I'm wondering if anyone knows any good physical models of how vortices created by wingtips behave? I've done some research on the subject but have not really found anything concrete. I'm interested in knowing if there are some equations calculating the forces of the vortexes behind an airplane, preferably taking wingsize/model, speed/g-force and angle of attack into account.
From what Jan said about induced drag: Is the energy of the wing-tip vortices exactly the same as that of the induced drag? How would I calculate this energy? I've found equations for the induced drag (for example: https://en.wikipedia.org/wiki/Lift-induced_drag#Calculation_of_induced_drag), but they all seem to include coefficients but never any actual equation to get a numerical value. To calculate the lift I need the lift coefficient, but the equations for the lift coefficient I've found all include the lift. Is it possible to calculate the lift coefficient or is that only possible during experiments?
EDIT2: Found this topic on induced drag (What is the formula for induced drag?) with an equation. It assumes straight and level flight. I want to be able to calculate the induced drag not for straight and level flight, but for different angles of attack and velocities. Is this even possible, or are more advanced methods needed (modelling in MATLAB etc)?