Hydrodynamics of Large Motor Yachts: past and...

II Simposio Internacional de diseño y producción de yates de motor y vela.

II International Symposium on yacht design and production.

Hydrodynamics of Large Motor Yachts: past and future developments

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Hydrodynamics of Large Motor Yachts: past and future developments Patrick Hooijmans[1] Guilhem Gaillarde[2] Nomenclature CB Block coefficient [-] Lpp Length between perpendiculars [m]

WLL Length on waterline [m]

L Ship length [m] g Gravitational acceleration [m/s2]

LgVFN ./= Froude number [-] TΦ Natural roll period [s]

EP Effective power [kW] V Ship speed [m/s] ∇ Volume of displacement [m3] µ Heading (180 deg is head seas) [deg] ω Wave frequency [rad/s] ρ Density [kg/m3] σ Cavitation number [-] p0 Atmospheric pressure [Pa] pv Vapour pressure [Pa] h distance to the water surface [m] Introduction For luxury motor yachts, aesthetics, comfort and operability are of major importance. Designers and shipyards have to meet the challenge of realising the owner’s dream but at the same time they have to work within technical and financial constraints. Aesthetics of the superstructure and the profile of the yacht must go hand-in-hand with technical requirements related to the expected operation of the ship. A yacht owner must be confident that his vessel can sail freely and safely in any part of the world and that it will also be comfortable and be able to realise the required range and speed. The Maritime Research Institute Netherlands (MARIN) has a large track record with respect to the hydrodynamic research on motor yachts. This is partly due to the fact that a large amount of yards dedicated to yacht business is present in the Netherlands, sometimes called the Yacht Valley. Every year a number of motor yacht

designs are investigated with respect to their powering, seakeeping and manoeuvring performances. Large luxury motor yachts have dedicated optimisation issues in calm water. Good propulsion characteristics mean low noise, low level of vibrations and attaining the required speed. Range also becomes an issue for these 40 to 100+ m vessels which need to sail long journeys (typically cross-Atlantic) to arrive at the desired location of the season. Some owners even require a certain range in combination with a required sustained speed, in order to arrive within a specified time at a specific destination without the need to refuel or restock. Regarding the manoeuvrability of the yacht, several aspects may be distinguished. When the yacht enters congested waterways, the controllability of the yacht determines the safety of the passage. When entering the harbour, the low speed manoeuvring ability of the yacht is of importance. With the current trends of ever increasing sizes of motor yachts and increasing service speeds of the yachts, better performance and improved safety is required for luxury motor yachts. These trends also lead to new technologies being implemented in the design, such as podded propulsion or hybrid propulsion systems. These systems all have their characteristic influence on manoeuvring properties. Seakeeping aspects are also of major importance as they characterise the motions and related comfort level in transit conditions and at anchor. Comfort in our perspective is here related to motions and seasickness level. Comfort at anchor has become one of the most important features for motor yachts over the last 10 years. Many techniques used to decrease the roll motions at anchor have been developed and will be discussed and compared. In transit conditions two aspects will also be developed, a comfort issue in moderate waves and a safety issue in more extreme

[1]Project Manager Ships-Propulsion [2]Project Manager Ships-Seakeeping Maritime Research Institute Netherlands MARIN (www.marin.nl)

II Simposio Internacional de diseño y producción de yates de motor y vela. II International Symposium on yacht design and production.


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conditions. The increasing displacement required for a given yacht length has increased their block coefficient and decreased their intact stability. Such combination may, in some extreme case, yield to relatively high rolling in stern-quartering seas and poor course keeping ability, even in moderate conditions. The influence of the steering system on the roll and course stability will be discussed in detail. The dramatic increase in size of motor yachts over the last 20 years has also increased drastically their range of operations and has increased at the same time the probability of being caught in severe storm. In such wave conditions risk of green water, bow flare slamming, course keeping ability and risk of broaching are becoming relatively important. To meet all these requirements, hull form design, weight distribution, choice of appendages and propulsion system must be made carefully. Hydrodynamics, used in the form of calculations and model tests, have proved to be a useful support for the shipyards and designers in the optimisation of this category of vessel. The following presents the numerical and experimental techniques and knowledge gained at MARIN on this type of vessels over the last 20 years. Trends and track-record of MARIN experience Powering Before diving into the hydrodynamic developments of luxury motor yachts, the following presents the trends observed at MARIN in the type of studied motor yachts. It also shows the amount of work related to this market at MARIN since 20 years. Looking back into MARIN files from 1986 to 2005, a total of 152 projects was conducted, corresponding to advice work (speed-power prediction, hull form optimisation and performance assessment by means of calculations or model tests). Some yachts were tested directly in their final configuration but, most of the time, a hull form optimisation was carried out prior to model tests. Figure 1 shows that yachts from 6 to 130 meters Lpp were studied over the last 20 years, with a large proportion of them in the range of 30 to 60 meters.

Figure 2 shows the range of ship lengths that was studied over the last 20 years (without giving details of the number of yachts per year). Projects of yachts over 80 meters have been studied steadily over the years. This figure is of course quite dependant on the number of projects per year, but hydrodynamic developments of yachts over 80 meters are not a recent fact, although their numbers increase each year. All these hydrodynamic developments have not all been finalised and built yet. Figure 3 provides an idea of the evolution of the block coefficients over the last 20 years. Although the scatter is rather large, some trend can be seen with an increase in block coefficient. New projects with block coefficients closer to 0.6 are observed, due to the increasing demand of displacement (due to onboard comfort level, outfitting and entertainment) while keeping reasonable ship lengths to enter most of small (charming) harbours. In-house information, summarised in Figure 4, suggests that block coefficients around 0.45 to 0.50 appear to be common practice. Figure 5 shows that a large scatter exists in the relation between beam or draft and length. The tendency is that smaller yachts have lower L/B and lower L/T ratios. For yachts larger than 40 meters, often called super or mega yachts, Figure 6 illustrates that these vessels are characterised by a length to draft ratio L/B around 5 (increasing to 6.5 to 7 for yachts over 80 m), and a beam to draft ratio B/T around 3. Also a lot of scatter exists in these ratios, which shows the variety of the designs but also illustrates the fact that they will not have the same performance in calm water, seakeeping and manoeuvring. Seakeeping and manoeuvring The first yacht tested in waves at MARIN was in 1972. A total of more than 50 projects were conducted since then, related to free sailing seakeeping and manoeuvring experiments. Figure 7 illustrates again the fact that yachts of all range were tested over the years. A large experience was gained since the opening of the new seakeeping and manoeuvring basin in 2000, with a total of 23 projects so far.




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The growing interest in seakeeping and manoeuvring studies probably originates from the combination of yard and designer’s wish to optimise their product and increasingly stringent requirements from owners for onboard comfort and motion control. It is important for the owner to know what he can expect from his yacht in all type of conditions and with any type of active devices he may fit onboard. Additionally, an increasing number of yards and designers identify seakeeping as an important issue in the quality of their product, which also becomes a selling argument. All test programs studying the seakeeping ability of the yachts comprised tests in transit condition and at anchor, for free sailing self-propelled models. All yachts were tested in particular in stern-quartering seas in transit in order to investigate course keeping ability and roll resonance. The manoeuvrability of yachts was generally verified using standard zigzag and turning circle manoeuvres combined with slow-speed astern tests to study the controllability of the ships when sailing astern. Models were also fitted with different types of propulsion system (propellers and/or water jets), steering systems (rudders with or without flaps, nozzles), active fin stabilisers of different sorts (high or low aspect ratio), anti-roll tanks (active or passive, usually U shaped) or other damping devices. Model tests in the early days were more orientated on observations and qualitative aspects. A great attention was then paid to the outfitting of the model, such as modelling of superstructure. A large emphasis has been given latter to the quantification of motions and comfort, implying increasingly complex measurements and analysis. This more scientific approach has allowed large progress in the understanding of the hydrodynamics and in the enhancement of performances. However, attention to details and observation of the behaviour in a seaway still stays rather important for designers, ship owners and ourselves, as shown by the photograph in Figure 8 taken in our new facility. Model tests are one of the first places where owners, captains or designers can face their design choices in realistic wave conditions and check the yachts behaviour in unrestricted conditions (even

those that the yacht should only face few time in her life time). Powering performance Hull optimisation In general the powering performance of a yacht can be divided into the performance of the hull (the bare hull resistance), the appendages (the appended resistance), the performance of the propulsion system and propeller-hull combination (open water efficiency and propulsive efficiency). In the following we constrain ourselves to the performance improvement of the hull and propeller-hull combination from a powering point of view. For motor yachts the most dominant factor for the performance of the hull is the ratio between the length on the water line and its displacement: 3/1/ ∇WLL . The longer the yacht becomes the lower its Froude number will be (forward speed relative to the length of the ship). The wave resistance is related to the Froude number NF . Larger Froude numbers will give higher wave resistance. Furthermore, increasing the length while maintaining constant beam and draught will increase the slenderness of the hull, which also has positive effect on resistance. An increase in displacement due to an increase in weight will have negative effect on resistance because more water has to be displaced from the forebody to the afterbody while sailing through the water. This means that the ratio between WLL and 3/1∇ must be as high as possible. Or in other words: longer and lighter is better. With these two dominant parameters the basic performance is fixed. In Figures 9 and 10 a comparison is given of the wave profiles along the hull for a yacht without bulbous bow with the same displacement but different waterline length and slightly different draught. The wave profiles are calculated by means of our non-linear potential flow code RAPID. Using this code it is possible to judge the hull lines based on the generated wave profile, velocity field and pressure distribution. The example illustrates the effects of differences



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in length/displacement ratio and optimisation of the forebody on wave interaction. The graphs show the wave profile along the hull (starting at the right and finishing at the left of the graph) together with the stern wave system starting at the stern. On the horizontal axis the ordinates of the yacht are given and on the vertical axis the dimensional and non-dimensional wave height is given. In Figure 10 the results of the yacht at the same displacement as in Figure 10 is presented, but with a more slender foreship and a somewhat increased waterline length (+1.5%). This second graph shows that the generated waves are lower and the interaction between the bow wave and forward shoulder has improved.

When further optimisation is required or when it is not possible to change the contour or slenderness of the bow due to the arrangement or aesthetics reasons, features such as bulbous bows and trim wedges can be used to further improve the performance of the hull. These features have the potential to improve the performance of the hull by about 10% to 15%. The application of bulbous bows A bulbous bow is a good alternative for a further improvement of the performance without changing the profile of the ship above the waterline. The basic principle of a bulbous bow is reducing the bow wave system by means of a good interaction between the wave system generated by the bulbous bow and the bow. Please note that, observing the previous graphs, the bow wave system is one of the most dominant wave systems generated by the yacht. Therefore, by reducing this wave system a lot can be gained in the total resistance for the hull. With our CFD code RAPID we are able to optimise the interaction between the bulbous bow and the bow wave system prior to carrying out model tests. The best way to optimise the bulbous bow within given restrictions is by means of our semi-automatic optimisation program “Fantastic”. With this method a systematic variation in length, width and height of the bulbous bow will be calculated with RAPID. Within the restrictions the best possible bulb will be obtained. By means of CFD optimisation the amount of modifications on a ship model for an

optimum bulb design can be minimised. An investigation into the bulbous bow design by means of model tests has shown that depending on the shape of the bow and the volume of the bulbous bow improvement in performance of 10% to 15% is possible. The application of trim wedges Besides improvements with respect to the forebody, further performance enhancement measures can be taken with respect to the afterbody. By introducing trim wedges on the afterbody between 5 to 15 degrees relative to the buttock angle on the centreline (see Figure 11) or interceptors the propulsive performance can be improved by 3% to 9% at design draught without a large penalty in the lower speed range. Trim wedges appear to become efficient from about Fn > 0.25. Moreover there is another important advantage with respect to the use of trim wedges. From a powering point of view the transom immersion should be as low as possible without creating to steep buttocks in the afterbody. It is however realised that stern slamming should be avoided at any case, especially while at anchor. In general, for motor yachts, this has resulted into a small transom immersion of about 300 to 500 mm. By combining this immersion with the application of a trim wedge, both an improvement in performance and transom immersion is achieved. Moreover, due to the trim wedge more shape and stiffness is introduced into the afterbody making it less favourable for stern slamming. Appendages and streamlines To improve the powering performance, appendage alignment to the flow is critical. Until recently paint smear tests were conducted on the bare hull model with dummy appendages to obtain an accurate description of the flow direction at key locations such as: strut and brackets, rudder headbox (see figure 11), stabiliser fins, bilge keels (see Figure 25) and tunnel thrusters. When top speeds become higher and/or the risk of large flow direction deviations becomes larger, the margins against strut and propeller cavitation become smaller. In these cases more detailed research is required by means of three dimensional wake surveys in the plain of the appendages.




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The advantage of this measurement above the traditional paint smear test is that not only flow direction is measured as a function of the distance to the hull, but also the flow speed itself. This information can be combined into non-dimensional cavitation numbers (σ, see following equation) and angles of attack.

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vp p g hVρ

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In addition to alignment, this information is used to optimise profile shape to increase the margin against cavitation. In order to satisfy comfort levels at both low and high ship speeds, it is not unusual that yachts are equipped with two pairs of stabiliser fins and bilge keels. Stabiliser fins and bilge keels must be carefully positioned in the streamline, their mutual clearance must be checked as well as the risk of creating a wake in the propeller disk and a minimum distance to the free surface must be kept to avoid risk of ventilation and damage in waves, especially for forward bilge keels. However, as the flow around the hull changes as a function of the ship speed, it is clear that prior to either paint smear tests or wake measurements a ship speed should be chosen for the alignment and profile optimisation. Usually this is the design speed of the yacht. However, a conflict of interest between the performance of appendages at cruising speed and at design (top) speed is evident. While CFD codes become more and more feasible from both a practical and economical point of view, they enable better compromise in alignment over a given speed range. For this purpose RAPID is already used to check (too large) deviations over the speed. However because RAPID is a non-viscous code and does not take into account any boundary layer, MARIN has introduced their Navier-Stokes code PARNASSOS for this purpose. A speciality with respect to the alignment of appendages for motor yachts is the longitudinal position of the exhaust pipe. To avoid too much backpressure on the exhaust system, a maximum water height is allowed above the exhaust exit. The local water height for a given speed is dominated

by the wave height along the hull. As a result the longitudinal position must be located carefully with respect to the accompanying wave system for a certain speed range. RAPID calculations for several ship speeds enable the designer to make the best compromise from both a hydrodynamic and general arrangement point of view. Noise and vibration Even if not yet standard for the hydrodynamic design of motor yachts, more interest is rising upon specific optimisation with respect to hydrodynamic induces noise and vibration. This noise and vibration is mainly caused by cavitating propellers (see Figure 12), short brackets, rudders, rudder headboxes and/or stabiliser fins. Reducing the risk of cavitation could therefore be very important to keep a high degree of comfort and silence onboard. The increasing demand in quality and noise level control on motor yachts may yield detailed flow measurements, profile optimisation and propeller cavitation studies to become standard for large motor yachts. New concepts With the demand for increasing length and displacement, also the demand for increased power arises. In order to meet the design speed, new concepts are being studied, such as combinations of propulsors, like a twin screw vessel with a booster jet for high speeds or a single screw vessel with two side pods to provide the required power. During model tests these concepts bring additional aspects as how to distribute the power over the various propulsors to come to the best solution from a propulsion point of view as well as from a comfort point of view. These aspects require more detailed research into power distribution, cavitation observations and hull pressure measurements. Another new concept is the use of two pulling podded propulsors (see Figure 13). There are quite some benefits from a propulsion point of view. The efficiency of podded propulsors can be higher that of conventional propellers. Furthermore, as no struts are in front of the propellers, a more homogene flow into the propeller disc is realised, resulting in a good wake distribution, and therefore less cavitation on



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the propeller blades can be realised and thus lower propeller induced hull pressures. This means a higher comfort onboard. Furthermore, as such propulsors are diesel-electric, more freedom for the engine room is created. Usually the engines are located at the most comfortable position on the yacht. Also generating the required power can be more efficient as several smaller power generators can be installed which can operate at their optimum rotation rates, instead of two main engines that sometimes have to operate at very low revolutions. Manoeuvring performance The manoeuvring performance of a ship can be categorised in the following items: course keeping, controllability, turning ability, slow speed manoeuvring and other safety and comfort issues such as manoeuvre-induced heeling angles, cavitation and noise. Course keeping The ability of the yacht to maintain its course is determined by the hull form, the efficiency of the steering arrangement (e.g. the size of the rudders) and the size of any other appendages such as centreline skegs. When the ship is not properly designed and the directional stability of the ship is poor, excessive helm action is required to maintain course. Due to the rudder action, added resistance is introduced resulting in added power consumption and therefore an increase in the running costs of the ship. Additionally, the directional stability may lead to excessive lateral motions in the aft ship and to noise of the machinery and due to oblique propeller inflow. Careful design of the appendages may avoid this. When properly sizing the centreline skeg and the rudders, a directionally stable ship can be designed, which needs only little rudder action to maintain course. Usually, reference data, simulation studies or model test data is used to determine the relation between the size of the appendages and the course keeping ability of the ship. Controllability and turning ability Collision avoidance and the reaction of the yacht to helm commands are naturally important for each type of ship. But because motor yachts often sail in congested waterways and in harbours, even more

attention needs to be paid to the controllability of the yacht. This means that not only sufficient course keeping ability must be obtained but also sufficient movable rudder area should be present to counteract or initiate any turning motion of the ship. Slow speed manoeuvring Motor yachts often have to manoeuvre in confined harbours or crowded mooring areas. To arrive at the desired location, an excellent manoeuvrability is required. Since luxury yachts are often moored with the stern directed to the quay, even the astern manoeuvring characteristics should be good. Not only should the manoeuvres be conducted accurately but also in a swift way, in order to avoid wasting the precious time of the owner. Nowadays, the size of motor yachts is ever increasing while the popular harbours in general remain the same. This results in changing the main particulars in relation to each other, such as for example increasing the beam while the draught remains the same (increasing B/T ratio) which significantly changes the manoeuvring performance of the yacht. Slow speed manoeuvring and the stopping characteristics of luxury yachts have also become important issues. Sometimes even closed loop DP-capability is required in order to hold station at for example mooring areas. Motor yachts have to be able to berth or unberth without assistance in a wide range of weather conditions. This requires appropriate sizing of the bow and possibly even stern thrusters in order to be able to manoeuvre sideways from or to quays or around the anchorage. In this respect the use of podded propulsion is attractive. When the yacht is equipped with pods, the need for stern thrusters does no longer exist. Compared to transverse stern thrusters, pods have a larger amount of power and a larger efficiency. Therefore, the crabbing ability of the ship (which is the ability of the ship to move purely sideways) will improve compared to a yacht with a conventional (twin) propeller-rudder and stern thruster arrangement. As an example, Figure 14 demonstrates a so-called crabbing ability footprint. In this figure, the maximum wind speed in which the ship can manoeuvre into the wind purely sideways without assistance is given for each wind direction. In this example, it can be seen that in bow quartering winds, leaving the quay is




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problematic in winds corresponding to Bf 5 or more. During the design phase of the ship, this can be improved by reducing the wind drag or wind area, or by increasing the power of the bow thrusters or pods. In most cases, it is found that the bow thrusters are the limiting factor in crabbing. Depending on the allowed changes to the aesthetics of the yacht, the possibility therefore exists to re-design the superstructure in such a way that the centre of effort of the wind forces is shifted aft, resulting in a relief of the required forces to be generated by the bow thrusters and an increase of the forces to be generated by the pods. However, since the pods are equipped with sufficient power for crabbing, this will in the end improve the crabbing ability considerably. Other safety and comfort issues Other aspects determining the safety and comfort onboard the yacht are heel angles and propeller noise and vibration induced by steering. When sailing at high speeds during manoeuvres, large heel angles can occur when the ship is not properly designed. Especially the increasing use of marble throughout the ship results in a reduction of the metacentric height and transverse stability of the yacht. Using fin stabilisers is an attractive way to increase the comfort and safety of yachts when sailing in a seaway or during high-speed manoeuvres. With the appropriate control system, able to reduce the roll acceleration and roll velocity but also the actual roll angle itself, the heeling angles during manoeuvres can be reduced. Applying a sufficiently large centreline skeg also reduces the drift angles and rate of rotation during manoeuvres. Due to the smaller drift angles and yaw rate, also the heel angles will reduce. Based on numerous tests, Figure 15 demonstrates the relation between the speed of the yacht and the maximum heel angle observed during a turn with maximum rudder angle. In this example, it is clearly seen that for high speeds, uncomfortable situations can occur when steering is applied. To avoid dangerous situations when sailing at high speeds, the maximum steering angles are sometimes restricted as a function of speed. However, for emergency situations, the possibility to use large

steering angles should always be possible without endangering both the ship and the crew and passengers. Due to large oblique inflow angles that can develop during manoeuvres, propeller cavitation, noise and vibrations can occur, compromising the comfort of passengers on the yacht and sometimes even leading to erosion of the propellers or rudders. During several research studies, it was found that the cavitation inception speed of a ship is dramatically reduced when sailing in off-design conditions, such as turns or in a seaway. To avoid unpleasant surprises these aspects can be investigated in the design stage of the yacht by calculations and model tests. Initial design stage In the initial design stage, when the first set of preliminary lines is drawn, an evaluation of the manoeuvring characteristics can be obtained based on reference yachts. Using databases of main particulars and appendage size statistics, an initial estimate of the required size of the rudders and centreline skeg is made. When optimising the hull lines from a powering point of view, it is the general trend to shift the centre of buoyancy aft in order to reduce the bow wave system. However, this has a negative effect on the yaw checking and course keeping ability of the yacht. During the service of the ship, this may increase the running costs due to the added resistance during the steering action or reduce the comfort onboard the ship. It is therefore important to make a balanced compromise between the powering, seakeeping and manoeuvring requirements of the yacht. When several different concepts or appendage arrangements are to be compared and the benefits or drawbacks of each concept should be qualified, numerical studies can be performed. For the manoeuvrability of the yacht, standard manoeuvres such as zig-zags or turning circles can be simulated after which the results can be directly compared to other concepts or reference yachts in the database. However, also dedicated scenarios can be performed, such as the approach and berthing manoeuvre in a selected harbour. The simulations can be conducted within a tight timeframe and can



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be conducted parallel to and in cooperation with other numerical studies, such as powering and seakeeping studies. Therefore a range of concepts can be thoroughly evaluated resulting in a balanced compromise between all the requirements of powering, seakeeping and manoeuvring. An example of such a study for a Hydrographic Survey vessel was published by Toxopeus et al. [2]. A detailed discussion about manoeuvring assessment studies can be found in Loeff and Toxopeus [3]. Final assessment Since numerical studies have their limitations in accuracy but sometimes also in applicability, it is strongly advised to assess the final performance of the yacht using actual model tests. Especially when new concepts (propulsion systems) or new combinations of main particulars are used, reference data from other yachts is non-existent which reduces the confidence in the numerical results. When a numerical study has already been conducted, the scope of the model tests may be limited to the situations at which critical performance is suspected. For manoeuvring, this mostly means that a limited set of zigzag and combined turning circle/pull-out tests is conducted, demonstrating the yaw checking and course keeping ability, the turning ability, the directional straight-line stability and the transverse stability during manoeuvring. With the increasing length of luxury motor yachts, also governmental requirements become important. Ships with a length between perpendiculars of 100 m or more now need to comply with the IMO criteria posed in Resolution MSC. 137(76) [4]. The criteria apply to certain characteristics to be obtained from zigzag and turning circle manoeuvres. In Figures 16 through18, examples are given of results of standard tests with motor yachts. The representative IMO criteria values are indicated in these figures. Based on these results, it is seen that in general, compliance with the turning criteria is easily achieved, while in some cases the manoeuvrability of a yacht did not comply with the criteria posed for the first overshoot during a 10/10 zigzag manoeuvre. Another example yacht did not comply with the criteria for the first overshoot during a 20/20 zigzag manoeuvre.

If the turning ability of the ship is to be improved, an increase of the rudder area is generally recommended. This will not significantly influence the yaw checking and course keeping abilities, but it will increase the steering forces that can be generated, resulting in improved turning ability and harbour manoeuvring. If the yaw checking and course keeping abilities are to be improved, either an increase of the centre line skeg or the rate of rudder application is proposed. Although the first option is usually very effective, it reduced the turning ability and harbour manoeuvring. If this is unacceptable, the increase of the rudder turning rate (by applying a more powerful steering machine) is a good alternative. Based on the requirements of the owner or yard, astern manoeuvres are sometimes conducted to demonstrate the ability of the motor yacht to sail astern, simulating astern berthing manoeuvres. During tests conducted in stern quartering waves, perhaps the most severe situation from a course keeping viewpoint can be studied. With the stern of the yacht in a wave crest the relative water velocity over the rudder reduces resulting in lower lift and hence reduced steering capability. For a certain range of yachts, a combination of ship length, wave length and ship speed, this is a dangerous situation which may lead to broaching or uncontrolled behaviour, as shown in the next section on seakeeping performance. This can be solved by increasing the rudder size, improving the autopilot, increasing the steering rate or by increasing the inherent directional stability of the yacht. The latter option is however the most rigorous one as the hull design and possibly the steering arrangement has to be redesigned.




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Seakeeping performance

This topic is usually characterised in many discussions as the most important aspect as it is related to onboard comfort and enjoyment while at anchor, vessel integrity and safety while crossing oceans (course keeping, green seas, structural loads), or feel good impression (perception and reality) of being on board a safe and seaworthy vessel. Being however not contractually defined (and not easy to check during sea trials) it is sometimes omitted from design study stage. Compared to powering optimisation, seakeeping of ships is not about small numbers and slight changes in hull form. Only relatively large modification of the main dimensions will yield a noticeable benefit to the behaviour in waves. Another influent parameter in the behaviour is also the selection of the appendages. Active appendages such as rudders or fins, passive ones such as bilge keels or skeg, and of course choice of loading conditions will affect greatly the future performance of the yacht. On top of the physical characteristics of the yacht (the hardware part), the selection and performance of the motion controls (the software part) is of prime interest. For example, an inherently bad hull form for course keeping ability can proved to be good when the steering control is very good. The same applies for rolling. In other words, a bad design from steering and rolling point of view can be “saved” by a smart motion control system, up to a certain level of course. As a matter of fact, seakeeping considerations will strongly influence items such as general arrangement, loading conditions and internal volumes used for fitting roll damping devices. When seakeeping becomes last in the design spiral, it becomes a simple design verification (which should just confirm that everything is alright) rather than a quest for further improvement and modifications are hard to make for designers when an undesirable behaviour is discovered. Ship design is by definition a balance of compromises. Adding a topic that includes so many parameters (waves, comfort, structure loads, ship handling, fatigue,

autopilots settings, etc) can look rather terrifying indeed for the designers. Trends, experience and design issues are discussed in this section, especially concerning motion controls (the ‘motion down, pleasure up’ aspect). The last part presents the developments we foresee as important and required in order to enhance the seakeeping quality of motor yachts. Hull form As shown in the first section of this paper, quite some scatter is observed in the main dimensions, such as B/T or L/B ratio. This scatter will also show up in the seakeeping performance. Even if the main dimensions for motor yachts are dictated by many aspects but not seakeeping considerations at first instance, it is good to know the consequences of the choices made in an early stage on the future performance and comfort level while going at sea. Figure 19 shows the influence of ship length and beam on the heave and pitch motions. The results were obtained by means of calculation with in-house developed 2D strip theory program SHIPMO. Vertical plane motions for monohull are fairly well predicted by means of calculations, with accuracy in the order of 10% for motions and accelerations. A typical motor yacht hull form was chosen, having the following main dimensions: Lpp=60.0 m, B=12.0 m and T=3.50 m. Calculations were performed for head seas at 14 knots in Beaufort 4 condition (Hs = 1.70 m and Tp = 6.1 s). The length and beam of the vessel was varied by +/- 10 % and the effect on heave, pitch and vertical accelerations at station 5 and 11.5 are shown (see Figure 20). The beam to draft ratio has a strong effect on vertical plane motions, as described by Dallinga [5] for ferry hull forms. Even if the excitation increases with increasing beam, the large increase in damping yield this result. However, please note that very slender monohulls (trimaran type hull) will however experience more pitch and vertical acceleration. This is due to the strong decrease in damping in vertical plane.



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An important statement is that the influence of the main particulars on ship motions and related comfort can be fairly well predicted. The large amount of parameters does not allow drawing final trends on how to obtain the optimum ship, but comparison between hull forms and verification of target performance can be achieved with model tests or calculations. General arrangement Even if surprising, the general arrangement will have a strong effect on the perception of the motions onboard. One of the major reasons is that the vertical accelerations, which are the prime reason of seasickness, are not the same at different longitudinal locations while the vessel is sailing. Figure 21 illustrates this point. Vertical accelerations can be twice high in front of station 13 than around station 7. Also the height has a large influence on the transverse accelerations. In fact, the traditional location of the engine room is quite close to the best location on a vessel in terms of comfort in transit conditions. Use of podded propulsion for example could yield additional freedom in the location of engine room, and hence use the best locations in terms of comfort for passengers. Appendages and damping devices The choice of appendages has a rather large influence on the future performance of the yacht. Appendages and damping devices are mainly used to reduce roll motion, which is the most undamped motion for monohulls in general. This means that any devices bringing additional damping will be beneficial. Vertical plane motions can however be reduced as well, especially for high speed vessel where trim tabs, T-foils or interceptors can used. For displacement or semi-displacement hull forms stabiliser fins can however be used in an unusual way as presented by Gaillarde [6]. Reducing pitch with stabiliser fins with a displacement or semi-displacement yacht will however only bring a 5 to 10% reduction in standard deviation, and even less for maximum amplitudes. For roll motions, for example, a rather large variety of damping devices exists, which will work relatively better when low damping is

provided by the hull itself. In other words, the best results and high percentage of efficiency for damping devices are obtained for the yachts having large roll motions due to the choices on the hull form. As a matter of fact, roll reduction in percentage is not a measure for the efficiency of a system as the number will vary depending on the yacht in which it is fitted. A 90% roll reduction is often given as a standard figure to judge a stabilisation system. Realistic values lay between 50 to 90% for good systems, a percentage that can vary for the same system depending on which wave is applied. There is probably an important feel-good factor of knowing that the damping devices yield 90% roll reduction instead of only 50%. However, from a quantitative point of view, the resulting roll angle and transverse acceleration felt onboard while laying at anchor or in transit should be the important issue. They are four main contributions than can yield damping to reduce roll: • the hull itself • passive appendages such as bilge

keels, rudders, shaft/brackets, fins... • active (moving) appendages such as

stabiliser fins or anti-roll tank (usually U-type tank).

Figure 22 shows approximate levels of contributions of these items in anchor and transit conditions. This graph only provides a trend of the contributions, as many variations will be obtained when changing appendages sizes, ship speed or wave conditions. The contribution of an anti-roll tank was not included in the graph, but its contribution at zero speed would be similar to active low aspect ratio fins. In transit condition, anti-roll tanks perform well in beam seas only but not anymore in stern-quartering seas when maximum roll motion is observed. The reason is that the tank will not only be excited at its own natural frequency (for which it will provide damping) but also at different frequencies where it will excite the motions. This is clearly measured during model tests and understood through calculations. Installing bilge keels of adequate size was the first measure that was introduced




133

regularly. The first step towards further improvement was the installation of a lightly dampened passive U-type stabilisation tank. In recent years active low aspect ratio fins were adopted frequently on new designs and also as re-fits on existing ships. Passive stabilisation tanks are well established as a means to reduce rolling. An important advantage of a U-tank is the low flow noise and the possibility to shut the tank down quickly when going to transit conditions. A drawback is of course the need for internal volume. The main design parameters are the volume, the duct height and the internal damping. Because of the low roll angles in design conditions (typically around 0.5 deg rms, roughly equivalent to maximum roll angle of +/- 2 deg) the internal damping needs to be rather low to obtain an adequate tank response. Typical roll reduction levels are around 70% of the rms values. Although counter intuitive the use of stabilisers at zero speed proved very effective. The system employs "extreme" low aspect ratio fins with a relatively eccentric fin shaft (typical aspect ratio of 0.4 and 70 to 80% axis eccentricity). In a “kicking” mode this type of fins produces relatively high inertia forces when accelerating (water) from rest to maximum velocity and a relatively high drag when moving at constant speed as shown in Figure 23. Design issues are the relative magnitude of the inertia and drag contributions and the timing of the fin response with respect to the roll motion. Typical roll reduction levels are also around 70%, for relatively low waves (up to around 1.5 meter significant wave height - about Beaufort 3 sea condition). Concerning fin stabilisers, the trend has been to reduce their span and aspect ratio quite considerably over the last year. Two reasons explain this trend: • The vessels have become fuller around

midship section, yielding the bilge radius to decrease considerably. Less space is left then to fit fins inside the limits of beam and draft.

• The success of using fins at zero speed

has pushed the manufacturer to improve the efficiency of the system. As a matter of fact the chord has drastically

increased with aspect ratio down to 0.4 as well as the eccentricity of the shaft.

It is important to realise that low aspect ratio produce less lift than high aspect ratio at similar fin area, which is illustrated in Figure 24. As a matter of fact, two pairs of fins are sometimes needed. The trend in fin design for their optimum use at zero speed has sometimes yield a decrease in performance in transit conditions. At zero speed, fins are effective when accelerating water and producing drag, which explains their actual design. In transit the fins are mostly effective when producing high lift forces. The two items have opposite requirements on fin dimensions. Use of retractable stabiliser fins could solve the issue of limited bilge radius. Even if many new things have appeared over the last 10 years to reduce effectively the roll of motor yachts, new damping devices and ideas are still coming up, as the market shows interest in innovation to gain comfort. Figure 25 finally shows a typical arrangement of two pairs of fins and bilge keels on a 50 m motor yacht. There is not yet a guideline for optimum set of damping devices on a motor yacht, as too many parameters are involved. From a hydrodynamic point of view, the performance of different systems can be compared very accurately. Two major aspects should be however checked in all kind of configurations:

• the bilge keels and fins should not be aligned on the same stream line, in order to avoid strong interaction.

• A minimum longitudinal clearance should be kept between each appendage, to avoid in particular lift degradation.

Clearance and streamline aspects can be observed on Figure 25. A comparison of stabilisation methods is not very straightforward because of the rather non-linear characteristics of the problem. It is clear that a meaningful comparison can only be made for a well-defined target wave condition. Figure 26 shows a comparison of the most used damping devices on motor yachts, active low aspect ratio stabiliser fins and



134

anti-roll tank. A full comparison was presented by Dallinga in [8]. More than the efficiency of the damping system, the most important still remain the absolute motion and induced seasickness felt onboard. A detailed investigation was presented by Dallinga and Levadou [9]. Performance in transit at sea With combining very high standard in terms of comfort (comparable to a large cruise vessel) together with relatively modest size ship (compared again to cruise vessel), motor yachts are one of the most difficult challenges in terms of seaworthiness and motion control. When discussing the sea state, in which the vessel will sail, there are usually two different approaches and scenarios: • normal sailing conditions during a

cruise, from one harbour to another. In that case, high standard of comfort must be fulfilled, as the owner may probably be onboard.

• severe wave condition that the yacht

may encounter during transit (North Atlantic crossing, North Sea or Bay of Biscay to reach yards in North Europe, Mediterranean Sea). These sea states have more to do with items such as vessel's integrity, course keeping in waves, slamming, green water loading, thus vessel's safety and controllability in general.

Head to bow-quartering seas Local vertical accelerations are related to the heave, pitch and roll motions and their mutual phasing. In practice this leads to an area with relatively low accelerations just aft of amidships and relatively high levels in the forward half of the ship. The relatively low damping of narrow hull sections magnifies this trend for ships with a relatively fine forebody. Figure 21 illustrates the trend for a 50 m yacht in head seas; the difference between the area just aft of amidships and the area around three-quarter ship length is nearly a factor two in acceleration level. In order to guarantee maximum comfort while sailing, sensitive area should always be placed around one third aft of the vessel. Stern-quartering to following seas

Concerning transverse motions, stern-quartering seas become the most critical when sailing at speed. This point is shared by all types of vessel and not only motor yachts. Any master has experienced difficulties in keeping his yacht on a straight course with low roll when sailing in such wave direction. On top of the roll motion due to resonance, a coupling with yaw usually appears for such headings. Roll resonance occurs when the encounter frequency is equal to the natural roll frequency of the vessel. The encounter frequency ωe as a function of the wave frequency ω is defined as:

)cos(..),(2

µωωµωω Vge −= (1)

Figure 27 shows this above equation at a speed of 15 knots. On the horizontal scale stands the wave frequency and on the vertical scale the heading (with head seas defined as 180 deg). The bold line is the natural frequency of the yacht (here corresponding to 7.9 s natural roll period). It clearly shows that for headings around 60 to 75 deg, a large range of wave frequency will be “seen” (encountered) by the moving yachts at her natural roll frequency. It also shows that the range of most unfavourable headings is quite narrow and that a change in course of about 30 degrees would “detune” the encounter frequency and natural roll frequency. The figure also shows the combination of headings and wave frequency at which the yacht travels at the same speed than the waves (zero encounter frequency). When calculating the roll response at a given speed as a function of heading and wave frequency, the graph shown in figure 28 is obtained. The maximum roll response follows the line of natural frequency. Large roll angles may also be observed at zero encountered frequency, with a strong coupling with roll and yaw. This point, however, can not be covered by linear theory as it involves non-linear aspects such as large amplitude motions, loss of stability and drastic change in course or strong speed variations due to surf-riding. The area of roll resonance and zero encounter frequency is of interest because it may yield broaching or capsizing in the most unfavourable cases. This point is crucial for example for frigates, as the risk in such




135

conditions is quite high (see de Kat [10], [11], [12], [13] and [14]). Even if less extreme than for long slender hull form such as frigates, similar effects are observed on motor yachts. In order to compensate for the coupled roll and yaw, rudders (for yaw) and stabiliser fins (for roll) are used. So far, these appendages are controlled separately on motor yachts (mainly because manufacturers also work separately). When the rudders react to the yaw motions they generate a transverse force that magnifies rolling. This increases the roll response in the quasi-static range with low encounter frequencies. The trend to increase rudder area and rudder efficiency (with high-lift rudders) magnifies this trend. It seems also clear that stabiliser fins placed forward on the vessel also generate longitudinal transverse forces (together with a vertical force). When both autopilot settings are wrongly phased, each appendage works against the other. Observations during model tests indicate that numerical models (also the foregoing results) tend to underestimate the roll response in the area of low encounter frequencies. This suggests that theory tends to underestimate the yaw and rudder induced roll excitation and to overestimate the effective stability. Reasons for an underestimation of the excitation may be related to the fact that even a small temporary drift angle has a large influence on the roll excitation and the yaw induced rudder or fin reaction forces that are often neglected. Reasons for a reduced effective transverse stability may be related to the steady wave system in the higher speed range (Figure 29) and to the waves themselves (Figure 30). The vessel will be “catch” between two wave crests (one at the stern, the other at the bow), when the projected wave length equals the ship length. Observations during tests suggest that in cases where the bow immerges temporarily the steady wave system becomes even more pronounced; this would imply that the foregoing estimate of the stability reduction is not necessarily conservative. It is quite clear from the previous figures that three factor in stern-quartering seas can yield unfavourable conditions in terms of rolling, steering and risk of broaching:

• encounter frequency tuned on natural roll frequency

• zero encounter frequency • wave length equal or slightly longer

than ship length These three cases are defined by the following equations:

−

= gVT

aVresonnance ..

2

cos),( 2ω

πωωµ φ (2)

=

VgaVencounterzero .

cos),(ω

ωµ (3)

= 2.

..2cos),(ω

πωµLpp

gaLpplengthwave (4)

All three components will hardly occur at the same time. They are plotted in Figure 31 for an Lpp of 45 meters and 17 knots. This type of simple graph allows a quick check on the most unfavourable combinations of headings and wave frequencies, for a given ship size and speed. Further calculations and model tests will quantify then the amplitudes of roll, the degree of course stability and the risk of broaching. From a variation of ship length and ship speed, it is also possible to produce a graph that will indicate, for example, if equations 3 and 4 can occur at the same time (if the red and blue line in Figure 31 cross each other or not). This is shown in detail for motor yacht in Figure 32. The limit for matching both a zero encounter frequency and a projected wave length equal to ship length corresponds to the maximum Froude number of 0.40. During surf riding, the vessels can increase their speed from about 16 to 20 knots, which will make them enter in the area with bad matching for potential course keeping problems. Design issues A basic characteristic of monohull motor yachts is the distribution of the vertical acceleration over the length of the vessels.



136

Regarding these characteristics it must be concluded that the acceleration levels can be reduced significantly by a full use of the favourable area just aft of amidships. A diesel-electric propulsion plant, combined with podded propulsion units, might solve the problems associated with a more forward location of the engine room. In anchored conditions podded propulsion units might also be very useful as a means to obtain and maintain a favourable heading and to avoid swinging behind the anchor. An alternative anchoring arrangement or a special superstructure (using the wind to stabilise the ship) may also be an option. The transverse stability has a significant influence on the roll and related transverse accelerations. A lowest level which is just “sufficiently” high to avoid problems in stern-quartering seas seems the optimum from a comfort point of view. Rolling can be reduced significantly with active stabilisation. Because the performance of bilge keels increases with increasing roll angles, bilge keels are highly desirable as a safety measure in extreme conditions. A problem in transit is the low efficiency of low aspect ratio fins and their interaction with the bilge keels. From a hydrodynamic point of view high-aspect ratio fins would be much more attractive. Of course the fact that low-aspect ratio fins are nowadays also used at zero speed is conflicting with the foregoing. A combination of high bilge keels, an anti-roll tank (for zero speed) and high-aspect ratio fins for transit may give the best performance if the required operational window is large. Although the basic physics of bow-flare and stern slamming are understood, the related discomfort levels due to hull girder vibrations and noise are hard to quantify. Despite this unsatisfactory state of the art it seems clear that a stern-wedge can contribute significantly in reducing aft-body impacts. Further developments Although many basic aspects of seakeeping are understood at a conceptual level a number of areas need further development. Model testing is still the only way to understand and check the design choices,

despite the continuous progress in numerical simulations. One area is the optimisation of fin control when used at zero speed. Even if promising results were obtained quickly with this type of stabilisation, more research on the topic would allow further progress on the control side and general efficiency of the system. Another area concerns course keeping and rolling in stern-quartering seas. A combined control system for rudders and fins seems the ineluctable way forward to control yachts in severe conditions. This point is anyway shared by nearly all kind of slender vessels. The hydrodynamic knowledge and testing capacity are available today to develop it for the maritime industry. Onboard system for captain's guidance should also be developed further, in order to guarantee an optimal use of the yacht in terms of comfort and safety limits. The introduction of podded propulsion in yachts will bring back the course stability in waves as one of the major items. Flatter aft body for pods combined with restricted pod angles of attack at high speed could cause alteration of the course stability in waves. Dedicated checks and correct designs of hull form, skeg, control settings must be realised to guarantee a good performance in waves. These checks and optimisation should of course be done during the design and conceptual phase more than being the result of a bad experience at sea. The transfer of fundamental insights in the careful compromise that characterises yacht design and in on-board ship-management is another major challenge. The development of general, robust and complete numerical models is a major investment.




137

Conclusions

This paper shows the wide range of application for hydrodynamic developments for motor yachts. The high demand on performance and the innovative attitude of shipyards and designers (which is more driven by the owner’s will than purely economical constraints) explains part of these developments. Hydrodynamic studies conducted through simulations and model tests have been identified by an increasing number of yards and designers as an important aspect of their work. From an owner’s perspective, these developments also tell him at an early stage of his project what he can expect from his vessel. The attention which is paid to the design of such vessel at an early stage also shows the maturity of the market, where the quest for quality integrates the use of modern research and development tools, quantification and qualification of design choices through hydrodynamic studies. Literature

[1] D. De Groot, “Weerstand en

Voortstuwing van Motorboten”, N.S.P Publication No. 93, 1951.

[2] S.L. Toxopeus, P.F. van Terwisga and C.H. Thill. "Mission Based Hydrodynamic Design of a Hydrographic Survey Vessel". Proceedings of Prads 2001 Conference, Shanghai, September 2001.

[3] G.B. Loeff and S.L. Toxopeus, "Manoeuvring Assessment in Concept Ship Design". Proceedings of NAV 2003 symposium, Palermo, June 2003.

[4] IMO Resolution MSC.137(76), "Standards for Ship Manoeuvrability", December 2002.

[5] R. P. Dallinga and M. Kanerva., “Recent changes in ferry hull from design and their impact on seakeeping”, Cruise & Ferry conference, London, October 1993

[6] G. Gaillarde, “Pitch reduction in transit by using stabiliser fins”, The Modern Yacht Conference, Royal Institution of Naval Architects, 2003, Southampton, UK.

[7] R.P. Dallinga, ” Roll stabilisation of motor yachts: use of fin stabilizers in anchored conditions”, Projects 99, Amsterdam, November 1999.

[8] R.P. Dallinga, “Roll stabilisation at anchor: Hydrodynamic aspects of the comparison of anti-roll tanks and fins”, Projects 02, Amsterdam, November 2002.

[9] R.P. Dallinga, M. Levadou, J.E. Bos, F. Gumps, “Seakeeping of motor yachts and passenger discomfort”, Projects 03, USA, 2003.

[10] J.O. de Kat, “The numerical modelling of ship motions and capsizing in severe seas”, Journal of Ship Research, 1990.

[11] J.O. de Kat and W.L. Thomas, “Extreme rolling, broaching and capsizing - model tests and simulations of a steered ship in waves”, Prads 98, Den Haag, 1998.

[12] J.O. de Kat, “Causes of yacht capsizing in heavy seas”, Workshop on Safety of Ocean Racing Yachts, Sydney, 1999.

[13] K. Mc Taggart and J.O. deKat, “Capsize risk of intact frigates in irregular seas”, SNAME Transactions, 2000.

[14] J.O. de Kat, D.J. Pinkster and K.A. Mc Taggart, “Random waves and capsize probability based on large amplitude motion analysis”, Proceedings OMAE'02, Oslo, June 2002



138

APPENDIX

0

10

20

30

40

0 20 40 60 80 100 120

Lpp

Num

ber

of v

esse

ls

Figure 1 : Lpp of vessels studied at MARIN

since 1986 in powering

Figure 2 : Range of Lpp encountered over

the last 20 years at MARIN

Figure 3 : Range of CB and trend over years

0

10

20

30

40

50

60

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cb

Num

ber o

f ves

sels

Figure 4 : Block coefficient CB

Figure 5 : Beam and draft as a function of Lpp

00.5

11.5

22.5

33.5

44.5

55.5

66.5

77.5

8

20 30 40 50 60 70 80 90 100 110 120

Lpp [m]

L/B

and

B/T

ratio

[-]

L/B ratio B/T ratio

Figure 6 : L/B and B/T as a function of Lpp

0

20

40

60

80

100

120

140

1970 1975 1980 1985 1990 1995 2000 2005

Lpp

[m

]

Figure 7 : Range of Lpp encountered for seakeeping and manoeuvring model tests

0

5

10

15

20

0 20 40 60 80 100

Lpp [m]

Bea

m o

r dra

ught

[m

Beam

Draught L/B = 3.5

L/B = 6.5

L/T = 12

L/T = 25

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Blo

ck c

oeff

icie

nt C

b [-

]

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Lpp

[m

]




139

Figure 8: Tests in the new Seakeeping and Manoeuvring Basin (SMB)

Figure 9: Motor Yacht A (length LA)

Figure 10: Motor Yacht B with LB = 1.015·LA

Figure 11: 3D wake measurement in the strut plane with the twisted strut as a result

after optimisation

Figure 12: Cavitation observation for twin-screw propeller in behind condition



140

Figure 13: Twin compacts pods

15.1 m/s

Bf 7

Bf 5

9.4 m/s

0°10° 20°

30°40°

50°

60°

70°

80°

90°

100°

110°

120°

130°

140°150°

160°170°180°

190°200°210°

220°

230°

240°

250°

260°

270°

280°

290°

300°

310°

320°330°

340° 350° Leaving the quay

Going to the quay

Figure 14 : Example of crabbing ability of a yacht with pods

0

5

10

15

20

0 5 10 15 20

Approach speed [kn]

Max

imum

hee

l ang

le [d

eg]

Reference ships Figure 15 : Maximum heel angle during

turning with maximum rudder angle

0

5

10

15

20

25

30

0 10 20 30 40L/V [sec]

10/1

0 Fi

rst o

vers

hoot

ang

le [d

eg]

IMO Res.MSC.137(76)Reference ships

Figure 16 : First overshoot angles obtained during 10/10 zig-zag manoeuvre

0

5

10

15

20

25

30

0 10 20 30 40L/V [sec]

20/2

0 Fi

rst o

vers

hoot

ang

le [d

eg]


Figure 17 : First overshoot angles obtained during 20/20 zigzag manoeuvre




141

0

1

2

3

4

5

6

7

0 10 20 30 40L/V [sec]

Tact

ical

Dia

m. /

L [-

]


Figure 18 : Tactical diameters obtained during turns with maximum rudder angle

-10.0%

-5.0%

0.0%

5.0%

10.0%

-10.0% -5.0% 0.0% 5.0% 10.0%

Lpp or Beam variations

Pitc

h SD

A

[deg

]

Effect of length and beam variation on heave and pitch (draft kept constant) in Beaufort 4 - head seas at 14 knots

-10.0%

-5.0%

0.0%

5.0%

10.0%

-10.0% -5.0% 0.0% 5.0% 10.0%

Hea

ve S

DA

[m

]

Lpp Beam

1.56

4.24

Figure 19 : Effect of Length and Beam on heave and pitch in BF4 in head seas at 14

knots

-10.0%

-5.0%

0.0%

5.0%

10.0%

-10.0% -5.0% 0.0% 5.0% 10.0%

Lpp or Beam variations

Vert

ical

acc

. St.1

2.5

[m

/s^2

]

Lpp Beam

Effect of length and beam variation on AZ (draft kept constant) in Beaufort 4 condition head seas at 14 knots

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

-10.0% -5.0% 0.0% 5.0% 10.0%

Vert

ical

acc

el. S

t.5

[m/s

^2]

Lpp Beam

2.46

3.42

Station 5

Station 11.5

Figure 20 : Effect of Length and Beam on

vertical accelerations in BF4 in head seas at 14 knots

Figure 21 : Vertical accelerations along ship length



142

0%

10%

20%

30%

40%

50%

60%

Hull (incl.skeg)

Bilge keels Rudders Passive fins Active fins

at anchor in transit condition

Figure 22: Roll damping contributions

Fin Angle

Fin Reaction Force

Acceleration

Stationary

Deceleration

Decay

Inertia Drag Inertia (acceleration) (constant speed)

(deceleration)

Figure 23: Principle of use of fins at anchor

Figure 24 : Typical CL for high and low

aspect ratio fins

Figure 25 : Typical fin / bilge keel arrangement

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.5 1.0 1.5 2.0 2.5Singificant Wave Heigth [m]

rms

Rol

l [d

eg]

passive fins active fins anti-roll tank

Figure 26: Comparison of fins and anti-roll

tank at anchor

LowEncounterFrequency

ResonantRoll

Normal WaveFrequency Range

Figure 27: Encounter frequency as a function heading and wave frequency

High aspect ratio fin

Low aspect ratio fin




143

Figure 28: Roll response as a function of

heading and wave frequency

Figure 29: Steady wave system obtained in

calm water, inducing a quasi-steady modification of the stability (change of GM)

Figure 30: Wave elevation along the ship in stern-quartering seas, inducing dynamic

modification of the stability (change in GM value)

0 0.5 1 1.5 2 2.5 30

30

60

90

120

150

180

Wave frequency [rad/s]

Hea

ding

[deg

]

natural roll period

Lpp / projected wavelength = 1 to 1.3

Zero encounter frequency

Figure 31: Combinations of heading and

wave frequency yielding bad tuning for risk of large roll or yaw

0 20 40 60 80 100 1200

10

20

30

Lpp [m]

Ship

spee

d [k

not]

.

Figure 32: Combination of speed and Lpp providing potential problems with course

keeping ability wave through reducing transverse stability

motor yachts

zero encounter + wavelength/Lpp=1

area of potential cour-se keeping problems



144

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