How would I calculate the spanwise location of the mean aerodynamic chord for a swept wing?
I see a general formula for an elliptical planform wing, but having trouble finding anything on swept wings.
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For a conventional trapezoidal wing the spanwise location of the mean aerodynamic chord has a simple equation and it can even be determined geometrically. The following picture (source - The original source of this picture is anyway the book Airplane design by Daniel P. Raymer) presents both methods ($\lambda$ is the taper ratio):
The spanwise location of the MAC is a meaningless thing.
Even the length of the MAC is fairly dubious.
The thing that matters is the location of the aerodynamic center (of a wing or a wing/tail combination).
The length of the MAC is used as a reference chord -- to non-dimensionalize moments. You can use any value so long as you are consistent. You can use the MGC (mean geometric chord) and everything will work out fine. Perhaps there is some empirical data out there that is fit to MGC that won't quite match your MGC use, but that isn't the end of the world.
We would typically like the c/4 of the MAC to align with the wing -- and even better if that is at the location where the wing's chord is equal to the MAC. However, there is nothing that defines that to be the case.
When I say that the spanwise location of the MAC is meaningless -- I mean that in terms of "What do you actually use it for". Perhaps I'm overlooking something, but I can't think of a use of that term in either roll or yaw calculations. I.e. it is something that looks important from the often geometric construction of the MAC -- but it doesn't actually matter.
Happy to be proven wrong on this.