= Leading-edge sweep angle
{title2=$\Lambda_{\rm LE}$}
The <leading-edge sweep angle> describes the inclination of a <leading edge> relative to a line perpendicular to the aircraft longitudinal axis. On one half-wing, take $x$ positive aft and $y$ positive outward. For a differentiable leading-edge curve,
$$
\Lambda_{\rm LE}(y)=\arctan\left(\frac{dx_{\rm LE}}{dy}\right).
$$
Positive slope denotes aft sweep and negative slope forward sweep in this convention. A coordinate reference must be supplied before the sign has meaning.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, planform coordinate sketch and equation (A-97)]{ref}
For a straight edge on a symmetric wing, let its tip be displaced aft from the root by $\Delta x$ and let $b$ be the full <wingspan>. Then
$$
\tan\Lambda_{\rm LE}=\frac{\Delta x}{b/2}=\frac{2\Delta x}{b}.
$$
For an original example, $b=12\,\mathrm m$ and $\Delta x=2.4\,\mathrm m$ give $\Lambda_{\rm LE}=\arctan0.4\approx21.8014\,{}^{\circ}$. Incorrectly using the full span as the root-to-tip run would give $\arctan0.2\approx11.3099\,{}^{\circ}$. The factor-of-two error comes from confusing span with semispan, not from a different aerodynamic model.
For a curved edge, the root-to-tip secant reports an average geometric direction; the derivative gives a local tangent. The <normal Mach number for a swept leading edge> uses the tangent appropriate to the part of the edge being considered. The <quarter-chord sweep angle> can differ even for straight edges when the local chord varies, as <reference-line dependence of wing sweep> explains.
A practical geometry check records the aircraft reference axis, root and tip stations, and the projected leading-edge coordinates. Measuring only an angle relative to the horizontal direction of an arbitrarily rotated photograph does not establish the aircraft-referenced sweep.
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