JD-EE
Quote:
Originally Posted by
JD-EE 
Kinetic energy is 1/2 mV^2. Potential energy is mgh. So the mass washes out of the equation. So a 3000' climb would give "gh" = 1/2 v^2 = 96000 ft^2/s^2 equals about a 438 '/s velocity change or about 300 MPH.
I am probably being a bit thick, but does this relate to the aircraft in question and if so, are you saying the aircraft lost 300mph in its climb?
Roughly speaking - I cheated on the math somewhat. Rudderrat posted the more correct equation from which mass drops out. I presumed a drop to zero velocity which is a cheat. It gives the general idea, though. A plane drops a staggering amount in the 3000' climb with no additional power input through the energy tradeoff.
Since we're working on the difference between the squares of two velocities it does vary. I'm not sure of the actual velocity of the plane to apply this to the AF447 case. (Too lazy to look up speed of sound at 37000'.) If the plane's physical speed was around 300MPH it'd have been dead stopped. If it started at 475 MPH the drop is probably around 120 MPH.
Again, the key takeaway is that the mass isn't part of the equation until you worry about flying bricks vs flying pillows of equal size and shape.