# Efficiency of a compressed air engine

I am doing some personal research on the efficiency of compressed air cars. I am currently trying to come up with an 'ideal' cycle to use as a reference for efficiency (c.f. Otto Cycle for petrol cars).

The best cycle I can come up with is isothermal compression of air at ambient atmospheric pressure to a compression ratio $r$, then an adiabatic (isentropic) expansion of the air and a constant pressure (isobaric) heating back to ambient temperature. In this situation the efficiency is defined as the ratio of the work extracted during the isentropic expansion to the work required to compress the gas during the isothermal compression.

I can't find any of the 'named' cycles that conform to this. A close analogue is the Brayton cycle, but I cannot satisfy myself that this is the 'ideal'. Is this because I haven't yet found someone who has or that I am approaching it the wrong way?