# Derivation of the Takeoff equation

I am trying to understand the derivation of some simple equations to calculate the neccecary takeoff speed for an airplane (under ideal conditions).

Which is taken from 15. Takeoff and Landing. My main issue is the derivation of the horizontal equation

To get from the first to the second line my guess is that we use

R = W - L   and    m = W / g


My main problem is understanding the details between what happens from line 2-3 and 3-4. I would love if someone could give me a brief explenation of the symbols used, what does S denote?

• What don't you understand from 2-3? It's just rearranging the algebraic terms. #4 replaces lift and drag with the lift and drag coefficients. – JZYL Jan 20 at 13:43