Page 36: of Maritime Reporter Magazine (May 15, 1974)

Ship Characteristics— eludes the curves of form, the bon- jean curves, trim calculations and a static bending' moment evalu- ation. In addition, the floodable length calculation and large-angle stability, both in the intact and damaged condition, are also de- scribed. All of these, and any other calculations requiring offsets or form definition, can be performed using as input the mapping co- efficients. It will be shown how, instead of performing numerical in- tegrations of curves defined iby off- sets, one can proceed as follows: '1. Apply conformal mapping tech- niques to determine a close fit to the section shapes up to the deck. 2. Hence, determine the mapping coefficients that define the sections. 3. Finally, compute analytically the area or centroid of each section to any waterline using the mapping coefficients.

The quasi-static calculations in- clude the effect of stationary waves on stability (intact and damaged), floodable length, and bending mo- ment and shear calculations. The quasi-static wave can be a tro- choidal wave, a sinusoidal wave or an irregular wave of any amplitude, phase and length.

The hydrodynamics category in- cludes the added mass and damp- ing coefficients for both vertical and lateral oscillation at finite and infinite frequencies which are necessary inputs for all ship motion and maneuvering calculations, as well as for determining the pressure distribution over the hull due to ship motion.

The pressure distribution in waves is a necessary input for the fourth category, i.e., the structural analysis of the ship using finite ele- ment techniques. In addition, the conformal mapping provides a geo- metric representation of the ship surface which is required for the generation of the mesh of nodal points to define the elements on the surface.

Conformal mapping representa- tion o'f ship lines, because of its concise form, is well suited for mini- computer systems placed on board many of today's ships. The moni- toring of loading and unloading of tankers, and a heavy weather dam- age avoidance and guidance sys- tem, are two on-board systems presently being introduced which use conformal mapping representa- tion as a data base.

The above described the more widely useful possible applications of conformal mapping, but it by no means includes all possibilities. For example, problems such as slam- ming pressures are also related to hull form, which, in turn, can be defined by the mapping coefficients.

It is intended therefore to use the coefficients as the basic data bank stored in the computer for the pur- pose of all ship calculations requir- ing ship form definition.

The introduction of the mini- computer to the commercial world has opened up a new larger scope for improvements and sophistica- tion of navigational aids in both

May 15, 1974 calm and high seas, as well as auto- mated control of ship loading, un- loading and stability, safety and control equipment, engine room monitoring and others.

In order to make such systems economically attractive to the ship owner the emphasis has been shift- ed to advances in software, i.e., computer programs and input-out- put information, rather than com- plicated expensive hardware which is not easily accessible to expert service due to ship schedules. One of the major considerations in the development of such systems is the limitation of computer core size to a minimum, as the cost of core can often determine the economical feasibility of the entire system. As mentioned before, with emphasis being on software, the ability to put the size of the programs and the input data required to operate the system without affecting the over- all efficiency and accuracy of the results is an absolute necessity.

Two specific applications of con- formal mapping coefficients input for on-board ship systems are 1. a static condition for monitoring stress and stability while loading and unloading of tankers, and 2. a dynamic application such as Heavy

Weather Damage Avoidance and

Guidance system. Other applica- tions in areas such as weather rout- ing, automatic loading control of tankers, and damage stability con- trol are presently being developed.

Conclusions

In the preceding presentation, the authors attempted to introduce the reader to conformal mapping tech- niques as well as to illustrate nu- merous new applications to ship system design in which it can be used.

The purpose of the paper is two- fold : 1. To present a tool of ultimate great potential in ship system de- sign. 2. To extend current practices using that tool to include new im- proved design procedures,, and new onnboard systems.

As a tool in ship design, the method presented is a suggested alternative to currently available techniques, a new approach that does not change the end product.

Though some distinct advantages of this method have been cited throughout the paper, the authors are naturally aware of its possible shortcomings, particularly the com- plexity of the mathematics required to generate the mapping coefficients in comparison to the simple nu- merical integration approach cur- rently used.

One of the great advantages of the approach is the generality of its use and the possibilities of explor- ing new design procedures. Al- though a rather comprehensive treatment of the use of conformal mapping in ship design is illustrat- ed in Figure 1, it is felt that other applications not mentioned exist as well. Such cases may include wet- ted surface and shell expansion calculations, the hydrostatic aspect of launching calculations or the definition of the lower portion of the hull as required for slamming pressure prediction. Once a physi- cal understanding of the -mapping coefficients is acquired, the impact on preliminary ship design may be considerable. When designers learn to work directly with the coeffici- ents, the full potential of the meth- od may be realized. This in turn will completely justify the adoption of the approach as a standard tech- nique for most ship calculations.

The accuracy and adequacy of the method have been proved be- yond a doubt, and the ability to store ship data bank on a minimum size core computer may be found very attractive to users utilizing their own small or mini-computers or time-sharing services.

It seems fair to conclude that this particular technique of mathemati- cal hull line representation is of rather general usefulness in ship system design. However, like any other tool, one should use it as a means for an end and properly se- lect its applications so as to improve current techniques rather than sim- ply to adopt it as a mathematical exercise.

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