= NACA 2412
{c}
<NACA 2412> is a <NACA four-digit airfoil> with maximum <airfoil camber> two percent of the <airfoil chord>, located at forty percent chord, and nominal maximum <airfoil thickness-to-chord ratio> twelve percent. It combines a nonzero <airfoil mean camber line> with the same nominal thickness parameter as <NACA 0012>.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A.1, NACA 2412 example and equations (A-4), (A-7)–(A-8)]{ref}
The construction is developed in <NACA four-digit airfoil>. A new calculation away from the maximum-camber station illustrates its normal offsets. At $x/c=0.2$, the mean line gives $y_c/c=0.015$ and $dy_c/dx=0.05$. The finite-edge thickness polynomial gives $y_t/c\approx0.05737543$. With $\theta=\arctan(0.05)$, the normalized surface coordinates are
$$
\frac{\mathbf r_u}{c}\approx(0.19713481,\,0.07230384),\qquad
\frac{\mathbf r_l}{c}\approx(0.20286519,\,-0.04230384).
$$
Their midpoint is exactly the construction point $(0.2,0.015)$ before numerical rounding. Their horizontal coordinates differ because thickness is placed along the local <normal vector>. Simply adding and subtracting $y_t$ vertically would produce a different geometry at this sloping station.
For a $0.50\,\mathrm m$ chord, these paired points are separated by $2y_t\approx57.3754\,\mathrm{mm}$. This local normal separation is smaller than the nominal $60\,\mathrm{mm}$ maximum thickness. <Airfoil thickness convention> explains why a projected or same-horizontal-station measurement must be distinguished from this paired normal distance.
The two-percent camber is not a two-degree incidence or a prescribed <lift coefficient>. Its aerodynamic effect depends on the mean-line slopes and the flow. A <wind tunnel> comparison with <NACA 0012> can hold nominal thickness and <Reynolds number> fixed while observing the change due to <airfoil camber>. Such comparisons follow the systematic separation of thickness and mean-line form in the original NACA investigation.<The Characteristics of 78 Related Airfoil Sections from Tests in the Variable-Density Wind Tunnel by Eastman N. Jacobs and others>[Summary and derivation of related airfoil sections]{ref}
Back to article page
