FPE vs Caliber and Port Sizes

[Gr8Gorilla]

Thanks for the complete and thorough answer Bob. I was trying to get an idea of the theoretical MAX and how long a barrel it would take to get there.

I would be happy to get 140 fpe and 5 shots @ that power. Is that too much?

[rsterne]

Thanks, Lloyd.... It's taken a lot of time to distill all the knowledge down to a few relatively simple concepts.... Every time I go over it, it seems I learn more, and get another piece of the puzzle and it makes a bit more sense.... Here is another way to think about the issue of caliber and long range....

You need the best BC possible to fight the wind, and maintain velocity (trajectory) and energy.... BC is a combination of SD and FF, in fact BC = SD / FF.... so for the best BC, you need a high SD (heavy for caliber) and a low FF (low drag shape).... If you maintain the SD as a constant, as you increase the caliber, the bullet gets fatter, but stays about the same length, so the shape has greater drag, and the FF goes up, reducing the BC.... If you maintain a constant shape (FF), as you increase the caliber the SD goes up in direct proportion to the caliber.... which increases the BC.... However, since there is a limit to the SD that you can push at any given velocity, with a given pressure and barrel length, you will a point where you can no longer drive the bullet fast enough because it is too heavy (ie too high an SD).... This produces an optimum caliber for any SD, to produce the best BC.... The larger calibers become the best choice only if the power available is enough to allow very high SDs.... as was the case with the 200 gr. Whiteout in .308 cal because of the Helium at high pressure.... For most airguns, a smaller caliber will be a better choice, providing you can get a fast enough twist barrel to use the proportionately long bullets.... That is why I had a 7" twist barrel made in .257 for my Monocoque PCP....

Shaun, I can't answer that question without knowing the reservoir size and the pressure range from fill to refill....

Bob

[Gr8Gorilla]

Bob,

Reservoir is 480cc 250 BAR max fill.

[Habanero69er]

I'm assuming you mean OČ & not breathing air when you advise against mixing helium & oxygen? Going on that assumption, would say a 50/50 or 25/75 mix of air & helium help velocity performance? My scuba shop will do an air/helium mix if requested.

[rsterne]

480cc = 29.3 CI.... You didn't state a refill pressure, but if you can maintain a stable velocity curve down to 75% (188 bar), that gives you 62 bar x 29.3 = 1817 CI of air to play with.... Typical PCP efficiency is about 1 FPE/CI, so that should give you about 1817 FPE, which if you are getting 140 FPE per shot is 13 shots.... so the 14 shots is indeed possible if you can get good efficiency, or a stable shot string below 2700 psi with a 3600 psi fill.... I had no idea the FLEX reservoir was 480 cc.... Is all the volume available to the valve, without restriction? (ie the plenum is effectively 480 cc)?....

Yes, I was referring to mixing O2 with He, not air and He.... If you mix them 50/50, the mass is going to be (4+29)/2 = 16.5, compared with He at 4 and air at 29.... I would suggest that your performance would be much closer to that with air than that with He.... I personally wouldn't bother using anything other than pure He or air, I don't see the point....

Bob

[Bill G]

Thanks, Lloyd.... It's taken a lot of time to distill all the knowledge down to a few relatively simple concepts.... Every time I go over it, it seems I learn more, and get another piece of the puzzle and it makes a bit more sense.... Here is another way to think about the issue of caliber and long range....

You need the best BC possible to fight the wind, and maintain velocity (trajectory) and energy.... BC is a combination of SD and FF, in fact BC = SD / FF.... so for the best BC, you need a high SD (heavy for caliber) and a low FF (low drag shape).... If you maintain the SD as a constant, as you increase the caliber, the bullet gets fatter, but stays about the same length, so the shape has greater drag, and the FF goes up, reducing the BC.... If you maintain a constant shape (FF), as you increase the caliber the SD goes up in direct proportion to the caliber.... which increases the BC.... However, since there is a limit to the SD that you can push at any given velocity, with a given pressure and barrel length, you will a point where you can no longer drive the bullet fast enough because it is too heavy (ie too high an SD).... This produces an optimum caliber for any SD, to produce the best BC.... The larger calibers become the best choice only if the power available is enough to allow very high SDs.... as was the case with the 200 gr. Whiteout in .308 cal because of the Helium at high pressure.... For most airguns, a smaller caliber will be a better choice, providing you can get a fast enough twist barrel to use the proportionately long bullets.... That is why I had a 7" twist barrel made in .257 for my Monocoque PCP....

Shaun, I can't answer that question without knowing the reservoir size and the pressure range from fill to refill....

Bob

Bob,
I don't want to get too far off the original topic but I think this is relevant.  Your point on the SD and FF  is so valid that I believe it is under considered.  If we are to use the information that you have graciously provided, I believe, performance and accuracy would improve. It seems that there is little need to fret about available twist rates on say .30 and up If you stay within the stated parameter for SD.  I see the .257 as a transitional caliber and the ability to make a platform that can drive fairly heavy slug, is not too difficult.  That being said, to max out the SD on a compatible platform results in a pretty long projectile, as you pointed out earlier.  So the long and short of it is power is truly relative to psi and barrel length and achieving ~.85 Mach.  To say that, "I'm going to build a X fpe rifle",  is to say that your going to build a rifle that has Y length barrel and runs on Z psi and shoots a projectile that fits the profile prescribed by your SD standards.  To Knife makers point, our fixation on FPE is a sort of cart before the horse approach.  If we move forward under the premise of achieving top accuracy from a platform, then push that platform for power, we would have a higher since of satisfaction with the product.  The fact is, the majority of those who are consumers of production and custom BB AG's, are victims of themselves and to some small extent, marketing. 

Something that I missed and seems like the chicken or the egg debate too me,  Form factor.  How is this derived?  Is there a formula for it and is it based on SD some how?       

[rsterne]

The Form Factor can be calculated, as it is in bullet design programs, or the Drag Coefficient can be measured and then the FF derived from that.... Empirical results always trump theory, of course.... Most often the FF is calculated from the reverse formula.... FF = SD / BC .... This formula is the easiest to understand if you consider the G1 projectile.... It is 1" caliber, weighs 1 lb., and by definition has a BC of 1.000.... It also has an SD of 1.000.... and hence a FF of 1.000.... If you had a bullet with the same SD but twice the drag, the BC would be 0.500 and the FF would be 2.000.... If you had a projectile that had an SD of 1.000 but only 2/3rds the drag, it would have a BC of 1.500 and a FF of 0.667.... IIRC, a sphere has a FF (G1) of about 1.55.... so it's BC will be about 64% of it's SD.... making it easy to calculate for a lead ball of any caliber....

The problem is, that if you use a different projectile for your model.... for example a sphere (GS) or a long spritzer boattail (G7).... while they can have the same SD, both the FF and the BC will be different, because you are using a different reference point.... So, just like the BC, the FF depends on the Drag Model used.... NOE's bullet design program calculates the FF (I presume using the G1 Model) and also the BC (which is G1 based), and has done so for all the designs I submitted.... The thing that is obvious is that the longer the bullet (in calibers) the lower the FF.... However, it is virtually the same number for a .224 cal BBT that is 4.0 cal. long as it is for a .457 cal that is 4.0 cal long.... What IS different is the BC, because the SD is higher for the larger caliber, when you scale a design up or down....

This puts the edge in BC towards the bigger calibers, if you hold the shape a constant.... The problem is that you can't drive a 4.0 cal long .457 cal bullet (~635 gr.) at a reasonable velocity with reasonable pressures and barrel lengths.... The Physics just won't allow it, because the SD affects the ACCELERATION inside the barrel just like it affects the DECELERATION outside the barrel....

Bob

[scottyhazzard]

I think I understand, which only makes me think I probably don't quite understand. So here goes: Given barrels of the same length, a BBT of 62 grains going through the barrels at the same 950 fps, using the same valves ports etc but two different calibers, one is .25 caliber and the other is .30 caliber... Then all things are equal except the sectional density. The SD of the .30 is higher so it's BC will be lower due to the higher drag.  Um, agh &^^&. Now I'm confused by the Form factor...

[Gr8Gorilla]

Bob,

I can't answer your question about the Flex plenum. I'll check with Travis. I can tell you that I shot 7, 57 grain slugs starting at 250 BAR & ending @ 3400 psi w/ an average velocity of 899 fps. The Sikes efficiency calculator gave me 2.0 fpe/cc. This is with the 17" barrel that is stock.

[Bill G]

The Form Factor can be calculated, as it is in bullet design programs, or the Drag Coefficient can be measured and then the FF derived from that.... Empirical results always trump theory, of course.... Most often the FF is calculated from the reverse formula.... FF = SD / BC .... This formula is the easiest to understand if you consider the G1 projectile.... It is 1" caliber, weighs 1 lb., and by definition has a BC of 1.000.... It also has an SD of 1.000.... and hence a FF of 1.000.... If you had a bullet with the same SD but twice the drag, the BC would be 0.500 and the FF would be 2.000.... If you had a projectile that had an SD of 1.000 but only 2/3rds the drag, it would have a BC of 1.500 and a FF of 0.667.... IIRC, a sphere has a FF (G1) of about 1.55.... so it's BC will be about 64% of it's SD.... making it easy to calculate for a lead ball of any caliber....

The problem is, that if you use a different projectile for your model.... for example a sphere (GS) or a long spritzer boattail (G7).... while they can have the same SD, both the FF and the BC will be different, because you are using a different reference point.... So, just like the BC, the FF depends on the Drag Model used.... NOE's bullet design program calculates the FF (I presume using the G1 Model) and also the BC (which is G1 based), and has done so for all the designs I submitted.... The thing that is obvious is that the longer the bullet (in calibers) the lower the FF.... However, it is virtually the same number for a .224 cal BBT that is 4.0 cal. long as it is for a .457 cal that is 4.0 cal long.... What IS different is the BC, because the SD is higher for the larger caliber, when you scale a design up or down....

This puts the edge in BC towards the bigger calibers, if you hold the shape a constant.... The problem is that you can't drive a 4.0 cal long .457 cal bullet (~635 gr.) at a reasonable velocity with reasonable pressures and barrel lengths.... The Physics just won't allow it, because the SD affects the ACCELERATION inside the barrel just like it affects the DECELERATION outside the barrel....

Bob

Backing into it based on the BC is how I had been doing it.  I have been using the Koble spreadsheet and I think that the calculated BC is a bit high.  none the less, it at least gives an ability to compare various weights and styles of slugs.  Ideally, I'm looking for a FF less than 1 and an SD that fits the psi and Barrel length as you have described. 

Bill

[rsterne]

Scott, you have the SD backwards.... For the same bullet weight, the larger the caliber the smaller the SD.... The formula for SD is....

SD = wt.(lbs.) / cal^2 = (wt.(gr.)/7000) / cal^2 because there are 7000 grains to the pound....

Since BC = SD / FF.... as the SD increases, so does the BC, if the FF is a constant (same shape)....

I think where you got confused is that for the same SHAPE (ie FF), as you increase the caliber, you get a higher SD, because the weight increases by the cube of the caliber, but the area only by the square.... This means the SD is proportional (exactly) to the caliber for bullets of the same shape and density....

Shaun.... 250 bar is 3625 psi, so 7 shots down to 3400 would 225 psi (15.5 bar).... a total of (29.3 x 15.5) = 454 CI to produce 7 x 102 = 714 FPE.... That works out to (714 / 454) = 1.57 FPE/CI, which is still really pretty stunning at over 100 FPE (but it isn't 2.0).... particularly with a 17" barrel.... I ran it through Lloyd's Internal Ballistics Calculator, and it might interest you to know that means the valve is closing when the pellet has only moved 3-4 inches (just over 3" at 3625 psi and just under 4" at 3400), and the overall efficiency of the gun is about 70%, which is excellent.... It shows what can be achieved by using tiny sips of very high pressure air.... Interestingly, with that tune, increasing the barrel length to 24" would only gain about 50 fps....

Bob

[Jim Holmgren]

There are a effecity loss with higher velocity and a rise with slower velocity, if I'm understand correct.

If one look at you graph, is it possible to dividing the fpe number with the speed increase to get a driffent number for driffent velocitys.

Lets say you have a .25 at 950 fps with a 0.141 port at 80 fpe, if we incresse the velocity with a lighter pellet to 1050 fps or decressed it to 800 fps with a heavier one, how would that impact the fpe number?


I understand this graph is just theoretical, but I find it quite accurate and intressting to find a "lofty goal" of prefomance.

[rsterne]

Yes, you are increasing the efficiency by using a heavier pellet because the air mass is a smaller percentage of the total.... Conversely, with a lighter pellet you are reducing the efficiency because the air mass is a larger percentage of the total mass.... Since the total energy input is the same, then you would expect to see more FPE with heavier pellets, travelling slower than 950 fps.... and less FPE with lighter pellets, travelling faster than 950 fps.... This in, in fact, the case, which is why virtually all of the cases where we see guys approaching 50% of the theoretical maximum FPE are shooting heavy bullets/pellets well below 950 fps, which is where my "lofty goal" is intended to work....

Bob