Why not just balance it on knife edges?

A question I hear regularly: why an instrument at all, when rotors were balanced on knife-edge prisms long before any electronics?

For some rotors that still works. Put the rotor on the prisms: the heavy spot turns down under gravity. Add a correction weight on the opposite side until the rotor rests indifferently in any position. That is static balancing — and for a narrow, disc-like rotor it can be enough.

Now take a long rotor with two equal unbalanced masses, M1 and M2, sitting in different planes along the length — on opposite sides of the axis. At standstill only gravity acts, and the masses balance each other: on knife edges this rotor looks perfectly balanced.

Spin it up. Centrifugal forces Fc1 and Fc2 appear — equal in magnitude, opposite in direction. But they are applied at different points along the shaft, not on one line, so they do not cancel each other. Together they form a moment that rocks the rotor once per revolution — which is why this is called couple (moment) unbalance. The uncompensated forces land directly on the bearing supports, can exceed the design loads considerably, and shorten bearing life.

This unbalance exists only in rotation. It is physically impossible to detect — let alone remove — on knife edges. To correct it, you need two weights creating a moment equal in magnitude and opposite in direction to the unbalance moment. They do not have to sit exactly opposite M1 and M2, nor match them in size — what matters is the moment they create.

In the general case M1 and M2 are not equal, so a real rotor carries a combination of static and couple unbalance — dynamic unbalance. And the theory here is clean: for a rigid rotor, two correction weights spaced along the length are necessary and sufficient — they compensate both the net centrifugal force (the static part) and the moment (the couple part).

That is exactly why Balanset-1A measures at two bearings and corrects in two planes: correction masses and angles are calculated from how the rotor behaves in rotation, not from how it hangs in gravity.