Working on my secret patent

Here I am figuring out the rod windings and solenoid windings for the re-invention of hybrid technology and realization of end to end electro drive for combustion energy,

Certain things come to mind in the engineering, like the need to share a common magnetic  core for both rod and solenoid; when converting the piston action into magnetic energy.

 How do I figure this out? As an eletrician can guess wire gauges in pictures of electric motors and solenoids. Then As a ham guy, I know this is low frequency, need iron core for magnetic conduction. Then I remember relative wiring on audio transformer, and pretend from there on end.