= Normal Mach number for a swept leading edge
{title2=$M_n=M\cos\Lambda_{\rm LE}$}
The <normal Mach number for a swept leading edge> is the incoming velocity component perpendicular to that edge divided by the local <speed of sound>. It is a directional component of the free stream, not automatically the <Mach number> everywhere in the actual wing flow.
Let $\mathbf e$ be a unit tangent along a straight <leading edge>, let $\mathbf U$ be the incoming <velocity>, and let $a$ be the <speed of sound>. Vector projection gives
$$
M_n=\frac{\lVert\mathbf U-(\mathbf U\cdot\mathbf e)\mathbf e\rVert}{a}.
$$
For a planar wing with flow aligned with its longitudinal reference direction and <leading-edge sweep angle> $\Lambda_{\rm LE}$, the component along the edge is $U\sin\Lambda_{\rm LE}$. Thus
$$
M_n=M|\cos\Lambda_{\rm LE}|,\qquad M=U/a.
$$
The cosine is nonnegative in the usual sweep range between $-90$ and $90$ degrees. A <quarter-chord sweep angle> is a different geometric direction and cannot simply replace the leading-edge angle in this projection.
For an original example, $M=1.2$ and $\Lambda_{\rm LE}=45\,{}^{\circ}$ give $M_n\approx0.848528$. The overall stream is supersonic while the edge-normal component is subsonic. For $M>1$, the boundary $M_n=1$ occurs at $|\Lambda_{\rm LE}|=\arccos(1/M)$, about $33.5573\,{}^{\circ}$ for $M=1.2$. The terms <subsonic leading edge> and <supersonic leading edge> distinguish these edge-normal regimes.
Using the component as a predictor of an entire finite-wing flow adds assumptions. Thickness, finite span, <angle of attack> and interference with the <fuselage> can all matter. Whitcomb's pressure and wake measurements found that shock-associated changes with sweep did not follow the simple cosine shift exactly.<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>[NTRS author abstract, comparison of observed changes with the cosine factor]{ref} The projection itself is exact for the stated vectors; the reduction of a three-dimensional aerodynamic problem to that single component is the approximation.
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