Supersonic leading edge (source code)

= Supersonic leading edge
{title2=$M_n>1$}

A \b[supersonic leading edge] has an incoming edge-normal flow component exceeding the <speed of sound>. For a straight planar edge at <leading-edge sweep angle> $\Lambda_{\rm LE}$ in the convention of <normal Mach number for a swept leading edge>, the criterion is
$$
M_n=M|\cos\Lambda_{\rm LE}|>1.
$$
It classifies a direction of the incoming <velocity>, rather than asserting that the same local <Mach number> holds over the whole <aircraft wing>.<Introduction to Aircraft Performance and Static Stability by Earll Murman>[PDF p. 9, Basic Sweep Concept, edge-normal Mach classification]{ref}

For an original example with $M=2$ and $\Lambda_{\rm LE}=30\,{}^\circ$, $M_n=\sqrt3\simeq1.732$. The condition can persist at larger sweep: at $M=2.2$, even a $60\,{}^\circ$ leading-edge sweep gives $M_n=1.1$: large sweep by itself does not establish a <subsonic leading edge>.

For $M>1$, the <Mach angle> is $\mu=\arcsin(1/M)$. On an aft-swept half-wing the edge's angle from the downstream streamwise direction is $\theta=90\,{}^\circ-\Lambda_{\rm LE}$. Thus
$$
M_n>1\quad\Longleftrightarrow\quad\theta>\mu,
$$
so the leading edge lies outside the downstream <Mach cone> from its apex in this ideal geometry. At $M=2$, $\mu=30\,{}^\circ$ whereas the example edge has $\theta=60\,{}^\circ$. Equality is the sonic boundary and belongs to neither strict inequality.

The classification helps select a high-speed flow model. It does not determine <shock wave> strength, <drag> or <flow separation> without the section shape and operating conditions. A measured <pressure coefficient> distribution or flow visualization can test those additional predictions; naming the regime alone cannot.