Firstly, in response to Tech's comment:
I have no interest in further complicating a switching system which already works well. When time and money permits I'll move to pressure drop switching, but the current setup hasn't given me any trouble so far.
I had some free time today, so I wrote a simple launcher simulator. It assumes the pressure gradient to be zero (i.e., local SOS >> muzzle speed), perfect flow through the "valve" (which is essentially the case here) and that there is no friction with the vessel walls. The expansion is assumed to be adiabatic (also reasonably accurate on a microsecond timescale). With high valve flow and low launch speeds in comparison to the SOS in the propellant gas, it agrees with GGDT to within 10%.
I don't claim this to be an accurate model, but it gave me some useful ballpark figures to work with. Picking a muzzle speed of 2600 m/s and a γ value of 1.14 (based on the scarce literature on pure ET guns with water as a working fluid), we get the following:
-Initial pressure: 43500 psi
-Travel time: 136 μs
-Velocity at joint between "chamber" and barrel: ~1950 m/s
-Barrel length needed to exceed Mach 1 with 6mm steel ball bearing: 1/4"
Note that the above is for a 3kJ shot, and that ETAv2.2 should be capable, with the necessary modifications, of running at least 6kJ.
At 48.4μF, the discharge current peak occurs at ~16μs, so the approximation based on instantaneous pressure generation produces a somewhat high value for initial chamber pressure. However, I suspect that the muzzle speed is likely over 50% of the SOS in the propellant gas, which will cause the estimated starting pressure to be considerably lower than the actual value. As such, I'll say that the current maximum chamber pressure is probably between 50000 and 80000psi, which is well within the capabilities of the chamber (which will yield at ~92% of its yield stress in internal pressure, or about 120000psi). However, I may need to upgrade to Grade 8 steel next summer.
It's not clear from what I know so far whether or not extending the barrel would be worthwhile, but I can say that I'm currently getting at least 75% of the possible muzzle energy (based only on varying barrel length), and probably quite a bit more when the pressure gradient is taken into account.
Assuming that the allowable maximum chamber pressure will not exceed 140 kpsi in the near future, the upper limit on the speeds achievable with an airsoft round will depend on the chamber volume, the stresses in the capillary tube area which may exceed the chamber pressure, the propellant gas composition and temperature, and the gains caused by the non-instantaneous pressure generation. By the looks of it, I'll probably run into energy input limitations before any of the above prevent further gains: at 1.2mL chamber volume and 965MPa starting pressure, the muzzle speed could exceed 5000 m/s. With a maximum 9kJ input, a more realistic upper bound on the speeds I might achieve next summer is 4000 m/s.
Any suggestions for improving the estimates for any of the quantities discussed above are appreciated. So far, it's clear that higher pressures and temperatures should be pursued as far as is possible without destroying the projectile and/or the chamber. Also clear is that summer 2011 will be a very interesting time of year around here
Spudfiles' resident expert on all things that sail through the air at improbable speeds, trailing an incandescent wake of ionized air, dissociated polymers and metal oxides.