= NACA 4412
{c}
<NACA 4412> is a <NACA four-digit airfoil> with maximum <airfoil camber> $m=0.04$ of the <airfoil chord>, its maximum at $p=0.4$ chord, and nominal maximum <airfoil thickness-to-chord ratio> $\eta=0.12$. Thus the first two digits specify a mean-line shape, while the last two specify a thickness-envelope parameter. The designation is geometric rather than a universal measured <lift coefficient>.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A.1, four-digit naming convention and equations (A-4), (A-7)–(A-8)]{ref}
For an original $c=0.50\,\mathrm m$ section, the maximum mean-line displacement is 20 mm at a station 200 mm aft of the mean-line origin. The nominal twelve-percent thickness is 60 mm. That thickness does not occur at every station and is not the same quantity as maximum camber.
A calculation away from the maximum-camber station makes the <airfoil thickness convention> visible. At the mean-line parameter $\xi=x/c=0.2$, the standard construction gives
$$
y_c/c=0.0300,\qquad dy_c/dx=0.1000,\qquad y_t/c\simeq0.05737543.
$$
Using the finite-trailing-edge thickness polynomial and normal offsets, the upper and lower points are
$$
(x_u/c,y_u/c)\simeq(0.19429093,0.08709069),\qquad
(x_l/c,y_l/c)\simeq(0.20570907,-0.02709069).
$$
Their different horizontal coordinates are part of the construction. Adding and subtracting the same half-thickness vertically would create a different profile at this station.
Compared with <NACA 2412>, the mean-line amplitude is doubled while $p$ and the prescribed thickness envelope are unchanged. <Thin airfoil theory> therefore doubles the camber contribution to its modeled <zero-lift angle of attack>; direct evaluation gives about $-4.1545\,{}^\circ$ for this ideal mean line. That number follows from the ideal model and is not a wind-tunnel measurement. It does not establish a universal <aerodynamic stall> angle or drag curve.
The physical motivation for a related family was to vary thickness and mean-line form systematically, then measure the resulting aerodynamic behavior under controlled conditions. The original NACA report describes such a comparison in a <variable-density wind tunnel> at large <Reynolds number>.<The Characteristics of 78 Related Airfoil Sections from Tests in the Variable-Density Wind Tunnel by Eastman N. Jacobs and others>[Summary, systematic variation of thickness and mean-line form]{ref} A performance statement about <NACA 4412> must still identify flow conditions, surface condition and the measured quantity.
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