Regulated FPE

[Kailua]

On a well tuned regulated airgun.  What is the max FPE lets say in .22 at 900,1000,1100 psi etc?

[toine]

There are so many variables out there... hammer weight, spring, transfer port size, valve efficiency, pellet type/weight...

[rsterne]

If you want to talk absolute maximum, then back it up to the size of the bore and the pressure.... A .22 cal barrel is actually 0.217", so the area is 0.037 sq.in.... Multiply that by the pressure in psi and you get the force that can be exerted on the back of the pellet.... To get any kind of efficiency worth bothering with, you have to close the valve at or before the pellet has moved half the barrel length, so assume a 1 ft. distance that force is acting through, and that force becomes the potential FPE that can be produced.... That simplfies to:

FPE = ~0.037 x psi

So, for 1000 psi that is 37 FPE, for 2000 is is 74 FPE, for 3000 it is 111 FPE, for 4000 it is 148 FPE, etc.... Now this makes a couple of assumptions, but it turns out to be pretty realistic....

1. You need bore size porting, ie the ports have to be 0.217" diameter (or equivalent area) all the way through from the valve seat to the pellet....
2. The above calculation is based on 100% efficiency over that foot of push (unrealistic).... HOWEVER it ignores the push from the expanding air after the valve closes.... It turns out that the two pretty much balance out for a barrel of about 24" long.... Longer barrels can actually exceed the above predictions....
3. You might think that leaving the valve open until the pellet exits would double the FPE because you have doubled the distance, but in fact the efficiency over the last half of the barrel travel is miniscule, all you do is waste air for a tiny gain in FPE.... That is why I ignore any push past the first foot....
4. It assumes that the pressure is a constant during the shot.... This requires a very large air reservoir, and in the case of a regulated gun that means a huge plenum between the regulator and the valve.... In practical terms, typical plenums will reduce the USEFUL pressure (and hence the FPE) by at least 10%, and with a really tiny plenum as much as 30-50%....
5. It is further assumed that the Sectional Density (ie weight) of the pellet/bullet is great enough to extract maximum FPE from the air.... That means, in general, bullets, not pellets....

How accurate is this formula?.... Well, I've done 83 FPE at 2000 psi with my Hayabusa in .224 cal with a 29" barrel firing 41 gr. bullets at 2000 psi, and 106 FPE at 3000.... Doing the same math for a .257 cal gives 0.052 sq.in., so 104 FPE at 2000 psi and 153 FPE at 3000.... I've hit 120 FPE usng 88 gr. bullets at 2000 psi and 160+ FPE at 3000 with my .257 Hayabusa with a 28" barrrel.... I think that's pretty good agreement with the theory.... Now what you have to do to GET to those FPE levels is a whole other story, IT AIN'T EASY !!! .... However, you did ask what was the MAXIMUM, right?....

Bob

[RatRacer]

All true on the variables.
My regulated .22 rainstorm was set at 2100 psi, and was good for 32 fpe w/21gr pellets for 30 shots. A Will Piatt tuned gun could do better fpe and a bit longer count without a reg, but I was naive about that until after I traded it.

[Kailua]

Kind of figured there would be many variables. But there must be a max FPE on a given bore size, barrel length, and pellet selection.  Just wanted some kind of idea and Bob as usual has given a formula to get some idea.  This just another thing to book mark. thanks

[rsterne]

For maximum FPE you want a big bore, lots of pressure, a long barrel, and heavy bullets.... oh, and big ports....

Bob