= Wing sweep
{title2=$\Lambda$}
\b[Wing sweep] describes the inclination of a chosen spanwise line in a <wing planform> relative to the direction perpendicular to the aircraft's longitudinal axis. It must name the reference line: a <leading-edge sweep angle> and a <quarter-chord sweep angle> can differ on the same <aircraft wing>. A <swept wing> therefore needs a reference convention, not just an unqualified angle.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, trapezoidal-planform geometry and sweep definitions]{ref}
Let $x$ increase aft, let $y$ increase from root toward one tip, and define the straight <leading edge> and linearly varying <airfoil chord> by
$$
x_{\rm LE}(y)=x_0+y\tan\Lambda_{\rm LE},\qquad c(y)=c_r+\frac{2(c_t-c_r)y}{b}.
$$
The line at chord fraction $f$ has $x_f(y)=x_{\rm LE}(y)+fc(y)$. Differentiating gives the exact geometric relation
$$
\boxed{\tan\Lambda_f=\tan\Lambda_{\rm LE}+\frac{2f(c_t-c_r)}{b}.}
$$
For $b=10\,\mathrm m$, $c_r=2\,\mathrm m$, $c_t=1\,\mathrm m$ and $\Lambda_{\rm LE}=20\,{}^\circ$, the <quarter-chord sweep angle> is $\arctan(\tan20\,{}^\circ-0.05)\simeq17.43\,{}^\circ$. This <reference-line dependence of wing sweep> is purely geometric.
There is also a useful high-speed approximation. Resolving the incoming <velocity> perpendicular to a swept straight <leading edge> gives the <normal Mach number for a swept leading edge>, $M_n=M\cos\Lambda_{\rm LE}$. Thus $M=0.9$ and $\Lambda_{\rm LE}=30\,{}^\circ$ give $M_n\simeq0.779$. This component is a guide to <compressibility> effects, not an exact prediction of <shock wave> formation on a finite wing with thickness and a <fuselage>.
In a 1947 experiment, <Richard T. Whitcomb> compared unswept wings with forward and backward sweep in the Langley 8-foot high-speed <wind tunnel>. Pressure measurements and wake surveys over <Mach numbers> from 0.60 to 0.96 showed shock-associated changes occurring later for the swept configurations. The reported shifts were not exactly the simple cosine prediction.<An Investigation of the Effects of Sweep on the Characteristics of a High-Aspect-Ratio Wing in the Langley 8-Foot High-Speed Tunnel by Richard T. Whitcomb>[Abstract, test configurations and comparison with the sweep cosine factor]{ref}
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