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I don't think I could make a diaphragm in this size but a piston is possible.
If I was doing this I think I would make some sort of electromagnetic shuttle valve that would deliver a defined quantity of fuel per pulse and then control the fuel quantity by varying the pulse rate.
My initial set up attempts will have to be much more practical.
Mike,I have done some rough calculations based on the Root engine:The control system would need to take into account rpm (not neccessary with my mechanical system), throttle position and ideally manifold pressure. I think I will leave that project to someone else Keep the thoughts coming
I'm not sure I actually need to know what the actual flows and pressures are
To me it will then be interesting to know / measure how much Air and Fuel goes through at those RPM's in order to see how much I'm away from the mark that would make it run - but I can also see the point in using an external Fuel metering device as found in many of the latest model airplane engines and just adjust it to make it run as it should @ max RPM first. That would allow me you to do it the next steps as you would have done in our youth