= Knife wedge angle
{title2=$\beta$}
The <knife wedge angle> $\beta$ is the included angle between the blade faces meeting at a cutting edge. It is a property of the edge geometry, distinct from the <knife clearance angle> produced by orienting the knife relative to the specimen. A final bevel can have a different angle from the broader blade body, so identify which faces define a quoted angle.<Knife Angle in Microtomy by Charles W. Scouten>[Ideal versus compromise: final bevel and cross-sectional wedge]{ref}
In <ultramicrotomy>, the wedge angle affects the tradeoff between reducing <section compression> and supporting a durable edge. Manufacturer descriptions distinguish $35^\circ$ and $45^\circ$ <diamond knives>; the lower-angle family is described as reducing compression. Guidance for polymer and brittle-material sectioning also emphasizes that lower angles leave a more sensitive edge and that some hard materials favor a larger angle.<Ultra diamond knives by DiATOME>[ultra35° and ultra45° descriptions]{ref}<Ultramicrotomy Techniques for Materials Sectioning by Leica Microsystems>[How to prepare high-quality sections of polymers; brittle-material discussion]{ref}
An original geometric comparison makes the difference concrete without pretending to predict cutting forces. On each face of an ideal wedge, mark a point a distance $s$ from the apex. The distance $d$ between those points is the base of an isosceles triangle:
$$
d=2s\sin\frac\beta2.
$$
For $s=1\,\mathrm{\mu m}$, this gives $d\approx0.601\,\mathrm{\mu m}$ at $35^\circ$ and $d\approx0.765\,\mathrm{\mu m}$ at $45^\circ$. The larger angle puts more material between the faces at that distance from the apex. This geometry is not an empirical law relating wedge angle to force, friction or a particular compression percentage.
Changing <knife clearance angle> rotates both blade faces together and leaves their included angle unchanged. Conversely, selecting a different wedge geometry need not mean that the same holder setting gives the same cutting conditions. A meaningful comparison records both angles, specimen material, feed and observed <section compression>. The two angle names should therefore remain separate even when an instrument discussion informally calls either one the knife angle.
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