Introduction
Guidelines exist for the design of sailing yachts; however, internationally recognized standards dictating the design and structural strength of yachts are yet to be established. This research was performed as part of a systematic review of existing data to establish standard design techniques and rules, for cruiser-class sailing yachts.
The hull form and other design information used in this paper was taken from a 31-foot trial ship due to be manufactured as a result of the project on ‘the development of the modern sailing boat of cruiser class for the Korean coastal sea based on the hull form of Korean traditional boat’ (Kim et al., 2006).
Based on the approach of L. Larsson and R. E. Eliasson when discussing the design of the YD-40 (Larsson and Eliasson, 2000), we assessed the stability, structural strength, and stiffness of this trial ship, verifying results in accordance with elective ISO design standards (ISO/DIS, 2004). Using these resources, the design load, thickness, stiffness and scantling of the yacht’s panels were decided upon. Through stress calculations with finite element analysis, the authors verified the yacht’s structural design to estimate the strength of the completed ship.
Structural design
Design limitations
The design restrictions in Australian standard 4132-1993 were applied to this ship, limiting the length of the hull bottom and side to 35 m as in Fig. 1.
In accordance with design standard 4132-1993, the design pressure of the hull bottom and sides was determined by selecting the largest expected values according to equations (1) and (2).
The design pressure for the hull bottom is defined as
The design pressure for the hull sides is defined as
The following guidelines were applied to the design of this ship:
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The scantling length of the yacht was less than 24 m, according to the ISO.
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Design load calculations based on the panel size of the ship’s structural members (stiffness, bulkhead, web frame etc.), the related coefficient of position, the calculated load, and the moment of inertia were to be within the minimum values required by the ABS.
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The thicknesses of the fiber-reinforced plastic (FRP) panels were calculated to ABS guidelines.
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ISO-defined FRP properties were used as per Table 1.
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Designs were based on the use of composite spray molding (CSM), with the weakest stiffness as shown in Table 2.
Scantling of panel members
Numerous panels must be constructed, including stiffeners, girders, bulkheads, the web frame, side and bottom shell plates, and the deck. Minimum values for the related coefficients of inertia and section modulus were calculated as follows:
With the exception of the deck, the area reduction factor Kar was applied to each panel.
The longitudinal and transverse impact factors kL and kV, used in the calculation of pressure acting on the ship’s longitudinal panel were defined as
for
and
where
where A = 1, B = 1, C = 0.9 and D = 0.8. A. The stability index was category four.
Design pressure of bottom, side and deck
The pressure distribution shown in Fig. 2 was used to find the design pressure of the ship’s bottom longitudinal.
The pressure distribution shown in Fig. 3 was used to find the design pressure of the ship’s side.
The design pressure of the yacht’s deck and bulkhead Pd was calculated as a function of their shortest dimension, independent of panel position.
Scantling of panel members
When the previously proposed design pressure was applied to a panel
The minimum section modulus and moment of inertia were calculated as follows:
The minimum thickness of sandwiched FRP material was calculated according to ABS guidelines:
where Ipanel is the moment of inertia, and SMpanel is the section modulus of each panel. The ultimate shear stress required of each panel was
The stiffener scantling has a close relation to the design pressure acting on each panel.
Yacht’s characteristics for analysis
The ship studied in this research was a 31-foot cruiser- class yacht, capable of housing 4–6 men. The yacht (BBHH971) had a CR class keel type fin and a masthead rig mounted for efficient sailing.
The principal dimensions of this yacht are as given in Table 3 and the finite element analysis modeling for each principal part (hull, deck, deckhouse, hull and keel) is shown in Fig. 4 (Ojeda et al., 2004).
Only the principal components affecting the ship’s structural strength were modeled (hull, bulkhead, deckhouse etc.). FEM modeling of less significant parts was not considered, but their weights were included in the principal components where appropriate.
Structural analysis
In this work, the yacht’s performance was analyzed in six scenarios:
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Travelling at a speed of 12 knots with the ship in an upright position.
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Travelling through a wave to consider the impact of slamming on the hull model.
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Travelling through a wave to consider the impact of slamming on the hull and keel models.
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The ship’s carrying state (transverse slope of 90°), due to the weight of the keel.
Structural analysis of the hull
Structural analysis, using previously published design recommendations (Shin et al., 2006), was carried out in still water conditions with the ship’s speed set at 12 knots. Figure 5 shows the stress distribution for each part of the hull. The maximum stress at the deck opening was 32.7 MPa. It is thought that the peak stress occurs at this point due the lack of bulkhead. The maximum stress in the parts of the hull connected to the keel was 19.7 MPa.
These stress values are, respectively, 28% and 17% of the tensile yield stress of FRP (115 MPa) meaning that there is no large impact on the hull.
Impact of slamming on the hull
In this section, we discuss the structural strength analysis of the hull and keel, and the effects of slamming. Two cases were considered: a Heeling angle of 0°, and a Heeling angle of 30°.
The distribution of design pressure in the longitudinal and transverse directions is shown in Fig. 2 and 3. Values given in the ABS guidelines were used in this analysis. The stress distributions for each part of the hull as a result of slamming at heeling angles of 0° and 30° are shown in Fig. and 6.
In Fig. 5, with a heeling angle of 0°, the maximum stresses in the deck and hull components were 47.8 and 25.3 MPa, respectively. In Fig. 6, with a heeling angle of 30°, the maximum stresses in the deck and hull components were 49.4 and 25.1 MPa, respectively. These stress values are 45% of the tensile yield stress of FRP.
Impact of slamming on the hull and keel
In case three, strength analysis was performed to assess the impact of slamming on the hull and keel, with heeling angles of 0° and 30°. Keel plates were modeled as solid elements.
The resulting stresses are shown in Fig. 7–9. The peak stress occurred near to the connection between the hull and keel, as shown in Fig. 9. The maximum equivalent stress was 50.5 MPa in the 0° case, and 54.8 MPa in the 30° case. All the resulting stresses were less than half the yield stress of FRP.
Strength analysis due to the weight of the ballast keel and keel
The carrying state of the yacht was then investigated in the case of severe loading.
The total keel weight used in this analysis was 1500 kg. Strength analysis was performed by applying mass to the keel, to confirm the structural safety of the connection point with the hull.
Fig. 10 shows the load distribution of the keel. Six loads, weighing 250 kg (2452.5 N) each, were evenly distributed about the center of the keel. Fig. 11 shows the resulting deformation of the keel shape, and Fig. 12 shows the Von-Mises stress distribution at the point of connection between the hull and keel.
A peak stress of 50.3 MPa, which is 43.7% of the yield stress of FRP, was measured at the point of connection between the hull and keel. According to these results, no serious damage to the hull or keel is expected.
Evaluation of analysis results
The resulting Von-Mises stresses for all cases described above are summarized in Table 4. The maximum stress of 54.8 MPa occurred in case five where the effects of slamming pressure on the hull and keel were considered at a heeling angle of 30°. The total stresses were shown to be less than half of the yield stress of FRP. Consequently, no issues are expected with respect to the structural strength.
Conclusion
This work has investigated the strength of the hull and keel of sailing yacht BBHH971 for the “development of a cruise class sailing boat based on a traditional design” task as a part of the Local Innovation Project for Man-power Training.
Patran (MSC Software Corp.) software was used to preand post-process data solved by Nastran. The initial conditions and example scenarios were based on ABS, ISO and Australian (4132-1993) standards. However, since there was no specific procedure for the structural analysis of yachts at the time of publication, the investigation was carried out with reference to other analysis examples. This study is therefore able to be used as yacht design reference material in the future.
Further examination of the localized strength analysis for the joint between the hull and keel, in terms of condition and material, is required as the highest stresses were found in this region. Strength and stiffness analysis should also be carried out for materials such as FRP.