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OK, I've got idea how it might work, but how would use the pump?
OK, so you calculate energy from speed. Than better question would be how you calculate the speed (v)?
Is this your hand pump?
Here is how speed of the shaft changes with distance:
For 20 cm Vlanikgun: v(s)=23,18*EXP(-0,8025425*s);
For 90 cm Vlanikgun: v(s)=30,21*EXP(-0,43568197*s).
The handpump can be seen in one of the photos at http://apox.ru/weapon/gun-handmade/19-besporshnevye-podvodnye-ruzhya-vlanik.
Dismantled components of "Vlanik 48" are shown in photo 8 of 16, handpump (Hacoc) is at the bottom.
The earlier "Vlanik" spearguns used much higher pressures, above 70 atm, which are difficult to produce with a handpump unless it has a very small bore. This small pump bore size requires many pump strokes to move the required volume of air into the gun in order to achieve very high pressure, so an alternative was to pressurize the gun with carbon dioxide gas instead. Carbon dioxide liquid transforms into a gas at around 900 psi or 60 atm. The compression ratio of the gun raises this chamber pressure to over 70 atm when the gun is cocked. A disposable carbon dioxide cartridge could be used to fill the gun provided that it was fitted into a suitable housing and I suspect that the last photo shows such a device rather than a pump.
To increase reliability of "sealed" tail cap design I would make something like this on drawing. Sealing o-ring is shielded from scratches as seen on the picture. Rubber plug makes friction to the cap so ensures more reliability in case of o-ring sealing failure. Air bubbles after shooting could indicate bad sealing.
This would be a mixture with Vladimir's design. I believe design with neoprene would also work.
There is an another problematic statement regarding performance of Vlanikgun. I do not believe that 28 cm long gun can have 2,8 m effective range. That range is obtained by calculation taking initial speed of shaft in air to be same in water, what is not true. According to that calculation, 70 cm long gun has range 5,6 m. That gun has about the same shaft acceleration distance as my Cyrano 850 (64 cm). My Cyrano (Tomba) with 100/7 mm shaft has effective distance to 4 m. Vlanik 70 might have to 4,5 m because of thicker shaft, not 5,6 m.
This not quite so...
The Resistance of water, influences upon initial velocity of the harpoon...
Though results close...
I like твои approaches in analysis of the work undersea ружей...
Can has already approached time and you itself изготовиш like handgun...
I certain, beside you are got...
Diagram posted just for interest as I had already mentioned it in my post #7 on this thread where I described the shortcomings of this "dual power" design. I only just found the diagram again. Not enough volumetric difference between inner barrel at 14 mm ID and outer tank at 20 mm ID.
It all seemed like a good idea at the time! Vladimir sent the drawing back (see attachment) with the inner barrel shown vented with port holes and the blades on the "turbine piston" reduced to stubs, the "power dial" arrangement being discarded. He was already working on the inner barrel idea when I wrote to him.