Theoretical Maximum Velocity in a PCP

[lloyd-ss]

CHEATER !!!

Bob

Com'on, Bob, that's the second time you've said that in the past week or so, LOL. 
How about we call it  "creative solutions"? 

[rsterne]

After you get this puppy past 2000 fps with air at room temperature.... I'd love to see what you can get with Helium.... a vacuum on the barrel.... heat it up red hot if you like.... *LOL*....

Bob

[I_like_Irons]

So, maybe we have some very well organized air molecules?.... The ones on the edge, near the barrel, are on the low side of the velocity distribution curve, while the ones in the middle are the fast ones, at the high end of the velocity distribution.... How very nice of them to co-operate like that, and not have to exceed the 1650 fps RMS velocity!.... J/K guys !!!

or am I?.... 

Bob

This is precisely why I thought that the tapered barrel may have merit.  The average temperature is not going to change much if at all.  Therefore the average speed of the molecules must remain the same.  Those near the barrel walls must be slowed down due to friction effects (which induces some heat, does it not?).  Thus the remaining molecules in the center must move faster.

With the tapered bore, you have a progressive reduction in area, and less force per say.  However, does this gain more speed possible due to the slowing of more molecules since they are dragging on the walls, which in turn makes those in the middle of the column faster moving? 

When observing the extrusion, pultrusion, and wire drawing processes, the material flows much faster in the middle while the material at the walls of the dies moves slower. 

Now for figuring out the force on the projectile as it travels down the tapered bore, you may have to apply calculus---a continuing decrease in area for travel.  The amount of taper,  however, will not be all that great.  Tapering a .257" bore to .240" in 36" should be more than sufficient to test this, I would think.  Therefore, an average may be a good enough approximation.

[K.O.]

Lloyd if ya really want to cheat/C.S. and since are using aluminum ammo stick with the 19-24 inch barrel but attach a short barrel (8-12 inch) extension that has embedded rails hooked up to a capacitor bank...

Can not help it even my little pumpers are hybrids...

[phoebeisis]

NASA LIGHT GAS GUN
used H2 or Helium for just the reason I suggested-the heavier molecules run out of speed-just as the physics book diagram showed
velocities were STUNNING- 6000 meters per second-
They are springers -but same idea-air -N2 O2- run out of speed-cut from somewhere-wiki maybe
Try helium  and a smooth bore

 light-gas gun works on the same principle as a spring piston airgun. A large-diameter piston is used to force a gaseous working fluid through a smaller-diameter barrel containing the projectile to be accelerated. This reduction in diameter acts as a lever, increasing the speed while decreasing the force. In an airgun, the large piston is powered by a spring or compressed air, and the working fluid is atmospheric air.

In a light-gas gun, the piston is powered by a chemical reaction (usually gunpowder), and the working fluid is a lighter gas, such as helium or hydrogen (though helium is much safer to work with, hydrogen offers the best performance [as explained below], and causes less launch-tube erosion). One addition that a light-gas gun adds to the airgun is a rupture disk, which is a carefully calibrated disk (usually metal) designed to act as a valve. When the pressure builds up to the desired level behind the disk, the disk tears open, allowing the high-pressure, light gas to pass into the barrel. This ensures that the maximum amount of energy is available when the projectile begins moving.

Light-gas gun
Diagram of a light gas gun
1 — Breech block
2 — Chamber
3 — Propellant charge (gunpowder)
4 — Piston
5 — Pump tube
6 — Light gas (helium or hydrogen)
7 — Rupture disk
8 — High pressure coupling
9 — Projectile
10 — Gun barrel
One particular light-gas gun used by NASA uses a modified 40 mm cannon for power. The cannon uses gunpowder to propel a plastic (usually HDPE) piston down the cannon barrel, which is filled with high-pressure hydrogen gas. At the end of the cannon barrel is a conical section, leading down to the 5 mm barrel that fires the projectile. In this conical section is a stainless steel disk, approximately 2 mm thick, with an "x" pattern scored into the surface in the middle. When the hydrogen develops sufficient pressure to burst the scored section of the disk, the hydrogen flows through the hole and accelerates the projectile to a velocity of 6 km/s (22,000 km/h) in a distance of about a meter.

NASA also operates light-gas guns with launch tube sizes ranging from 0.170 inches (4.3 mm) to 1.5 in (38 mm) at Ames Research Center. These guns have been used in support of various missions beginning with Apollo reentry studies in the 1960s and most recently for high-speed thermal imaging. Velocities ranging from 1 km/s up to 7 km/s can be achieved. The largest of these involves a 6.25-inch (160 mm) diameter piston weighing more than 46 pounds (21 kg) to compress the hydrogen.

[rsterne]

They are a firearm, for a start....

One particular light-gas gun used by NASA uses a modified 40 mm cannon for power.

This thread is about PCPs, which rely on the EXPANSION of air, not it's rapid, Adiabatic compression by an explosion.... As I've said before, pretty much comparing apples to orange juice....

Bob

[phoebeisis]

Helium molecules are going faster at room temperature-maybe 3x as fast-at ALL temps-they have a BIG speed advantage-
which is why they used the lightest gas possible-H2-which is too dangerous for home use
at 1745fps his pellet is outrunning more than 70%  of his propellant molecules
This isn't my idea-NASA- thought the same thing-everyone would come to the same conclusion
if you want max speed from a gas gun-use the lighest gas
otherwise your projectile will outrun  most of your propellant molecules-
DESPITE still having PLENTY of energy and MV
you can't hit what you can't catch
I give up-I'll leave you guys alone

[rsterne]

Actually, you can go ahead and use Helium in a PCP, and you still won't achieve the theoretical maximum discussed at the beginning of this thread.... It is based solely on pressure, barrel length, and caliber.... Read through it and you will (or should) understand....

This thread is not about the highest velocity you can achieve by ANY means.... it is about PCPs.... Hope that clears it up.... Nobody is trying to pretend light gas guns don't work, they do, and extremely well....

but they aren't PCPs... 

Bob

[phoebeisis]

rsterne
Thanks for your polite reply.
I get it  room temp     just   air    14.5 cc volume     4500 psi   .22 caliber 
 so weight  friction  are about it in respect to improvements
your propellant is  just about out of gas
but a why not a smoothbore-and a nod to aero shape for the short chronograph distance -
I will leave you folks alone-no offense meant
Thanks
Charlie

[rsterne]

I would point out that the maximum theoretical FPE with a .22 cal at 4500 psi with a 23.3" barrel is 332 FPE..... Once you subtract the mass of the air that needs to be accelerated, and the pressure loss from a finite reservoir you lose a huge percentage of that.... but even at 1745 fps, with a 7.5 gr. pellet, Lloyd is only at 51 FPE.... Using Helium, with no other changes, might double the FPE.... but that still leaves us a HUGE distance from the theoretical maximum....

Bob

[phoebeisis]

Yikes
Long thread-parameters-set-air 4500 psi- barrel length-chamber size-rifling not rifling
OP calculated theoretical maximum-and is doggedly shooting nibbling away-

Went thru some of it-noticed helium mentioned way back #25 or so(scotchmo maybe)- plastic bullets  too
My apologies-  too much water under the bridge a thread to drop in on-
I will just eyeball it occasionally to see how the 1745 changes
Thanks for your patience-
Charlie

[lloyd-ss]

Hey Charlie, Yes, these long threads cover a lot of territory, and wander, but usually  come back to the original topic. Like herding cats sometimes.  And there is always a ton of information buried within the various replies.

You might want to take a look at this other thread (Sonic Choke, Sonic Joke),
http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.180

which is an offshoot of this thread you are reading now. (Theoretical Max Vel in a PCP)

The real topic in the other Sonic Choke, Sonic Joke, thread is dispelling existing theories/notions  of specific velocity limits in PCPs.  Or, to put it more bluntly, if someone is going to state as a fact that there is a velocity limit, they need to back it up with real evidence.   If they are going to say they think "there might be a velocity limit," even that needs to be backed up with some amount of credible reference material. None of us here are youngsters    who just got their first $99 springer at Walmart and can be fooled into swallowing random anecdotal statements.  This is a smart, thinking group     with commons sense and book and hands-on experience who really love the challenge of these guns.  And we see the challenges that most other airgunners don't.  This is serious fun, among a great bunch of folks. 
I'll get down off my soapbox now.  See what I meant about herding cats, LOL. 
 
Lloyd

[phoebeisis]

Lloyd
Ha,ha-not fair
1) we have 3.5 cats and a retread greyhound-they are about equally un-herdable
2)And I literally JUST(2 hr ago) bought a Crosman phantom NP break barrel $92.74 delivered with a $10 rebate-so $83.24 with the
stamp

This sure  is an exotic sub forum-someone designing building a springer cannon?

I will follow this thread-curious just how much over 1745 fps you can get-
Thanks
Charlie

[rsterne]

Here's a simple thought for you to consider.... The maximum FPE potential of a PCP is proportional to the total amount of air you cram into the barrel.... Think about it like uncorking a bottle.... The energy is volume times pressure.... which is ultimately the total volume used at 1 atmosphere.... This is consistent with what we discussed above....

Maximum FPE = Force (lbs) x Distance (ft) = Bore Area (in^2) x Pressure (lb/in^2) x Barrel Length (ft) = Barrel Volume (in^3) x Pressure (lb/in^2) / 12 (in/ft)

In terms of the maximum FPE potential, it doesn't matter if you have a .25 cal barrel that is 4 feet long, or a .50 cal barrel that is 1 foot long.... They both have the same potential to produce energy at the same pressure.... The bottom line is.... how much air are you cramming in the barrel?.... More volume, more power.... More pressure (ie more air), more power.... Multiply the two together, and you just end up with the amount of air at one atmosphere you used tp fill the bottle before you uncorked it.... 

Bob

[Scotchmo]

Bob,
true, but:

The maximum projectile FPE approaches the original FPE of the air volume -  as the projectile mass approaches infinity. (highest muzzle-energy efficiency)

The maximum projectile FPS approaches the maximum possible for air - as the projectile mass approaches 0. (lowest muzzle-energy efficiency)

Maximum FPS is at odds with maximum FPE.

[rsterne]

Not really.... because in real PCPs we aren't working with 100% efficiency in either case.... Don't forget, that "Maximum FPE" must include accelerating the mass of air in the barrel as well.... The whole point of this thread, and it's consequent discussion about maximum FPE.... was the THEORETICAL MAXIMUM EXCLUDING LOSSES.... and that's also what I am dealing with above.... In practical terms, the FPE that ends up in the bullet is almost always less than 50% of the theoretical maximum when using air.... Lloyd's last 2035 fps shot with a 5.6 gr. projectile in a .278 cal, 46" barrel at 4500 psi, only achieved 51.5 FPE out of the maximum possible, which was 1047 FPE, if you just look at the projectile.... That's only 5%.... The rest of the energy went into accelerating the air out the muzzle, and losses....

In practical terms, it will be easier to get a given FPE out of a .50 cal with a 1 foot barrel than out of a .25 cal with a 4 foot barrel.... but the theoretical maximum is the same in both cases, at equal pressure....

Bob

[lloyd-ss]

Sorry for dropping out of sight for so long.  I hope to get back on this project after things settle down around Thanksgiving.

Scott and Bob, your posts bring out some thoughts that have similarities to the conundrum that both conservation of energy and conservation of momentum within a system must be maintained.  But because air is compressible, that sort of comparison really isn’t realistic. And add elastic and inelastic modifiers to the momentum constraints makes it even more confusing.

BUT, just speaking of generalities, I have to agree that Scott’s statement that achieving/approaching  ACTUAL maximum velocity is at odds with also achieving maximum energy.

Again, just speaking in generalities, and trying to relate the output to the input, consider this:

For energy, given that  KE = ˝*mv2         
If the input energy is kept  the same, to achieve 10 times the velocity, the mass must be reduced to one one  one hundredth.  But we know empirically that if we use one one hundredth of the mass that we will probably get less than 10 times the velocity. For arguments sake let’s say we get 5 times the velocity and the rest of the energy is transferred to the system.

For conservation of  momentum, with input being m1 and v1:
For a perfectly elastic momentum collision, Input m1*v1 = Output m2*v2.
For an inelastic momentum collision, m1*v1 = m2*v2 + losses
Making a leap that the inelastic situation has some relevance to the discussion, and using the thoughts from the energy paragraph above:
For the heavy, slow bullet,  Momentum Input  m1*v1 = Output  m2*v2
For the light, fast bullet,  Input  m1*v1 = Output m2/100 *  5*v2 + large energy losses
Therefore, in this extreme example, the momentum of the light, fast bullet is only 5% of the momentum of the heavy slow bullet, and a substantial portion of the energy does not go into the KE of the bullet.

Now, everything I said above might be garbage, but  it seems that at every turn, the laws of physics predict humbling, diminishing increases as the velocities creep higher and higher.
Lloyd

[rsterne]

I think I follow your reasoning, and that is an excellent explanation of why the "real" velocity cannot keep up with the theoretical as the projectile gets lighter.... I was merely trying to point out that in terms of the maximum theoretical FPE, it can be simplified to barrel volume x pressure.... which simplifies even further to the amount of air (mass, or volume at NTP) the barrel would contain at that pressure before firing....

I agree 100% that heavier projectiles will retain more of this theoretical FPE.... if for no other reason, because there is a considerable mass of air moving down the barrel.... However, this has no effect on the basic calculation of the maximum theoretical FPE.... It just means that the lighter the projectile, relative to the mass of the air driving it, the lower will be the share of the KE given to the bullet....

Bob

[Euro2]

Guys, please check my logic if it makes sense. Energy of pellet and air pushing pellet

(m*v^2)/2 = (M*V^2)/2

m - mass of pellet
v - pellet muzzle velocity

M - mass of air per shot
V - average velocity of air in barrel

V = v *sqrt(m/M)

I'm metric guy.

Air density=0.001225gramms/cc.

Air rifle data from the net.

.25 marauder, data from:

newbielink:http://www.gatewaytoairguns.org/GTA/index.php?topic=59041.0 [nonactive]

25grain Pellet(=1,62gramms), pressure 3000psi(=206bar), muzzle velocity 853fps(=260m/s), cylinder volume 215cc, 62 psi/shot(=4.27bar/shot)

Mass of discharged air per shot = (206*215*0.001225)/(206/62)=1.13gramm

Average air velocity in barrel

V = 260*sqrt (1.62/1.13) = 311m/s

.458 air force texan, data from

pyramydair com /blog/2015/02/airforce-texan-big-bore-rifle-part-3/
(GTA wont let me post external url, I guess I do not post enough)

215 grain pellet(=13.9gramms), pressure 3000psi(=206bar), muzzle velocity 853fps(=260m/s),
cylinder volume 490cc, 256psi/shot(=14.8bar/shot)

Mass of discharged air per shot = (206*490*0.001225)/(206/14.8 )=8.88gramm

Average air velocity in barrel

V = 260*sqrt(13.9/8.88) = 325.29m/s

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

So we see that average air velocity in barrel of air rifle is about same 311m/s vs 325m/s. sonic speed is 343m/s. Note barrel length is irrelevant.

Practical max pellet speed (including supersonic) can be calculated by changing m - mass of pellet.

I think there are pretty interesting conclusions can be made, but 1st - do you see any misses in logic above.

[rsterne]

Is your basic assumption that the energy pushing the pellet and the energy pushing the air which is pushing that pellet are equal?.... In other words that the energy produced by the expanding air must somehow be equally divided between the two?.... Your math looks fine, from a quick glance, but I question the initial assumption.... assuming I understood it correctly....

Bob