What Makes Sense for PCPs?

[rsterne]

I've been thinking about this for a while.... What makes sense trying to accomplish with PCPs and what is basically a waste of time tryng to accomplish with any hope of doing so efficiently?.... There are a couple of things that, while they don't present HARD limits, seem to me to be the point where pushing beyond them is prone to a (sometimes severe) loss of efficiency in the energy delivered to the target for the amount of air expended....

1. Velocities over Mach 0.9.... Bullet drag increases drastically once you are over 900-1000 fps.... therefore less FPE delivered downrange....
2. Port velocities over Mach 1.... Shock waves inside the ports drastically increase the drag, dropping the efficiency in FPE/CI....

RE #1, I realized some time ago that the BC of waisted pellets dropped significantly in that velocity range.... What I found out recently was that bullets suffer the same fate.... The velocity at which the drag suddenly increases varies between Mach 0.75 and Mach 0.9 depending on bullet shape.... My point is, why bother trying to go supersonic when our source of power is so limited (compared to a PB) when the bullet tends to give it all back in the first few yards?....

RE #2, this was recently brought into clearer focus by Steve in NC where he set out a formula for "optimum transfer port sizes" based on the point where the flow goes supersonic.... It is based on the idea that if you know the velocity of the air in the barrel (the bullet velocity) you can calculate the velocity in the transfer port, and when it goes supersonic, the drag takes a big jump.... It's not that you CAN'T push past that point, it's just that doing so EFFICIENTLY is extremely difficult.... In a carefully design, axial flow gun (like the Condor) in theory it MAY be possible to design a convergent-divergent nozzle (think rocket nozzle) that would accelerate the airflow past Mach 1.... but until the CFD types figure that out, we are left with trying to keep all of the flow under Mach 1 to keep the efficiency up, IMO.... Steve's formula is very simple:

Port diameter = Caliber (Muzzle Velocity / Speed of Sound) ^0.5 .... ie take the muzzle velocity, divide by 1130 fps, take the square root of the result, and multiply by the bore size.... When the muzzle velocity equals Mach 1, you need ports that are bore-size.... For CO2, use 917 fps, and for Helium use 3200 fps (all at 20*C).... Here are some other values....

Mach 0.8 (904 fps) : Port 90% of caliber
Mach 0.85 (961 fps) : 92% of caliber
Mach 0.9 (1017 fps) : 95% of cailber (valve throat = caliber)
Mach 0.95 (1074 fps) : 98% of caliber

Incidently, in my testing I have found that having the throat slightly (10%) larger in area than the remainder of the ports seems to help the efficiency.... I'm thinking that since the critical part of the flow that starts the pellet acceleration occurs before the 1/4 diameter "curtain limit" on the lift, that larger throat helps keep shock waves from forming at that critical time as the pellet acceleration is beginning.... but I can't prove it.... I digress....

So, let's assume for a moment that we use bore area porting and limit the velocity to around 950 fps, where the FPE is easy to calculate, it's twice the weight of the projectile.... So that we don't push the ports too close to Mach 1 (as I'm sure the drag starts increasing well below that anyway), let's use bore-size porting.... If the gun was 100% efficient, we could calculate the maximum FPE we can get per foot of acceleration once we know the force on the base of the pellet.... That force is the bore area times the pressure....



OK, so we know the force, what else do we need to calculate the acceleration, and the velocity after a foot of travel?.... Well, we need the mass, but not just of the bullet, but of the air in the barrel that is accelerating as well, which is considerable.... How about if we use the barrel volume of air at that pressure, assuming a foot of barrel?.... At 21*C, that is 1.2 kg/cu.m. at 1 bar.... let's convert that to grains per cu.in.... We get (7000 x 2.204 x 1.2) / 61023 = 18514/61023 = 0.303 grains / cu.in times the pressure in bar.... We can calculate the weight of air inside the barrel at various pressures, from the cailber and the barrel length.... For a 12" long slug of air (you'll see why later), this works out to:

Wt. (gr.) = 0.303 x (cal ^2 x PI / 4) x 12 x pressure (bar) = 2.86 x P x C^2

Here is what that works out to, in the same format as above....



Now we need the weight of the projectile.... For a high performance PCP, a roundball isn't heavy enough, IMO, so here is a graph, again in the same format, giving similar bullet weights graphed against the caliber....



I left off the 4x roundball weight over .357 cal because the bullet weights just seemed unreasonably heavy.... Really all the lines are just to give you some examples.... Can you see where I'm going with this?.... Good, because my train of thought has left the station and it's time for me to stop for a while and regroup.... *LOL*.... I think I was getting off track (in fact I know I was) but I'll leave the graphs here anyway just because some may find them useful....

Bob

[rsterne]

OK, fresh start.... Back to the basic math, I hope I've got it right.... Sorry I hit the "post" button before I was done.... Starting with the equations for constant linear acceleration:

F = ma .... Force F = mass m x acceleration a .... solve for a you get .... a = F/m

E = 1/2 m v^2 .... Energy E = one half the mass m times the velocity v squared....

v^2 = 2as .... starting at rest, the velocity v = twice the acceleration a times the distance s .... substitute 2as for v^2 in the energy equation above....

E = 1/2 m (2as) .... the 1/2 and the 2 cancel and we get E = mas .... now substitute F/m for a....

E = m (F/m) s .... the m's cancel out, and you are left with E = Fs .... the energy E in Ft.lb equals the force F in lbs. times the distance s in ft.

Now, let the distance be 1 ft., and we get E = F.... so, going back to the original graph of Force vs. Caliber, if we apply that force over one foot of travel, we now have FPE vs. Caliber....



I feel that this represents a reasonable goal for modern PCPs.... Now you may say that our barrels are more than a foot long, but remember that to get any reasonable efficiency we have to close the valve before the pellet/bullet travels more than half the length of the barrel.... Then you will point out that the air keeps expanding after the valve closes, adding more energy, to which my answer is that makes up for the less than 100% efficiency assumed in my calculations.... Well, what about barrels longer than two feet?.... OK, you got me there, in a three foot barrel maybe you should be able to get 50% more FPE than the graph suggests.... You can lug around something that long if you wish....

I know this is going to be controversial, and that's fine.... This is, after all, the Geek Gate, and I expect to have you guys be tough on me.... So, have at it !!!

Bob

[Airgun.Sniper]

 Very well detailed...had to put it on a seperate document to be able to make clear thoughts

[wwonka]

and you are left with E = Fs .... the energy E in Ft.lb equals the force F in lbs. times the distance s in ft.

Now, let the distance be 1 ft., and we get E = F....

It has been a while since I've had to put my old physics degree to use, Bob: but Energy = Force X Distance is pretty much a definitive equation for energy (a force exerted across a distance), "aka the ability to do work".

So - yep, you're right. But I don't' think you needed to derive that all over again from the basic Newtonian equations 

[rsterne]

Not everyone is a math whiz (and I'm certainly not) so I figure if it helped me to work through it and have to explain it to others I would make sure I didn't make any glaring error.... The fact that the units worked out in the end was the validation I was looking for.... Yes, you're completely correct, Energy is force x distance, so maybe it should have been obvious, but hopefully my explanation was slightly clearer than a muddy pond....

Bob

[wwonka]

It was very well explained. I really enjoy reading your posts, graphs, data, etc. Seems you've achieved some pretty groundbreaking results translating this stuff into actual real-world shot strings, etc. Very cool stuff.  Makes me want to send you my Rainstorm .357 for a tune.

[rsterne]

Just a few interesting data points for my Hayabusa.... All the below have 28-29" barrels, running at 3000 psi....

.224 cal maxed out at 106 FPE.... full boresize porting.... right on the blue line
.257 cal maxed out at 160 FPE.... full boresize porting.... right on the blue line
.308 cal maxed out at 207 FPE.... 92% porting.... about 5% below the blue line
.357 cal maxed out at 257 FPE.... 80% porting.... about 13% below the blue line

Based on that data, I feel the chart above is pretty good as a goal.... and to achieve it you likely have to go with pretty much boresize porting and a barrel over 24"....

Bob

[wwonka]

Yes, very interesting data points. The combination of shot count, performance, ES and efficiency you squeeze out of the .308 and .357 seems to beat a lot that's out there in the market.

The stock barrel on the Rainstorm .357 is is 21.5".  The stock shroud doesn't project much more than 2 inches over that. But if you're willing to give re-barreling, re-porting, etc a shot - I think this would be a worthy platform to try them on. I'd honestly pay to see what could be done with some of your techniques on this very nice Rainstorm platform    I don't hunt, but I do enjoy long-range target - so that rapidly sloping shot string isn't ideal - which is why I like the fine balance of ES consistency and performance that you're able to achieve in your projects without a regulator.

[David.Soliman]

Where is the like button when you need one  . Some very useful information you put there Bob and I think is pretty helpful to modders and DIYers

[PakProtector]

IFF force is not constant...E=integral(force x distance)...but we seem to have it relatively constant...

I was pleased to see my .224 with bore area porting running quite efficiently at 80 FPE. Which validated the experiment on opening both sides of the valve up...inlet at ~5x port area, and outlet at bore area at the smallest. Now to get it to put one on top of the other...tried many different shape pellets; all the way to 47 gr weight and still no joy. Next thing is to examine the barrel harmonics.

If it were easy everybody would be doing it.
cheers,
Douglas

[45Bravo]

They promised me there would not be any algebra on this forum.......

[Big Bore Bart]

They promised me there would not be any algebra on this forum.......

   Where is that written?    This is the GEEK Gate.

[45Bravo]

   Where is that written?    This is the GEEK Gate.
[/quote]

Oh, I am a geek, and a nerd.

I have been working on computers since the TRS-80 came out

And still do today for a living..
(Not working on the TRS 80's, but mostly pc's)

[TimmyMac1]

Nice work. I see so much start to happen in the Transitional velocity range from Mach .82 to 1 but it is hard to say what is happening in the ports. You can induce supersonic flow to help a valve shut quicker. There is always a point of max restriction which will be your highest air speed. It will normally be at a port restrictor if you are using that to throttle it.
Convergence on a contoured bolt probe where I like to accelerate the flow so it scavenges the air through the TP. That's my theory. If you can create the point of max restriction at a point other than the port redirection in the valve or barrel it creates the most fluid flow. What I consider a pop rather than a belch or bark rather than a burp is what the ear hears when the charge value is dead on
THE MASS OF OUR PELLETS AND THE SMALL MASS OF OUR CHARGE is why we need to be so efficient and not play with the supersonic thing. We can do it but it is a massive energy zapper. We find efficientcy and accuracy holding hands so often they are a harmony you see a lot in good Airguns. Standing on it will cost you in General. More sometimes than others.

TimmyMac1

[wwonka]

Oh, I am a geek, and a nerd.

I have been working on computers since the TRS-80 came out

And still do today for a living..
(Not working on the TRS 80's, but mostly pc's)

Ha ha, that picture's a blast from the past. I do software today too. Even before high school I was sneaking upstairs while the family slept to code on my brother's TRS-80 Level II 16 K "microcomputer" (older than the one in your pic). Brother told me he'd kill me if he ever caught me touching his computer - but I guess he never caught me.

That TRS-80 and my old rock-solid Chinese break-barrel .177 were my two things.  Tinkering with computers is a lot like tinkering with airguns. OK - back to airguns...

[PakProtector]

Since I am nearly at 3x roundball weight in .224, I think I should get a few; that would make for a neat close-in chipmunk killer...or squirrels, or... which BTW is one way to establish power plant capability---put more light boolits in and examine delivered velocity.
cheers,
Douglas

[rsterne]

If you want to look at what bullet weight does, check this out.... Gun settings maxed out, starting at 3000 psi for all strings....





Note that I didn't have quite enough hammer strike to max out the velocity with the heavier bullets, so their maximum FPE should have been even higher....

Bob

[Sfttailrdr46]

  Every time I do this (read your Geek Posts) I end up talking to myself and wishing I had taken mechanical engineering rather than electronics. Then I would not have to think so hard

[PakProtector]

Every time I do this (read your Geek Posts) I end up talking to myself and wishing I had taken mechanical engineering rather than electronics. Then I would not have to think so hard

Yeah...riiiight. Variable gate-drain capacitance based on drain-source voltage? No thanks. I am quite happy with the easy ME stuff...LOL
cheers,
Douglas

[Tad]

rsterne-"The fact that the units worked out in the end was the validation"

It always feels good, doesn't it?  The first thing they try to beat into your head in physics class is to be sure to use dimensions throughout your calculations, and the last thing a student wants to do.

The courses I took used both English and metric units.  So, you could have a problem where 5 of the units were metric, and one English unit snuck in.  Always screwed you if you were not paying attention to the units.