The mathematical treatment of grid-survey data for land levelling
Netherlands Journal of Agricultural Science
2. Sources of errors and their elimination 1. Introduction 2.1. The mathematical error in grid squares where cut changes to fill 2.2. Elimination of the mathematical error in grid squares where cut changes to fill 2.3. The evaluation of volumes of cut and fill in grid squares traversed by the plot's boundaries 2.4. Some practical examples 3. Tentative comparison between calculated and true volumes Summary The accuracy of three methods of calculating the volumes of earth movement for land
... ng on account of grid-point data is investigated, viz. of the summation, four-point and stereometric method. Two sources of errors appear to be responsible for obvious inaccuracies caused by the applica tion of the summation method : a. a systematic error in grid squares, where cut changes to fill ; b. a statistical inaccuracy when evaluating the volumes of earth movement in grid squares trav ersed by the boundaries of the plot to be levelled. It is demonstrated that the four-point method is subject to a similar deficiency as mentioned under a, though to a much lesser degree than the summation method, but does not show the deficiency mentioned under b. The stereometric method appears to be free from both deficiencies. In grid squares with all corners either in cut or in fill and not traversed by the plot's boundaries, each calculation method gives the same results. When the deficiency mentioned under b is eliminated, all three calculation methods give the same earth-work balance for a plot to be levelled. The stereometric calculation as such being too complicated for practical application, it is found to be practicable to correct the summation method in such a way as to obtain results which are identical to those of the stereometric method, especially, when tabular aids or nomographs are used and the survey is made with the aid of a triangular net instead of a net of grid squares. When the number of grid squares, where cut changes to fill, is comparatively small, results iden tical to those of the four-point method are obtained more quickly by applying a correction to the summation method than by applying the four-point method as such. The various calculations with the aid of corrections are demonstrated by practical examples. A tentative comparison is made between calculated and true volumes. The stereometric calculation appears to give the closest approximation.