Theoretical Maximum Velocity in a PCP

[Scotchmo]

I have question. Is that true that none of side injected (aka transfer port is 90 deg to barrel) PCPs are not capable of super sonic  projectile velocities? I know that inline injection i.e. AirForce/Huben are capable of supersonic.

My thinking is that 90 deg air injection creates way too much turbulence and there's no sonic choke, so air flow never crosses sonic. Inline injection models have natural air choke that is capable to produce super sonic air flow.

Am I way off?

The straight inlet has less flow resistance. Either way, straight or angled, the flow out of a pressurized vessel becomes "choked" at mach 1.

A flowing column of air will also undergo expansion in the barrel. The maximum expansion rate is also about mach1. Under the right conditions, the inlet will approach mach 1 relative to the stationary air in the tank. The expansion front, would approach mach 1 relative to the flowing air. The velocity of the expansion front relative to the stationary air is then about mach 2.

[Euro2]

Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!

Let's say .17 rifle has 15ftlbf energy. By your theory 0.4 g plastic pellet will leave barrel at full blown Mach 4 - 4100ft/s.

And because of REALL BAD BC pellet energy will drop to 2ftlbf and velocity to 1300ft/s in just one ft before it reaches chronograph?

I think to confirm that you can move chronograph one ft further? Should see dramatic drop from 1300 ft/s?

[rsterne]

By your theory 0.4 g plastic pellet will leave barrel at full blown Mach 4 - 4100ft/s.

I don't think anyone suggested that.... If you really want to, you can calculate an approximate BC for the felt pellet.... The SD is 0.4/7000/0.177/0.177 = 0.0018.... Using the rate of velocity decay for a cylinder (Drag Profile GC) from ChairGun, if the BC is 0.018 it would decay from 2000 fps to 1327 in 8 yards.... which means for a BC of 0.0018 the distance for the same deceleration would be 0.0018/0.018 x 8 = 0.8 yards x 36 = about 29".... Therefore, for a measured (average velocity between 12-24 " from the muzzle, the muzzle velocity must be less than 2000 fps.... If we consider the deceleration rate to be uniform, and use an average distance of 18" (0.5 yd), and an average velocity of 1365 fps, my best guess for the MV is 1760 fps....

Bob

[Euro2]

I don't think 2000 ft/s has ground under it. 15lbft will send 0.4 g at 4100ft/s. So speed out of barrel shoul be 4100.


To my understanding losing 3 Mach of speed in 1ft will most probably evoporize plastic pellet:)

But as I said experiment is pretty easy - move crony one more ft away. Bob your calculation should tell speed at 2 and 3 ft.

I'll see if I can order same/similar e plastic pellets to fire from Huben.

[rsterne]

In my experience, as the weight of a projectile goes down, so does the FPE it will be launched at, from a given PCP.... If you are curious why, perhaps you need to look at the mass of the air, compared to the mass of the pellet, as one of the reasons for the drop in efficiency.... Another will likely be that as the pellet moves progressively faster down the bore (because it is lighter and easier to accelerate), the valve (which should have near constant dwell) will be closing later in the pellets travel down the barrel, and at some point, after the pellet exits.... Unless I have a misunderstanding of physics, once the pellet is no longer in the barrel, the air can't accelerate it to your 4100 fps....

I have a copy of Lloyd's Internal Ballistics Spreadsheet, and starting with a .177 cal PCP that shoots an 8 gr. pellet at 15 FPE, on 1500 psi of air from a 16" barrel.... changing ONLY the projectile weight to 0.4 gr predicts 1820 fps and 2.9 FPE.... Any projectile lighter than 1.2 gr (MV = 1615 fps) will be leaving the barrel while the valve is still open.... After that, the losses in FPE are huge, because you have less and less air actually driving the pellet before it leaves the muzzle.... and more and more air blowing out the end after Elvis has left the building....

I see you altered you distances to having the screens at 2 ft. and 3 ft, so the average distance would be 2.5 ft.... If the MV was indeed 1760 fps, and my BC is correct, you should measure an average velocity of about 1170 fps....

Bob

[Euro2]

Oh, I probably was not clear.

We have experimental fact - 0.4 g pellet shows 1300ft/s at chronograph one ft after muzzle from 15lbft rifle,

My speculation was that pellet travels in barrel at sub sonic speed. Muzzle acts as choke and right out of muzzle pushes pellet a bit supersonic.

Motörhead on other hand has his theory;

Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!

Note that he says that dwell is short - so he speculates that valve closes pretty fast and all mass of air pushes .4 g pellet. This is where I derived theoretical 4100fps. His "MAJORLY slowing down" I read as very bad BC....

But I may have misunderstood him - we can let him explain.

[rsterne]

If you are suggesting that the pellet is accelerated AFTER leaving the barrel, I would ask you to explain how that happens.... If you are saying that the choke at the muzzle is pushing the pellet supersonic, how do you explain my shots from an unchoked barrel at over Mach 1.5 ?

I tried to explain that a gun with a short dwell cycle (with normal pellet weight) no longer has a short dwell cycle with an extremely light pellet, the valve will close after the pellet leaves the muzzle.... I guess I failed....

I wish you luck in your speculations....

Bob

[Motorhead]

Oh, I probably was not clear.

We have experimental fact - 0.4 g pellet shows 1300ft/s at chronograph one ft after muzzle from 15lbft rifle,

My speculation was that pellet travels in barrel at sub sonic speed. Muzzle acts as choke and right out of muzzle pushes pellet a bit supersonic.

Motörhead on other hand has his theory;

Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!

Note that he says that dwell is short - so he speculates that valve closes pretty fast and all mass of air pushes .4 g pellet. This is where I derived theoretical 4100fps. His "MAJORLY slowing down" I read as very bad BC....

But I may have misunderstood him - we can let him explain.

I smell a TROLL who wishes to CREATE conflict among us ... of which quite honestly only responded to Euro2's post in thread because I had easy access to take a few shots over the chrony.  Honestly I could care less about the theory & data of perceived or real status quo thinking.
Really could care less being said testing and collected data simply DOES NOT apply to shooting of an air gun with normal pellets in any practical sense.

Indeed I've got my own thoughts on this subject and getting into it as with most outside the box thinking is best left to those persons and places where such application and testing can prove or disprove fact from fiction.
The under lying FACT the speed limitations thought as the speed limit has been dis-proven ... so are those contributing reasons for the original assumption being now questioned beyond the accepted physics involved.

[Euro2]

I smell a TROLL who wishes to CREATE conflict among us ... ... DOES NOT apply to shooting of an air gun with normal pellets in any practical sense.

Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!

Well if that's all that you have to say to defend your statement quoted above, I'm fine with that. I asked question - none of you guys hanging on forums for years posting same stuff every single day had answer. Cause answer is not written on google and hurts your pride as every day guru here:)

In case if you cool down, please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment - it is good subject and wrong place to call people trolls.

[Motorhead]

Please excuse my "troll" smelling  ... that is just shy of calling someone out.

The internet forums are all subjected to a non stop barrage of those seeking definitive black/white resolve of varied subjects that many times like politics what works for them, does not for you & thus conflict of ones perception to which viewpoint is correct comes into heated debate.

I will say this and then I'm done ...
A pulse of high pressure has a front that bears against the ambient pressure.  In a barrel this Pressure as well Amplitude is strongest right at the valve where the HP is subjected to the ambient LP.  A Felt pellet of such low mass gets swept up and moved along with the Front of the pressure pulse.  As this pulse expands into greater volume of the barrel it's amplitude is diminishing. The felt offers little to no resistance and does not create drag to cause compression pressure behind itself but moves with the pulse energy of the expanding air.

In front of the felt pellet is a column of ambient air that upon the felt getting pushed out barrel is compressed as it gets forced out ahead of the felt ( Pellets too ) This compression of the air column ABSORBS energy and further the felt moves towards muzzle greater is the resistance felt pellet feels.  My take is that the Felt pellet having so little weight & mass it SNAPS up to speed near instantly slowing down as the amplitude of the pulse energy driving it falls off as volume is gained while compression losses of the air it is displacing ahead of it is increasing slowing it down.  Once felt pellet exits muzzle the column of air it compressed on it's way to muzzle blows clear, but static ambient pressure air is still very effective in slowing it down at very high rate ... Yea the BC is Terrible !!!

JMO ...

[Rocker1]

 Now my head hurts lol!!  whats bad is I understood it. David

[rsterne]

Here is your question....

I have question. Is that true that none of side injected (aka transfer port is 90 deg to barrel) PCPs are not capable of super sonic  projectile velocities? I know that inline injection i.e. AirForce/Huben are capable of supersonic.

My thinking is that 90 deg air injection creates way too much turbulence and there's no sonic choke, so air flow never crosses sonic. Inline injection models have natural air choke that is capable to produce super sonic air flow.

Am I way off?

Scott and I both answered it, but apparently you didn't like our answers, which both proved that you can drive something faster than Mach 1 (in fact over Mach 1.5) with a conventional side-ported PCP where the air turns 180*.... Then you made the (very antagonistic) statement....

none of you guys hanging on forums for years posting same stuff every single day had answer

All I see is someone who has their own ideas (and more power to you for that) that is unwilling to accept experimental evidence, or reasoning, that does not agree with you.... I would strongly suggest that when you make a statement, or have a theory, you be prepared to prove it.... Theories are only valid until they are disproved by empirical evidence (just like the 1650 fps limit was).... Then it's time for new theory.... IMO....

In case you don't get it yet.... empirical results will NEVER match theory.... all they can do is prove that the theory is wrong if the number predicted is too low....

Bob

[rsterne]

To take us back to where this thread started.... here is Lloyd's original post, with the numbers changed to reflect the test shot being recently discussed.... ie .177 cal with a 0.4 gr. "pellet" in a 16" barrel, using 1500 psi....

Example of Calculating Maximum THEORETICAL Velocity-

Let’s assume  .177 cal, 0.4 gn,  16” (1.33 ft) barrel, and 1500 psi.
We want to solve for “v” in the equation we rearranged above:
v = (F/m) x {sqrt ([2 x d x m]/F)}

Here is one way to solve it:
First, find the force, “F”, that is accelerating the bullet.  F  is the product of the bullet’s cross sectional area (.0246 sq in for a .177 cal bullet) times the pressure, so the force on the bullet  = .0246 sqin x 1500lbs/sqin = 36.9 pounds of force trying to push, i.e., accelerate, the bullet through the barrel.
F = 36.9 pounds


Next, calculate the mass, “m” of the bullet.  Mass is the weight of the bullet in pounds, divided by the gravitational constant “g”.  (We need the mass of the bullet, not the weight.) 
Mass= (0.4 gns/7000 gns per pound)/32.174 = .00000177 slugs ( the slug is the imperial unit of mass, a bit confusing).
mass  = .00000177 slugs

Now, plug those calculated values for F and m into the velocity equation:
v = (F/m) x {sqrt ([2 x d x m]/F)}
v= (36.9/.00000177) x {sqrt ([ 2 x 1.333 x .00000177]/36.9}
v = (20,847,457) x {sqrt (.000000127}  [note that 20,847,457 is the acceleration in ft/sec2, or 647,960 g’s]
v = 20,847,457 x .000356
v = 7,422 feet/sec MAXIMUM THEORETICAL MUZZLE VELOCITY  for this example.

And to take it one step farther, the MAXIMUM THEORETICAL MUZZLE ENERGY for this example is:
FPE = (bullet grains x velocity x velocity ) / 450,240 = 49 ftlbs

By way of double checking the results, we can use the formula for the Maximum FPE that can be produced by 1500 psi in a .177 cal barrel that is 16" long....

FPE = Force (lbs) x Distance (ft.)
= area (sqin) x pressure (psi) x barrel length (in) / 12
= (0.0246 x 1500) x (16 / 12) = 36.9 x 1.333 = 49 FPE

As you can see, achieving a "mere" 1365 fps is nowhere NEAR what the Theoretical Maximum is.... which was the whole point of this thread.... Somehow it got turned into a discussion of what we have "achieved", or that might be "achieveable" in the real world.... rather than how far we are from extracting the theoretical maximums.... which while interesting, is far from the original intent of the thread.... IMO....

Bob

[Scotchmo]

...please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment - it is good subject and wrong place to call people trolls.

"please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment"
The maximum observed velocity is about 2160fps per Lloyd's experiments.

"please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment"
My best theoretical maximum is about 2500-3300fps depending on the driving pressure.

A repeatable experiment will never exceed the theoretical maximum. It won't even reach it. If it does, the theory is wrong.

[phoebeisis]

Slight aside
What is the current fastest shot here
The last time i "LOOKED" it was 2300fps or so I think
and the shooter was planning a 2nd or 3nd generation "gun" of bigger diameter-about .27" I think-a smoothbore I think
and maybe it was going to have a different pellet release/trigger-no longer going to use claws to grab the pellet-so the pellet could be lighter
so current max for a PCP?
Thanks
Charlie
ps-I think the builder was a little disappointed with the barrel stock that arrived-it was well off claimed inside diameter

[rsterne]

I believe 2162 is the fastest Lloyd recorded.... The thread is right here in the Geek (R&D) Gate.... http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0

Bob

[phoebeisis]

Bob
Thanks-2160-

[MJP]

Well subject is "Theoretical Maximum Velocity in a PCP" so I think anything counts:)

Can you please chronograph cleaning pellet next time you fire it? Is it almost sonic or way supersonic?

This isn't a cleaning pellet but speed is above mach1 from conventional 180 deg turn valve.


Marko

[Scotchmo]

Well subject is "Theoretical Maximum Velocity in a PCP" so I think anything counts:)

Can you please chronograph cleaning pellet next time you fire it? Is it almost sonic or way supersonic?

This isn't a cleaning pellet but speed is above mach1 from conventional 180 deg turn valve.


Marko

366 m/s (1200fps) is common with alloy pellets.

http://www.gamousa.com/product.aspx?productID=235

Some airguns can even do it with lead pellets.

[MJP]

Well its a 67 grain lead bullet, I think it counts as a lead pellet.

Marko