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Effect of AFR on Power.
So between lambda AFR of 0.86, 0.90 and 0.95, which AFR target should I choose the best? Is it the leanest one since it makes the same power?
And how do I know if I need to make the combustion temperature cool enough?
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Your choice will come down to the way the engine will be used, as well as the specific power level. For example if it's a street engine then you're unlikely to be able to sustain maximum power for much more than 5-10 seconds if you value your licence. This limits the load the engine will be subjected to and we don't need as much cooling effect from the fuel - In this situation you could favor a leaner mixture. On the other hand for a competition engine that will be seeing sustained high load, I'd favor a richer mixture.
If the engine is naturally aspirated (which based on those lambda targets I'll assume it is), I would typically target around 0.88-0.90. My general rule of thumb is to aim for the richer side of the range where the engine makes best power as this is understandably safer for the engine. Unless you're using the engine in a situation where it is seeing extreme levels of high load operation (land speed racing for example), I wouldn't see the need to run as rich as 0.86.