= Quarter-chord sweep angle
{title2=$\Lambda_{1/4}$}
The <quarter-chord sweep angle> is the sweep of the spanwise line joining points one quarter of the local <airfoil chord> aft of the <leading edge>. It is a wing-planform reference direction, not the <angle of attack> and not the <mean aerodynamic chord>'s quarter-point location.
For chordwise coordinate $x$ increasing aft,
$$
x_{1/4}(y)=x_{\rm LE}(y)+\frac14c(y),\qquad
\tan\Lambda_{1/4}=x'_{\rm LE}(y)+\frac14c'(y).
$$
The <reference-line dependence of wing sweep> gives the general relation. On a straight-edged trapezoidal wing with full <wingspan> $b$, root chord $c_r$ and tip chord $c_t$,
$$
\tan\Lambda_{\rm LE}=\tan\Lambda_{1/4}-\frac{c_t-c_r}{2b}.
$$
Mason explicitly relates sweep at different chord fractions in the planform geometry.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, equation (A-100), with quarter-chord fraction 1/4]{ref}
For an original inverse calculation, let $b=8\,\mathrm m$, $c_r=2\,\mathrm m$, $c_t=0.8\,\mathrm m$ and $\Lambda_{1/4}=15\,{}^{\circ}$. The leading-edge tangent is $\tan15\,{}^{\circ}+0.075$, giving $\Lambda_{\rm LE}\approx18.9294\,{}^{\circ}$. With the root leading edge at $x=0$, the root quarter-point is at $0.5\,\mathrm m$. The tip quarter-point is $0.5+4\tan15\,{}^{\circ}\approx1.57180\,\mathrm m$ aft of that origin, while the tip leading edge is $0.2\,\mathrm m$ farther forward.
This calculation uses the full span in the chord-gradient formula and the semispan in the root-to-tip displacement. It also shows why the <normal Mach number for a swept leading edge> needs its own leading-edge direction: a reported fifteen-degree quarter-chord sweep does not make the leading edge fifteen degrees.
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