Abstract: In general, in one aspect, a measurement system has measurement instrument having a first and second component. The first component is mechanically coupled to a first point on a shaft. The second component is mechanically coupled to a second point on the shaft. The measurement instrument is configured to generate an electrical displacement signal indicative of a displacement between the first and second components. A processor is in data communication with the measurement instrument, and the processor configured to: receive the displacement signal from the measurement instrument; receive a velocity signal indicative of a velocity; and based on the displacement signal and the velocity signal, produce an electrical power signal indicative of at least one of a torque applied to the shaft, or a power applied to the shaft.