Knife wedge angle ($\beta$)

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.^[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.^[ref][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:For $s=1\mu \mathrm{m}$, this gives $d\approx 0.601\mu \mathrm{m}$ at $35^{\circ }$ and $d\approx 0.765\mu \mathrm{m}$ 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.