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Lifting-line theory represents a finite aircraft wing by a spanwise bound vortex whose circulation varies with position. The trailing vortex filaments induce downwash, reducing the local effective angle of attack. In its classical form, the model assumes steady, incompressible potential flow, a comparatively large wing aspect ratio, small sweep and locally approximately two-dimensional section behavior.^[ref]

Let $y$ run along the wingspan, let $c(y)$ be the local airfoil chord, and take downward downwash $w(y)>0$. Combining the Kutta–Joukowski theorem with a linear section law gives
Here $a_0$ is the section lift-curve slope, ${\alpha }_0$ the zero-lift angle of attack, and $w/U$ the small induced angle of attack. Because the wake induced by the entire circulation distribution determines $w(y)$, these equations couple different sections. Solving independent two-dimensional airfoils and adding their lift misses that coupling.^[ref]

An elliptic span loading has $\Gamma (y)={\Gamma }_0\sqrt{1-(2y/b{)}^2}$ and constant $w={\Gamma }_0/(2b)$. Integration gives
This is the unit span efficiency factor case.^[ref] For stipulated $b=10\mathrm{m}$, $U=30m/s$, $\rho =1.2kg/{\mathrm{m}}^3$ and $L=6000\mathrm{N}$, it gives ${\Gamma }_0\simeq 21.22{\mathrm{m}}^2/s$, $w\simeq 1.061m/s$ and $D_i\simeq 212.2\mathrm{N}$.

A proposed test compares sectional surface pressure integration for airfoil lift with a traverse of the downstream velocity field. The two observations test the predicted loading and wake, rather than only one total force. Flow separation, strong sweep and compressibility require further modeling; the classical calculation does not predict all drag or aerodynamic stall.