The Geometry of Ships

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56 THE PRINCIPLES OF NAVAL ARCHITECTURE SERIES these spaces is an important aspect of the design of any ship, so that it meets its capacity objectives with respect to both mass and volume of each type of cargo as well as overall mass and center of gravity when fully loaded. The subdivision also plays a major role during loading and unloading, to ensure that freeboard and longitudinal strength criteria are met throughout the operations. In practice, a large majority of partitions lie on planes parallel to the principal coordinate planes of the ship: • decks on horizontal planes • transverse bulkheads (often referred to simply as “bulkheads”) on transverse planes • longitudinal bulkheads on planes parallel to the centerplane. Most compartments are therefore bounded by orthogonal planes on most of their sides; but most have at least one face that is a portion of the curved hull surface. In rare cases, curved surfaces are involved as interior partitions; for example, in some liquefied natural gas (LNG) carriers, the cargo is contained in spherical insulated tanks. Subdivision is fundamentally a solid modeling problem: taking a solid region (the interior of the ship) and subdividing it into smaller solids (the compartments). In almost all cases, a compartment can be defined as the Boolean intersection of the ship’s interior volume with a simple rectangular solid aligned with the axes. (A different form of subdivision is breaking a ship down into units or modules for construction purposes.) 13.3 Compartment Volumes and Centroids. In the analysis of capacity, the primary geometric quantities of interest are the volumes and centroids of the individual compartments. Values are most often required for the compartment filled to capacity, but there may be a need to evaluate them for partially filled compartments, up to an arbitrary waterline level Z. These quantities are calculated by any of the volume calculation methods discussed in Section 9.4. 13.4 Dry Cargo Capacity. Dry cargo spaces have capacities that depend somewhat on the nature of the cargo. Such spaces are usually fitted with battens (ceiling) on the inside of frames, and are also restricted somewhat by the intrusion of other structural members; for example, beams under the overhead deck, or stiffeners on a bulkhead partition. Such encroachments have slight impact on the volume available for a granular bulk cargo, but interfere significantly with stowage of cargo packed in crates, bags, bundles, and bales. Consequently, a distinction is made between: grain capacity: the molded volume of the compartment, less a small deduction for volume of included structure bale capacity: the volume of the compartment inside the batten line, and below the deck beams Dry cargo capacities are often calculated in terms of the stowage factors of various cargoes. Stowage factor is an inverse effective density (cubic meters per ton), taking into account packing fraction as well as the inherent solid or liquid density of the material. 13.5 Tank Capacity and Contents. Tanks are compartments used for carrying fluid consumables (fuel oil and fresh water), fluid cargoes, and waste water. A tank’s full capacity is basically its volume, less the volume of any structure, piping, etc., interior to the tank. A tank that has significant interior obstructions can be assigned a “permeability,” usable volume / total volume of the space. For any contents besides water, allowance must be made for thermal expansion. For oil, this is a deduction of typically 2 to 3 percent of the tank volume. (Of course, water expands too, but the difference is that an overflow of water is relatively harmless.) During loading and operation, it is necessary to know the fullness of each tank. Various devices are used to measure the location of the free surface in a tank. A pressure gauge at the bottom of the tank is the simplest method; this provides a direct indication of the height of the free surface above the gauge. The hydrostatic pressure in the tank is g(Z z g ), where is the density of the tank contents, g is acceleration due to gravity, Z is the free surface level, and z g is the vertical coordinate of the pressure gauge. Other methods involve sonic sensing of the free surface height, or lowering a float until it reaches the surface. In some cases, there may not be an accessible location that allows a vertical measurement for all possible levels in the tank. In that case, a tube may be provided inside the tank to guide a sounding chain. Tank capacity tables or charts must be developed that relate the volume and centroid of the tank contents to the measurement method. Ullage is a term for the empty space in a tank, above the surface of the fluid, or the vertical extent of this space. Ullage tables express the tank capacity as a function of ullage rather than depth of fluid. 13.6 Tank Stability Effects. When a vessel changes attitude (heel and trim), the liquid in a partially filled tank shifts to a new equilibrium position, taking a new shape (while maintaining its volume and mass). Therefore, its center of gravity shifts in a complex way depending on the shape of the tank. This shift of center of gravity has important stability effects that go under the name of free surface effects. For large attitude changes, calculation of free surface effects requires treating the complete tank as a solid at a specified attitude, and solving for the free surface height that makes the solid volume below the free surface equal to the current volume contents of the tank. For small attitude changes, there is a useful linearized approximation similar to initial stability (equation 106). Free surface effects are properly accounted for by treating the liquid mass as if its vertical center is at a metacenter located above the center of gravity of the liquid at a distance (metacentric radius) I/V, where V is the volume of liquid and I is the moment of inertia of the free
THE GEOMETRY OF SHIPS 57 surface about a longitudinal axis (for heel) or transverse axis (for trim), through the centroid of the free surface. As in initial stability, the metacentric radius is generally different for heel and trim. The metacentric radius vanishes if the tank is either empty or full, because there is then no free surface. 13.7 Container Capacity. Today, a great deal of maritime freight is carried in containerships loaded with standard containers. The modular nature of the cargo is a profound driver of the geometry of these ships. The starting point for a design will generally be a stack of the requisite number of containers with minimum clearances between them. Then, as the hullform is developed around the envelope of the containers, it is critical to check lower outboard corners to be sure they are inside the hull surface and framing. The three most common container sizes (stacking dimensions, length width height) are: 20-foot: 6.096 2.438 2.591m 40-foot: 12.192 2.438 2.591m 45-foot high cube: 13.716 2.438 2.896m, but 48- and 53-foot containers are also in use. Ship capacity is often stated in terms of “twenty-foot equivalent units,” abbreviated TEU; this is the capacity for one standard 20-foot container. Forty- and 45-foot containers are both considered as 2 TEUs, and container height is not taken into account in this measure. REFERENCES Abt, C., Birk, L., and Harries, S. (2003). Parametric Hull Design: The FRIENDSHIP-Modeler. Intl. Conf. on Ship and Shipping Research. NAV 2003, Palermo, Italy. Bai, Yong. (2003). Marine Structural Design. Oxford: Elsevier Science Ltd. Bartels, R. H., Beatty, J. C., and Barsky, B. A. (1987). An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Los Altos, California: Morgan Kaufmann. de Berg, M., van Kreveld, M., Overmars, M., and Schwarzkopf, O. (2000). Computational Geometry Algorithms and Applications. Berlin: Springer. de Boor, C. (1978). A Practical Guide to Splines. New York: Springer. Couser, P. (2006a). Selecting a Suitable Hull Definition Package. The Naval Architect, April 2006, 42–46. Couser, P. (2006b). Selecting the Optimum Hull Definition Package. The Naval Architect, May 2006, 6–10. Couser, P. (2006c). Selecting an Optimum Hull Definition Package. The Naval Architect, July/August 2006, 66–70. Faltinsen, O. M. (1990). Sea Loads on Ships and Offshore Structures. Cambridge: Cambridge Univ. Press. Farin, G. (1999). Curves and Surfaces for Computer Aided Geometric Design (5th ed.). San Francisco: Morgan Kaufmann. Faux, I. D., and Pratt, M. J. (1979). Computational Geometry for Design and Manufacture. Chichester, U.K.: Ellis Horwood Ltd. Galli, A. M., and Qualich, G. (1997). Experiences in Numerical Fairing of Hull Surfaces. Intl. Conf. on Ship and Marine Research (12th ed.). NAV97, Sorrento, Italy. Gibbons, A. (1985). Algorithmic Graph Theory. Cambridge: Cambridge Univ. Press. Gillmer, T. C., and Johnson, B. (1990). Introduction to Naval Architecture. Annapolis: Naval Institute Press. Hoffmann, C. M. (1989). Geometric and Solid Modeling: An Introduction. San Mateo, California: Morgan Kaufmann. Kikuchi, N. (1986). Finite Element Method in Mechanics. Cambridge, U.K.: Cambridge Univ. Press. Kilgore, U. (1967). Developable Hull Surfaces. Fishing Boats of the World, Vol. 3. New York: United Nations F.A.O. Knupp, P., and Steinberg, S. (1994). Fundamentals of Grid Generation. Boca Raton: CRC Press. Kreyszig, E. (1979). Advanced Engineering Mathematics (4th ed.). New York: John Wiley & Sons. Kreyszig, E. (1959). Differential Geometry. Toronto: Univ. of Toronto Press. Kuo, C. (1971). Computer methods for ship surface design. London: Longman Group Ltd. Lamb, T. (ed.) (2003). Ship Design and Construction. New York: SNAME. Lamb, T. (1995). Shell Development Computer Aided Lofting — Is There a Problem or not? J. of Ship Production. Vol. 11, No. 1, 34–46. Larsson, L., and Eliasson, R. (2000). The Principles of Yacht Design (2nd ed.). London: McGraw-Hill. Larsson, L., and Raven, H. C. (2009). Resistance. In: Paulling, J. R., (ed.), Principles of Naval Architecture: The Series. Jersey City, New Jersey: SNAME. Letcher, J. S. (1972). A New Approach to Numerical Fairing and Lofting. Marine Technology. Vol. 9, No. 2, 223–230. Letcher, J. S. (1993). Lofting and Fabrication of Compound Curved Plates. J. of Ship Research. Vol. 37, No. 2, 166–175. Letcher, J. S., Shook, D. M., and Shepherd, S. G. (1995). Relational geometric synthesis: Part 1 — Framework. Computer-Aided Design. Vol. 27, No. 11, 821–832. Moore, C. S. (2009) Intact Stability. In: Paulling, J. R., (ed.), Principles of Naval Architecture: The Series. Jersey City, New Jersey: SNAME. Mortenson, M. E. (1995). Geometric Transformations. New York: Industrial Press. Mortenson, M. E. (1997). Geometric Modeling (2nd ed.). New York: John Wiley & Sons. Newman, J. N. (1977). Marine Hydrodynamics. Cambridge (Mass.): M.I.T. Press. Nolan, T. J. (1971). Computer Aided Design of Developable Hull Surfaces. Marine Technology. Vol. 8, No. 8, 231–242.
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Page 92 and 93: Index Terms Links seakeeping 2 31 3
Page 94 and 95: Index Terms Links surfaces (Cont.)
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The Geometry of Ships

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