That is a good question. Chapters have been written on the subject. I
suspect there is no direct analogy with a piston engine because
of the moving combustion chamber. Here is some stuff from Yamamoto. Also
a drawing of an old idea I had. Won't work as it will suck
HP to compress the air required. Unless of course the air compressor is
run off the waste exhaust energy alone.

Paul Lamar

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After thinking about it some more my air injection idea above
won't work as combustion pressure will leak above the apex seal across
the air injection hole. It is going to take some real ingenuity to
get stratified charge to work on a moving combustion chamber.

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On third thought if I move the hole up so the trailing apex seal
just passes the hole before the plugs fire there will be no  combustion
pressure leakage across the hole. I have done away with the solenoid
valve and replaced it with a synchronized piston air compressor.
The piston is phased such that the
injected fresh  air reaches max velocity and pressure just before the
trailing apex seal passes over the air injection hole. The piston
compressor is geared to the e-shaft of course. Here is a 3D.
The one way side ball valve is the fresh air intake valve.
The other one way ball valve prevents the piston from
sucking in fuel/air mixture from the main intake chamber.
In a way this has a slight supercharge effect.

The question remains. Will the compressor suck more HP than
it will improve the BSFC?

Paul Lamar