Math question.

A .357 air gun regulated to shoot 81 grain JSB'S @ 900fps, also equates to 97 grain slugs at 850fps. It starts at a 4200psi fill and gives (pm info, no way of telling if all gauges are on) roughly 16 good shots, ending at 2700psi.

Now, let's just say 15 good shots & assume they're all within a 10fps spread at most. I know, everything has to be sorted, weighed, no blow by, etc to get single digit spread.

My main questions are as follows, and please understand I truly have a math disability. This equates to 100 psi per shot. I'm guessing the reg is set at 2700psi, but I don't think it takes 2700psi on a 81 grain .357 surface area (it would be over 2x the pressure as it's under 1/2 inch, almost 1/3rd so maybe triple 2700psi?) to move a 81 grain pellet at 900fps.

Now, besides the fact that most people don't want a 4-5' rifle, or longer, so companies give on efficiency by gaining appeal in a shorter barrel. I don't know the formulae for optimal air usage L=length/D=diameter/W=weight/P= pressure; but I'd sure like to learn it. Anyway, this subject is a .357 WAR with Cothran valve & Cobra regulator. I don't know barrel length.

I'm asking what it really takes in pressure to push this 81 grain at 900fps. I noticed my usual rule of thumb, add or subtract 10fps for each grain, did NOT apply here according to members info of 900fps w/ 81 grain & 850fps, same setting on a 97.? Morrill slug. I'd have estimated a drop roughly of as much as 170fps. Maybe this 10fps per grain works for spring guns, but I'm obviously way off here as he only dropped 50fps.

So besides the general math question of formulae, how much pressure is really pushing on that 81g .357, what rifles are most efficient, most powerful, most consistent, AND, most importantly, most accurate? Let me make an observation.

I think most of us know, slugs & Diabolo skirted pellets are VERY different. Very few barrels can shoot both pellets & slugs accurately at all distances. Let's assume all ammo is perfect & consistent. The pressure (this is my main question, remember?) Created by my Sumatra. 25 simply shreds the skirt right off soft lead JSB King 25.43's at anything past TP#6-7 max. In fact, TP#1 is just enough to send it through the barrel and bounce off a pillow or sink to bottom of 5 gallon bucket. It mics exactly at .251. I've re-shot these "sized" pellets and they'll do well. They hit higher though on TP#4 where I shoot the Kings normally at 32 yards. Less friction, higher POI. 

I can switch to 33.95 soft JSB'S and these have larger, thicker skirts. I can turn power up on these to maybe TP#9-10.

Now, the only slug I've tried so far is what came with this LNIB Sumatra from Mr. Lindt. Thank you SO much. As good as they come to deal with. The slugs in question are now discontinued but they're Air Venturi blue plastic box 50 grain .253 solid core, round nose, 90° back that is concave to a depth of 0.030" (Starrett depth gauge). If swage they take a bit of pressure but will size out at .251.

Starting with a .251 slug, of 40 grains maximum, and a design that's air gun friendly for high pressure (where the diabolo skirt was never meant for these speeds, initial blast to get it going) why is it that we seem to have problems getting anywhere near even 0.100 let alone around 0.120-0.140BC like a .22LR, short?

I don't know. Any answers? As I wrote this I found out none of my CPHP'S are even engaging the 10 year old barrels L&G's. Looked under a scope. Not the least bit. It's amazing it shoots as good as it even does but time to get a Maximus barrel on her as I have like 5K CPHP'S in tins. $7.00 @ Wally World & good to 30-50 yards out of any of my .22's












 
I think a glass of really good bourbon will put things in proper perspective. I don't know if you're "overthinking" it or not, but you're sure thinking beyond my level. I've read the posts twice and still don't understand the question. Which is just as well, as I certainly don't have the answer. But good luck in your search. 
 
A gun is filled to 3000psi. That's 3K on every sq inch. Pellets, slugs, aren't 1", let's just simplify this and use a quarter bore and say it's truly 0.25"

In reverse, my question is how does a hand pump pump 4500psi. By using very small piston in 3rd stage. Even though it's a tiny piston there's around 200lbs of pressure to pump that sucker towards the end. It got divided by a smaller size so pressure went down. Is it whatever your fill pressure or regulator are at, or does the smaller diameter pellet equate to more than your fill pressure?

You see what I'm asking?

There's reasons. Look at what some extreme cases have gotten. Heavy 20mm made over 3Kftlbs. .82 on Helium over 1800fpe. These are no higher files than 4350psi at most, and even the Huben is now rated at a 5K fill. an 06 hits 55K for a few milliseconds to push that sucker out at 2700fps. Think about this. 55K is NOT really needed.

I've heard that physics won't let an air projectile go over 1650fps. I don't know about this. Even if we could reach 1650fps and stay above 1100 out to 200 yards, that would be great as far as I'm concerned if it were a .22LR 36-40 grain with the same BC. I'd be even more happy with just 1050-70fps standard sub sonic velocity and a BC of 0.137

I think it can be done a lot easier than most think. One of the reasons it hasn't is you'd have to accept being tethered for any number of consistent shots. I'd have no problem with that as a BR or varmint shooter with a bipod on a blanket. I have no idea how many 1070fps constant shots one could get with a 88CF 4500psi tank tethered to a rifle equal to a .22LR standard velocity. I've been told I need a .257 Texan. No, I don't think I do.

I think I need a very good .22 caliber air gun with a barrel meant for similar .22LR bullets with a high BC, and just have a big tank with a good external regulator.

Anyone want to build something like this? 
 
Absolutely cannot answer this question without barrel length...and port size....



a .357" cal pushing an 81 gr @ 2700 psi with 28" barrel and .3 port = 1030~ fps..

a .357" cal pushing an 81 gr @ 2700 psi with 23.5" barrel and .3 port = 985~ fps..

a .357" cal pushing an 81 gr @ 2700 psi with 19.5" barrel and .3 port = 937 ~ fps..



What it takes to move 81 gr 900 fps?



2400 psi with 19.5" barrel .357 cal 81 gr .3 port

2000 psi with 23.5" barrel .357 cal 81 gr .3 port

1700 psi with 28" barrel .357 cal 81 gr .3 port



The above was done with a large plenum volume..



I am much too lazy right now to write out my formula, I have threads where I have shared it in the past. I can actually calculate the above with 2 separate calculations. One based on air usage (provided you know this figure) and the other based on parameters such as pressure(force), caliber (surface area), barrel length (distance), pellet weight (mass), plenum volume (pressure drop), and port size (correction factor) 



The fastest verified velocity obtained by an air rifle is around 2200~ FPS with a 7gr projectile...several have taken shots over 1650. 1650 is the RMS speed of air @ a specific pressure meaning AVERAGE...which suggests there is air moving slower, and air moving faster. If you fire a projectile that weighs LESS than the mass of air being shot, then its quite possible and likely the projectile will exceed the RMS speed of air...because its taking advantage of the air that is traveling well above the RMS value..