= Chord-axial aerodynamic force
{title2=$A$}
The \b[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 $\boldsymbol e_x$ point aft along the chord, and let $\boldsymbol n$ point outward from the body. Pressure and <viscous stress> give
$$
A=\boldsymbol e_x\mathbin{\cdot}\int_S(-p\boldsymbol n+\boldsymbol\tau\boldsymbol n)\,dS.
$$
NASA's primary explanation motivates integrating locally normal pressure forces before resolving the resultant into flow axes.<Aerodynamic Forces by NASA Glenn Research Center>[Variation in Pressure and Definitions of Lift and Drag]{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 is
$$
A'_p=\int_0^c\left(p_u\frac{dz_u}{dx}-p_l\frac{dz_l}{dx}\right)dx.
$$
The 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 $A'_p$.
An original vector example takes $A=-5$ N, $N=80$ N and $\alpha=20\,{}^\circ$. The <airfoil force-axis transformation> gives $D\simeq22.66$ N and $L\simeq76.89$ 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.
Back to article page
