 Chord-normal aerodynamic force

In the airfoil section plane, the 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.^[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,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 $D\simeq 67.32\mathrm{N}$ and $L\simeq 76.60\mathrm{N}$. 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 $N_p^{\prime }=\int (p_l-p_u)dx$ 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.