Chord-axial force coefficient ($C_A=A/(qS)$)

The chord-axial force coefficient is the dimensionless chord-axial aerodynamic force:Here $S$ is the stated aerodynamic reference area, $\rho$ the reference mass density and $U$ the reference speed. The chord axis and its positive direction accompany the normalization. A signed coefficient can be negative even when the flow-relative drag coefficient is positive.

An original example uses $\rho =1.2$ kg/m${}^3$, $U=25$ m/s, $S=0.40$ m${}^2$ and aft-directed load $A=9$ N. Then $q=375$ Pa and $C_A=9/(375\cdot 0.40)=0.060$. Reporting that load with area 0.80 m${}^2$ instead gives 0.030. The reference-area scaling of aerodynamic coefficients changes the reported coefficient without changing the balance reading.

For a section, axial load per unit span $A^{\prime }$ is instead normalized as $c_a=A^{\prime }/(qc)$ using airfoil chord $c$. The denominator $qc$ has units N/m, whereas $qS$ has units N. A per-span load divided by a finite area does not produce the same dimensionless quantity.

With common references, the inverse airfoil force-axis transformation isFor stipulated $C_D=0.040$, $C_L=0.60$ and $\alpha =5{}^{\circ }$, this gives $C_A\simeq -0.01245$. The subtraction shows why labeling a body-axis coefficient as drag can change even the sign of the apparent result. NASA defines lift and drag relative to the flow, which is the physical basis for keeping these axes distinct.^[ref]

At fixed area, density and measured force, a small fractional speed error contributes approximately $-2\delta U/U$ to the coefficient's fractional error. Normalization consequently does not replace measurement calibration or an uncertainty assessment of the reference flow.