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Originally Posted by brucepick
Its the cube of the airspeed.

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With a doubling of speed the drag (force) quadruples per the formula.

So two times faster increases air drag four times? That's squared, not cubed. Two times two.
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Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times a [the] work in half the time requires eight times the power.

Four times the force already figures in the double speed, why is the double speed considered twice? If you are keeping a constant time, then the distance is double and thus the power exerted over the same time increases by the cube.
80 mph for one hour uses 8 times (2x2x2) the power of 40 mph for one hour. That's a cube, but the distance (displacement) is double.
80 mph for 40 miles uses 8 times (2x2x2) the power of 40 mph for 40 miles (a fixed displacement or distance), but for half as long. 2x2x2x.5 is the same as 2x2. 2x2 is a square, not a cube.
To me that's logical. If I'm wrong, why does it make sense to me?