,
Thanks for putting a bug in my ear.  I seem to work on projects serially, not in parallel.  I've be hitting some that I need to get out the door and this one has set idle.  Plus, I am working on a 13' long oak dining table that my wife asked for about 3 years ago.

The first item when I get back on this project is to try and get some shots above 1700 fps.  Its just something that needs to be done.

For collecting some meaningful test data, the number of variables needs to be limited.  With the dump shot setup that I am using, each shot takes about 10 minutes, not including making the bullets. But for a single caliber and a single bullet weight, I think 2 or 3 barrel lengths should be used; 3 or 4 pressures; and 3 or 4 port sizes.  Instead of orifice plates to simulate T-ports, I think that short tubes should be used to more closely simulate the effect of smaller valves and T-ports.  Plenum volume would be a nice variable, but the number of shots needed is getting unmanageable. The dump valve setup I have is good for max velocity shots, but it isn't practical testing that requires a large number of shots. 
A more "test friendly" setup is needed.
Lloyd

[jeff76]

in theory.  if there was a way to seal the muzzle and create a vacuum in the barrel, and break that seal at the same time or a few milliseconds after the pellet begins to move, that the pellet would be pushed as well as pulled at the same time?  kind of like when you go to push a door open at the same time someone on the other side is pulling it open and you "dang" near rip it off at the hinges.

[rsterne]

The additional force created by the vacuum (15 psi) would be tiny, compared to the 4500 psi available pushing the bullet.... increasing the force on the bullet by only 1/3%.... IMO, not worth the bother.... True, you wouldn't have to push the air out of the way in front of the bullet, inside the barrel, but Lloyd already addressed that earlier in the thread with some numbers.... again, not worth the trouble....

In your analogy with the door, you are doubling the force because the pushing and pulling forces are roughly equal, no so in this case, the pushing force is 300x greater....

Bob

[Bill G]

Lloyd,  The tube idea is a good idea toward the traditional valve set-up.  personally I'm trying to move away from the passages toward an orifice or even CD nozzle. As to the data variable of plenum volume,  A max plenum size of what ever you were to choose altered by a series of progressively shorter spacers to take up volume.  But like you said, that's a bunch more shooting with 10min intervals for every shot.  This is a very large undertaking when you really start thinking about it.  With regard to the method you are using, it is about as instantaneous as I could imagine.  I can see where loading can be difficult and time consuming, not to mention how involved making the test projectiles can be.  You sir have chosen to carry a large burden. I thank you for the undertaking and the exchange of data. 

Bill     

[Buldawg76]

I was lost on the first page along with Rocker1 but still manage to pickup the overall theory and reason for the testing and learning all the time form you guys so it does help me improve my projects more than not and always follow with great enthusiasm even if I don't post as I tend to lurk and learn at my own slow pace.

Thanks as always for great thinking material but time for that whiskey and icepack. LOL

Mike 

[lloyd-ss]

Lloyd,  The tube idea is a good idea toward the traditional valve set-up.  personally I'm trying to move away from the passages toward an orifice or even CD nozzle. As to the data variable of plenum volume,  A max plenum size of what ever you were to choose altered by a series of progressively shorter spacers to take up volume.  But like you said, that's a bunch more shooting with 10min intervals for every shot.  This is a very large undertaking when you really start thinking about it.  With regard to the method you are using, it is about as instantaneous as I could imagine.  I can see where loading can be difficult and time consuming, not to mention how involved making the test projectiles can be.  You sir have chosen to carry a large burden. I thank you for the undertaking and the exchange of data. 

Bill     

We've really got about three topics going in this thread, but that is about par for this group, LOL.

One is the project of trying to shoot something with compressed air as fast as possible.  For that, the instantaneous release cam seems to be a good set-up. 

Then there is the data collection/data base development, for  shot velocity/fpe with all the various variables.

And finally, the ongoing development of an algorithm for predicting the internal ballistics of a PCP.  Several of us are working on that and getting decent results, but are still looking for further refinements.

So all in all, that's a whole 'nother Cardew book, LOL.

Bill G, please help me out with your mention of the CD nozzle in the path between the valve and bullet.  If the goal is to keep maximum force on the bullet all the way down the barrel (I think that is the goal, correct?), how does the CD nozzle come into play? I know that it can increase the velocity of the airstream, but will it increase the force on the bullet in this closed system? I am having trouble wrapping my head around that question.
Lloyd

[rsterne]

As I understand it, a CD nozzle is used to create a situation where the velocity of the gas reaches Mach 1 at the narrowest part of the restriction.... That allows the gas to continue to accelerate beyond Mach 1 downstream of the restriction.... By definition, the flow is choked, and you must get a pressure reduction of 1.89:1 across the system.... ie the outlet pressure cannot exceed 53% of the inlet pressure.... and in addition, there is a maximum mass flow that occurs once Mach 1 is reached in the nozzle.... The only way you can increase the amount of gas flowing through the system after choking occurs is to increase the upstream pressure.... Reading through this thread may help refresh your memory....  http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0

Since the goal is to maintain the greatest force against the bullet, and that requires pressure and air mass.... we should be avoiding restrictions in the system.... However, trying to understand how those restrictions affect the results is a sensible goal, because we use that as part of the tuning process sometimes....

Bob