Originally Posted by
tomato coupe
The original statement was "Air resistance [drag] increases exponentially with speed." That is incorrect -- drag is a quadratic function of speed. You introduced P, and made a statement that "It is cubic. It is not squared, exponential or quadratic." I was simply clarifying that aerodynamic drag is a quadratic function of speed, and the power required to overcome drag is a cubic function of speed, as some people may not have realized that you had changed the topic from drag to power. I stated exactly what you repeated in your 3rd paragraph.
I think it is less confusing to simply state that drag is proportional to v squared and Power is proportional to v cubed.
To me (maybe being UK educated in maths?) a quadratic function implies a quadratic equation of the form ax^2 + bx + c = 0 which the drag equation isn't.