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Determining max compression ratio on GDI engines

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I have a Hyundai Lambda II 3.8 V6 engine I'm building for time attack purposes. It's a GDI setup and it's not knock limited. Currently 11.5:1 CR. I'm boring it out to 4.0L and I want to increase the CR to squeeze some more power from it, but I'll be running on 91 octane and not sure what it will handle. This is an NA build, but with occasional nitrous use.

Are there guidelines, info or math on determining what the limit will be? I'm aware that other things come into play such as cam and ignition timing.

Something else to consider, I have a nitrous wet system setup (50 shot) for straight line fun, it's an occasional usage type of thing, but I'm concerned that it might cause an issue with a higher CR.

Modelling the engine behaviour to this level unfortunately is a little beyond the scope of our courses and as you've rightly noted, the CR is only one factor that plays into the overall performance (and knock resistance) of an engine. In general due to the way the fuel is introduced directly into the combustion chamber, DI engines tend to do a better job of using the fuel to reduce charge temp and hence they are less knock prone than an engine with the same CR and port injection.

For an example the FA20 uses a 12.5:1 CR and this is lightly knock limited on our local 98 octane fuel. We still manage to run 8 psi boost on this CR and pump fuel with conservative timing with no trouble. Your nitrous is going to have a similar effect to boosting the engine. Personally I'd consider a bump in CR to 12 or 12.5:1 but just understand that your tuning will need to be on point to handle the nitrous safely.