INFLUENCE OF THE BOW SHAPE ON LOADS IN HIGH AND STEEP WAVES

Transcription

1 Proceedings of 29 th International Conference on Ocean, Offshore and Arctic Engineering OMAE 2010 June 6-11, 2010, Shanghai, China OMAE INFLUENCE OF THE BOW SHAPE ON LOADS IN HIGH AND STEEP WAVES Günther F. Clauss Ocean Engineering Division Technical University Berlin Germany Marco Klein Ocean Engineering Division Technical University Berlin Germany Matthias Dudek Ocean Engineering Division Technical University Berlin Germany ABSTRACT To ensure survival of floating structures in rough seas, a precise knowledge of global and local loads is an inevitable integral part for safe design. One of the key parameters is the vertical bending moment. Not only vertical forces but - as previous investigations revealed - also longitudinal forces significantly contribute to the vertical wave bending moment. Three segmented ships, equipped with force transducers, are investigated systematically in high and steep regular waves and in harsh wave environments at several cruising speeds to identify the structural loads. The model tests are carried out in the seakeeping basin of the Technical University Berlin at a scale of 1:70. To cover possible influences of the bow geometry, three different types of vessels are chosen, a bulk carrier with a full bow, a Ro/Ro vessel and a container vessel with a V-shaped frame design. For identifying the influence of the wave height and steepness on the vertical bending moment, model tests in regular waves with different crest/trough asymmetries are performed with the Ro/Ro vessel and the bulk carrier. The program can be subdivided into three parts, each characterized by the same wave lengths with varying wave steepness. The first test series includes regular waves with small amplitudes, thus linear wave theory can be applied. In the second part the same (regular) wave lengths have been generated with increased wave heights, i.e. increasing crest/trough asymmetries and wave profiles within Stokes II domain. During the last part of the experimental program the wave heights are further increased to reach wave profiles within Stokes III domain. For the evaluation of the test results in regular waves - in particular in high steep waves - the results are compared to the respec- Address all correspondence to this author. tive Response Amplitude Operator determined by the transient wave package technique. Here the focus lies on the asymmetry of the hogging and sagging loads with respect to the wave steepness and the bow geometry of the two investigated ship models. Furthermore, the influence of the freeboard height on the vertical bending moment is analysed. For this purpose the container vessel is investigated with two different freeboard configurations in a harsh wave environment. This paper presents a detailed overview of the results of these model tests including investigations in frequency and time domain. INTRODUCTION Since ships are exposed to harsh wave environments one of the key parameter in ship design is the vertical wave bending moment. Reports on ship losses (e.g. Erika (1999) and Prestige (2002)) and encounters with freak waves (e.g. Bremen (February 2001) [1] and Voyager (February 2005) [2]) illustrate that a precise knowledge of the occurring maximum local and global loads is indispensable. During the last few years studies have been published, presenting investigations on the vertical bending moment due to rogue wave impact, comparing numerical simulations and model tests with the IACS Common Rules ( [3 5]). For the design process the IACS-Common Rules [6] provide empirical formulae to determine a design vertical wave bending moment which is one of the main parameters in the dimensioning process of ships. Depending on the block coefficient, the hogging - sagging criterion leads to higher sagging than hogging moments. This nonlinearity 1 Copyright c 2010 by ASME

2 is mostly associated to the nonlinear geometry of the hull [7] and increases with decreasing block coefficient. Watanabe et al. [8] investigated experimentally the influence of the nonlinear effects on the vertical bending moment of a container vessel and showed that the vertical bending moment for large bow flares is nonlinear. Fonseca and Guedes Soares [7] compared numerical and experimental results of wave-induced vertical ship motions and loads, revealing that the geometry of the bow flare in combination with the wave steepness significantly influences the global loads, in particular the sagging loads. Within the framework of the project Handling Waves, funded by the European Union, the influence of the bow geometry of three different types of ships on the vertical bending moment is systematically investigated in high, steep, regular waves as well as in an extreme wave sequence. The tests are carried out with a bulk carrier, a container vessel and a Ro/Ro vessel covering head seas. EXPERIMENTAL SETUP The model tests are conducted in the seakeeping basin of the Ocean Engineering Division of Technical University Berlin at a model scale of 1:70. The basin is 110 m long, with a measuring range of 90 m. The width is 8 m and the water depth is 1 m. On one side a fully computer controlled electrically driven piston type wave generator is installed. For investigations of the influence of wave height on the vertical bending moment - with special emphasis on effects resulting from the forecastle geometry - three ship models are investigated, in example a Ro/Ro vessel, a bulk carrier and a container vessel. Table 1 shows the main dimensions and load conditions of the three investigated ships. The wooden models are subdivided into segments being connected with three force transducers at each cut. Two of them are installed close to the deck level, one underneath the bottom of the model. The force transducers register the longitudinal forces during the model tests. Based on the measured forces and the given geometrical arrangement of the three force transducers, the resulting vertical wave bending moment and the longitudinal forces are obtained. On this basis, the superimposed vertical wave bending moment including the counteracting vertical bending moment caused by the longitudinal forces with respect to selected vertical levels is determined. Two of the wooden models are divided into three segments intersected at L pp /2 and L pp /4 (measured from forward perpendicular (f.p.) - Ro/Ro vessel (see Fig. 1, top)), bulk carrier (see Fig. 1, middle). The container ship model (see Fig. 1, bottom) consist of two segments intersected at L pp /2. During the tests the models are towed with an elastic suspension system using a triangular towing arrangement. The longitudinal motions are restricted by a spring in front of and a counter weight behind the model. The suspension system is connected with the ship models by a thin elastic cross bar, which is mounted on the deck FIGURE 1. MODELS OF THE INVESTIGATED SHIPS (Ro/Ro VESSEL (TOP), BULK CARRIER (MIDDLE) AND CONTAINER VESSEL (BOTTOM)). FIGURE 2. COMPARISON OF THE MEASURED VERTICAL BENDING MOMENT AT L pp /2 (TOP) AND L pp /4 (BOTTOM) MEASURED FROM F.P. WITH AND WITHOUT SUSPENSION SYSTEM. of the aft segment (centre of gravity in x-direction). With this arrangement, heave and pitch motions remain unrestrained. For the evaluation of the suspension system, i.e. to ensure that the measurements are unaffected by the suspension system, the Ro/Ro vessel is investigated with and without the suspension system. The Ro/Ro vessel with its high freeboard is chosen since a possible influence of the suspension system on the vertical bending moment depends on the lever arm of the mounting point to the neutral axis (waterline level). Thereby the Ro/Ro vessel is investigated in a high, steep regular wave (H = 13 m) with a wave length of L w /L pp = 1.1 to select a worst case wave length regarding the maximum vertical bending moment as well as the asymmetry of the vertical bending moment. Fig. 2 illustrates the measured vertical bending moment of the Ro/Ro vessel with the 2 Copyright c 2010 by ASME

3 TABLE 1. MAIN DIMENSIONS AND LOADING CONDITIONS OF THE THREE INVESTIGATED SHIPS container vessel bulk carrier Ro/Ro vessel Length between perpendiculars [m] L pp Breadth [m] B WL Draught [m] D f p Displacement [t] Block coefficient [-] c B Longitudinal centre of gravity [m] x cg Vertical centre of gravity [m] z cg Transversal metacentric height [m] GM t suspension system (blue lines) and without the suspension system (black lines). The top diagram shows the vertical bending moment at L pp /2 and the bottom diagram the vertical bending moment at L pp /4 (bottom) measured from f.p.. Comparing the mean values between t = 900 s and t = 1100 s reveal a variance of approx. 1.2 % for the absolute vertical bending moment and approx. 2 % for the vertical hogging moment. This proofs that the influence of the suspension system is negligible. EXPERIMENTAL PROGRAM AND RESULTS For identifying the influence of the bow shape on loads in high, steep waves, different model tests have been performed. The Ro/Ro vessel with its V-shaped frame design and the bulk carrier with its full bow are chosen for systematical investigations of the influence of the bow geometry in high and steep regular waves at different cruising speeds. Furthermore, the influence of the freeboard height on the vertical bending moment is analysed. For this purpose the container vessel is investigated with two different freeboard configurations - the design freeboard and a freeboard extension (cf. Fig. 1 (bottom) and Fig. 3) - in the New Year Wave, a harsh wave environment with an embedded rogue wave. The freeboard extension is approximately 10 m, which is high enough to ensure that the highest wave (crest height H c = 18.5 m) of the irregular sea state is not spilling green water over the weather deck. Regular Waves The investigated discrete regular wave lengths (L w ) have been chosen in order to cover the complete range of interest in frequency domain - from L w /L pp = 0.6 to L w /L pp = 3.1. With regard to the influence of the wave steepness on the vertical wave bending moment, the test program has been divided into three parts. Each part comprises the same wave lengths with varying wave steepness. The wave height and steepness have been selected to obtain wave profiles with different crest/trough asymmetries and to evaluate the influence of different wave profiles (asymmetries) on the vertical bending moment. Fig. 4 illustrates the regions of validity of various gravity water wave FIGURE 3. MODEL OF THE CONTAINER VESSEL WITH FREE- BOARD EXTENSION. THE HEIGHT OF THE FREEBOARD EX- TENSION IS APPROX. 10 m IN FULL SCALE. FIGURE 4. BREAKING WAVE HEIGHT AND REGIONS OF VA- LIDITY OF VARIOUS GRAVITY WATER WAVE THEORIES [9]. 3 Copyright c 2010 by ASME

4 theories with regard to the wave profile. The relative water depth is plotted on the x-axis and the relative wave height on the y-axis. It is shown that for small amplitude waves the linear wave theory can be applied whereas for increasing wave heights (and hence increasing crest/trough asymmetries) the Stokes II and Stokes III theories become valid (the relative water depth of the investigated wave lengths is between < d/(g T 2 ) < (cf. Fig. 4). The first part of the experimental program includes regular waves with small amplitudes. The relative wave heights of the investigated waves are between H/(g T 2 ) = assuming linear wave theory (cf. Fig. 4 - red stars). In the second part the same (regular) wave lengths have been generated with increased relative wave heights between < H/(g T 2 ) < where the wave profile is within the Stokes II domain (cf. Fig. 4 - green stars). During the last part of the experimental program the wave heights are further increased to generate high, steep waves and thus the relative wave heights are between < H/(g T 2 ) < where the wave profile is within the Stokes III domain (cf. Fig. 4 - blue stars). For the following investigations the small amplitude waves and all related results are subsequently labelled with the abbreviation WH1, the Stokes II domain results are labelled with WH2 and the FIGURE 5. COMPARISON OF THE RESPONSE AMPLITUDE OPERATOR (RAO) FOR THE VERTICAL BENDING MOMENT AT L pp /2 DE- TERMINED WITH THE TRANSIENT WAVE PACKAGE TECHNIQUE (BLUE DASHED CURVE) AND THE RESULTS IN REGULAR WAVES (BLACK CURVE) FOR THE Ro/Ro VESSEL (LEFT) AND THE BULK CARRIER (RIGHT) FOR F n = 0. THE RED STARS DENOTE THE HOGGING MOMENT (2 M hogging /H), THE BLACK CIRCLES THE SAGGING MOMENT (2 M sagging /H). THE TOP DIAGRAM PRESENT THE RESULTS FOR WH1, THE CENTRE FOR WH2 AND THE BOTTOM DIAGRAM FOR WH3. 4 Copyright c 2010 by ASME

5 Stokes III domain results are labelled with WH3. All the investigated regular waves are illustrated in Fig. 15. The respective RAOs (black curves) of the Ro/Ro vessel (left) and the bulk carrier (right) are shown in Fig. 5 for L pp /2 and Fig. 6 for L pp /4. In addition the sagging (black circle) and hogging moments (red stars) are separately registered in both diagrams to evaluate the asymmetry of the measured bending moment compared to wave steepness. All results are compared to the Response Amplitude Operator (blue dashed curve in Fig. 5 and Fig. 6) determined by the transient wave package technique. The top diagrams of both figures show the results for small amplitude waves (WH1), the centre diagrams for wave profiles in the Stokes II domain (WH2) and the bottom diagrams for wave profiles in the Stokes III domain (WH3). The agreement for the vertical bending moment at L pp /2 of the RAOs determined in regular waves ( sagging moment + hogging moment - black curves) and in transient wave packages (blue dashed curves) for both vessels is fair. For the Ro/Ro vessel, however, the vertical bending moment in regular waves tends to induce higher loads for higher steeper waves. This observation is verified by the results of the vertical bending moment at L pp /4 (Fig. 6). Here, the loads significantly increase with increasing wave height. With regard to the asymmetry of the hogging and sagging FIGURE 6. COMPARISON OF THE RESPONSE AMPLITUDE OPERATOR (RAO) FOR THE VERTICAL BENDING MOMENT AT L pp /4 DE- TERMINED WITH THE TRANSIENT WAVE PACKAGE TECHNIQUE (BLUE DASHED CURVE) AND THE RESULTS IN REGULAR WAVES (BLACK CURVE) FOR THE RO/RO VESSEL (LEFT) AND THE BULK CARRIER (RIGHT) FOR F n = 0. THE RED STARS DENOTE THE HOGGING MOMENT (2 M hogging /H), THE BLACK CIRCLES THE SAGGING MOMENT (2 M sagging /H). THE TOP DIAGRAM PRESENT THE RESULTS FOR WH1, THE CENTRE FOR WH2 AND THE BOTTOM DIAGRAM FOR WH3. 5 Copyright c 2010 by ASME

6 moments, it is clearly identifiable that the asymmetry between sagging and hogging increases with increasing wave height, in particular for the Ro/Ro vessel. The bulk carrier shows a different trend. For medium wave heights (WH2) the asymmetry increases as well but for the highest waves (WH3) the asymmetry of the vertical bending moment remains on the same level at L pp /2. The results at L pp /4 (Fig. 6 bottom right) illustrate a special feature the asymmetry switches its direction for the highest waves and the hogging moment is higher than the sagging moment. In this context it must be noted that green water effects are observed for the highest waves at the stern and at the forecastle of the bulk carrier. Furthermore the sagging as well as the hogging loads are higher as the loads predicted by linear theory in contrast to the Ro/Ro vessel (higher sagging and lower hogging loads) which was also observed by Guedes Soares and Schellin ( [10]). Nevertheless, the strongest influence of the bow geometry and wave steepness is observed for the Ro/Ro vessel. Therefore the effect of wave steepness on the vertical bending moment of the Ro/Ro vessel is subsequently investigated in detail. At first, the Ro/Ro vessel is additionally investigated with forward speed. Fig. 7 shows the measured vertical wave bending moment of the Ro/Ro vessel at L pp /2 (left) and at L pp /4 (right) with forward speed, the top diagrams for WH2 and the bottom diagrams for WH3. Here, the x-axis FIGURE 8. RELATIVE CREST HEIGHT RANGES AT THE BOW OF THE RO/RO VESSEL. shows the ratio between the encounter wave length and the length between perpendicular which results in shorter waves. The black curves denote the total load, the red stars the hogging moments and the black circles the sagging moments. Fig. 7 clearly shows higher loads for the cruising ship in comparison to the results at stationary conditions. Furthermore, the detected asymmetry increases strongly as well which results in two times higher sagging loads for L pp /2 and four times higher sagging loads for L pp /4. The relative surface elevation at the FIGURE 7. RESULTS OF THE MODEL TESTS IN REGULAR WAVES (BLACK CURVE) FOR THE RO/RO VESSEL AT L pp /2 (LEFT) AND AT L pp /4 (RIGHT) FOR F n = 0.13 IN COMPARISON TO THE HOGGING MOMENT (2 M hogging /H - RED STARS) AND SAGGING MOMENT (2 M sagging /H - BLACK CIRCLES). THE TOP DIAGRAMS ORESENT THE RESULT FOR WH2 AND THE BOTTOM DIAGRAMS FOR WH3. 6 Copyright c 2010 by ASME

7 bow of the Ro/Ro vessel (measured by a dedicated wave probe) is presented in Fig. 8. The illustration marks the measured crest heights at the bow for the three different wave steepness ranges. The orange lines denote the relative crest height range for WH1 (which is very narrow), the green lines denote the range for WH2 and the blue lines for WH3 for F n = 0. The respective dashed lines show the maximum relative crest heights at the bow for F n = The lower limit of each range is related to the shortest wave lengths (L w /L pp = 0.6). The relative crest height increases with increasing wave length up to the maximum by approximately L w /L pp = 1.1 for F n = 0 before the relative crest height slightly decreases with further increasing wave length. Due to the encounter frequency of the cruising vessel the relative crest height reaches its maximum by approximately L w /L pp = 0.6 for F n = With increasing crest height the wetted surface at the V-shaped bow increases rapidly which results in a huge bending moment asymmetry with clearly higher sagging loads. The experimental data are now analysed in frequency domain to obtain the harmonic components of the vertical bending moment ( [8]) depending on the wave steepness and the forward speed. Fig. 9 shows the analysis procedure for the three wave steepnesses (Ro/Ro vessel). The procedure starts with the measured vertical bending moment in time domain (top left diagram) which is then transformed into frequency domain (top right) via Fast Fourier Transformation (FFT) to obtain the harmonic components of the vertical bending moment. Analysing the exemplarily shown vertical bending moment (top left) in frequency domain, the FFT results in very sharp bending moment spectra with high spectral energy peaks at the first order wave frequency accompanied by higher order peaks, which are more significant at steeper waves (blue and cyan line in the top right diagram). Beside these results, the asymmetry of the vertical bending moment - with higher sagging moments and lower hogging moments in steep waves - is documented by energy contributions (red line in the top right diagram) at very FIGURE 9. FREQUENCY DOMAIN RESULTS OF THE VERTICAL BENDING MOMENT FOR THE THREE WAVE STEEPNESSES FOR F n = 0. THE THREE CENTRE DIAGRAMS SHOW THE RESULTS AT L pp /2 FROM WH1 TO WH3 (FROM LEFT TO RIGHT) AND THE BOTTOM DIAGRAMS FOR L pp /4. EACH DIAGRAM SHOWS THE (NORMALIZED) AMPLITUDE OF THE FIRST (BLUE LINE) AND THE SECOND HARMONIC (CYAN LINE) AS WELL AS THE OFFSET (RED LINE) OF THE BENDING MOMENT FOR THE RESPECTIVE INVESTIGATED WAVE LENGTHS. 7 Copyright c 2010 by ASME

8 low frequencies close to zero (similar to the effect of an offset in the registration) ( [7, 8]). The frequency domain results for the three wave steepnesses are illustrated in the six lower diagrams. The three centre diagrams present the results at L pp /2 from WH1 to WH3 (from left to right) and the bottom diagrams for L pp /4. Each diagram presents the (normalized) amplitude of the first (blue line) and second harmonic (cyan line) as well as the offset (red line) of the bending moment for the respective investigated wave lengths. The normalized bending moment amplitude of the first order wave frequency is approximately the same for the three different wave heights at L pp /2, in contrast to the vertical bending moment at L pp /4. There the normalized bending moment amplitude increases with increasing wave height. The second order amplitudes and the offset have a minor influence on the vertical bending moment for WH1 and WH2, but for the highest waves both increase significantly. Fig. 10 presents the results at forward speed for WH2 and WH3. The great influence of the second harmonic amplitude as well as the offset is already high for WH2 and increases significantly for WH3. Altogether, the bow geometry of the Ro/Ro vessel causes vertical bending moment responses with high energy contributions at very low frequencies depending on the wave steepness and length which results in the observed sagging - hogging asymmetry. Irregular Waves Besides the systematical investigation of the influence of the bow geometry of a bulk carrier and a Ro/Ro vessel in regular waves, the influence of the freeboard height in high, steep irregular waves is investigated as well. Therefore a container vessel is investigated with two different freeboard configurations - the design freeboard and a freeboard extension (cf. Fig. 1 (bottom) and Fig. 3). For identifying the influence of the freeboard height, a dedicated irregular sea state with an embedded rogue wave is chosen - the so called New Year Wave. This giant single wave (H max = m) with a crest height of H c = 18.5 m has been FIGURE 10. FREQUENCY DOMAIN RESULTS OF THE VERTICAL BENDING MOMENT FOR WH2 AND WH3 FOR F n = THE TWO TOP DIAGRAMS SHOW THE RESULTS AT L pp /2 AND THE BOTTOM DIAGRAMS FOR L pp /4. EACH DIAGRAM SHOWS THE (NORMALIZED) AMPLITUDE OF THE FIRST (BLUE LINE) AND THE SECOND HARMONIC (CYAN LINE) AS WELL AS THE OFFSET (RED LINE) OF THE BENDING MOMENT FOR THE RESPECTIVE INVESTIGATED WAVE LENGTHS. 8 Copyright c 2010 by ASME

9 ζ (t) [m] t [s] New Year Wave recorded in the North Sea New Year Wave generated in the wave tank FIGURE 11. COMPARISON OF MEASURED MODEL WAVE TRAIN AT TARGET POSITION AND THE SEQUENCE RECORDED AT THE DRAUPNER PLATFORM (ALL DATA FULL SCALE). ultimate vertical bending moment (M u = γ M WV ). Since each segment features almost the same weight and centre of gravity, the measured vertical bending moment is nearly identical in both test runs. But the impact of the New Year Wave results in different sagging loads since the crest of the extreme wave is higher than the design freeboard of the container vessel thus the crest can act on a larger area/displacement at the freeboard extension. The sagging load due to the impact is approximately 20% higher with the freeboard extension. Comparing the maximum vertical recorded during a storm on January 1, 1995 at the Draupner platform in the North Sea [11] and occurred in a surrounding sea state characterized by a significant wave height of H s = m (H max /H s = 2.15) at a water depth of d = 70 m. To transfer the real-sea measurement into the wave tank, an optimization approach for the experimental generation of tailored wave sequences with predefined characteristics is applied [12]. This method enables the generation of specific, tailormade wave groups superimposed to irregular seas. During the experimental optimization, special emphasis is laid on the exact reproduction of the wave height, crest height, wave period as well as the vertical and horizontal asymmetry of the target wave. Fig. 11 shows the measurement in the wave tank in comparison to the original wave sequence recorded at the Draupner platform. Fig. 12 shows the container vessel during the impact of the New Year Wave at the forward perpendicular. The top picture displays the impact with freeboard extension and the bottom picture with design freeboard. The height of the freeboard extension is approximately 10 m and therefore ensures that the crest of the New Year Wave (crest height H c = 18.5 m) is not spilling over the weather deck. For a better comparison of the two investigated configurations the total weight and the centre of gravity of each segment is almost the same (< 0.5%) during both test runs, but the radii of inertia are different. The investigations comprise model tests at stationary conditions (F n = 0) and at forward speed (F n = 0.13). Fig. 13 shows the results for F n = 0. The target location of the New Year Wave is at the forward perpendicular. The top diagram displays the surface elevation at the forward perpendicular - here this extraordinarily high wave is clearly identifiable. The blue curve denotes the measurements with the freeboard extension and the red curves without the extension. The centre diagram displays the surface elevation at the mainframe. Both diagrams show that the position of the container vessel within the tank is identical in both test runs. The bottom diagram presents the vertical bending moment. To discuss the measured results in time-domain they are compared to the design bending moments according to the IACS-Common Rules [6]. The cyan dashed lines denote the vertical design bending moment and the black dashed lines the FIGURE 12. SNAPSHOT OF THE CONTAINER VESSEL TAKEN DURING THE EXPERIMENTS. THE TOP PICTURE SHOWS THE CONTAINER VESSEL DURING THE IMPACT OF THE NEW YEAR WAVE WITH THE FREEBOARD EXTENSION AND THE BOTTOM PICTURE WITHOUT THE EXTENSION. 9 Copyright c 2010 by ASME

10 FIGURE 13. COMPARISON OF THE MODEL TEST RESULTS IN THE NEW YEAR WAVE WITH (BLUE LINE) AND WITHOUT (RED LINE) THE FREEBOARD EXTENSION FOR F n = 0. THE TARGET LOCATION OF THE NEW YEAR WAVE IS AT THE FOR- WARD PERPENDICULAR. FIGURE 14. COMPARISON OF THE MODEL TEST RESULTS IN THE NEW YEAR WAVE WITH (BLUE LINE) AND WITHOUT (RED LINE) THE FREEBOARD EXTENSION FOR F n = THE TARGET LOCATION OF THE NEW YEAR WAVE IS AT THE FOR- WARD PERPENDICULAR. wave bending moment with the design vertical bending moment reveals that both configurations exceed the design vertical bending moment slightly. Fig. 14 shows the results for F n = The top diagram displays the surface elevation at the forward perpendicular and the centre diagram the surface elevation at the mainframe. The blue curve denotes the measurements with and the red curves without the freeboard extension. Both diagrams reveal that the cruising container vessel encounters the same waves in time and space. The bottom diagram presents the vertical bending moment. Here, two wave group impacts are observed during the experiments which causes higher wave crests compared to the design freeboard of the container vessel - the impact of the New Year Wave (t = 860s) and the wave group at t = 758s. Both cases clearly show higher sagging loads for the vessel with freeboard extension - 20% at t = 758s and 30% during the impact of the New Year Wave. The maximum sagging loads are clearly higher for the standard freeboard configuration in comparison to the design bending moment but is within the limits considering the safety factor γ whereas the sagging loads for the freeboard extension slightly exceeding the design bending moment including the safety factor γ. CONCLUSIONS This paper presents a comprehensive study on vertical bending moments for different types of ships. The influence of the bow shape on loads in high, steep regular waves has been investigated systematically with a Ro/Ro vessel and a bulk carrier. Furthermore, the influence of the freeboard height on the vertical bending moment is analysed. For this purpose a container vessel is investigated with two different freeboard configurations in a harsh wave environment with an embedded rogue wave, the so called New Year Wave. The model tests are conducted with segmented wooden ship models, intersected at the mainframe, and the Ro/Ro vessel and bulk carrier are additionally intersected at L pp /4 measured from the bow. During the tests, the models are towed with an elastic suspension system using a triangular towing arrangement, whereby the heave and pitch motions remain unrestrained. The model tests in regular waves reveal that the vertical bending moment (total load and the hogging - sagging asymmetry) of both investigated ship models at L pp /2 shows a good agreement with the Response Amplitude Operator (RAO) in moderate relative wave heights (WH1 and WH2). But with further increasing relative wave height (WH3) the hogging - sagging asymmetry increases significantly, in particular for the Ro/Ro vessel with its V-shaped frame design at the bow. Furthermore it is shown that the effect of a large asymmetry between hogging and sagging loads is clearly more distinctive at L pp /4 for the Ro/Ro vessel which also results in higher total loads as predicted by the RAO. In addition it is pointed out that the hogging - sagging asymmetry depends strongly on the relative wave steepness and the bow geometry. Investigations in frequency domain revealed that the observed sagging - hogging asymmetry of the Ro/Ro vessel is presented by high energy 10 Copyright c 2010 by ASME

11 contributions at very low frequencies. Altogether it is shown that the influence of the wave steepness is more significant for the Ro/Ro vessel due to its V-shaped frame design at the bow and the high freeboard ( [8]). The container vessel is investigated in an irregular sea state with embedded rogue wave and two different freeboard configurations at stationary conditions (F n = 0) and with cruising speed (F n > 0.13) with the impact location of the rogue wave at the forward perpendicular. The investigations reveal that the impact of the rogue wave is severe for the container vessel. The impact of the New Year Wave results in different sagging loads for the two configurations. The freeboard extension reveals significantly higher sagging loads (up to 30%) for wave crests which exceeds the design freeboard since the crest can act on a larger area/displacement during the impact at the bow. ACKNOWLEDGMENT This paper is published as a contribution to the project HANDLING WAVES, which is founded by the European Commission, under the contract TST5-CT We highly acknowledge the support of this research project. Furthermore we would like to thank our project partner - Grimaldi Group Naples, HSVA, Instituto Superior Tecnico, Navigation Maritime Bulgare,Portline, RINA, Rodriquez Cantieri Navali SPA, St. Petersburg State University, Technical University of Varna - for the valuable teamwork. [7] Fonseca, N., and Guedes Soares, C., Comparison of Numerical and Experimental Results of Nonlinear Wave- Induced Vertical Ship Motions and Loads. Journal of Marine Science and Technology, 6, pp [8] Watanabe, I., Keno, M., and Sawada, H., Effect of bow flare on shape to wave loads of a container ship. J Soc Nav Archit Jpn, 166: [9] Clauss, G., Lehmann, E., and Östergaard, C., Offshore Structures, Vol. 1: Conceptual Design and Hydrodynamics. Springer Verlag London. [10] Soares, C. G., and Schellin, T. E., Nonlinear effects on long-term distributions of wave-induced loads for tankers. Journal of Offshore Mechanics and Arctic Engineering, 120(2), pp [11] Haver, S., and Anderson, O. J., Freak Waves: Rare Realization of a Typical Population or Typical Realization of a Rare Population?. In Proceedings of the 10th International Offshore and Polar Engineering Conference (ISOPE), pp [12] Clauss, G. F., and Schmittner, C. E., Experimental Optimization of Extreme Wave Sequences for the Determinsitic Analysis of Wave/Structure Interaction. In OMAE th International Conference on Offshore Mechanics and Arctic Engineering. OMAE REFERENCES [1] Schulz, M., Ich spürte den Atem Gottes. Der Spiegel, December. No. 51/2001. [2] Bertotti, L., and Cavaleri, L., Analysis of the Voyager storm. Ocean Engineering, Vol. 35(1), pp [3] Clauss, G. F., Schmittner, C. E., Hennig, J., Guedes Soares, C., Fonseca, N., and Pascoal, R., Bending Moments of an FPSO in Rogue Waves. In OMAE rd International Conference on Offshore Mechanics and Arctic Engineering. OMAE [4] Guedes Soares, C., Fonseca, N., Pascoal, R., Clauss, G. F., Schmittner, C. E., and Hennig, J., Analysis of wave induced loads on a FPSO due to abnormal waves. In OMAE Specialty Conference on Integrity of Floating Production, Storage & Offloading (FPSO) Systems. OMAE- FPSO [5] Clauss, G., Klein, M., and Kauffeldt, A., Limiting Loads and Motions of Ships in Extreme Sea States. In IMAM th Congress of Intl. Maritime Assoc. of Mediterranean. [6] GL, Germanischer Lloyd. In Rules & Guidelines. 11 Copyright c 2010 by ASME

12 Appendix A FIGURE 15. REPRESENTATION OF ALL INVESTIGATED REGULAR WAVES, COMPREHENDIN WAVES WITH SMALL AMPLITUDES (WH1 - LINEAR THEORY - RED LINE), WAVES WITH MEDIUM AMPLITUDES (WH2 - STOKES II DOMAIN - GREEN LINE) AND STEEP WAVES WITH HIGH AMPLITUDES (WH3 - STOKES II DOMAIN - BLUE LINE). THE INVESTIGATED WAVES ARE SHOWN FOR BOTH VESSELS, RO/RO VESSEL (LEFT) AND BULK CARRIER (RIGHT), IN GROUPS ACCORDING TO THE RELATIVE WAVE LENGTH 0, 6 L w /L pp 2,1. 12 Copyright c 2010 by ASME