Predicted Dwell Times?

[NCmountainShooter]

This is my first post to Geek Gate, though I feel at home from everything I've read so far. I'm trying to do the math for a perfect airgun and valve. From the discussion of "what works for PCP", I'm taking 950fps  as a good efficient speed and max predicted FPE as my goal:

Caliber, weights (max), FPE:
.177 cal - 35gr - 70 FPE
.224 cal - 55gr - 110 FPE
.257 cal - 75gr - 150 FPE
.308 cal - 115gr - 230 FPE
.408 cal - 200gr - 400 FPE
.457 cal - 250gr - 500 FPE
.510 cal - 300gr - 600FPE


 My question then is how do I determine the necessary dwell time to achieve those goals? I'm assuming the valve closes by the time the pellet/bullet travels around 1/3 length of the barrel. Let's start with a 24" barrel. The throat is at minimum 0.308 and lift is at minimum 0.077".  I don't have any hammer or spring numbers to go by, so I want to start from a performance ideal to get the dwell time. Lift could also be increased if needed.

Thanks!
Chris

[rsterne]

Lift and dwell are interrelated in a "smack open" valve.... The lift will have to scale up as the throat diameter increases, of course, to keep in proportion to the volume of air the valve has to flow.... Typically the lift is roughly twice as great at the low pressure end of the shot string as it is at the beginning.... and the amount of lift at the beginning of the string is around 1/4 of the throat diameter.... These values vary by a wide margin, but those might be considered "typical" values in a PCP that is working efficiently....

The dwell is quite closely related to the muzzle velocity (you wanted 950 fps) and the position of the pellet when the valve closes.... If the valve closes as the pellet exits, the dwell, of course, equals the lock time (used in this case to represent the time of the pellet in the barrel, not between trigger pull and valve strike).... As the valve closes sooner, the dwell is a smaller percentage of the lock time.... For the case where you have a 24" barrel, 950 fps muzzle velocity, and the valve closing at 8", the dwell is roughly 1.8 milliseconds.... and the lock time is roughly 3.5 milliseconds.... What changes, to meet those requirements, is the pressure and the efficiency of the gun.... In other words, only a small combination of values will produce a result where the muzzle velocity for a given weight pellet is 950 fps in a 24" barrel and the valve also closes at the 8" point....

Every time you change the reservoir volume, you change the average pressure during the shot.... If the volume was infinite, the pressure would remain the same until the valve closed.... The smaller the reservoir, the more the pressure drops during the shot.... The volume between the valve and the pellet is wasted volume, and causes a pressure drop before the air even hits the pellet.... Then there is the drag of the pellet down the bore (sliding friction) and the starting friction, plus of course the major effect of pellet weight.... As the pellet weight increases, it requires more volume of air to accelerate it to 950 fps, and this normally means more dwell is required.... Even the weight of the air changing (it is also accelerated) makes a difference.... If you use a different pressure in the reservoir, or if the gun is more, or less, efficient, either the muzzle velocity changes, or you have to change the dwell to keep it the same.... Unfortunately, the list goes on and on, so there is no simple answer to your question....

In addition, the values you listed in your table, which are pretty much maximums for a 24" barrel using 3000 psi, are not likely to be achieved with the valve closing at the 8" point at that pressure.... Remember, I said they were goals, and ones that were difficult to achieve.... something that is not likely to happen while closing the valve early....

Bob

[NCmountainShooter]

Bob,
Thanks the the ballpark figure. I get that those really are max values and don't necessarily correspond to the more efficient goals of 950fps or dwell = 1/3 lock time.  I'm sure a .22 won't need the same dwell time using the same valve dimensions as a .308. The more I tinker with these numbers and the math the better of an understanding I get for how these work.

Chris

[NCmountainShooter]

Maybe a better question is to ask for a range. What are the ranges of dwell time and for lift, from efficient but functional to powerful but inefficient?

I understand that for a throat diameter of 0.308", any distance of lift above 0.077" won't increase flow any further, just dwell time.
Therefore, I'll assume 0.077" lift is the minimum lift needed to take full advantage of that throat diameter. What amount of lift might be required to maximize FPE? Double, 0.154"?

Chris

[rsterne]

As you state, increasing the lift doesn't increase the flow, only the dwell, and the shape of the lift/dwell curve.... This is what happens as the pressure drops....



The black line is your 0.077" lift where the flow rate doesn't increase.... The amount of air through the valve is the area under the curves and also under the black line.... As shown, the difference in pressure between the beginning and end of the string is 2:1.... In fact, you are likely to have less than that for a useable pressure range.... The range of usable dwell for a PCP runs from about 1-2 milliseconds, depending on pressure and barrel length, but that is typical....

You are correct that dwell time will be less for a smaller caliber, and also for a lighter pellet within a given caliber.... Absolute maximum usable dwell will equal the lock time, beyond that the valve is still open after Elvis has left the building.... but the efficiency even then is only about 0.4 - 0.5 FPE/CI.... For any kind of decent efficiency, you want to close the valve before the pellet reaches half way down the barrel.... Even then, you will only be getting 0.7 - 0.8 FPE/CI.... That is about where the velocity plateau starts.... The knee of the curve in a regulated gun is likely where the valve closes at about 1/3 barrel length, and the efficiency approaches 1.00 FPE/CI.... I assume you have seen this type of curve for a regulated PCP?....



Studying how the velocity and efficiency interrelate on that graph will give you a good idea of what the dwell is.... +4T is about 100% dwell, +1T is about 50% dwell, 0T is about 33% dwell, and -1T likely about 25% dwell.... Those are just estimates of the barrel position when the valve closes, of course....

Bob

[Bill G]

As you state, increasing the lift doesn't increase the flow, only the dwell, and the shape of the lift/dwell curve.... This is what happens as the pressure drops....



The black line is your 0.077" lift where the flow rate doesn't increase.... The amount of air through the valve is the area under the curves and also under the black line.... As shown, the difference in pressure between the beginning and end of the string is 2:1.... In fact, you are likely to have less than that for a useable pressure range.... The range of usable dwell for a PCP runs from about 1-2 milliseconds, depending on pressure and barrel length, but that is typical.... ]

Bob imagine how useful your graph could be if we could plot the PSI at the top and the volume used at the right. This could allow one to optimize porting for a given cal based upon maximum efficiency vs flow requirements for desired performance.  Basically, help decide what size porting is required to attain a performance level while maintaining as flat as possible velocity curve.  We currently make the porting as large as possible and manipulate the flow by hammer/spring.  Essentially, the gun would work at max efficiency/power for a chosen pellet and without all the trial and error that we currently do.  Also allow us to choose a caliber that is suited for a given job as opposed to trying to overdrive a particular caliber. 

This is what I have been trying to do with my modeling tool for years.  I think that my model is fairly accurate(1.3% or less with correct variables) but am currently wrestling with Dwell prediction based on hammer mass, spring force and the like.  Doing it on a reged system is much easier and very accurate. 

[rsterne]

Some of your suggestions are already covered in this thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=57828.0 .... It deals a lot with how pressure and caliber relate to FPE and bullet weight....

The minimum porting question is partly covered here.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0 .... with other info on port size and how it relates to potential FPE in a given caliber in the first thread....

If you are talking about the pressure in the exhaust port, then I would suggest that above the "clipping" point it is virtually equal to reservoir pressure, assuming the ports (including the throat) are large enough to avoid sonic choking.... At just a few thou of lift, there is no air yet flowing due to boundary effects, so the pressure in the exhaust port is essentially zero.... On the opening cycle, between the two, the flow rate increases very quickly, and so does the pressure.... On the closing cycle, due to the onset of sonic choking, the drop in flow and pressure is even faster once the curtain area is reduced to the point where the flow reaches Mach 1 for the gas and pressure being used....

Bob

[Bill G]

Yep.... that boundry effect along with popet flex and sonic choking at the end are what gives our math models fits.  At that point, the math is beyond my ability.

Bill

[rsterne]

X^2....

Bob