Stoti, I don’t have the mathematical solution, but I think I know where you’re going with this(I think). On my Airhog tank that was bought in kit form, it came with a 5’ whip, with an exterior blue armor shield. When tuning my Marauder years ago I found myself having to go get it topped off twice a week. There had to be a better way, as I knew I was losing a lot of air during the bleed off.
Then I discovered the Regman tethering regulator from airtanksplus.com He’s local to us(more so to me, as he’s in Sacramento) so I drove over to Gene Webber’s(one of two owners) place to check it out. Great guy, btw.
Shooting tethered, wether while target shooting or adjusting for velocity over a chronograph, I find my tanks air lasts longer between fills. Cool thing also, when shooting my hatsan hercules Bully which is a non regulated gun with a max fill of 3,650 psi, i was able to adjust the Regman to find its sweet spot of air pressure and accuracy, which was at 3200 psi.
Some folks try the method of shooting tethered to their tank by just closing off the tanks valve, and checking on the guns pressure gage after every so many shots, then cracking the valve open to re top off their gun. That’s an ok method I guess, but with the Regman it’s worry free and no head bopping to check the guns gage constantly. A cool feature about the Regman, also, is with the appropriate tees and misc fittings, you and your two shooting partners can shoot tethered all together to the one tank(provided you all have guns that shoot at about or close to the same pressures), and the only air you’ll waste is the bleed off at the end of the shooting session. Try shooting with two shooters tethered to the tank where you close off the tanks valve, and see how that goes.
Every once in awhile a topic on the forums comes up, where it’s asked what the best tool or piece of gear is had by an airgunner, and my Regman is always posted up. It truly is the best investment of a tool that I’ve made to add to all my gear.
https://airtanksplus.com/product/regman2-external-pcp-airgun-regulator/