# Calculations

• For example, compressed air at 2,900 psi (~197 atm) has an energy density of 0.1 MJ/L calculated from P*deltaV. 
• Pressure - N/m2 - 3000 psi = 2E7 Pa. Delta V - of 1 liter or E-3 cu meter - to 214E-3 cu meter.
• PdeltaV=2E7*214E-3=214E4=2E6 = 4MJ for that one expanded liter, as max possible work - but this is just PdeltaV without considering real thermodynamics underneath. Ballpart ok.
• Need to use PV-Work Calculator -https://www.geogebra.org/m/KAZHEN8c
• See formula for energy density - . This shows 50MJ/m3 = 0.05 MJ/l at 50% efficiency
• From 
• Type K Gas cylinders are 50l, or 1/20th cu m. Bottom line for compressed air: at about 3000 PSI - energy in a cylinder is 50MJ/m3 at 50% extraction efficiency. Thus, one Type K cylinder has 2.5MJ of energy storage - or 0.7kW hr. WTF????? Right. That is theory, but off-the shelf parts (see Air Motors), even piston ones - are rather pathetic. The Air Motors piston motor gets me 35 minutes of 150W - ar about 75Whr - whereas the calculation of stored energy is 0.7 kWhr above- making the piston engine only 11% efficient. Where are event the 30% efficiencies of air motors coming from? The actual calculation of stored energy based on pressures for a given volume - get us 0.7kWhr. This is a harsh reality - but real for adiabatic expansion. It would be 30% efficient for isothermal expansion - such that we need to tap the isothermal efficiencies somehow. Teh CAES Calculator shows 0.54 kWr - so 0.075 kWhr is a 14% efficient engine based on the calculator.
• Does this check? 20,000*ln(20/0.1)=100,000 kJ/M3 = 100MJ/m3 at 100% efficiency, or 50MJ/m3 with 50%.
• This is rather impressive - 50% efficiency of expansion gets 0.7 kWhr - but heat must be added here to increase the energy output of the expansion engine.

# Summary

• Practical (adiabatic) energy extraction appears to be super low, at 10-15%. Isothermal must be a start from the get go- and then it needs to be a magical 70% which by comparing CAES Calculator to isothermal - we get 1.5 kWhr. If we are close to that with highly efficient expansion engines - that would be practical energy. But the adiabatic prediction is simply not matched by reality - the practical air engines completely suck at an apparent <15% mechanical efficiency, excluding the thermodynamic efficiency in the CAES Calculator. So we need to achieve good mechanical efficiency, and good thermodynamic efficiency of isothermal.