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Author Topic: Revised CUPS  (Read 178 times)

poorman plinker

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Revised CUPS
« on: August 21, 2017, 10:18:52 AM »
Hi Mr. Sterne,

I know you worked long and hard on your CUPS assesment of airgun efficiency and I think you have even revised it.

I tried to dumb the whole thing down for a general (non-specific) use comparison model...
What do you think about using the following:

EFFECIENCY HPA and PCP
This formula calculates the volume of air per shot FPE. This formula can be used for HPA and PCP airguns:
VE  = (VR * (FP-RP) / 15) / (E*S)
Where:
VE = Volume of air per shot energy
VR = Volume of Reservoir (cu.in.)
FP = Fill Pressure (PSI)
RP = Refill Pressure level (PSI)
E = Cumulative average FPE per shot
S = Number of Shots
15 = PSI per one atmosphere
A stock Discovery shoots as follows:
(8.2 * (2000-1200) / 15) / (22.8 * 25) = (8.2 * 800 / 15) / (570) = 0.77 Cubic Inch Per Shot

Pump Airguns can use this formula to calculate the volume of air per shot FPE:
VE  = ((VP*P) / E) * K
Where:
VE = Volume of air per shot energy
VP = Volume of pump (cu.in.)
P = Number of pumps
E = FPE per shot
K = Constant (57%)

Using a Crosman 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 with 14.3 gr. JSB Express pellets in a 14" barrel:
10 pumps = 541 fps = 9.30 FPE
((1.1 * 10) / 9.30) *57% = .67 cubic inch per shot

CO2 The amount of CO2 contained in a 12-gram powerlette can be calculated into cubic inches at Standard Temperature and Pressure. There are .454 kilograms of CO2 in 8.743 cubic feet of gas. The .454 kilograms equals 454 grams. One cubic foot equals 1728 cubic inches. Or, 454 grams equals 15108 cubic inches. Dividing both  by 37.83 results in 12g = 399.37 ci.
VE  = (VR / E*S) / K
Where:
VE = Volume of air per shot energy
VR = Volume of Reservoir (cu.in.)
E = Cumulative average FPE of all shots
S = Number of Shots
K = Constant (4)

In a normal Crosman 2240 configuration, the CO2 gun shots above 390 FPS produced
31 shots  that averaged 431 FPS (5.9 FPE).
(399.37 / 5.9*31) / 4 = (399.37 / 183) /4=  2.18 /4 = .55
The average cubic inch per FPE result in HPA is .70. The CO2 result of .50 is 27% less than .70. When the FPE of a .22 caliber 14.3 grain pellets was shot in a 24" barrel with both CO2 and HPA using roughly the same PSI the resulting FPE differed by 27%. The factor of 4 is used to make the results relate to the HPA formula.


I have given you credit for the CUPS idea that this was borrowed from... and I know this is not perfect just simple. Maybe too simple


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rsterne

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Re: Revised CUPS
« Reply #1 on: August 21, 2017, 01:55:44 PM »
The efficiency factor for a pumper adjusts for pumping losses.... The 57% was typical for relatively high numbers of pumps with the stock (flexible) pump cup on the 13XX/2289's.... It is likely too low for the 39X series, or the the 13XX/2289's at low numbers of pumps, or if a rigid Flat Topped Piston is installed....

CO2 is better calculated assuming that a 12 gr. cartridge provides 400 CI of expanded gas at room temperature.... Therefore, if you get 400 FPE, that works out to an efficiency of 1.00 FPE/CI....

CUPS (Cubic Inches Per Shot) is a flawed idea because it depends on the FPE per shot.... so using Barcc/FPE, or the inverted version I came up with of FPE/CI is a much better way to measure efficiency....

Bob
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poorman plinker

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Re: Revised CUPS
« Reply #2 on: August 22, 2017, 12:26:56 PM »
Mr. Sterne,

Do you have a copy of your FPE/CI formulas you could post here or give me a link so I can check it out?

 8)
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rsterne

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Re: Revised CUPS
« Reply #3 on: August 22, 2017, 07:23:44 PM »
Total FPE = avg. FPE per shot times shot count (or if you have it, the sum of all the FPEs of all the shots)....
Total air used (std. CI) = pressure drop (bar) x reservoir volume in CI .... One standard CI is one in^3 of air at 1 bar pressure....

Pressure drop (bar) = pressure drop (psi) / 14.5 (psi/bar)
You also use the HP reservoir volume in a regulated PCP, providing you don't shoot below the setpoint pressure.... because the plenum pressure doesn't change....
Reservoir volume (CI) = reservoir volume (cc) / 16.4 (CI/cc)

Efficiency in FPE/CI = Total FPE / Total CI

If you shoot below the regulator setpoint, you need to correct for the pressure drop in the plenum.... You are starting with TWO volumes (HP reservoir and plenum), at different pressures (fill pressure for reservoir, and setpoint pressure for plenum).... and ending up with the total volume (reservoir plus plenum) at the ending pressure....

The density of CO2 gas at room temp (70*F), is 1.83 g / L.... Therefore a 12 g. cartridge contains ( 12 / 1.83) litres x 61 (CI/litre) = 400 std. CI once expanded (and a 90 g. contains 3000 CI), so you can use that for the CI to calculate the efficiency.... If you know the weight in of CO2 in a bulk fill gun or tank, you can use this formula....

Expanded volume of CO2 at STP = 33.3 CI per gram = 945 CI per oz.... Do not assume a 9 oz. tank has 9 oz. of CO2 in it, you must use the actual weight of CO2....

There are two ways to calculate the efficiency of a pumper.... You can do it just like a PCP, using the valve volume and the pressure inside it before the shot (which requires a pressure gauge), which tells you the efficiency of the SHOT itself.... Alternately, you can do it using the amount of air pumped into the valve (swept volume times number of pumps), which takes into account the pumping efficiency of course.... If the pumper dumps ALL the air in a single shot, the calculations are straight forward.... If it retains air, then to use the PCP method, you need to know not only the volume of the valve, but also the pressure at the end of the shot as well as at the beginning of it.... If you are calculating the efficiency based on the swept volume and number of pumps, then for a retained air pumper you would use the number of pumps used to refill the valve between shots....

Lastly, you can use a similar method for a Springer.... Since they are typically one pump (cocking motion) per shot, you can use the swept volume of the compression chamber (area of ID times piston stroke) as the Total CI.... Note, however, that you will get MUCH HIGHER values for the FPE/CI efficiency than for a PCP, because you get Adiabatic compression occurring, which heats the air being delivered to the pellet.... This increases its energy more, so you will get far higher values than for a PCP, where the expanding air actually cools and loses energy that is then not available to provide FPE to the pellet....

HTHs....

Bob
« Last Edit: August 22, 2017, 07:48:42 PM by rsterne »
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oldpro

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Re: Revised CUPS
« Reply #4 on: August 22, 2017, 11:11:43 PM »
 This should help http://www.calc.sikes.us/1/
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poorman plinker

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Re: Revised CUPS
« Reply #5 on: September 03, 2017, 10:16:04 AM »
THANK YOU BOTH  :)
 8)
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