Size Matters! But how much?

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Lets take my .25 cal marauder for example, it sports a 19.5" barrel, .225" ports and 53 cc plenum @ 2100~ psi. All the graphs shown are with 33.9 gr.

What happens with various barrel lengths at plateau power? Well for one, if you chop the Marauder barrel in half, it will output basically half the energy, if you double the barrel, it would nearly double the energy, with the right weight projectile, or if you add 10% barrel length, you will add nearly 10% energy potential to the system. This wouldn't come for free, and you would need to dwell and keep the valve open nearly twice as long to get twice the air into a system with twice the barrel of course to obtain twice the energy...

So when someone asks, how many fps will 1" of barrel add? Well that depends on your existing barrel length! For a 10" barrel, 10% FPE, for a 20" barrel, 5% FPE, then you can determine your velocity/fps increase based on that. Clearly adding 1" to a 6" barrel increases FPS a lot more than adding 1" to a 28" barrel.


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What happens with various port sizes? Well if I half my port size from .225 down to .1125, I would get half the power at plateau...same applies in reverse, you double power output. 10% increase/decrease should relate closely to a 10% change in energy. Likewise you would use more air as power increases, or less as it decreases at plateau as you're expending more or less appreciable air behind the pellet before it exits the muzzle, provided you adjust your hammer strike. Largest port possible closest to bore diameter allows the shortest dwell time possible in a system as the lift generated to expel for example 1000 mg of air through a .25" equal port for a .25 cal takes less time than that of a .2" equal port or less, thereby increasing dwell time / the pressure pulse making it less efficient than a system with larger porting closer to bore diameter.

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Half the pressure? Half the power!

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All this to say, energy increase is fairly linear with Pressure, Barrel Length changes, and Port sizing changes until you reach limitations placed by physics, be it speed of sound, or otherwise, such as exceeding the diameter of bore on air flow path, or exceeding regulator setting/fill pressure. However doubling the caliber would provide closer to 4x the power increase if you're on the hunt for power.

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And projectile weight where power stops increasing once pellet weight is 1/2 the FPE in grains and velocity is 950~ fps. This can be seen middle of chart.

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And of course, plenum changing alone...

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Where the graph goes off the chart its flat and shows no real gains to be had, beyond 3 fpe/ci shows no real gains for a pcp's air delivery system, however a good sweet spot for max power is a bit over 1 fpe/ci with a good workable range being .4 fpe/ci to 1.6 fpe/ci. One could supplement smaller plenum volumes with increases pressure by that is not the point of this discussion as one could simply run longer barrels as well, or larger ports, it all provides more energy if plenum volume won't get you there, unless you want to max everything out, then you should be at your max regulator setting anyhow and that discussion is moot. Hope this helps some tinkers out there understand changes they can or have made to their airguns.


Regulator refresh rate? Oh ya, theres that too...it effects your pressure during the shot cycle!

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-Matt
 
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I appreciate the effort, but I'm curious about the math - in all cases of barrel length, port size, and pressure, you state that half the size is half the power, and I'm sure that not is true. It is not linear, so at a minimum it matters where you start.

Also, on the port sizing, you report half the diameter as half the size, and that is incorrect - half the diameter is only half the diameter, not half the area as the area is "Pi R Squared" - half the area of 0.225 would be about 0.159, not 0.1125 inches in diameter.

I get and appreciate the intent, but some of the specifics might need tweaking . . .
 
It is not linear, so at a minimum it matters where you start.
True, because the weight of the air filling a longer barrel to accelerate the projectile is itself an added weight that must be accelerated. Analogous to the rocket problem...more fuel is necessary to carry a rocket to a greater altitude, but the fuel adds weight which offsets the benefit.

So it would be true that the gains from a longer barrel will not scale linearly at the same state of tune, but I suspect Matt is describing what is possible if you increase dwell to shove more air into the barrel.
 
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I appreciate the effort, but I'm curious about the math - in all cases of barrel length, port size, and pressure, you state that half the size is half the power, and I'm sure that not is true. It is not linear, so at a minimum it matters where you start.

Also, on the port sizing, you report half the diameter as half the size, and that is incorrect - half the diameter is only half the diameter, not half the area as the area is "Pi R Squared" - half the area of 0.225 would be about 0.159, not 0.1125 inches in diameter.

I get and appreciate the intent, but some of the specifics might need tweaking . . .

You're actually right in the port sizing, it was late last night and I forgot to correct for surface area opposed to diameter alone. .159 is half the surface area of .225, and half the flow rate which would result in half the power, or half the mass ejected! I will correct the post to reflect this. (***EDIT***)

Oddly in my tests however, its closer to how I have orginally, so I will not edit it. Stock marauder valve was .14" ported and could do way over half the power of what I have at .225....but if I restricted it to .1125, it does closer to half the power of .225.

@ .157" porting at 2100 psi the marauder did well over 40 fpe, and at .225 porting 63 fpe.

RIDDLE ME THAT!


Barrel size being halved will result in half the potential energy in the system, with factors such as approaching the speed of sound and friction aside. In its simple form, a 10" barrel will make half the power of a 20" barrel if you tune to keep the valve open till the pellet reaches the end of the barrel.

Pressure is not entirely linear as you increase, high pressure contains a bit more energy than low pressure, however its marginal and I felt I'd keep things rather simple here and not delve into the minor gains or losses at either end of the spectrum

-Matt
 
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True, because the weight of the air filling a longer barrel to accelerate the projectile is itself an added weight that must be accelerated. Analogous to the rocket problem...more fuel is necessary to carry a rocket to a greater altitude, but the fuel adds weight which offsets the benefit.

So it would be true that the gains from a longer barrel will not scale linearly at the same state of tune, but I suspect Matt is describing what is possible if you increase dwell to shove more air into the barrel.

For barrel length, I made it abundantly clear you're increasing energy potential of the system and more dwell is necessary...the issue will only come once you approach the speed of sound or are overcome by inability to keep your valve open long enough due valve design (non blow open calculated dump)....the closer you approach the speed of sound, is when the equation makes large changes. Also the first few inches but I don't see people building pcp's with 1-3" barrels...so for all purposes this 'rule of thumb' applies...

Also raising pellet weight to avoid speed of sound will greatly keep the linearity of growth going until...you hit the physical limits of reasonable projectile length in that caliber...which I made clear as well to some degree, but it was late and honestly I hit 'save'/'post' before I was even ready to and just let it ride...
 
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I want to make it clear, I am here showing various changes to each variable that determines energy output of a pcp, and how relatively linear some of these variables are, when used within our scope.

That is to say, plenum volume changes, pellet weight changes, regulator refresh rate change, and most importantly caliber changes are far from comparable in near linear growth, as I have demonstrated... the linearity falls off on either extreme for pressure and barrel length, but that doesn't dismiss that in the Goldilocks zone we operate, there is a fair amount of linearity going in either direction when changing barrel or pressure. Reducing 10% of your set point will very much result in nearly 10% energy loss just as chopping off 10% of your barrel would, however adding 10% more plenum will not result in 10% power increase, no where close...

To get 10% more power from plenum you would have to increase the pressure your plenum can maintain on average through the cycle by 10%, which is an entirely different equation that depends on your air mass released, plenum volume, ect, that can't be simplified...but for example, to reduce my power 10% alone with plenum, I would have to reduce my plenum volume from 53 cc to 27cc, and if I wanted to take it down 10% again from 27 cc, I'd have to go down closer to 17cc which is less than half...and another 10%, down to 13cc plenum which brings it to 45 fpe, and again much less than half plenum to achieve 10% drop...and now I'm rambling.


-Matt
 
The ugly mess of an equation that I use to calculate the energy output of a pcp

H166 = Pellet weight
H165 = Port diameter
H161 = Barrel length
H162 = Caliber
I223 = loss % due to friction
I225 = % of barrel volume used
B87 = Average pressure while valves open

Things that effect average pressure? Initial pressure/set point, plenum volume, port size/throat diameter, volume between valve seat and pellet, and regulators refresh rate.

What effects % of barrel volume used most? Typically barrel length, a shorter barrel will use a larger % of its barrel, and a longer barrel will use a smaller %, due to the nature of our projectiles traveling 900~ fps, the math there is rather simple, as the pellet reaches near its terminal/nominal velocity of 900~ fps, its too far down the barrel to have any more air expended from the valve to contribute energy behind it, in very short barrels where that higher 900~ fps velocity is never even met, it is most certain you will use a larger portion of barrel than a long barrel reaching or exceeding 900 fps.

=IF(H166*2 < ROUNDDOWN((H162^2 * 3.14159/4)* B87*((H161)/12*(I225/100)),2), ROUND(SQRT((ROUND(((H166*2)+ROUND((H162^2 * 3.14159/4) * B87*((H161)/12*(I225/100)),2))/2,0)*450240)/H166)*(1-(I233/1000)),0) , ROUND(SQRT((ROUND((H162^2 * 3.14159/4) *B87*((H161)/12*(I225/100))*450240)/H166)*(1-(I233/1000))) ))


No witchcraft, sorcery, ****ery or the like. The IF statement determines if you're exceeding the pellets weights max energy, I forgot how I elegantly came up with it, but it works. If I put in 33.95 gr, I get 63 fpe @ 913 fps . If I put in 48 gr I get 768 fps also at 63 fpe, opposed to 78.5 fpe @ 848 fps using the standard equation, which is what I get in real life with 48 gr here beside me. Your max energy will be near 950 fps with 1/2 gr per fpe, so for me that is 31.5 gr @ 950 fps which makes 63 fpe.

-Matt
 
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Yes Matt,
Good Stuff :) ->

Your plenum information was very important in deciding to make a DIY plenum for my RAW's.
Since I limit my barrel TP to .75 Pellet Diameter (no pellet damage please), I limit my other TP to .75 PD also. Efficiency is improved too.

- I pick the most accurate pellet weight, tune for (900/915 fps) velocity at .95-.97 of max. at lowest regulator set-point to obtain needed power.

Lately, sticking to basic, optimal settings standards has greatly helped removing uncertainty. Now, I'm the BIG uncertainty in the equation :whistle: .
 
Yes Matt,
Good Stuff :) ->

Your plenum information was very important in deciding to make a DIY plenum for my RAW's.
Since I limit my barrel TP to .75 Pellet Diameter (no pellet damage please), I limit my other TP to .75 PD also. Efficiency is improved too.

- I pick the most accurate pellet weight, tune for (900/915 fps) velocity at .95-.97 of max. at lowest regulator set-point to obtain needed power.

Lately, sticking to basic, optimal settings standards has greatly helped removing uncertainty. Now, I'm the BIG uncertainty in the equation :whistle: .

75% port width of pellet diameter is playing it ultra safe. I personally push it to about 85% and oblong my ports, although 75% is better safe than sorry, its not practical for near full bore porting, that would require a .03125" long by .1875" wide port to get full bore, where as 85% requires .2875" Long by .215" wide porting.

Most of this context applies to tuners/builders/tinkerers which not everyone is, some just want to pick up a pcp and shoot, and I get that...

Even some tuners would rather 'feel' all the effects I am doing the math for opposed to trusting a spreadsheet, although, in many cases having a data model to follow for a clear path towards a goal is always beneficial to any tinkerer/builder.

-Matt
 
Yeah, it's an engineer's nature to double check all the details (y).

However, when the concept makes perfect sense to me, I know most of the other stuff is usually marginal.

That's why I usually only TRUST: Bob Sterne, Motorhead, Hector Medina, Jason, Mark, Bucket Boy, Mubhaur and .... You.
 
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Yeah, it's an engineer's nature to double check all the details (y).

However, when the concept makes perfect sense to me, I know most of the other stuff is usually marginal.

That's why I usually only TRUST: Bob Sterne, Motorhead, Hector Medina, Jason, Mark, Bucket Boy and .... You.

There are quite a few experienced veterans in our sport that I highly respect, and others I do not due to personality issues, but at the end of the day it is always beneficial to the community to share and exchange information that stands the test of time, which improves the sport and keeps the innovation ball rolling. If the statements you make today can remain true in 10, 100 years, you're doing a good service!

-Matt