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Setting aside ignition timing, is there any way to use the cranking compression reading in order to figure whether an engine is able to use pump gas?



I usually shoot for 160 psi cranking pressure.
Usually if your at higher pressure you could use a larger cam or your starting off with fairly high static compression, and usually if your below you are giving up low end torque.

Also, and oil that might get in the chamber from bad rings, valve guides, intake, etc. will reduce the octane of the fuel and may cause detonation,