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
If you would like to see another bulletin created regarding a specific topic,
please email Creative Systems, Inc. at firstname.lastname@example.org.
Copyright (C) 2011
Creative Systems, Inc.