It frequently happens during the design of a ship that unexpected requirements which were not foreseen necessitate a change in dimensions without changing the coefficients of form. Examples are an increase in breadth to provide greater stability, a decrease in design draft to allow entering a port with restricted water depth, or an increase in length to reduce wavemaking resistance. If this should happen after preliminary lines are faired, it seemingly requires that a completely new set of lines be drawn and faired. However, by making systematic changes in the offsets, it may be possible to accomplish the desired transformation without disturbing the fairness of the lines, and without necessitating complete recalculation of the curves of form.

For example, a simple respacing of body plan stations leads to an elongation or shortening of the lines at constant breadth and draft, with displacement changing in direct proportion to the station spacing; the form coefficients , , , and will not change, and the fairness of lines will be preserved. Of the curves of form, changes will be experienced only in those quantities which depend upon length and displacement, including . Correspondingly, an increase in waterline spacing leads to a proportionate change in displacement with no change in , , , and and . Those curves of form which are dependent upon displacement and draft are the only ones which will change. Similar conclusions are reached insofar as changes in buttock spacing that is, changes in halfbreadth are concerned.

The combined effect of two or more of such changes is multiplicative. For example, if the length of the vessel were to increase 10 percent by an increase in station spacing, the breadth were to increase 5 percent by an increase in halfbreadths, and the draft were to decrease 8 percent by a reduction in waterline spacing, the resulting volume of displacement would be obtained from , the initial volume of displacement, by,

A new body plan, waterlines plan and profile could be drawn directly, in which new longitudinal distances are obtained from old longitudinal distances by new halfbreadths are obtained from old halfbreadths by ; etc.

Changes in the more important curves of form, would give,

Wetted surface, which depends upon girthed distances, does not vary in a simple manner and would have to be recomputed for the transformed design.

Methods have been developed (Rawson & Tupper, 1983) to estimate modifications to the geometrical quantities on the basis of partial derivatives. Inasmuch as these methods assume infinitesimal changes in the independent variables, L, B, etc., they may lead to inaccuracies in practical use. On the other hand, direct calculations to find the transformed quantities are by their nature both exact and correct, and therefore they are recommended.

A traditional and practical way of shifting the LCB of a new design without changing displacement is known as the method of swinging stations. Figure A

shows the sectional area curve of a ship and the centroid of the area under the curve, the latter having been found from both axes ( and ). If the centroid now be moved forward (or aft) a distance , and a straight line be drawn through the shifted position and original base, it will establish an angle by which all points on the curve may be similarly shifted so that the desired shift of LCB occurs. Any original body plan station such as station 3 must then be shifted by distance . This allows one to find the shift of any offset (height or halfbreadth) forward or aft directly from the transformed sectional area curve. Hence, the waterlines and profile views on the lines plan may be redrawn without refairing being required. From the redrawn waterlines and profile a new body plan, with equally spaced stations, may then be constructed.

A somewhat similar transformation can be done to the separate ends of a sectional area curve with some parallel middle body if one wishes to change the fullness of the design. Let us suppose the fore body of a given sectional area curve has a prismatic coefficient of but it is desired to increase this by respacing stations to gain more displacement. The new fore body prismatic is to be . Thus . Then it can be shown (Lackenby, 1950) that if is the dimensionless distance from the left-hand axis of the curve, where lies between 0 and 1.0, the shift forward to give the required new prismatic coefficient of the forebody is obtained from,

or

This procedure, which is known as the one-minusprismatic rule, is illustrated in Figure B

(Lackenby, 1950. Having modified the sectional area curve in the indicated way, body plan stations must now be shifted the indicated amount. Thus, the waterlines and profile views in the entrance may be redrawn, with a new body plan for the fore body to suit equally spaced stations. It should be noted, however, that having first transformed the forebody a similar transformation of the afterbody in general leads to a combined longitudinal center of buoyancy of the entire ship which will differ from that of the basic ship before the transformation.

Soding, et al (1977) show an extensive transformation of an existing containership design to a design of widely different particulars nofollowing generally the methods of Lackenby (1950).

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• Developable and Straight Frame Lines - 2009-05-02 - 01:27:07
• Offsets In Ship Geometry - 2009-05-02 - 12:10:24
• Developing a Set of Lines In Ship Geometry - 2009-05-01 - 01:34:25

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