MH, your first calc assumes constant current, which is not how a resistor behaves. Cut the voltage in half, and the current drops in half also, resulting in 1/4 power.
Aerodynamic power is the cube of speed, but that doesn't seem to match these switching fans. I just measured a Yate Loon 120. Feeding it 6V instead of 12 reduced the current by half. So that matches the resistor model nicely. Not matching the aero power calc is not intuitive for me. Do you need a scope to measure these switching motors properly?
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