 Chord-axial aerodynamic force

The chord-axial aerodynamic force $A$ is the component of the net aerodynamic force parallel to an airfoil chord, with positive direction here chosen aft. The perpendicular body component is the chord-normal aerodynamic force $N$. These two components resolve one load vector; flow-relative lift and drag resolve it in a different basis when the angle of attack is nonzero.

Let ${\mathbf{e}}_x$ point aft along the chord, and let $\mathbf{n}$ point outward from the body. Pressure and viscous stress giveNASA's primary explanation motivates integrating locally normal pressure forces before resolving the resultant into flow axes.^[ref] The explicitly outward normal in this equation fixes the pressure-force minus sign.

For a two-dimensional section whose upper and lower surfaces are graphs $z_u(x)$ and $z_l(x)$, the pressure-only axial load per unit span isThe surface slopes determine how much locally normal pressure projects onto the chord. A pressure force is normal to its local surface, rather than necessarily normal to the chord. Skin friction supplies a further contribution and is not included in $A_p^{\prime }$.

An original vector example takes $A=-5$ N, $N=80$ N and $\alpha =20{}^{\circ }$. The airfoil force-axis transformation gives $D\simeq 22.66$ N and $L\simeq 76.89$ N. A forward-directed axial component is therefore compatible with positive drag. It is not, by itself, evidence that the body supplies net propulsive power.

A proposed measurement compares a body-axis balance with integrated surface pressures after matching the angle of attack, sign conventions and support tare. Disagreement can include omitted shear or instrument effects; changing from body axes to flow axes does not remove those physical or measurement contributions.