In a nutshell the problem is this: 1) We want to preserve the charge on the tank in stop-start situations
2) (Obviously the available work eventually venting to the atmosphere will be less than the potential energy stored in the tank. This is not the question for those not sharp enough to understand what is going on. You can't turn 100% of the pressurized energy into work) 3) When driving a certain amount will be lost to wind, rolling resistance etc. Since this is low speed it ain't much. 4) It is fair to say that in short stop-start conditions most of the kinetic energy at the wheels ends up in the brakes as heat. 5) There is no law preventing us from conducting most of that heat back to the tank but the difference in temperatures and ratios of the heat capacities of the brakes to the tank. On engineering terms 'all' the heat could go back to the tank if the brakes had low heat capacity and were very hot. We could elect to send the heat back with a heat engine and compressor but heat flow does this more gracefully. Not all dissipative heat flow is a dead end for engineers. 6) Imagine a continuous stop-start cycle where we can compute the average energy out from the tank and the average energy back into it. It would seem that if the outflow from the tank is O and the inflow is I, then the new outflow is O - I. 7) Naively 6) should preserve the life of the tank charge: The tank temperature is linear in I, E = mcT And the work from the tank is f(T) and nRTln P1/P2 for an isothermal process at least. So linear in T too. If the whole plant function was very sensitive to the tank temperature (higher order terms in T) then the process would be worthwhile. 8) In the steady state the assumption at 6) is probably correct because of (7) 9) Realistically stop-start cycles won't be 'regular'. The temperature will not reach equilibrium and there will be very little change in the tank temperature at next power demand despite our feedback. In short the thing would be sluggish. It probably would be better to have a SMALL high pressure reserve tank to capture the braking energy that then rapidly give it out on the next power demand. 2pm and that probably is the answer without detailed work. May look at it again in a few days.
