| ACCURACY CONSIDERATIONS IN SELECTING STATION SPACING |
| For displacers
(hulls), a minimum station density is enforced in order to prevent
accuracy problems resulting from trapezoidal integration of the section
area curve. The maximum allowed station spacing is 5% of the overall
length, which, for normal area curves at maximum draft leads to displacement
volume errors on the order of 0.1%. It is left to the user to decide
whether greater accuracy is required. Decreasing the station spacing
by a given factor can be expected to reduce the volume error by the
square of that factor. In some conditions of loading, the number stations which are actually immersed may be significantly fewer than the total number of stations, leaving the area curve to be represented by a lesser number of points. This, of course, results in more error in terms of the present volume, but not necessarily more error relative to the volume at normal draft. Increasing the number of stations always improves accuracy, but at some point, the improvement obtainable by adding any more stations will be less than the errors from other sources, such as the approximations involved in the station curves themselves. Centers and surface properties are also affected by station spacing. Waterplane properties, especially the longitudinal center and moment of inertia, are commonly less accurate than volumes and volume centers. A particular source of inaccuracy in waterplane properties is in determining the outline of the interpolated end of a waterplane - - that area which occurs after the last station cut by the waterplane but before the end of the hull. This area is normally approximated as a triangle (corresponding to a waterplane which narrows to a point). However, square-ended waterplanes occur when the bottoms of the stations in the region of the waterplane ending are parallel to the waterplane (e.g. no deadrise in the bottom combined with a zero heel angle). In this case, the blunt waterplane ending is determined by extrapolating the width of the waterplane at the neighboring stations. Nevertheless, the accuracy of this procedure is not as good as that which results from adding stations (reducing the size of the area which must be determined by extrapolation). This effect is most noticeable with barges which have no deadrise in one or both of the rakes. It may be necessary to use 10 or more stations within the rake in order to produce LCF and KM of sufficient accuracy to appear as smooth curves when plotted as a function of draft or displacement. Tank volumes, centers and their surface properties are calculated using the same procedures used to find the displacement, center of buoyancy and waterplane properties of the hull. Therefore, the same accuracy considerations apply to containers which apply to the displacer parts. The maximum station spacing for tanks is the same as for hulls. Therefore, a tank whose length is one 5% of the length of the hull could have as few as two stations. Depending on the shape of the tank, its level of loading and the attitude of the surface, the error involved could be quite substantial in terms of the tank itself -- though it would not necessarily be significant in terms of the overall ship. With only two stations where their areas are very dissimilar, the volume error could be as high as 20%. Therefore, a good practice is to ensure that major components in all parts have at least four stations, reducing the error liability (due to station spacing) to about 5%. If accurate tank properties are required independent of the tank's size relative to the size of the ship, then the overall length of the tank itself should be used as the guide in selecting the station spacing. The usual process of creating a tank component within a hull involves the "FIT HULL" process which provides the resulting component with stations at the locations of intervening hull stations (in addition to its own end stations). If more stations are required, the SPACING statement can be included within the CREATE command. |
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