CO222's recent posts about his extremely efficient one-of-a-kind bigbore that can produce 195 foot-pounds from only 1242 bar-cc of air = 6.37bar-cc/fpe, raises this question: Ignoring all practical limitations like pneumatic and mechanical friction, pressure ratings, finite barrel length, speed of sound related issues, etc. etc.

Where is the limit? Just what is the absolute theoretical limit of PCP efficiency?

http://www.network54.com/Forum/79537/thread/1211559328/At+6.37bar-cc-fpe+and+195fpe%2C+is+this+the+most+efficient+airgun+on+the+planet-

The way I ran the numbers suggests that, for PCPs, the answer is: 3.875 bar-cc/fpe.

Here's where that number comes from.

In a PCP, the process of propelling the pellet occurs in two basic (idealized) phases:

1. Isobaric = constant pressure.
2. Adiabatic = constant energy.

In phase 1, the valve is open. This connects the breech and bore behind the pellet with the air reservoir. If air the reservoir is very large (effectively infinte) and if the valve and air passages cause no pressure losses, then the pressure pushing the pellet will equal the constant reservoir pressure.

Under these (ideal) conditions, the maximum kinetic energy in fpe delivered to the pellet by each bar-cc is 14.5psi / 2.54^3 / 12 = 0.0737fpe.

In phase 2, the valve is closed. So the fixed charge of air now trapped between the valve and pellet expands as it continues to accelerate the pellet, causing both its pressure and temperature to drop. Because the expansion is so rapid that no significant heat can transfer from the barrel to the air, the only energy available to push the pellet is the initial thermal energy of the molecules in the charge. This means that the sum of the energy of the pellet and the molecules is constant, as one speeds up at the expense of the other slowing down.

Under these ideal conditions and assuming that expansion cools the charge all the way to -459.58F (absolute zero), the maximum possible energy delivered to the pellet per bar-cc = 0.1843fpe

Add #1 and #2 together, and we get 0.258fpe/bar-cc = 3.875bar-cc/fpe

So even CO222's remarkable achievement leaves a little headroom for future progress.

Even if it's precious little.

Steve

time of a pcp valve,given a desired output,a given reservoir pressure, a given bore length and caliber, and assuming adequate average lift for the needed flow?I suppose you'd need to pretend left and closing was instantaneous,(and that you wouldn't muzzle gases exiting at below zero...lol)

...would the striker parameters - i.e., mass and hammerspring energy - needed to get that dwell time.

And, for my money, at least one useful facts about striker parameters is prettymuch proven: Valve dwell time is proportional to striker momentum = Mass x Velocity.

This leads to two predictions.

1. For any given striker spring energy (i.e., spring stiffness, preload, and stroke), striker momentum and therefore valve dwell time are proportional to the square root of striker mass/weight. Double striker mass and you get 41% more dwell. Halve it, and you get 29% less.

2. For any given striker mass/weight, dwell time is proportional to the square root of spring energy. Double spring energy mass and you get 41% more dwell. Halve it, and you get 29% less.

Steve

as much as needed to get adequate momentum,is there a way to figure minimum striker mass? Or,looked at from another direction,is it possible to get the striker light enough to not yield too long a dwell(for maximal efficiency oat a given power level)

wouldn't it make sense to settle on a reasonable hammer mass, then adjust your hammer
spring until you reach the required dwell?

I.e., BOTH hammer momentum AND kinetic energy.

The former changes power, but the latter changes the sweet-spot pressure. Only hammer weight changes momentum alone and therefore power alone.

Interesting, isn't it, that despite all the decades folks have been tuning PCP valves, these simple rules aren't common knowledge?




Steve

...then exactly three variables are left with which to tune a PCP.

1. Hammer kinetic energy = hammer spring energy (=average force x stroke) which sets the "sweet spot" pressure. More spring = higher pressure.

2. Hammer mass which, at a given spring energy determines momentum and therefore valve dwell and therefore the volume of air released with the shot and therefore muzzle energy. More mass = more air = more muzzle energy.

3. Fill pressure which, at a given hammer energy and momentum, determines shot count per fill and extreme spread. Optimum fill pressure is always higher than the sweet spot, but the greater the difference then the farther down the bell-curve of velocity vs shot count the first shot on a fill will be - which defines the left end of the velocity curve.

And that's the whole story.

If you want to run at higher fill pressures, get more spring and/or stroke. If you want more power, make the hammer heavier. If you want less velocity spread, move the fill pressure closer to the sweet spot.

Anything else will lead to interactions and side effects. For example, if you try to raise power by increasing the hammer spring preload, power WILL go up, but you'll ALSO raise the sweet spot pressure. Guaranteed. Etc.

Steve

In the QB's with cutaway valves, I think I'm still getting excess gas usage.(too much dwell)PCP tube,porting is conservative,delrin valve head,factory spring,wire probe,but no matter how much lighter I make the striker(whittled down stock striker at 1.3 oz compared to 2 oz factory weight,the minimum that looks strong enough)power doesn't drop off in the 900 to 2000 psi range.(900 fps or so with 14.3 pellets)That implies the striker could be lighter yet?
It also implies the factory setup was designed with other priorities...

...tried the old tried-and-tested method of changing just one thing at a time, and fully characterizing the effect.

For example, I'd suggest running full shot-count curves with identical springs, preloads, pellets, etc. etc., that differ ONLY in using two hammer weights that are as far apart as possible.

Note that hammer momentum is proportional to the square root of mass, so a 20% change in mass only changes momentum and dwell by 10%.

Have you done a simple controlled experiment like that?

Steve

...changing the hammer weight - and nothing else - did to my .177 Disco.

Hammer weights are 48gms (DIY ground-down) and 39gms (James Perotti bore and refill with Delrin).




Note that sqroot(48gms/39gms) = 1.11, and 15.8fpe/14fpe = 1.13

So the theory's prediction about the effect of momentum wasn't perfect, but then 948fps is close enough to the speed of sound that other effects (e.g., Sonic Horizon) cloud the picture a little.

Steve

...than changine spring energy, simply because you can quantitively measure weight with a simple scale - but measuring hammer energy is harder.

Steve

They only work well together.A wire probe does very little on an otherwise stock gun,a light striker in a stocker does reduce power,a cutaway valve with a factory striker is a huge gas hog...
So where I am now,optimized as best I can for power,I can't get the power to drop off by lightening the striker,all I can do is use more gas(with little power gain) by putting a heavy striker back in.
It's not horrible,the pcp version with a 25" HW .20 caliber barrel just gave me ten shots between 990 and 980 fps using crosman brown box premiers.(2300 psi fill) None of the other .20 caliber pellets shot worth a dam.

In the rest of the gunworld, "dwell time" usually refers to the time interval the projectile spends accellerating the length of the barrel.

And, in my experience, if I want the valve to close more quickly, so as to save a bit of air and widen the power curve, I often increase valve return spring weight. I don't see this being bandied about here much, in fact, it seems to be nearly unknown, but its perhaps one of the most useful tuning tools in the bag a tricks.

(if there are other options) since when the return spring forces become a significant part of the closing forces,self regulation ability falls off.

Scot explained perfectly clearly what he meant by "valve dwell," and IMO it adds no information but only wastes bandwidth to carp over irrelevant minutia.

For example, suppose I were to correct your incorrect use of the term "weight" for the elastic force generated of a compressed spring? Springs have mass and therefore actually do have weight, so one can only guess that you meant to sloppily refer to the former and not the latter. How much information would that criticism add?

Meanwhile, increasing the force of the valve closure spring of course does mimic some of the effects of lightening the hammer and has the advantage of being easily reversible. So it works better with a trial-and-error/hack-and-patch approach to tuning.

But it's fundamentally inferior to reducing hammer mass, because it wastes hammer spring energy - making cocking more difficult, increasing trigger sear loading, and worsening wear and tear on the valve stem.

Steve

How can such intelligent me get caught up in such childish antics? If you don't mind changing the subject, Steve, I have a new post for you regarding the theoretical force of the hammer in a Talon and the effect it may have on accuracy.



James

he may stay the king.
as a matter of idle speculation, there must be a healthy market for retrofit gizmos for all the popular models. chuck would be one of the enthusiastic kiddies willing to shell out cash.
is this great or what.

comin' at you from the supply side

Chuck if you're referring to fitting my hammer damper to other guns, unfortunately
there's too much modification required. It was a simple procedure in this gun which
was designed for it, but not for others. I would like to try it with a 22xx at
some stage, with a lengthened tube or pivoting hammer to see what can be had
from a single powerlet.

pretty easy to mod.

comin' at you from the supply side

I'm positive there's a bit of room for improvement still, in practical terms (i.e.
before we start seeing bits of air-ice at the muzzle) as the muzzle report is still
on the loud side, and there's a bit of blow-by at the single bolt o-ring. The overall length
of the rifle is under 1m so a bit of extra barrel wouldn't hurt.

A while back I wrote a programme (in BASIC) to estimate energy of an airgun,
but my mistake was to not treat the adiabatic and isobaric phases separately
as you have. I just considered the total potential and added in a sort of
fudge factor based on bore volume from empirical data.
I think that given the hammer energy / duration relationship you discussed
and some empirical data, I might be able to write a more accurate programme
for energy predictions. This might help out some new builders.
But as usual, experience can give the best estimate. I haven't built that many
guns, but I'm quite pleased how close I came to my 200 ft-lbs target.