Airfoil mean camber line ($y_c(x)$)

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.^[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 satisfyAdding and subtracting gives ${\mathbf{r}}_c=({\mathbf{r}}_u+{\mathbf{r}}_l)/2$ and $2y_t=\Vert {\mathbf{r}}_u-{\mathbf{r}}_l\Vert$. The pair shares a construction parameter, not necessarily the same physical chordwise coordinate.^[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 $\sqrt{0.01^2+0.03^2}\approx 0.031623\mathrm{m}$. 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.