 Wing sweep

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.^[ref]

Let $x$ increase aft, let $y$ increase from root toward one tip, and define the straight leading edge and linearly varying airfoil chord byThe line at chord fraction $f$ has $x_f(y)=x_{\mathrm{LE}}(y)+fc(y)$. Differentiating gives the exact geometric relationFor $b=10\mathrm{m}$, $c_r=2\mathrm{m}$, $c_t=1\mathrm{m}$ and ${\Lambda }_{\mathrm{LE}}=20{}^{\circ }$, the quarter-chord sweep angle is $\arctan (\tan 20{}^{\circ }-0.05)\simeq 17.43{}^{\circ }$. 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, $M_n=M\cos {\Lambda }_{\mathrm{LE}}$. Thus $M=0.9$ and ${\Lambda }_{\mathrm{LE}}=30{}^{\circ }$ give $M_n\simeq 0.779$. 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.^[ref]