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.
Formula for Elliptal WIng:
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1$\begingroup$ Basically I think you do a weighted average based on the wing chord width. Will let someone with more expertise post the actual answer. Interested to see if anyone has anything to say about how to take twist (washout) into account. For example, what if the outer fifth or quarter of wing is so washed out as to be negatively lifting at moderately fast airspeed (moderately low AoAs)? I've seen this happen with hang gliders, and not primarily due to the wing flexing. In such a case do we say the MAC moves inboard (and thus forward) as the AoA decreases? Maybe grounds for a new question... $\endgroup$– quiet flyerAug 15 at 21:41
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1$\begingroup$ Take a look at skybrary.aero/articles/…. Take it with a grain of salt though, for example I think "measured parallel to the normal airflow over the wing" is wrong. You measure parallel to the aircraft centerline. I assume they are just giving the formula for an average, weighted according to chord length. In the case of linear leading edges and trailing edges it should be fairly simple. $\endgroup$– quiet flyerAug 15 at 21:53
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2 Answers
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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):
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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.
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$\begingroup$ I'm using it to calculate moments for a novel aero body with a swept tail surface. So I ultimately need the moment arm distance from a specific point to the cp of the tail. In my case, the cp would be at 25% of the mac (since it's a symmetric airfoil). Knowing the spanwise location of MAC would allow me to calculate the chordwise location from the root leading edge using trig. $\endgroup$– SethAug 16 at 1:22
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1$\begingroup$ I do not believe most methods of deriving the MAC will yield the spanwise position -- and if it did, there is no requirement that the MAC lie 'on' the wing. It can lie in front of or behind the wing. I suggest you use a LVM code like VSPAERO, AVL, XFLR5, Tornado, etc. to perform a simple pitch stability calculation for your configuration. $\endgroup$ Aug 16 at 3:18