In the sport of indoor rowing (and probably others) I know that to double your speed you must increase your power output by a factor of eight.
I am wondering why this is the case. The indoor rower works by measuring data from a fan e.g. speed of fan, deceleration, acceleration etc.
Normally with objects moving through air there are (I believe) two factors to consider when speed is doubled. One is that you will hit the air twice as fast and the other is that you will hit twice as much air. Hence the power required increases by a factor of four.
What is the additional factor I'm forgetting to consider in the case of indoor rowing?