Lloyd Conquers the VanDerWaals Equation !
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Lloyd Conquers the VanDerWaals Equation !
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Topic: Lloyd Conquers the VanDerWaals Equation ! (Read 2440 times))
farmerjoe99
N.U.A.H Marksman
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Posts: 2458
Real Name: Joseph
Re: Lloyd Conquers the VanDerWaals Equation !
«
Reply #20 on:
August 19, 2018, 11:05:18 PM »
Many Thanks to Lloyd for his work and Bob for sharing,
I know I've just learned a few things that I'll be thinking on for a few days.
Now I don't know how calculable this would be, but is it possible to estimate just what kind of efficiency
would be gained using 4500psi instead of say 2000psi at small bore pcp levels,
for instance a 40fpe .25 or 30fpe .22 marauder or would it only be slight gains that wouldn't show much
difference unless you were at further ends of the spectrum say 6000+psi
Or in other words how big of a role can air pressure/density play in possible efficiency?
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QVTom
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Re: Lloyd Conquers the VanDerWaals Equation !
«
Reply #21 on:
August 19, 2018, 11:15:32 PM »
Obviously I'm having trouble applying this information. At the higher pressures we get more pressure with fewer molecules; pressure is our motive force and we have less mass. So, this pressure/density relationship does support higher efficiencies at pressures above ~3k4 mark.
Thanks Bob
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rsterne
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Bob and Lloyd
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Re: Lloyd Conquers the VanDerWaals Equation !
«
Reply #22 on:
August 20, 2018, 01:26:24 PM »
It's complicated, and the answer is yes, and no.... Each shot can have a greater efficiency (more power from the same number of air molecules)…. but you will see a greater pressure drop per shot at very high pressures.... If you are calculating the standard CI of air used by using Boyle's Law and the pressures are high, you could get a false sense that the efficiency is lower because of that greater pressure drop.... where in fact if you use VanDerWaals to convert to the standard CI of air used, you would be correctly calculating greater efficiency....
The above effects, because they are contradicting, make it difficult to estimate how high pressure affects the efficiency, based on the density vs. pressure relationship not being linear.... However, there is a much greater overlying effect that is the reason for high pressures being more efficient in producing a given FPE from any particular PCP.... If you compare two setups in a PCP that are producing, for example, 100 FPE, one using 2000 psi and the other using 4000.... and assuming that in both cases the valve is closing before the bullet reaches the muzzle.... then the higher pressure shot is accelerating the bullet using a short, high pressure pulse, rather than a long, show push over a greater distance.... Since most of the acceleration occurs early in the bullet's travel down the barrel, intuitively you would expect high pressure to produce more FPE, and you would be correct....
If you released the same amount of air in both cases (ie the same CI of air at STP), the bullet would be APPROXIMATELY twice as far from the breech with the lower pressure shot when the valve closes (half the pressure, twice the barrel length and therefore volume).... The closer the bullet is to the muzzle, the less distance (and volume) there is for the air released from the valve to expand.... That expansion adds additional FPE to the bullet, while lowering the residual muzzle pressure (and hence the report)…. Additional report (noise) is wasted energy of course.... It seems a bit counter-intuitive that starting with a lower pressure ends up being louder, for the same FPE produced, but that is indeed the case.... Consider this chart for a Disco at the beginning, middle, and end of the shot string.... Over the course of the string the velocity is within a 4% ES, even though the pressure starts at 2000 psi and ends at 1200.... The lines with the "step" in them are the pressure curves as the pellet travels down the barrel (left to right)…. The valve is closing at the end of the straight part on the left, where the pressure turns sharply downwards....
At 2000 psi (red), the valve is closing when the pellet has only moved about 2", and the residual muzzle pressure is about 200 psi....
At 1700 psi (green), the valve is closing at about 4", but the muzzle pressure has increased to about 300 psi....
At 1200 psi (magenta), the pellet has reached nearly 8" when the valve closes, and the residual pressure at the muzzle is nearly 400 psi....
Although all 3 shots produced nearly the same velocity and energy, there was more air released by the valve at lower pressures, and the report was louder as well (proof of wasted energy)…. If you calculate the efficiency over the entire string, you might get (for example) 1.2 FPE/CI.... However, if you broke it down by pressure, you would find that the gun was a lot more efficient at the beginning of the string (maybe 1.5 FPE/CI) and less efficient at the end of the string (maybe 1.0 FPE/CI)….
This is simply how all PCPs convert air pressure into energy.... The higher the pressure, for a given FPE in a given gun, the sooner you can close the valve, releasing less air, and the more efficiently that air is used.... THAT is why PCPs can be more efficient at higher pressures.... Any changes due to the VanDerWaals effect are drastically overshadowed by the basic way a PCP works.... However, when you look at shot count, at very high pressures it will fall, due to there being less air stored if a given volume tank or reservoir at those high pressures....
Bob
«
Last Edit: August 20, 2018, 01:29:21 PM by rsterne
»
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PakProtector
GTA Senior Contributor
Posts: 2890
yes
Real Name: Douglas
Re: Lloyd Conquers the VanDerWaals Equation !
«
Reply #23 on:
December 09, 2018, 06:48:11 PM »
That is some fine work...
The application to the firing event is interesting. I recall digging this up for a much more altruistic purpose: The cubic foot ratings for the charging cylinders varies greatly depending on who sells it. Manufacturers list the compressed air capacities, and the 'water' volume of the tanks themselves. Applying just Boyle to 88's leaves us numbers like 97 and other exaggerations. Applying 'The Whole Thing', aka the adjustment from van der Waal, shows that the 88 is actually just an 88. Now the 88 thing matters not to me personally, as I prefer to use 44's.
cheers,
Douglas
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Lloyd Conquers the VanDerWaals Equation !