posted by Carlos on .
An airplane of a certain density and shape flies at a constant speed. To do so, it must fly with a certain velocity v0. If the size of the airplane is scaled up in length, width, and height by a factor of two, it can only fly above a new velocity v1. What is v1/v0?
Plane mass increases by a factor of 2^3 = 8.
Plane lift increases by a factor 2^2 = 4
Plane drag increases by an unknown factor between 1 and 2. Engine power will have to increase to compenstate for increased prssure drag and boundary layer friction.
The plane's velocity will have to increase by v1/v0 = sqrt2 so that the new lift (4*2 times higher than before) will match the increased weight (8x higher).
Elaboration on drwl's answer: since p∼ρv^2 via Bernoulli's equation