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 are measured and combined to a flatness measurement. The measurement of two center lines is commonly omitted in the evaluation and only used to determine so-called closure errors. These two lines can be incorporated in the measurement evaluation in a least-squares sense, giving an 18% reduction of the uncertainty. 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 a further reduction of 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.