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I didn´t understand so weel when you mentioned about the scenario when running 0.75 lamba on supercharged and 0.85 on aspirated. Could you explain this a bit better?
Supercharged or Turbocharged cars require more fuel to safely keep the cylinder temps lower than a NA engine needs, hence why you target lower lambda on a forced induction engine.
Tommy has summed this up perfectly - We need to match the fuel delivery to the engine load. As we increase the load on the engine we need to add more fuel and run a richer mixture to control the combustion temperature.