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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.

Camber describes the departure of an airfoil mean camber line from the straight airfoil chord. A common scalar measure is the largest normal distance from that line to the chord, often divided by chord length. Its sign, position and full chordwise distribution matter when specifying a profile. A symmetric airfoil has zero airfoil camber under the corresponding midpoint convention.^[ref]

For an original camber-line model, let $\xi =x/c$ and chooseIts derivative is $d{y}_c/dx=4m(1-2\xi )$, so the maximum is at $\xi =1/2$, with $y_c/c=m$. With $m=0.03$ and $c=0.4\mathrm{m}$, the maximum displacement is $12\mathrm{mm}$. Doubling all lengths doubles this displacement while preserving the three-percent camber. This full-chord parabola is a stipulated example, not the piecewise mean line of NACA 2412.

Camber height is not itself curvature. In this example $y_c^{\prime \prime }=-8m/c$, so the midpoint curvature magnitude is $8|m|/c$ because the slope there vanishes. Uniform geometric scaling preserves the camber-to-chord ratio while changing curvature inversely with scale. Nor does the maximum height alone determine the mean-line slopes at other stations.

In thin airfoil theory, the mean-line shape shifts the zero-lift angle of attack; finite positive lift can occur at zero incidence. Determining that shift requires the mean-line distribution, rather than substituting a camber percentage for an angle. The independent shape choices in the early NACA programme were tested by measuring aerodynamic characteristics while systematically varying thickness and mean-line form.^[ref]

NACA 0012 is a NACA four-digit airfoil with zero specified airfoil camber and nominal maximum airfoil thickness-to-chord ratio $0.12$. Its upper and lower thickness envelopes are reflected across the airfoil chord, making it a symmetric airfoil. The designation describes section geometry; it is not a measured lift or drag specification.^[ref]

To construct it, set the airfoil mean camber line to zero directly and use the standard thickness envelope in trailing edge with $\eta =0.12$. No mean-line location parameter is needed. For the finite-edge convention, the normalized half-thickness at $x/c=0.5$ is $y_t/c\approx 0.052940252$. An original section with $c=0.30\mathrm{m}$ therefore has surface heights $\pm 15.8821\mathrm{mm}$ at that station and full local thickness $31.7642\mathrm{mm}$. The nominal maximum thickness is about $36\mathrm{mm}$; twelve percent is not the thickness at every station.

Its nose-radius formula is $r_{\mathrm{LE}}/c\simeq 1.1019(0.12{)}^2$. The same $0.30\mathrm{m}$ chord gives $r_{\mathrm{LE}}\simeq 4.7602\mathrm{mm}$. The finite-edge polynomial also leaves a small nonzero rear gap; closing that endpoint changes the coordinate specification. These are consequences of the stated construction, not independent manufacturing measurements.

A useful physical test records pressure and section lift while varying angle of attack at controlled Reynolds number. Thin airfoil theory predicts a zero zero-lift angle of attack for the symmetric ideal model, but it does not supply a universal aerodynamic stall angle. The original NACA experimental programme systematically compared related shapes in a variable-density wind tunnel, providing a reason to identify both the section and the flow conditions when citing results.^[ref]

A NACA four-digit airfoil encodes three quantities: maximum airfoil camber $m$ in hundredths of the airfoil chord, its position $p$ in tenths of the airfoil chord, and nominal maximum airfoil thickness-to-chord ratio $\eta$ in hundredths. Thus NACA 2412 means $m=0.02$, $p=0.4$ and $\eta =0.12$; NACA 0012 has zero airfoil camber and the same nominal thickness ratio.^[ref]

With $\xi =x/c$, the airfoil mean camber line isFor a symmetric airfoil, take $y_c=0$ directly; do not divide by the zero position parameter. The half-thickness $y_t$ follows the polynomial in trailing edge. If $\theta =\arctan (d{y}_c/dx)$, the upper/lower coordinates areThickness is placed along a normal vector to the mean line, rather than simply added vertically.^[ref]

For an original NACA 2412 calculation at $\xi =0.4$, the mean-line slope is zero, $y_c/c=0.02$ and the standard finite-edge polynomial gives $y_t/c\simeq 0.0580301$. Hence the surface points are approximately $(0.4,0.0780301)$ and $(0.4,-0.0380301)$ in chord-normalized coordinates. A 12-percent designation does not mean the section is 12 percent thick at every chordwise position.

The trailing-edge convention must also be specified. The usual coefficient $-0.1015$ leaves a small finite thickness; the modified $-0.1036$ closes the endpoint. With a sloping mean line, the upper and lower endpoint coordinates can differ in both components, so directional measurement of trailing-edge thickness must state which separation it reports. These constructions define geometry, not a universal aerodynamic performance curve.

A symmetric airfoil has upper and lower surfaces that are reflections across its airfoil chord. Its airfoil mean camber line coincides with that straight reference, so its airfoil camber is zero. Symmetry constrains shape; it does not require zero lift at every angle of attack.^[ref]

In chord-aligned coordinates, a graph representation satisfies $y_l(x)=-y_u(x)$. Reflection changes the sign of incidence and transverse force. For an otherwise reflection-symmetric flow problem and corresponding reflected solutions, the section lift coefficient is odd in incidence, $c_l(-\alpha )=-c_l(\alpha )$, while drag is unchanged. At zero incidence, the symmetric solution has zero lift. An asymmetric nearby wall, control-surface setting or flow history can break the symmetry of the complete problem.

Under the attached-flow assumptions of thin airfoil theory, the zero-lift angle of attack is zero and $c_l\simeq 2\pi \alpha$, with $\alpha$ in radians. For an original ideal calculation, take $\alpha =3{}^{\circ }$, mass density $\rho =1.2kg/{\mathrm{m}}^3$, speed $U=30m/s$ and airfoil chord $c=0.5\mathrm{m}$. ThenThe reflected incidence gives the opposite lift per unit span in this model. These are illustrative section calculations, not measured data for a manufactured wing.

NACA 0012 supplies a standard geometric example. A wind tunnel comparison can measure lift at equal positive and negative incidences while controlling Reynolds number and surface condition. Comparing the reflected measurements tests the symmetry of the whole setup as well as the section; it does not extend thin airfoil theory through aerodynamic stall.