Posted by **Carlos** on Saturday, June 1, 2013 at 11:59pm.

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?

- Physics -
**drwls**, Sunday, June 2, 2013 at 1:21am
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).

- Physics -
**exactly**, Sunday, July 21, 2013 at 7:07am
Elaboration on drwl's answer: since p∼ρv^2 via Bernoulli's equation

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