Moody Revisited: Least-Squares Solutions of the Union Jack Surface Plate Measurement Method

For the calibration of surface plate, the classical Moody method is still commonly used. In this method the straightness of a number of lines over a surface plate in a union-jack configuration is measured and combined into a flatness measurement. The measurement of the two center lines is used to determine so-called closure errors. A shortcoming of this method is that it gives an ambiguous value for the central height and that the measurements of the central lines are not involved in the evaluation. This research shows how the lines can be incorporated in the measurement evaluation in a least-squares sense. This gives a measurement redundancy leading to an 18% reduction in the uncertainty. Also, it is shown that a further reduction in the uncertainty is possible when using the gravity vector as a common reference, as can be done when using electronic levels. A least-squares evaluation of measurements taken in this way gives an even further redundancy, leading to a reduction in the uncertainty of 29% relative to the traditional evaluation according to the Moody method. This is illustrated with an actual measurement example and additional Monte Carlo simulations.