= Mean aerodynamic chord reference position
A <mean aerodynamic chord reference position> locates the reference segment whose <length> is the <mean aerodynamic chord>. Its chordwise origin and spanwise placement are additional geometric data. The length alone does not specify a point on a wing or determine its <aerodynamic center>.
For a symmetric <wing planform>, let $c(y)$ be the local <airfoil chord>, $x_{\rm LE}(y)$ its leading-edge coordinate and $S=2\int_0^{b/2}c(y)\,dy$ the <wing area>. A standard area-weighted half-wing placement is
$$
y_{\rm MAC}=\frac2S\int_0^{b/2}yc(y)\,dy,\qquad
x_{\rm LE,MAC}=\frac2S\int_0^{b/2}x_{\rm LE}(y)c(y)\,dy.
$$
The definition averages leading-edge positions themselves; it does not generally substitute the average station into a nonlinear leading-edge curve.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, pp. A-27–A-28, equations (A-88)–(A-92)]{ref}
The <quarter-chord reference of a mean aerodynamic chord> then has
$$
x_{1/4}=x_{\rm LE,MAC}+\bar c/4
=\frac2S\int_0^{b/2}\left[x_{\rm LE}(y)+\frac{c(y)}4\right]c(y)\,dy.
$$
The last identity follows directly from the definition of $\bar c$. It is a geometric area-weighted average of the local quarter-chord positions, without assuming a uniform aerodynamic loading.
For an original curved-leading-edge example, take constant chord $c=0.4\,\mathrm m$, span $b=4\,\mathrm m$ and $x_{\rm LE}(y)=ky^2$ on the positive half-wing, with $k=0.05\,\mathrm{m^{-1}}$. Then $S=1.6\,\mathrm{m^2}$, $\bar c=0.4\,\mathrm m$, $y_{\rm MAC}=1\,\mathrm m$ and
$$
x_{\rm LE,MAC}=\frac{k(2\,\mathrm m)^2}{3}=0.066667\ldots\,\mathrm m,
\qquad x_{1/4}=0.166667\ldots\,\mathrm m.
$$
Evaluating the leading edge at the mean station would instead give $x_{\rm LE}(1\,\mathrm m)=0.05\,\mathrm m$, moving the quarter reference forward by $16.667\,\mathrm{mm}$. For a straight leading edge the two operations agree, as in <mean aerodynamic chord of a trapezoidal wing>.
The positive half-wing station is a placement convention; the whole symmetric planform's spanwise <centroid> remains zero. Reporting a chord-reference position should identify its coordinate origin, planform-area convention and the chosen fraction of the reference chord.
Back to article page
