= Reference-line dependence of wing sweep
<Reference-line dependence of wing sweep> means that different spanwise lines on one <wing planform> can have different sweep angles. Naming the line is therefore necessary to specify the geometry. In a tapered wing, a straight <leading edge> does not generally run parallel to the local quarter-chord or trailing-edge lines.
Let $x$ increase aft and $y$ run outward on one half-wing. If the local <airfoil chord> is $c(y)$, the line at a fixed chord fraction $f$ is
$$
x_f(y)=x_{\rm LE}(y)+fc(y),\qquad
\tan\Lambda_f(y)=\frac{dx_f}{dy}=x'_{\rm LE}(y)+fc'(y).
$$
For two fixed fractions $f,g$, subtraction gives
$$
\tan\Lambda_f-\tan\Lambda_g=(f-g)c'(y).
$$
This is a relation between tangents of angles, not the angle difference itself. Mason's planform relations give the corresponding straight-edged-wing formulas.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, pp. A-28–A-29, equations (A-97)–(A-101)]{ref}
For an original example, take <wingspan> $b=8\,\mathrm m$, root chord $3\,\mathrm m$ and tip chord $1\,\mathrm m$, varying linearly. Then $c'=(1-3)/(8/2)=-0.5$. Choose a leading-edge slope $x'_{\rm LE}=0.125$. Its <leading-edge sweep angle> is $\arctan(0.125)\approx7.1250\,{}^{\circ}$, but its <quarter-chord sweep angle> obeys $\tan\Lambda_{1/4}=0.125-0.125=0$. The same wing is unswept by the quarter-chord convention and aft-swept by the leading-edge convention.
For constant chord, $c'=0$ and the local angles agree at all chord fractions. For curved edges or nonlinear taper, the angles can also vary with $y$, making a local tangent distinct from a root-to-tip secant. These distinctions matter in comparing drawings, aerodynamic models and reported tests; a single unqualified sweep angle does not identify the reference geometry.
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