= Airfoil mean camber line
{title2=$y_c(x)$}
An <airfoil mean camber line> is the reference curve midway between the upper and lower surfaces of an <airfoil>, using a specified surface-pairing convention. It separates the bending of the profile from its thickness. In a <symmetric airfoil>, the mean line lies on the <airfoil chord>.<Wing Geometry by NASA Glenn Research Center>[Airfoil Geometry, mean camber line]{ref}
For the normal-offset construction used in a <NACA four-digit airfoil>, let the mean-line point be $\mathbf r_c=(x,y_c(x))$, let $\mathbf n$ be its <unit normal vector>, and let $y_t$ be the local half-thickness. The paired surface points satisfy
$$
\mathbf r_u=\mathbf r_c+y_t\mathbf n,\qquad
\mathbf r_l=\mathbf r_c-y_t\mathbf n.
$$
Adding and subtracting gives $\mathbf r_c=(\mathbf r_u+\mathbf r_l)/2$ and $2y_t=\lVert\mathbf r_u-\mathbf r_l\rVert$. The pair shares a construction parameter, not necessarily the same physical chordwise coordinate.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, equations (A-1)–(A-3)]{ref}
For an original local example, take paired coordinates $\mathbf r_u=(0.30,0.08)\,\mathrm m$ and $\mathbf r_l=(0.32,0.02)\,\mathrm m$. Their midpoint is $(0.31,0.05)\,\mathrm m$, and the half-thickness is $\sqrt{0.01^2+0.03^2}\approx0.031623\,\mathrm m$. The separation direction is proportional to $(-1,3)$, so the corresponding tangent direction is proportional to $(3,1)$. It would be incorrect to call either endpoint's horizontal coordinate the common construction station.
For surface data tabulated as two graphs at the same $x$, the vertical midpoint $(y_u(x)+y_l(x))/2$ defines a useful alternative convention. It need not exactly invert a normal-offset construction with a sloping mean line. Extracting a mean line from measured coordinates must therefore identify the pairing and interpolation rule. <Airfoil camber> summarizes its departure from the chord; <directional measurement of trailing-edge thickness> shows the related directional ambiguity at the rear endpoint.
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