= Chord-normal force coefficient
{title2=$C_N=N/(qS)$}
The \b[chord-normal force coefficient] normalizes the <chord-normal aerodynamic force>:
$$
C_N=\frac{N}{qS},\qquad q=\frac12\rho U^2>0.
$$
The reference <dynamic pressure>, <wing area>, body axis and sign convention accompany the coefficient. For sectional force per unit span, use $c_n=N'/(qc)$ with <airfoil chord> $c$. Mixing total force and sectional normalization gives different units.
With stipulated $q=500\,\mathrm{Pa}$, $S=0.40\,\mathrm{m^2}$ and $N=100\,\mathrm N$, \b[$C_N=0.50$]. Reporting the same force with reference area $0.20\,\mathrm{m^2}$ gives $C_N=1.0$. This <reference-area scaling of aerodynamic coefficients> changes a reported number without changing the measured load.
When <chord-axial force coefficient> $C_A=A/(qS)$ uses the same references, the <airfoil force-axis transformation> gives
$$
C_D=C_A\cos\alpha+C_N\sin\alpha,\qquad C_L=-C_A\sin\alpha+C_N\cos\alpha.
$$
For $C_A=0.10$, $C_N=0.50$ and $\alpha=30\,{}^\circ$, the <drag coefficient> is approximately $0.3366$ and the <lift coefficient> is $0.3830$. Neither equals the normal coefficient.
Normalization does not remove measurement error. At fixed <mass density> and reference area, a small fractional <speed> error contributes approximately twice that fractional error to $q$, and hence the opposite fractional error to $C_N$ if $N$ is otherwise fixed. The usefulness of a dimensionless coefficient depends on retaining the measured references and their <measurement uncertainty>.
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