Air usage Efficiency Calculator for PCPs ??? (another calculator added 9/7)

[melloroadman]

Lloyd .Thank you again . And we all know the fisherman stories will happen . But it will be a useful tool for most . Marvin

[tworr]

Lloyd, I asked our programmers and they said the easiest way was to use Google Docs and make it available online.

They said that once you get the form ready to let them see it and they could build it java script.

BTW, when this post hits page three, I'm holding this train up and hijacking it!! 

[lloyd-ss]

Lloyd, I asked our programmers and they said the easiest way was to use Google Docs and make it available online.

They said that once you get the form ready to let them see it and they could build it java script.

BTW, when this post hits page three, I'm holding this train up and hijacking it!! 

tworr,
Thanks for the warning, I'll be watching my back for suspicious activity!  

I've got  a php script calculator partially finished right now and will make that available as soon as I get it going.
After that I'll take a look at the google docs. Thanks for the offer on the programming, that might be the direction to go.
Lloyd

[lloyd-ss]

OK folks, here is the link to the calculator.  

calc.sikes.us

Just click on it.  There is no www in front of it.
Right now the only calculator is for PCP Air Usage Efficiency, but I'll be putting some others up shortly.  Bob (rsterne) is the serious statistician on that stuff and taught me a lot about it.
The efficiency calculator basically tells you how much pellet energy you are getting from the air that the gun uses.  There are two ways of measuring it:

FPE per cubic inch of air (bigger number is more efficient)

and

bar-cc per FPE   (smaller number is more efficient)

They are pretty much the same thing, but one is the inverse of the other with the cc-cuin conversion thrown in.

This calculator can be a tool for working with PCPs.
Bob gave me some  ranges that you might expect to see from different types of PCPs:

Loud, overpowered, inefficient.... 0.6 to 0.8 FPE/CI (20-27 Bar-cc/FPE) - (big power at a high air cost, just a few shots per fill)
Powerful, useable efficiency.... 0.8 to 1.1 FPE/CI (15-20 Barcc/FPE) - eg. Modded Disco, MRod, Hatsan
Moderate power, good efficiency.... 1.1 to 1.4 FPE/CI (12-15 Barcc/FPE) - eg. Stock Disco, MRod, Hatsan AT44
Low power, high shot count, excellent efficiency.... 1.4 to 2.0 FPE.CI (8-12 Barcc/FPE)

Enjoy it folks, and let me know if you have questions or suggestions.
Lloyd

[Rescue35]

Nice work, Thanks for putting in the time to do this.

[melloroadman]

Thanks again . Marvin

[melloroadman]

Lloyd I just took a better look at it .Make sure you tell the wife thanks too .Marvin

[lloyd-ss]

Lloyd I just took a better look at it .Make sure you tell the wife thanks too .Marvin

Marvin,
You bet!  And thanks for your suggestions, too.  I hope folks will find his useful.
Lloyd

[rsterne]

The Calculator works great, Lloyd, and many thanks to your wife as well.... The numbers I gave you are based on the work I've done on .177 to .25 cal PCPs.... I only have very limited data on Bigbores, and only time will tell how they compare to the smaller calibers....

I have so far found that there seems to be a edge in efficiency as the caliber increases in the same (or similar) gun.... ie .25s seem to be slightly more efficient than .22s which have an edge over .177s.... The one 9mm I have built also follows this trend, but when you consider it's quite low powered (2260 based carbine) the extra efficiency could well be because of that.... Even though it's nearly triple the FPE of a Disco, it's pretty tame for a 9mm....

The one obvious difference with Bigbores is that with their huge barrel, they can really eat a lot of air.... From some of the limited data I have seen so far, efficencies can be much less than 0.6 FPE/CI.... More data will enable us to get a much better feel for how Bigbores fit in, efficiency-wise....

Bob

[rsterne]

Some further thoughts about how to compare different calibers.... that might give us a better handle on what to expect.... Let's say we establish a "baseline" FPE relative to the caliber.... How can we do that?.... Well I'll throw out this idea.... Let's take the weight of a bore-sized lead ball and fire it at 950 fps.... Why that speed?.... Well, it's about as fast as is reasonable to stay out of the transonic region.... In addition, it makes it REALLY easy to figure out the FPE.... it's twice the weight of the ball.... Here are the weights and FPE for the various calibers....

.177 - 8.3 gr. - 17 FPE
.20 - 12.0 gr. - 24 FPE
.22 - 15.3 gr. - 31 FPE
.25 - 23.4 gr. - 47 FPE
.30 - 43.8 gr. - 88 FPE
.35 - 67.8 gr. - 135 FPE
.41 - 103 gr. - 207 FPE
.45 - 143 gr. - 286 FPE
.50 - 182 gr. - 364 FPE
.58 - 292 gr. - 585 FPE

OK, bear with me for a minute.... Look at the .22 cal at 31 FPE and the .25 cal at 47 FPE.... Those are pretty healthy numbers, and I have evidence of lots of guns that can shoot at that level at an efficiency of right around 1.0 FPE/CI with pellets of about that weight.... It is reasonable to assume that larger calibers should be able to meet that air usage at the power levels given, no?.... So just for the heck of it, let's for a minute consider that to be a "standard gun".... What range of power levels do we realistically have, and what are the efficiency levels for those?....

Let's take a gun half as powerful.... 8 FPE in .177, 15 FPE in .22 cal, 68 FPE in 9mm.... I've tested guns in those power ranges and they tend to be about 1.50 FPE/CI give or take.... How about a gun twice as powerful.... Well, I've done a .22 cal at 52 FPE and it was 0.6 FPE/CI.... so at 62 FPE I'm betting 0.5 FPE/CI might be pretty good going.... See what I'm getting at.... some way to "catagorize" your gun and get some idea of how much air it might use.... Whether or not this will hold true for Bigbores I don't know.... but it will be fun finding out.... 

Bob

[lloyd-ss]

Bob,
With the shooting I've done with my bigbores, I have seen the efficiencies run off the charts at both ends.  From less than .7 FPE/cuin for a high velocity shot to more than 4 FPE/cuin for a slow moving heavy weight.
It will be interesting to see what reports we get.
Lloyd

[melloroadman]

Lloyd I know you have recorded the psi per shot as well . How did they fare with the numbers you mentioned . Marvin

[melloroadman]

Lloyd forget that last question . I looked at your test mule charts . When I am tethered and get a psi per shot on the converter you have given us is there a way  I personally can convert that over to what the psi per shot average would be to a tank around 300-500 cc as you have done in your charts ? Marvin

[lloyd-ss]

Lloyd forget that last question . I looked at your test mule charts . When I am tethered and get a psi per shot on the converter you have given us is there a way  I personally can convert that over to what the psi per shot average would be to a tank around 300-500 cc as you have done in your charts ? Marvin

yes.  I will work on that today at lunch and post something.
Lloyd

EDIT-
Marvin,
I had a chance to work on it:
If you have data from a tethered tank and want to convert it to the guns actual volume, this will give a reasonable estimation.

(tank vol + gun vol) / gun vol = tank ratio

tank ratio x psi used = psi for gun tank only

Example: 
1200 cc (water volume) tethered tank, 300cc gun, 12 psi/ shot used

(1200 + 300)/300 = 5

12 psi x 5 = 60 psi with only the gun tank

This is an approximation, and even though the psi for the shot will be different, the efficiency calculation should give the same result.  However, tethered tanks do make guns behave differently. A similar calculation technique can be used to approximate what the usage would be if the gun had a larger or smaller tank.
Lloyd

[lloyd-ss]

Lloyd I know you have recorded the psi per shot as well . How did they fare with the numbers you mentioned . Marvin

Marvin,
I think you found that info on the test mule thread.  DO notice that I was using different tank volumes for each set.  I have filler plugs I put in the tank.
I have to get back on that project and post some more, BTW.
Lloyd

[melloroadman]

Lloyd thanks again . Marvin

[airpuffhunter]

the calculator works excellent

thank you marvin and bob

[melloroadman]

The thanks goes to Lloyd . Marvin

[lloyd-ss]

Some further thoughts about how to compare different calibers.... that might give us a better handle on what to expect.... Let's say we establish a "baseline" FPE relative to the caliber.... How can we do that?.... Well I'll throw out this idea.... Let's take the weight of a bore-sized lead ball and fire it at 950 fps.... Why that speed?.... Well, it's about as fast as is reasonable to stay out of the transonic region.... In addition, it makes it REALLY easy to figure out the FPE.... it's twice the weight of the ball.... Here are the weights and FPE for the various calibers....

.177 - 8.3 gr. - 17 FPE
.20 - 12.0 gr. - 24 FPE
.22 - 15.3 gr. - 31 FPE
.25 - 23.4 gr. - 47 FPE
.30 - 43.8 gr. - 88 FPE
.35 - 67.8 gr. - 135 FPE
.41 - 103 gr. - 207 FPE
.45 - 143 gr. - 286 FPE
.50 - 182 gr. - 364 FPE
.58 - 292 gr. - 585 FPE

OK, bear with me for a minute.... Look at the .22 cal at 31 FPE and the .25 cal at 47 FPE.... Those are pretty healthy numbers, and I have evidence of lots of guns that can shoot at that level at an efficiency of right around 1.0 FPE/CI with pellets of about that weight.... It is reasonable to assume that larger calibers should be able to meet that air usage at the power levels given, no?.... So just for the heck of it, let's for a minute consider that to be a "standard gun".... What range of power levels do we realistically have, and what are the efficiency levels for those?....

Let's take a gun half as powerful.... 8 FPE in .177, 15 FPE in .22 cal, 68 FPE in 9mm.... I've tested guns in those power ranges and they tend to be about 1.50 FPE/CI give or take.... How about a gun twice as powerful.... Well, I've done a .22 cal at 52 FPE and it was 0.6 FPE/CI.... so at 62 FPE I'm betting 0.5 FPE/CI might be pretty good going.... See what I'm getting at.... some way to "catagorize" your gun and get some idea of how much air it might use.... Whether or not this will hold true for Bigbores I don't know.... but it will be fun finding out.... 

Bob

Bob,
I tend to disagree, because this scale is regressive against the larger calibers.  Here is why:
As you increase the bore dia, the area of the bore goes up with the square of the increase, but the weight of the ball goes up with the cube.  Because the force applied to the bullet is proprtonal to the area of the bore, the increase in force will lag far behind in the larger calibers.

For example, going from the extremes of .177 to .58, the dia goes up by a factor of 3.3, and the bore area goes up by 10.7, but the weight of the bullet goes up by a factor of 35.2.  So the .58 caliber is at a 3.3 to one weight disadvantage.

To equalize things you would have to reduce your velocity goal for the larger calibers by dividing the baseline velocity by the square root of the increase in diameter.  That would give a more level playing field.

So the target velocities would be
.177  950 fps
.20  893 fps 
.22  852 
.25 799 
.30 729 
.35 675 
.41 624 
.45 595 
.50 565 
.58 524 fps

That will make the " force density??" on the bottom of the bullet the same in all calibers.  That means if the pressures and barrel lengths are equal, so will the velocities.....theoretically. 

That might have screwed up what you were trying to accomplish but it does make for a more fair comparison.  If you wanted to keep the velocities equal, you would have to drop the weight of the bigbore bullets way back. 
Driving the bullets to 950 fps is a lot harder for a big caliber than it is for the little calibers.

Lloyd

[rsterne]

I know exactly what you are saying.... and I agree with everything you are saying IRT the "force density" on the base of the bullet.... However, we have both seen what appears to be big advantages in efficiency in favour of the Bigbores.... for whatever reason.... We know because we have to play with that (efficiency factor) in our calculations....  You have results where you were pushing a 143 gr. roundball in .458 cal at ~950 fps and efficiencies of well over 1.0 FPE/CI.... I was just trying to come up with a "target" set of numbers that is somewhat in agreement with real world results....

As an example, using your velocities.... the .45 cal shooting a 143 gr. roundball at 595 fps is only 112 FPE.... I don't think anyone would consider that to be of the same relative power level as a .25 cal MRod shooting at 47 FPE.... but rather as a "low powered" gun.... However, at 950 fps, it's 286 FPE, which although not a high power level for a .45 cal (the DAQ is 500 FPE+) seems to me to be a relatively easily attainable, and yet signficant power, comparable with that MRod.... That DAQ would then compare to a .25 Condor in relative terms....

The math may not be right.... but because Bigbores are more efficient.... I think the concept is.... I once asked a long time PCP builder what he used as a benchmark for performance, ie his goals.... His reply was "a bore sized roundball at 1100 fps and a bullet of twice that weight at 880 fps"..... I think those are pretty good targets.... The .308 DAQ fires a bullet nearly 3 times roundball weight at 850ish (200+ FPE) .... and the .458 DAQ shoots a bullet of 3 times roundball weight (432 gr.) at 732 fps (500+ FPE).... I'm betting that the Rogue isn't breaking too much of a sweat to hit 135 FPE and will probably deliver over 1.0 FPE/CI doing it....

All I'm doing is trying to come up with a guideline "standard" of performance in a PCP.... that hopefully, with enough data will show relatively similar levels of efficiency across all calibers.... There will always be exceptions to the rules, of course.... and maybe someday we'll understand enough about all the factors that affect efficiency to make sense of it all....

Bob