Derivation and Guide to the Uncertainty in the Angle Between Two Planes

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Abstract

Coordinate metrologists need to plan their measurements and estimate the resulting uncertainties before data collection in order to achieve needed precisions. We present the mathematical relationship between the calculated angle between two planes, least square fitted from measurements of two surfaces, and the uncertainties in the employed measurements. Various types of measurement uncertainty are considered, including centering error, and instrument, network, and targeting uncertainties. Calculations assume that all uncertainties are small and normally distributed. We also provide a guide to the process of simulating the measurement uncertainties before the measurements are taken in order to plan the measurement and select instruments and tools.