= Chord-normal aerodynamic force
{title2=$N$}
In the airfoil section plane, the \b[chord-normal aerodynamic force] $N$ is the component of an aerodynamic <force> perpendicular to the <airfoil chord>. The <chord-axial aerodynamic force> $A$ points along the chord, chosen positive aft. These body directions differ from the flow-relative <lift> and <drag> axes.<Aerodynamic Forces by NASA Glenn Research Center>[Definitions of Lift and Drag]{ref}
Choose $z$ toward the upper surface and let the incoming flow direction have body components $(\cos\alpha,\sin\alpha)$. Resolving the same <vector> in the two orthonormal bases gives the <airfoil force-axis transformation>,
$$
\begin{pmatrix}D\\L\end{pmatrix}=\begin{pmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{pmatrix}\begin{pmatrix}A\\N\end{pmatrix}.
$$
The <rotation matrix> preserves the squared <Euclidean norm>: $A^2+N^2=D^2+L^2$. An original example with $A=20\,\mathrm N$, $N=100\,\mathrm N$ and $\alpha=30\,{}^\circ$ gives \b[$D\simeq67.32\,\mathrm N$ and $L\simeq76.60\,\mathrm N$]. Calling the 100-newton normal reading lift would confuse two different components. The transformation is kinematic; it does not assert that a particular wing produces those loads at that angle.
For a pressure-only reconstruction, the chord-normal component is $N'_p=\int(p_l-p_u)\,dx$ per unit span when upper and lower surfaces are graphs over the chord. The total $N$ can also include <viscous stress>. A force balance resolving body axes and a pressure reconstruction therefore need matched axes and a stated load decomposition before they are compared.
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