# Models/equations for wingtip vortices/wake turbulence [closed]

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.

EDIT:

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)?

## closed as too broad by ymb1, fooot, DeltaLima, SMS von der Tann, GerrySep 16 at 11:47

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Welcome to aviation.SE. I'm sorry, but your question seems to be a bit broad. Did you have a look at previous questions that used the wing-tip-vortex tag? Could you try to refine your question and make it a bit more specific? – Federico Sep 14 at 12:49
• The total energy in the vortices is easy, because that's just the induced drag (plus suitable velocity and time terms to match the dimensions). However the same energy can correspond to very different velocity profiles in the vortex and you need something with enough granularity to calculate it. And that means a numerical integration, something like the vortex lattice method. – Jan Hudec Sep 14 at 18:51
• Thanks for your comments. I've looked at the other topics relating to wing-tip vortices and I did not really find was I was looking for. I guess what Jan was talking about is more in the right direction, so I'll elaborate from that. So is the induced drag only caused by wingtip vortices? If I know the energy of the induced drag is that exactly the same energy as for the wing-tip vortices? The equations for induced drag include a the coefficient for lift, which I can't really seem to find a good way to calculate. Perhaps I'm a bit naive in thinking it's easy to calculate this? – Jonathan Persson Sep 20 at 7:38
• Your question was initially put on hold for being too broad. In my opinion, you made it even more broad with your latest edit. What exactly do you want to know? You're allowed to post more than one question, so you can ask a separate question about specific problems you run into. Specific example questions could be, "Is the energy per meter in the wake vortex of an aircraft equal to the work done by the induced drag divided by the airspeed?"; "How to estimate the induced drag coefficients for different AoA and velocity?". Be sure to check for duplicate questions. – Sanchises Sep 20 at 9:12