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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.^[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 givesUsing the finite-trailing-edge thickness polynomial and normal offsets, the upper and lower points areTheir 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.^[ref] A performance statement about NACA 4412 must still identify flow conditions, surface condition and the measured quantity.

Robert M. Pinkerton investigated airfoil aerodynamics at the National Advisory Committee for Aeronautics. He coauthored the related-section study with Eastman N. Jacobs and Kenneth E. Ward and later compared measured surface pressure distributions with potential flow calculations.^[ref][ref]

His 1937 report describes a 5-by-30-inch NACA 4412 model in a variable-density wind tunnel, with 54 pressure orifices at the middle of the span. Seventeen angles of attack, from −20 to 30 degrees, were tested at a Reynolds number of approximately$3\times 10^6$. These readings test the distribution of pressure, not merely whether the total lift happens to agree with a calculation.^[ref]

An original simplified example explains the extra information. If a thin airfoil has a constant difference $C_{p,\mathrm{lower}}-C_{p,\mathrm{upper}}=0.8$ over its chord, its surface pressure integration for airfoil lift gives the normal-force approximationWith dynamic pressure $q=500\mathrm{Pa}$ and airfoil chord $c=0.20\mathrm{m}$, the normal force per unit span is $qc{c}_n=80N/m$. A different distribution can give the same integral while producing a different pitching moment or boundary layer behavior. These are invented uniform data, not Pinkerton's measurements.

Finite pressure-tap spacing and pressure-tap position error can change the inferred integral. A measured distribution therefore offers both a stricter test of potential flow and a way to see where its assumptions cease to describe the actual fluid flow.

The zero-lift angle of attack is an incidence at which the relevant lift coefficient is zero. For a two-dimensional airfoil in its approximately linear attached-flow regime, writeThe slope $a$ and intercept ${\alpha }_{L=0}$ are different properties. A cambered section can produce positive lift at zero geometric angle of attack, so its zero-lift incidence can be negative. Flow conditions and the distinction between a section and a finite wing must accompany an experimental value.

In thin airfoil theory, $a=2\pi$ per radian. With $\xi =x/c=(1-\cos \theta )/2$ and mean-line slope $z^{\prime }(\xi )=d{y}_c/dx$, the camber contribution isThe weighting means that the full airfoil mean camber line, rather than only maximum airfoil camber, determines the ideal incidence. The originating lecture notes derive this result from the first two Fourier coefficients of the tangency condition.^[ref]

For an original parabolic mean line $y_c/c=4m\xi (1-\xi )$, the slope becomes $4m\cos \theta$. Since ${\int }_0^{\pi }\cos \theta d\theta =0$ and ${\int }_0^{\pi }{\cos }^2\theta d\theta =\pi /2$, direct integration givesAt $m=0.02$, this is $-0.04$ radians, or about $-2.292{}^{\circ }$, and the modeled zero-incidence lift coefficient is $4\pi m\simeq 0.2513$. This parabolic example is not the piecewise mean line of NACA 2412. Substituting the actual piecewise mean line of NACA 4412 instead gives about $-4.1545{}^{\circ }$ within the same ideal theory.

An experimental estimate varies incidence while recording a force balance or integrating measured surface pressure, then locates the zero crossing in a suitable flow regime. For two stipulated linear data points $c_l=0.10$ at $-1{}^{\circ }$ and $c_l=0.30$ at $1{}^{\circ }$, linear interpolation or extrapolation gives $a=0.10$ per degree and ${\alpha }_{L=0}=-2{}^{\circ }$. These invented observations illustrate the reduction, not a particular profile measurement. Reynolds number, Mach number, surface condition and incidence calibration belong in a real comparison.

Zero lift does not require zero drag or zero pitching moment. Nor does extending a linear fit beyond aerodynamic stall establish another valid zero-lift prediction. The definition concerns the chosen lift component under specified conditions.