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February 2003

Article selected from our quarterly magazine dedicated to the largest and most luxurious boats with information, interviews, technical articles, images and yachting news



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Article by
Angelo Sinisi


As I said in the previous article, if the project-problem data (volume, weight, speed) are such to warrant a round bottom, from a hydrodynamic point of view, a ship designer must have the following fundamental objectives:

  • achieving a certain speed, given among the project initial data, with the least "expenditure" of power possible;
  • ensuring good sea-keeping;
  • ensuring good static and route stability as well as good handling.
The aim to focus on in determining the geometric characteristics of the ship's bottom is that of meeting the requirements of the project theme with the least displacement (weight) possible.

Care must be taken not to misunderstand and/or consider obvious, if not futile even, the above affirmation. "Meeting the requirements" means proceeding with equilibrium, proportioning at the right pace, calculating with due safety margins. "The least possible displacement" is the compromise between the various often contrasting needs, called for by the theme, avoiding the use of volumes and machinery as a result of this compromise that do little or nothing to meet the requirements of the theme itself.


Fig. 1 - Systematic series

Nordstrom methodical series

Series 63 methodical series

Series 64 methodical series

SSPA methodical series

NPL methodical series

Limiting displacement does not mean "saving" in the realisation of the project, but not "wasting" volumes, areas and weights, obviously without skimping on safety, a fundamental quality at sea. In fact, reducing the weight of a boat for the purposes of resistance to progress (speed) and/or for cost purposes, at times leads to a decrease in the thickness of the planking or the structures, while still remaining within or even reaching the maximum limit for permitted vibrations, there is consequently a lesser margin of structural safety, which is by far more serious than having a little extra weight, which is not a synonym of "waste". Therefore, after having set weight and volume, the designer must optimise the elements on which the ship's hydrodynamic behaviour depends, that is the bottom (nude hull and additions) and the propeller, giving them the best combination possible.

Forecasting a ship's hydrodynamic behaviour while still at the design stage still presents considerable difficulties today. The choice of the bottom for the ship being designed may be arrived at through various methods. Using Systematic Series bottoms (see Fig. 1) experimented by several Naval Craft such as:

  • the Taylor Series, by Admiral Taylor at the Experimental Model Basin in Ashington
  • the 60 Series by F.N. Todd
  • the 64 Series
  • the NPL Series
  • the Nordstrom Series
  • the 63 Series
  • the SSPA Series
The Taylor series (see Fig. 2) is still today held to be the most complete research into the effects on Pe (effective power) with variation in some coefficients and significant ratios with an original bottom. The data were presented (see Fig. 3) as a residual resistance curve, measured in pounds per ton of displacement, based on the longitudinal fineness coefficient Cp, of the displacement-length ratio D / (0,01 . Lwl)³; each diagram is valid for width-draught and speed-length ratios. Taylor examined eighty models and from the total resistance values obtained from tests on these models, he subtracted the friction resistance calculated according the Tideman formula.

Fig 2 - Taylor sistematic series model

With direct drawing of the same, using mathematical systems such as regression analysis. This method is used when it is necessary to resolve a very particular problem and it is not possible to refer to a similar bottom. In this case, however, it is almost necessary to start out with a systematic series, obviously depending on the skill of the designer.

Fig 3 - Taylor sistematic series type graphics

Making use of existing ships' bottoms, adapting them to the displacement and length desired. I will try to give a simple explanation of the residual or wave resistance, arrived at using the above methods.

A body that moves on the undisturbed surface of the water produces a wave system. This system is generated by the field of pressure around the body and the energy possessed by the waves is given to them by the body itself. This transfer of energy from the body to the surrounding system generates a directional force opposite to that of the movement, which is our wave resistance.


Fig. 4

Schematic diagram of the wave system generated by the bow and the stern

Fig. 5

Sketch by W. Froude of the wave train characteristic of the bow

Fig. 6

Graphics of the progress of the Wave Resistance Ro, where the positions of the troughs and the crests are highlighted

There are two kinds of wave systems generated by ships, diverging ones that form laterally to the ship that have inclined crests with respect to the ship's symmetrical level and transversal ones that form at the bulwarks of the ship that have perpendicular crests with respect to the centreline (see Figs. 4 and 5). This wave system, divergent and transversal, is generated by both the stern and the bows. The interference between these waves systems creates the characteristics ups and downs based on speed-length ratio in the wave resistance curve. Considering only the transversal waves, in a simplistic but indicative way, it can be said that wave resistance is given by the difference between the pressures at the bow area, in the direction bow-stern, and the pressures at the stern area in the direction stern-bow. While the bow-stern pressure system increases constantly with the increase in , the stern-bow pressure system is variable (in other words it can be positive or negative) depending on the interference between the wave systems at bows and stern. There will therefore be a crest in the wave resistance when there is a (wave) trough at stern and vice versa a trough in the wave resistance when there is a (wave) crest at the stern (see Fig. 6). Based on the above, we can see that a ship's wave resistance depends on the speed, length and shape of the bottom, in other words on the penetration angle of the water lines and the distribution of volume in a longitudinal, transversal and vertical direction.

Fig 7

The bulbous bow (see Fig. 7), as it modifies the penetration angles and volume distribution, represents an effective means for reducing wave resistance. So the bulbous bow's own wave system interferes with the ship's wave system. The longitudinal position of the bulbous bow defines the interference phase, while its volume determines the width of its wave system.

A certain shape of bulbous bottom is excellent only in design conditions. Usually at low speeds the effect of the bulbous bottom is negative, while as the Froude number (FN) increases it becomes positive and increases up to a maximum value, from this point on, for FN, which tends to the infinite, the bulbous effect tends to zero.

Thus the decision for or against the adoption of a bulbous bow depends on an analysis of costs and benefits. However, it can be affirmed that the good hydrodynamic shape of a bottom with moderate wave formation does not usually need a bulbous bow, while this is necessary in the presence of a considerable wave formation due to the poor "starting" of the bottom shapes. Obviously "starting" does not mean geometrically but hydro-dynamically. In fact if geometric starting were sufficient, a computer with starting programmes for bottoms would have resolved all the problems. But unfortunately good hydrodynamic start up depends on the skill and experience of the designer and the specialist in naval architecture (a subject that includes the study of boat statics and the dynamics).

In fact the starting of shapes creates pressure and depression components that act on the bottom and which generate a rise or lowering in the water level, when the value of the pressure undergoes a positive or negative variation. The water lines that define the bulb towards the prow must have a well started hydrodynamic profile, to avoid separation of the fluid filaments. The upper part of the bulb must be connected with the body of the ship well so that the water, flowing over the body of the bulb itself, can interfere favourably with the residual bow wave. For each bulbous bottom, there is an optimal condition, corresponding to a speed that can be determined experimentally. From all this it is evident that the influence of the bulb must not be considered limited to the bow wave formation, but that it extends to the so-called separation or shape resistance, that is the viscous type resistance that, together with wave resistance, is referred to in the term residual resistance, including pressure viscous resistance, resistance due to vortexes, cavitation, etc.

Moreover, an opportunely started bulb, due to its high damping characteristics, considerably reduces the bow acceleration due to pitching and therefore has a positive effect on sea keeping. Optimum choice of a round bottom depends on the skill of the designer in achieving the best compromise between weight, volume and speed. As always the designer's ability is fundamental, from whose skill in realising the best compromise between weight, volume and speed depends the optimum choice of a round bottom.