# Deriving lift equation from scratch

I am trying to derive a model for how the lift of an airplane depends on its speed, surface area of wings, and air density. I used the Buckingham Pi Theorem and some dimensional analysis to come very close to the actual lift equation:

$$L=C \times v^2 \times S \times p$$

where $L$ is lift, $C$ is a constant, $v$ is velocity, $S$ is surface area of the wing, and $p$ is air density. I know for a fact that the actual lift equation is this with $C=1/2$. Other than experimentation, how does somebody figure the constant $C$?

• The only way would be to go back to first principles and derive this equation from them. Then, you should be able to collect constants to determine what makes up C.
– user237392
Sep 28 '16 at 3:48 is your coefficient of lift which varies generally between 0.5 and 1.5. It's based upon airfoil camber and angle of attack.
In the lift formula 1/2 is just another coefficient mutliplied with , velocity squared ( ), density ( ), and wing area ( ).