4.6 Integration of the equations of motion
5.1.1 Model design objectives
Large high speed passenger ferries present a range of technological problems that have either emerged for the first time or have been exaggerated by the increased demands of higher speeds. One of these issues is seakeeping. Poor seakeeping occurs when resonance of motions occurs in combination with significant excitations. The resonant frequency and associated damping ratio of a given boat, although a function of parameters such as speed and loading, does not change greatly under different conditions. On the other hand as the boat speed increases this frequency is encountered (for head seas) in longer waves. For conventional hulls at slow speeds the waves corresponding to the heave and pitch resonant frequencies are generally shorter than the hull length, and the associated heave force and pitching moment are small or even negligible. This is a consequence of cancellation effects when integrating pressures over the hull (at certain wavelengths, where equivalent volumes of the boat may be at wave troughs and wave crests, the net force may be close to zero) and of the decay with depth over a length scale proportional to the wavelength of the non-hydrostatic component of pressure. The wave force for a given wave height will be at a maximum, and equal to the equivalent hydrostatic force, for wavelengths significantly longer than the hull, and any vessel fast enough for this to coincide with its natural frequency has potential for seakeeping problems.
Early development of high speed ferries naturally focused on resistance and propulsion. In terms of meeting contract obligations these problems have been largely overcome, although they continue to be of interest as builders and operators demand bigger, faster, or more efficient vessels, and tighter design margins, in order to secure an advantage over their competitors. On the other hand these vessels have developed a reputation for poor seakeeping, and consequently there is now a greater emphasis on motion prediction in the research activities. There is also a rapidly growing interest in dynamic sea loads and their influence on structural fatigue.
The effect of motions on passengers may be quantified in terms ofmotion sickness incidence
or motion sickness index (MSI), defined by Mandel [65] as “the percent of individuals who would vomit if subjected to motions of prescribed characteristics for a given time intervalt1”,
and discussed also in [66] and [78]. Figure 5-1 shows MSI as a function of frequency and acceleration for sinusoidal vertical motions. This shows the worst range of frequencies to be about 0.06–0.4Hz (0.4–2.5r/s). Unfortunately this coincides with the typical range of natural frequencies for most large high speed passenger ships.
0 1 2 3 4 5 6 RMS vertical acceleration (m/s2) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Frequency (r/s) MSI = 35%, t1= 2 hrs MSI =20%, t1= 2hrs MSI =10%, t1= 2hrs MSI =10%, t1= 4hrs
Figure 5-1: Contours of motion sickness incidence as a function of frequency and vertical accel- eration (based on tabulated data in Mandel [65]).
In addition to passenger comfort is the problem of dynamic structural load and slamming. The high speed of these vessels means that dynamic structural loads and slamming events are likely to be both more severe and more frequent than for conventional vessels. Slamming, as well as introducing very high local stresses, initiates high frequency global vibrations with very low damping, which in turn is associated with high global stresses ([2] and [12], as well as preliminary results of research in progress by Roberts, Watson and Davis at the University of Tasmania). This has serious implications for fatigue, particularly as this type of vessel is generally made of aluminium in order to overcome the increased drag or decreased payload capacity associated with excess structural weight.
The dynamic load and slamming problem is a major concern in the classification of high speed ferries, and the lack of a sufficiently large body of related research has meant that many
of the design rules are extrapolated from research on more conventional types of boats. Naturally in such cases the classification societies have to be conservative in making the rules, while the builders are concerned about unnecessary structural weight and the impact it has in terms of speed reduction, lost payload, or additional propulsive power requirements. Unlike civil engineering construction for example, where the regulatory bodies have a monopoly, there is open competition in the market for boat classification, and therefore the builders and the classification societies both have an active interest in better load prediction and less conservative rules based on accurate and more comprehensive information. The prediction of dynamic sea loads follows as a logical consequence of the computational methods developed in this thesis. However, slamming, if defined as the high local loads that develop rapidly (inertia dominated) when hull surfaces of significantly non-vertical inclination impact with the free surface, accompanied by significant wave breaking, would demand a more customised local analysis that is not directly the subject of the present thesis. Nevertheless the methods developed here have potential application to the prediction of slamming loads, and also to the damping and decay of the higher frequency global modes of vibration which have recently been observed to be initiated by slamming events.
The usual solution to the seakeeping problem is to install a ride control system, either active or passive, which make use of lifting surfaces. Considerable research has already been done and is still being undertaken in the area. However appendages have disadvantages, including additional drag and proneness to damage. In the last few decades designers have been considering alternative hull forms to minimise motions. One such form is the small waterplane area twin hull (SWATH), and, more recently, shapes intermediate between this and conventional hulls (semi-SWATH) have also been tried.
Examples of semi-SWATHs include boats designed and built in Australia by Austal Ships (in Fremantle, Western Australia) and NQEA (in Cairns, Queensland, who have originated theSeajet design built in Denmark), as well as the 128m “HSS” built for STENA in Finland. The Australian built example has been at a scale where an element of speculation has been possible without too much financial risk, as the semi-SWATH treatment in the Austal design is little more than a modest submerged bulbous bow faired into the underwater hull. The HSS however is not only considerably larger than anything else of its type in the world, but it in particular represents a very substantial departure from a conventional hull form, with a significant reduction of waterplane area along the whole hull length and a large submerged bow. However in spite of being the subject of considerable research it has not met the expectations of all observers. In particular this vessel, as well as theSeajetand other vessels without substantial reserve buoyancy above the waterline forward, have shown themselves to be very prone to nose- in incidents in following seas or even during crash stops. This illustrates the overall complexity of the design process, as the consideration of such events involves significant surge inertia terms which are not the subject of the present work. However, there is potential for the computational methods developed here to provide a basis for analysis of these aspects.
The basic premise of the SWATH concept is that a lower natural frequency (due to reduced hydrostatic stiffness for the same or similar effective mass) has associated with it lower accel- erations for a given amplitude of motion. This is partly offset by increased motion amplitudes due to an increased wave force associated with the longer wavelengths at resonance (this will be described in detail in the following chapter), and possibly also due to slightly poorer damping characteristics of SWATH type hull forms. Generally however for high speed vessels there is a significant net reduction in accelerations. Motion sickness incidence is basically a function of acceleration and frequency, but for frequencies near the natural frequency of typical ships in heave and pitch the motion sickness incidence is near its maximum and is only weakly frequency dependent. Therefore a reduction in accelerations will in general improve comfort for passengers. It does not necessarily imply however an improvement in the structural aspects of seakeeping, although global dynamic sea loads and impact velocities in slamming events will probably also be lower. Also a lower natural frequency allows more response time for ride control systems, as well as smaller force requirements.
Obviously, given that conventional boats are still far more common, the seakeeping advan- tages of SWATHs are gained at some sacrifice. The buoyant part of the hull form, being largely submerged, creates smaller waves than conventional hull forms due to its dynamic motions. As a consequence there is less damping near the natural frequencies, and motions may be large. Furthermore the lower natural frequency means that resonance occurs in longer waves, also con- tributing to larger motions. In terms of passenger comfort there is usually still a net benefit, but structural or safety problems may arise. Therefore SWATHs are rarely built without some form of ride control system (although the HSS has hull appendages designed to reduce vertical mo- tions and does operate without an active ride control system). Other disadvantages of SWATHs include sensitivity to load (hence ballast and/or appendages are required, which contribute to drag), higher resistance (although wave resistance is usually less, the frictional resistance and other viscosity related components more than offset any gain), difficulty of manufacture (they tend to have more curved surfaces than conventional hulls), and machinery arrangement is more difficult (because the narrow waterplane restricts free access to the hulls).
The semi-SWATH concept is an obvious opportunity to exploit the positive aspects of both SWATH and conventional hulls, but without a better understanding of which major features of the hull (which is basically an infinitely variable surface) are important, and how they affect global behaviour, there is no guarantee that such a hybrid will be better than either of its antecedents. Fundamental questions include whether to have waterline beam reduction for the whole length of the boat or only for part of the length (for example only for the forward half), whether or not to have a submerged or bulbous bow (and if so the shape, size, and depth), the optimum use of flat surfaces, curved surfaces, and chines, design for slamming, and safety against nose-in incidents in following seas. Even in this list there is considerable scope for variations, and as there is yet no “normal” semi-SWATH design.
Seakeeping studies have been done on specific SWATH hulls, but unfortunately there is not a great amount of information publicly available about the general behaviour of this class of vessel (such as the type of extensive systematic series data frequently seen for conventional hull forms) and there is even less publicly available for semi-SWATHs. Some exceptions to this include Doctors [24] and Schack [85]. Rapid progress therefore requires intelligent interpretation of results and not just a mass data or trial and error approach. Once the relative importance and general effects of various features have been identified systematic studies may be beneficial in refining and optimising design.
The models tested as part of this project are intended to represent a significant departure from the conventional, with the object of gaining a better understanding of some semi-SWATH design issues.
Finally, one of the objectives of the strip theory of the previous chapter was the modelling of high speed vessels, as was highlighted in the section dealing with the strip theory assumptions, and there is an obvious application to the high speed ferries of the type discussed above. There- fore, in addition to addressing some issues associated with unconventional hull forms, and in particular semi-SWATHs, the models tested in the experimental programme were also designed to providing a challenging test case for the validation of the new strip theory.