Sorry, once again, you totally lost me.... You need to draw it out and figure all the forces on all the moving parts, and if you are convinced it will work build one to see how well....At stage 3, the middle chamber? at 0 psi isn't pushing back against the piston, so there is still 1/3 of the 2K force on the piston pushing it towards the VC....The efficiency was never better than about 1.33 times what we can get conventionally at 2K, let alone at 3K.... so basically ANY wasted air makes it not worth the bother, IMO....Bob
Here is a sketch of the basic idea using a stepped piston like that in a regulator, only acting backwards like a typical pressure booster.... Black lines are the stepped cylinder, blue the stepped piston, and red an airflow passage and check valve (located in the cone shape in the small end of the piston).... The 2K chamber on the left is supplied from the regulator.... The 6K chamber on the right is the firing chamber, vented by a dump valve to the barrel....The dashed blue line is the piston in the compressed (firing) position (ie to the right), it is sitting up against the shoulder in the cylinder, (actually against a light return spring in the middle portion of the cylinder, not shown).... When the gun is fired, the 6K chamber drops to zero (guage), and the 2K cylinder at the left is full (up to the dashed line) with 2K air.... Because of the extremely short response time of the shot, I do not want the piston to move during the shot to cause any variations in velocity.... Since the pressure is so high (6K), even a small movement would make a big difference.... In order to move the piston back to the cocked (decompressed) state (ie to the left), three things have to happen....1. The volume of 2K air in the low pressure chamber must decrease (note air cannot flow backwards into the regulator to accomplish this)2. The pressure in the firing chamber must reach 2K3. The pressure in the middle chamber must also reach 2KConditions 2 & 3 are required to equalize the pressure across the piston.... Condition 1 would be achieved by venting it to the port where the red arrow is on the top of the cylinder.... The air would flow into the middle portion (where the spring is) and through the piston and check valve into the firing chamber.... With equal pressure on both sides of the piston, the spring would recock it.... NO AIR IS WASTED IN THIS COCKING STROKE (the air simply moves from the left side of the piston to the right side, into the middle and firing chambers).... The passage between the low pressure chamber and the middle chamber would then have to be closed, and the middle chamber vented to the atmosphere.... The check valve in the piston would close and as the pressure in the middle chamber bleeds off, the regulator would top up the low pressure chamber, moving the piston to the right and compressing the air in the firing chamber back to 6K.....The problem with this design is that the volume of 2K air used for every shot is the volume of the low pressure (left) chamber over the entire stroke of the piston.... which is 3 times what actually goes out the barrel.... 2/3rds of the air, all of the 2K air used to cock the piston in the middle chamber, is vented to atmosphere on the compression stroke.... Obviously, that is terribly inefficient, and renders the whole exercise useless.... Your task, should your choose to accept it, is to eliminate that wasted air.... *grin*Lloyd's spreadsheet is proprietary, he was nice enough to give me a copy.... I don't have any way to superimpose two shot cycles as you suggest.... Bob
As I tried to explain, doubling the amount of air when the bullet has already achieved 87% of it's velocity at 17" down the barrel will do virtually nothing.... However, cutting the volume of the 6000 psi chamber by 50% would drop the energy down from 224 FPE to less than 180 FPE, still using the 30" barrel....Bob
Yep you keep missing that you have to have the same force on both sides of the piston to reset it for the next compression stroke.... Force = pressure x area.... If you just open a valve between two chambers of equal volume, one at 2K and one at zero, you get both at 1K.... the air doesn't move completely from one to the other, only half of it does....The 180 FPE was just for the 6000 psi x 5.15 cc and the 2000 psi point would now occur earlier at about 8.5" down the barrel.... If you have the 2nd chamber dump at that point, you will get more out of it than before, the two chambers will work (from that point on) as if it was 20.15 cc at 3022 psi.... You will gain a few FPE instead of basically nothing, but you are still using a LOT of air to do it.... and your velocity is down 100 fps from your goal.... None of these dual chamber setups are as efficient as a straight 3000 psi conventional PCP with the valve closing at 50% (15" of travel).... I have to tell you, I'm growing a bit weary of this.... You need to do some drawings and work out the math for each step and figure out how to move the piston without losing any air.... or it's a waste of time.... I'm going to take a break from this thread for a while and let you ponder it.... Bob
Perhaps a totally different track?.... Don't worry about the efficiency.... Build the gun to use a 6K dump valve with a volume of 50% of the barrel volume.... Carry a 4500 psi Pony tank into the field, regulated down to 3000 psi and equipped with a 2:1 pressure booster (or the two combined into a regulated pressure booster if such a thing exists) so that it has a 6K output.... Use hoses and fittings, and a gun, designed to hold 6K in the valve.... Fill, shoot, and repeat.... The gun is a single shot, but it gets incredibly light, even with a 30" barrel, because it has no reservoir.... Using an 18cc dump valve at 6K should be able to push a 150 gr., .308 cal bullet about 950 fps (300 FPE).... The efficiency of the shot is 0.66 FPE/CI (better than most big bores) but when you include the air vented from the booster, it drops to about 0.44 FPE/CI, still in the range for many big bores.... You will lose some 6K air from bleeding the hose, though....If instead of the dump valve you can control the dwell accurately using a balanced valve (so that the hammer energy doesn't get overwhelming) you can, of course, drastically increase the efficiency.... If you can close that same 18 cc valve when the bullet exits the muzzle you would have the same power, and the efficiency would be 0.98 FPE/CI.... Close the valve at 50%, the velocity only drops 20 fps and the efficiency jumps to 1.26 FPE/CI.... However, you have the added complication of filling the gun to exactly 6K for each shot.... although a smaller amount of air would be wasted by the (smaller) booster.... Bob
OK, so before you start jumping off the walls, that is FAR from a dump valve, in fact the dwell is so short the valve is closing when the pellet has only moved less than an inch.... To get back to about where we were for power and efficiency, and with a dump valve, we need to reduce the plenum (in this case valve) volume.... I had to do some trial and error, but here is what I came up with.... It turns out you only need about 1/10th the volume, 1.67 cc of air at 6000 psi to get back to 50 FPE with a dump valve....Regulated, compressed to 6000 psi, 1.67 cc valve with dump shot.... 50 FPE @ 1.29 FPE/CI.... So the answer is yes, what you are proposing should work.... IF you can build it....Unfortunately, that's a big IF.... You need to start with 5 cc of air (0.305 CI) at 2000 psi and then compress it 3:1 to 6000 psi.... Let's say that you use a piston 1/2" in diameter, which is 0.196 sq.in.... you need a cylinder 1.56" long, and a piston with a 1.04" stroke to increase the pressure 3:1.... At the end of the compression stroke, the force on the piston would be 1178 lbs. so you would need quite a leverage system to achieve that.... If the lever was a foot long, you would still have a 100 lb. load.... You could trade off smaller diameter for longer stroke, or larger diameter for less stroke on the piston, but you still end up with a 100 lb. load on the end of a 1 foot lever to compress that 5 cc of 2000 psi air to 6000 psi.... So the answer to your question is, yes, by using a much higher pressure you can make a dump valve as efficient as a conventional PCP.... The question then becomes, can you build and operate it?....Bob
Sorry, I still don't see it.... When one booster is on the compression stroke, ALL of it's force is required to raise the pressure of the firing chamber to 6K.... There can be NO pressure in the middle chamber at max. stroke.... However, in the other booster, returning the piston to it's uncompressed position (against 2K pressure) requires 2K of pressure on both it's firing chamber (1/3rd of the area) and middle chamber (2/3rd of the area).... Connecting the two middle chambers together would see the volume move back and forth, but there would still be 2K of pressure in both middle chambers.... so no compression could occur.... In addition, the large (low pressure) side of the chamber that is on the cocking stroke is full of 2K air, which in my design would flow into the middle and firing chambers.... If the middle chamber is being filled by the air from the middle chamber on the other booster, then that excess air has nowhere to go.... unless you vent it....BTW, in my suggestion of having the booster external to the gun, I realize that there is an air loss during recocking the booster, and mentioned that as a loss of efficiency.... The other alterative, of course, is to build a PCP that runs on 6K and figure out how to fill it safely.... There are big bores safely running 4500 psi now, it's only a matter of time before they go higher.... The problem currently is a safe way to store air at an even higher pressure to fill them.... or use a booster....ob