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 $C$?