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As the fan spins faster and faster, the angle of attack of the fan blades, relative to the airflow, increases. If the fan spins too fast, the angle becomes too great, and the airflow will separate off the trailing edge of the blade. This separation makes noise. The dimpled surface will cause a turbulent boundary layer, that will help keep the airflow attached longer (arcsine has this pretty much correct) - so in theory, the dimples should work. But for a fan that spins at a set speed, why not just design a blade that works well at that speed?
Rex
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1975 911s
1997 Saab 900s
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