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rsterne · Moderator

I've been trying to think of a way to measure / discuss the efficiency of PCP Airguns.... a way to relate the air usage to the power of the gun and the number of shots.... I came up with the following suggestion, open to discussion, which is the reason for this post....

This is the formula I came up with to calculate the volume of air used for each shot per FPE.... I decided to work in "English" units instead of Metric.... The variables are:
Volume of Reservoir in cu.in. (V)
Fill Pressure in psi (F)
Refill Pressure (or regulator pressure if regulated) in psi (R)
Average FPE per Shot (E)
Number of Shots (N)

The first three give the amount of air used for a shot string....
Volume of air at one atmosphere = V x (F-R) / 15
eg.... 13 cu.in. x (3000 psi - 1500 psi) / 15 psi = 13 x (1500) / 15 = 1300 cu.in.

The second two give the total energy in the shot string....
Total energy = E x N
eg.... 26 FPE x 50 shots = 1300 FPE

If we divide the amount of air used by the total energy, we get the volume of air per FPE....
1300 cu.in. / 1300 FPE = 1 cu.in. per FPE

The complete formula is therefore:
V x (F-R) / (15 x E x N) .... for the heck of it, lets call the units CUPS (for Cubic Inches Per Shot).... Laughing

I'll go first.... my Regulated 22XX PCP produces the following numbers:
13 x (3000-1600) / (15 x 26.9 x 70) = 13 x 1400 / (15 x 1883) = 0.64 CUPS

My stock Disco was as follows:
8.2 x (2000-1200) / (15 x 22.8 x 25) = 8.2 x 800 / (15 x 570) = 0.77 CUPS

My favourite tune on the Disco produced:
8.2 x (2000-1350) / (15 x 28.8 x 20) = 8.2 x 650 / (15 x 576) = 0.62 CUPS

Flat-out tune on the Disco produced:
8.2 x (2000-1500) / (15 x 35.8 x 10) = 8.2 x 500 / (15 x 358) = 0.76 CUPS

A very mild setting on the Disco produced:
8.2 x (1800-1000) / (15 x 18.6 x 33) = 8.2 x 800 / (15 x 614) = 0.71 CUPS

A couple of comments on these results:
First, they are in a pretty narrow range, I think because the volume of the valve is the same for all of the above....
Secondly, it is possible to get more performance and yet use the air more efficiently.... eg. the best tune on my Disco was 24% more efficient than the stock gun.... :wink:

Anyhow, for what it's worth, here is a way to compare different guns, and different states of tune within the same gun.... I know it doesn't mean anything in the real world, but I enjoy it.... Anybody else want to post their numbers?.... Cool

Bob

oddtodd · Silver Status Member

Bob, your post always make my head hurt. lol Just kidding, they are actually useful. thank you for spending your time trying to level the playing field.

sniper · Silver Status Member

WE'RE NOT WORTHY!!

i talked to tim (mac-1) the other day about this relating to the marauder. he says it's peak efficiency is around 18-20 fpe. though it can max far beyond that with power, accuracy will likely suffer and air will be wasted.

so it might do 30 full power shot at max power but the sweet spot might give 45+. i look forward to racking my brain around with the math when i get it. 20 fpe will kill a rat as dead as 30fpe Twisted Evil

.

of course my analysis won't rival that of the all mighty BOB, THE CALCULATOR! Laughing

Slavia · Moderator

I came home this morning after a 12-hour shift, and rsterne's numbers just started to dance around the screen. Now that I'm rested:

The final number is the cubic feet of air (at one atmosphere) per FPE produced - am I getting that right?

How long is the 22XX barrel (i.e., is it comparable to the discos)? I am assuming all the examples were in .22 caliber.

Say you have a MPP (like a 1377 or the like). Assume a FTP and the valve body dropping to 1 atmosphere after each shot. Would the swept volume times the number of strokes be equivalent to your PCP volume calculations?

It might also be interesting to calculate the swept volume of a springer, just to see how it compares.

Nice work. I'm still digesting it.

Jaxom · Senior Member

ACK!!!!! MATH!!!! and I told my highschool algebra teacher I would NEVER use it again after her class....the woman must own an ag!

rsterne · Moderator

HI Slavia....

You got it right (except cubic inches, not feet).... the final number (CUPS) is the amount of air (at one atmosphere) that it takes per FPE developed.... My 22XX PCP has a 24" barrel, the same as the Disco, both in .22 cal.... Cool

RE the MPP comparison, the formula also works, but the numbers don't take into account pumping losses.... With the MPP, I had a spreadsheet designed to calculate the pressure inside the valve based on swept volume, headspace, valve volume, and number of pumps, and it seemed to work reasonably well.... There are the inevitable pumping losses due to headspace, flex, heating of the air during compression and subsequent cooling before the shot, etc. etc.... Because of this, I had to use a "fudge factor" of 57% efficiency in my pressure formula to make my spreadsheet agree with the real world pressures my buddy measured with a valve fitted with a guage.... but back to your question.... Shocked

Using a 2289, the swept volume is about 18cc, and the valve about 1.6 cc.... If you call it 1.1 cu.in (at one atmosphere) per stroke, here is what I get with 14.3 gr. JSB Express pellets in a 14" barrel....

5 pumps = 403 fps = 5.5 cu.in./5.15 FPE = 1.07 CUPS
10 pumps = 541 fps = 11 cu.in./9.30 FPE = 1.18 CUPS
16 pumps = 636 fps = 17.6 cu.in./12.85 FPE = 1.37 CUPS
beyond that it starts retaining air.... Wink

On first blush, it seems that an MPP is less efficient, but don't forget this is with a 14" barrel, not 24".... If you use my 57% "fudge factor" to adjust the above, it actually gets pretty close to the range I found for my PCPs.... but that doesn't really matter in the real world.... What matters is that yes, the idea works for MPPs as well.... just not good to compare directly to PCPs.... The pumping losses in a PCP don't show up because you are measuring the result (ie pressure) in the reservoir AFTER those losses have already occurred.... Rolling Eyes

This is kind of like using the total energy extracted from a CO2 powerlet to give an idea of efficiency.... Wink

Good point about the Springer, BTW.... anyone have some numbers for that?.... Question

Bob

Slavia · Moderator

That makes sense that pumping losses in a PCP would be external to the gun.

Just for fun, I went back to your post for the "dual power hammer" where you said you got 604 FPE (through 150 shots) from a 12 gram CO2 bulb:
http://www.airgunhome.com/agforum/viewtopic.php?t=2651&highlight=

Take the density of CO2 gas at 1 Atmosphere to be 1.977 grams per litre:
http://encyclopedia.vbxml.net/Carbon_dioxide
This is at 0 Degrees Celsius, but I'll use it as a rough approximation. Use 61 cubic inches per litre, and you get 0.61 FPE per cubic inch of CO2.

It's not even the same gas (air being predominantly nitrogen), but it's interesting that 0.61 FPE per cubic inch compares closely to your PCP values.

rsterne · Moderator

Looks good, you've got a good handle on this.... Mr. Green

Using your numbers, to calculate the volume of CO2 gas, you take 12 g divided by 1.977 g / L = 6.07 L.... You can double check this by taking one Mole of CO2 (44g) which is 22.4 L at STP.... 22.4 L x 12g/44g = 6.11 L.... Lets call it 6.1 L x 61 cu.in./L = 372 cu.in..... Then you divide that by 604 FPE, and you get 0.62 CUPS.... which I agree is pretty efficient, comparable to a PCP.... Cool

If you look at a standard 2240, though, you will find that the efficiency is a LOT less.... in the 250-300 FPE area.... which works out to 1.2-1.5 CUPS.... Steve in NC claims the best he got was 516 FPE, which works out to 0.72 CUPS.... Wink

Bob

Slavia · Moderator

fritz · Silver Status Member

I think that the higher psi guns would be more efficient because they use less air for the same pressure. Leaving more for other shots.

I've been reading this whole thread and Bob you are amazing, you must spend a lot of time doing all the tests and putting the numbers together (which are correct). It must take great *cough*addiction*cough* dedication to bother recording all the data. I would just shoot and forget to write things down.

rsterne · Moderator

The most efficient shots I have seen are those where the reservoir is at high pressure and only a very short, sharp pulse is propelling the pellet.... You can see this in the stock Disco, where the first 5 shots only drop the pressure by about 100 psi.... By the time you are down to 1600 psi, from there on you lose about 200 psi in 5 shots.... The proof of this is in the difference in the sound.... the first few shots are much quieter for nearly the same velocity.... Shocked

One word of caution.... If you take a longer shot string by allowing the minimum velocity to fall further.... eg. allowing a minimum velocity of 90% instead of 96% of the maximum.... the gun will probably be more "efficient" when you calculate the CUPS.... As an example, if I use a longer shot string (down to 90%) on the "mild Disco tune" from my first post, you get the following:

8.2 x (1975-850) / (15 x 17.9 x 52) = 8.2 x 1125 / (15 x 930) = 0.66 CUPS

By taking a longer shot string, the efficiency has increased from 0.72 to 0.66.... basically because you have relaxed your criteria of what constitutes a "good" shot.... My data for CO2 was taken to the point in the velocity curve where it "went over the knee" and that is typically at about 90% (or less) of the maximum for high power settings, and about 93-94% for the low power (very efficient) settings.... This is technically not quite consistent with a PCP, but it is "real world" in that it is the way people shoot CO2.... Wink

I think it's really Cool

that you can basically use this formula for PCPs, pumpers, and CO2.... Mr. Green

Cost per FPE.... hmmmmmmmmmmm.... I'll have to leave collecting that data to those who don't pump their PCPs by hand.... Rolling Eyes

Bob

Slavia · Moderator

fritz · Silver Status Member

I would be interested in knowing the efficiency of pumpers, in like pumps per fpe, but how much effort (I guess in fpe) it takes to do the pumping.

I could probably do this myself, but these tests seem to rely on a chronograph.

rsterne · Moderator

There is some information on this a few posts above:

yourdaddyjoe · Supporting Member

Bob..... Do you have a "PCP Efficency for Dummys" version?