Sonic Choke? Maybe not. 2162 FPS

[rsterne]

So you pulled the nose right off that Delrin bullet, parting it at the O-ring groove?.... Maybe PEEK would be strong enough?.... I'm sure you will figure it out, possibly drilling the aluminum one for a hollow nose and tail?.... (just stay away from the O-ring groove) *LOL*.... If you can get the weight down to 7.8 gr. you should be able to break 1700 fps with your current setup....

Lloyd, when you build a spreadsheet with my {square root (bore diam. x transfer port diam.) } used in the calculations, please send me a copy, I'd love to run some of the data I have and see how it tracks.... I have one gun here (my Disco Double) that has a variable barrel port (the bolt retracts and I can control how far quite accurately), so it is easy to get data....

Bob

[rsterne]

I thought I would try to see how my idea of using the "area" of the bore x transfer port diameters would work over the entire range of TP diameters, from 0-100% of bore size.... I used Lloyd's spreadsheet, input .25 cal, 25" barrel, 3000 psi, infinite reservoir volume and no losses except the mass of the air, and used TP diameters every 10%, to calculate the velocity and FPE with 25 gr., 100 gr., and 400 gr. bullets (to get various speed ranges).... Here are the results....



There was obviously something strange going on.... I expected to see the velocity parabolic and the FPE linear, but all three graphs had a discontinuity at about 450 fps.... That made no sense, so I went looking for a cause.... It turns out that the J4 version of Lloyd's spreadsheet I was using stopped integrating at 891 lines, which with the barrel length and pressure I chose worked out to about 450 fps.... so any velocity below that gave an incorrect result .... There is a definite smooth curve relationship between velocity and TP diameter, but I don't know yet if that is an accurate model of what happens in the real world....

Bob

[Scotchmo]

I went to sleep thinking about the 1640fps limit.

Where did it come from?

I speculated that it was from the calculated velocity that freely expanding air might achieve. Instead of a cylindrical expansion that is restricted to a barrel, imagine a spherical expansion. I did a little internet research and that's where I now think it came from.

We are concentrating the flow in a cylindrical barrel, so it seems velocities higher than 1640fps should be predictable and doable.

I looked into supersonic wind tunnels. They use a dump tank similar to Lloyd's experiments. Speeds of mach 4 are obtainable without additional heating.

https://en.wikipedia.org/wiki/Ludwieg_tube

https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Supersonic-en.svg/2000px-Supersonic-en.svg.png

[lloyd-ss]

Bob,
Check that again. 
Each iteration is .00001 sec, so with the arbitrary limitation of 891 iterations, any locktime over approx .0089 sec will be truncated.  The truncation is time related, not velocity or distance related.  That happens with the 400gr .25 cal because it is too slow to get out of the barrel in .0089 sec, but the other combinations you have presented should be correct.  The .0089 maximum lock time covers all plausible caliber/weight combinations. That is what my Rev J4 version is doing, anyway.
Lloyd

[lloyd-ss]

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

 

[Scotchmo]

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
 

After further reading, the Ludwieg tube appears to use a vacuum chamber. Different than a typical supersonic wind tunnel which uses a pressurized chamber. The following might be more typical:

[rsterne]

Lloyd, using the 100 gr, and reducing the "caliber" number I get the following for the last few lines in the spreadsheet....

100% - .25 cal - 1012.1 fps (constant)
60% - .15 cal - 662.2 fps (constant)
50% - .125 cal - 561.8 fps (constant)
40% - .1 cal - line 880 - 446.3; line 885 - 447.6; line 890 - 448.6; line 891 - 448.8
30% - .075 cal - line 880 - 259.4; line 885 - 260.9; line 890 - 262.3; line 891 - 262.6

As you can see, the velocity is still increasing in the last two examples, so the integration is not complete.... This is version J4.... Even the 25 gr. pellet runs out of lines at the 20% TP size (cal = 0.05).... 448.8 fps and still increasing....

Bob

[lloyd-ss]

OK, so one uses a big vacuum tank and the other a HPA tank, but both use flow thru a converging-diverging nozzle to drop the pressure and increase the air velocity on the down stream side of the nozzle.  They are using what amounts to an open ended system to create high velocity air, but without regard to the pressure drop..... maybe? I don't know.
We have a closed system (until the bullet exits the muzzle) and want maximum pressure behind the bullet until it exits.  But there must be a pressure drop (lower pressure directly behind the bullet) to make the air flow in the barrel.  So, the hypersonic tubes want maximum air velocity in the tube and we want maximum velocity of the projectile.  Are this goals common, or mutually exclusive.  I don't know.
Lloyd

[lloyd-ss]

Lloyd, using the 100 gr, and reducing the "caliber" number I get the following for the last few lines in the spreadsheet....

100% - .25 cal - 1012.1 fps (constant)
60% - .15 cal - 662.2 fps (constant)
50% - .125 cal - 561.8 fps (constant)
40% - .1 cal - line 880 - 446.3; line 885 - 447.6; line 890 - 448.6; line 891 - 448.8
30% - .075 cal - line 880 - 259.4; line 885 - 260.9; line 890 - 262.3; line 891 - 262.6

As you can see, the velocity is still increasing in the last two examples, so the integration is not complete.... This is version J4.... Even the 25 gr. pellet runs out of lines at the 20% TP size (cal = 0.05).... 448.8 fps and still increasing....

Bob

Bob, OK, I think I see what you mean.  Let me change the time increment and make a J5 version and send that to you in a few minutes.  This is curious.
Lloyd

[rsterne]

I tried Version K1 and got the same results.... The maximum lock time on both is 0.00878 sec.... That is occurring before the bullet reaches the muzzle if the velocity is less than about 450 fps....

Bob

[lloyd-ss]

I tried Version K1 and got the same results.... The maximum lock time on both is 0.00878 sec.... That is occurring before the bullet reaches the muzzle if the velocity is less than about 450 fps....

Bob

Correct, 450-500 fps is about the low limit with a 25" barrel  with the way I have the time increments set.  The J5 version I just sent should handle really slooooooow bullets.   

The barrel toggle in column O should switch from zero to 1 when the pellet leaves the muzzle.
Lloyd

[Bill G]

I left my jump drive in my desk at work so I don't have my newest iteration of spread sheet.  So, without it in front of me, I'll try to convey some findings.  I discovered that when I compared the possible flow through the specified port, at a specified pressure, to the chamber size at the same pressure, I could derive an "efficiency factor" (Better term welcome). It is expressed as a percentage.  What I discovered is that I can alter that percentage based on the pressure, proportionally, and it smooths the velocity differences from pressure to pressure or port area to port area.  It appears linear. Trying to change both port area and pressure just makes me get lost. 

I'll try to get back on once I get the jump drive in hand and have the numbers in front of me.  I may just have to follow along in the near future due to having to travel for work in the near future and I won't be able to keep up with the conversation in a meaningful way. You guys are all over this thing at the ragged edge of my ability.  I gotz sum lernnin to do. 

Bill

[rsterne]

Lloyd, that worked just fine.... Here are the new graphs....



You will notice an overall difference in shape of the velocity curve as well.... because in the first set I used the TP diameter, instead of sq.rt.(bore x TP)....  .... These curves are smooth right down to the point where the TP is only 10% of the bore (0.025"), not surprising they go in to the dumper after that....  .... Remember, that without the TP correction, the predicted velocity and energy would be a constant, not falling off as the TP gets smaller.... Note that for the light bullet, the velocity curve is more horizontal at the top end, as it should be.... while for the heavy bullet it is straighter.... This is consistent with reality.... Also note that although all the criteria are the same in every case with the exception of the bullet weight, the maximum FPE drops off dramatically for the light bullet going supersonic, just as we find in the real world.... For the 400 gr. bullet, wide open ports, we get 280 FPE, for the 100 gr. it is 230, but for the 25 gr. it is only 140 FPE (half the power for 1/16th the bullet weight).... That is a function of your calculator (there is no TP correction when wide open).... and one of the reasons I like it so much - it really works well....

Bob

[Airsnipe]

I'm not sure if this has been accounted for (or is significant) but I don't know if the pressure on the atmosphere side of the projectile is being considered. There is 14.whatever psi on the low pressure side of the projectile. I was thinking you have this somewhere in one of those formulas? But I would imagine that as the projectile speeds up, the low pressure side of the pellet also increases in pressure. Is that force being considered in these formulas? Or is this just as insignificant as the weight of air in the barrel?   

[rsterne]

The weight of the air in front of the bullet is insignificant, and the molecules can get away from the bullet at an average of 1650 fps anyway.... The weight of the HP air DRIVING the bullet, however is VERY significant, not only is it dense (~200-300 x normal), but it must be accelerated out the muzzle.... It MUST be included or the calculations are wayyyyyyyyyyyyy off.... That was mentioned earlier in this discussion....

Bob

[Airsnipe]

OK but what about the atmospheric pressure? There is one atmosphere of pressure countering the HP side. This is a very low value (once again maybe not significant) but the lower the HPA side the more significant it becomes. Say at 1400psi the atmospheric pressure is countering about 1% of the pressure accelerating the pellet.

[lloyd-ss]

.............................. You guys are all over this thing at the ragged edge of my ability.  I gotz sum lernnin to do. 

Bill

Bill G, ha, ha, I think we are all on the ragged edge of our abilities.  This is definitely pay as you go!

Bob, Please email me how you think the T-port compensation should be added into the spreadsheet, because I am not 100% positive.  I want to make sure I understand so that I might get it right the first time.  Or at least close    )

Airsnipe, I think the force of the air on the atmospheric side of the pellet is still pretty insignificant.  At rest, the atmospheric air exerts about .55 pounds of force on the pellet.  Lets say the pellet is fired and by the time it is a half inch shy of the muzzle, 3/4 of the air in front of it has flowed out the muzzle and the remaining 1/4 has become pressurized (stacked up) in front of the pellet, that is about 3.3 pounds of force, but that is only in the zone very close to the muzzle.  That is equivalent to about 90psi.  So maybe not totally insignificant depending on how the air in front of the bullet does move.  This is kind of in the realm of pellet drag values.
Lloyd

[Scotchmo]

OK but what about the atmospheric pressure? There is one atmosphere of pressure countering the HP side. This is a very low value (once again maybe not significant) but the lower the HPA side the more significant it becomes. Say at 1400psi the atmospheric pressure is countering about 1% of the pressure accelerating the pellet.

When we specify tank pressure, it is the pressure over and above air pressure.  1400 PSIG gauge is really 1414.7 PSIA, so the ambient air pressure is accounted for.

[Scotchmo]

The TPort affects the flow from the start so flow restriction during the iteration is really required. But maybe not really needed to get a good enough answer.

For Transfer Port compensation, at the backend of the calculation, what about something like:

If TParea2/TParea1 = .XX

FPS2/FPS1 = .XX^(1/8)
FPE2/FPE1 = .XX^(1/4)

It seems about right.

[rsterne]

I got the new version of Lloyd's spreadsheet this morning (J7) and right after breakfast I used some data I had for a Disco with various size transfer ports to test it.... The data was taken a few years ago, in a stock .22 cal Disco with 14.3 gr. pellets, at 3 pressures, 1600, 1200, and 850 psi.... with no adjustments to the gun between shots (ie same hammer spring preload), just the different size TPs.... I did six tests at 1600 psi, but only three at the lower pressures.... I tested larger size transfer ports as well, but since the barrel port and valve ports were stock, they did not increase the velocity to any significant degree, so I deleted them from this data as they were not a true test of the port diameter....

I set up Lloyd's new J7 spreadsheet using the criteria for a Disco.... .22 cal, 14.3 gr, 135 cc reservoir, 0.02CI transfer volume, 24" barrel, 0.140" TP diameter, 1 lb. drag and 2 lb. breakaway, air mass included, and 0.70 efficiency.... I used Isothermal expansion while the valve was open and Adiabatic after it closed.... I then adjusted the dwell until I got the same velocity as with the test results with the stock 0.140" port at each pressure.... and then changed the port size (only) to get the predicted velocities with the smaller ports.... Here are the results....



I was pretty disappointed, as the method I had Lloyd put into the spreadsheet, which works well for maximum FPE (essentially a dump shot) predicts too low a velocity with the smaller transfer ports.... ie it overcorrects for them.... Just for the record, here are the dwells I used for the three pressures to get the actual Disco velocities with the 0.140" TP, and the resulting predicted FPE/CI....

1600 psi - 0.0018 sec - 1.13 FPE/CI
1200 psi - 0.0025 sec - 1.02 FPE/CI
850 psi - 0.0035 sec - 0.90 FPE/CI

Those efficiency numbers are slightly low, but certainly in the ballpark for a stock Disco at those pressures.... so my guess of using 0.70 for the "fudge factor" in the J7 spreadsheet was pretty close, and not the reason for the divergence of the spreadsheet predicitions from reality.... 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.... Realistically, it predicts velocities on the low side about as much as no compensation would on the high side (which would predict no loss in velocity as the TP changed - ie straight lines at the maximum velocity)....

Bob