I am not going to claim to have full understanding of the calculus behind how projectile velocity determines effective barrel length, but this thread will briefly go over what I have learned, and how pellet weight and most importantly pellet velocity alone greatly impacts the 'effective barrel length' in a pcp (and most airguns).
Generally speaking, a well tuned airgun rifle's valve will close by the time the pellet reaches between 30-50% of the barrel length, however this applies to rifles with the common 18-24" barrel, and just happens to coincide with physics. Some may notice, a heavier pellet will produce more FPE than a lighter one. The physics here is easy to explain, as the heavier pellet moves slower, it spends more time in the barrel (pellet dwell), which allows the mass of air ejected to transfer more energy to the projectile, and likewise, if you go really light, you'll notice a huge decrease in energy, because the pellet is traveling down the bore so fast, the 'effective barrel length' is reduced, however marginal it may be, it is physics and a race of air molecule velocity versus your pellet velocity.
"Bobs lofty goal" formula from the GTA does not take this effective length into account whatsoever, hence why short barrels crush his lofty goal, because it assumes 50% barrel use, where short barrels will exceed this.
Do note, it takes a huge shift in projectile weight to drastically shift the effective barrel length, and the science behind the mass of air working on the mass of lead within the barrel is not simple. Once projectile velocity decreases below 950 fps the effect becomes more and more noticeable The GK1 really brought to light to many, myself included, just how impactful this is, hence why a 8-9" barrel can really pack a punch, the first 9" of any airgun is commonly their peak 'effective' range for the common sub 30gr pellet, but for big bores and the like, getting up heavier and heavier in ammo (100gr+), they really begin to take advantage of much longer barrels, producing gobs of power and pushing the effective barrel distance towards much further than 9-10", meaning many heavy ammo shooters greatly benefit from 30"+ barrels (provided they desire a fairly non-violent shot cycle airguns are known for while producing gobs of power).
Below is an example of the pressure and fps/energy gradient of a very standard airgun.
22 cal, 19.5" barrel, 25 cc plenum volume, 2000 psi set point, .187" ported, shooting 18.1 gr. (also to be noted, the effective barrel length used @ 19.5"/495mm opposed to 20" @ 500mm is because we're measuring the pellets traversal distance, which is from where it sits in front of the transfer port to muzzle.)
The valves closure distance here is at 9.3" or 47.5%~ of the barrel length, why 47.5% and not 45% or 50%, well, because I said so! LOL (for demonstration and based on my tests of 19.5" barrels with nominal pellet weights)
But what happens when we compare this to a GK1 that has all identical features (and a theoretical regulated 25 cc plenum), where we only reduce its barrel length to 8.2"
Say whaaaaaat? The difference in power between the two power plants here is minimal, and its simply the calculus of air molecules chasing the pellet down the bore, where the gk1 is able to use upwards of 90-100% of its barrel length effectively, the 20" barrel uses 45%-50% to transfer energy, where the remainder is primarily reducing pressure for muzzle noise/flip. The above graphs are not 100% actual representations, rather theoretical, for demonstration only.
So what about really long barrels and heavy ammo? Well, I am not claiming to have it all figured out, and the mad men that do have it all figured out, well feel free to chime in! The below is a 36" barrel that would in theory use 35% of its barrel length, however, I have done zero tests to even begin to grasp very long barrel lengths, as I am simply fudging numbers based on theoretical peak projectile velocity and estimated pellet dwell extrapolated from that, so take the actual figures below with a grain of salt, where the above figures are fairly reasonable.
In any case, with all pcps, the moment the valve shuts, the bore experiences a sharp drop in pressure, and the gradient of this pressure is one reason that makes our pcps so delightful to shoot, from minimal muzzle noise, to minimal muzzle flip. I hope this helps paint a picture how projectile velocity greatly effects the 'effective barrel length' in pcps, where the majority of energy transfer occurs sharply in the first 10", and as the projectile outpaces air, energy transfer greatly stagnates.
This concludes my Ted Talk for the day.
-Matt
