THE SIXTH INTERNATIONAL SYMPOSIUM ON
PRACTICAL DESIGN OF SHIPS AND MOBILE UNITS
SEPTEMBER 17-22. 1995
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STRUCTURAL DESIGN OF SAILING BOATS: A CASE STUDY
D.N. DIMOU, V.J. PAPAZOGLOU Shipbuilding Technology Laboratory,
Department of Naval Architecture and Marine Engineering, National Technical University of Athens,
9 Heroon Polytechniou Ave., GR-15773 Zografos, Greece
ABSTRACT
A methodology for the structural design and heuristic optimization of racing sailboats using the finite element method is presented. After a brief introduction, general aspects concerning structural design considerations of such boats is given. Emphasis is placed on the design
criteria to be used, which include adequate strength, high hull rigidity and appropriate weight distribution. This is followed by guidelines on the structural modeling using available finite
element method packages. Asan illustration, the methods described are applied in thecase of the 470 class racing boat, for which indicative results are provided both for the hull and the
rigging system. It is concluded that with present day tools, a designer is able to perform complex calculations, leading to improved structural designs for sailing boats.
INTRODUCTION
Sailing yacht structural design poses a great challenge for the designer. Cruising and racing sailboats have different requirements, hence different solutions should be employed. Cruisers
are the least demanding, so the focus here sets on the racers. Assuming that its hull shape is hydrodynamically correct, a racing sailboat must also be strong enough to withstand the various imposed loads without failure. At the same time, the hull should be adequately stiff,
deforming minimally, to enable it to act as a rigid platform for the sailplan while keeping a fair shape. The hull weight must be kept low and carefilly distributed so that the ends, especially
the bow section, remain as light as possible. Considering that racing yachts are generally
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Racing yachts fall into three categories: One-Design (O.D.) classes, yachts racing under a rating system, and level racers. The first category indudes mostly small sailboats, while the
other two involve offshore racers. In each One-Design class, all boats are "copies" of the
same design, they race together, and are built under special rules controlling the construction
and the dimensions of this class. Some classes are strict O.D., with tight rules, while others are development classes, less tightly controlled. The optimization ofan O.D. racing sailboat poses the greatest difficulty for the designer because he must push the rules to their limits,
exploiting every possible loophole, while playing with tolerances of a few millimeters. Rating
systems, such as the International Offshore Rule (IOR) or the International Measurement
System (IMS), are used to classify yachts according to their abilities, thus permitting yachts of
varying sizes and types to race together when an appropriate time allowance system is used.
Level systems look like development O.D. classes bound by rating systems, as for example in
the case of Ton yachts. The designer in.these two latter categoriesis far less constrained than
in an O.D. class because the limitations are fewer and with completely different purposes. The complicated geometry of most boats and the multitude and complexity of the
imposed loads force the designer to either
use a simplified theoretical model or usesophisticated computer-based methods, such as the Finite Element Method (FEM). This
paper presents an effort to use the finite element method of analysis for sailboat structural
design. With today's advances in computer technology, a designer can perform on his personal computer types of analysis previously feasible only on workstations or mainframes.
Using a 486 or Pentium-based PC and a proven FEM analysis package, linear, non-linear,
static or dynamic and buckling analyses of complicated models can be performed with relative ease.
STRUCTURAL DESIGN CONSIDERATIONS
There are two basic tasks a designer is asked to deal with: either to undertake a completely new design or to try various improvements on an existing boat type. In either case, hull, rig
and keel/centreboard-rudder models can be checked individually or combined in a complete
model. In most cases, a complete analysis consists
of strength, stiffness and weightcalculations, modal analysis having no practical interest. Stress maps of the hull reveal potential stress concentration areas, showing clearly where to expect possible failures and
thus, prompting for correcting actions. When using special "laminated" plate or shell elements, one can get layer (lamina) stresses, core crushing stresses (for sandwich elements), failure estimation based on various criteria, such as the Tsai-Wu criterion, and even residual thermal stresses due to the curing process.
Accurate material data is, however, required in order to obtain all this information, a
task which in most cases is quite difficult to accomplish. Today, the majority of sailboats is
made of composite materials rather that wood or aluminum. To obtain exact composite material mechanical properties, one must perform special tests on samples cut from the actual structure; there exist, of course, various analytical methods for property prediction and these can be utilized as a first estimate.
Nodal displacements define the stiiThess characteristics of the hull as a beam and various configurations of different stiffener arrangements or different materials can be tested against each other in order to increase the rigidity of the boat hull. With a special mass properties
processor, both total hull weight and radius of gyration can be obtained, indicating whether a boat is under- or over-weight and giving a measure of the weight distribution, that is whether
the hull ends are light or not. In the case of keels and rudders, the same type of information can be made available, but rigs (masts with rigging) should be also checked for buckling,
either global or local, by using appropriate models [1, 2].
One critical aspect of an accurate and realistic sailboat strength analysis is the
determination of the loading conditions of the structure in question. There are many different
forces acting on a sailing boat: dynamic wind forces carried to the hull through the sails and
mast; rig pre-tension; hydrostatic pressure on the immersed areas of the hull and wave impact
pressures on the bow section; loads due to dynamic lift of the centreboard or the keel; the weight of the keel; concentrated loads from certain fittings and crew members [3]. Most of these loads are dynamic and difficult to predict. Sail forces are the prime example: frequent wind velocity and direction changes, in combination with the motion of the hull through waves, create a highly complicated, continuously changing situation. During the last few years, serious attempts have been made to analyze and understand these loads, especially in
America's Cup research and development projects [4-6] or through industry sponsored
programs [7, 8]. However, most of these projects are highly classified and little is known about their results and conclusions. Thus, unless one has the ability to experiment and take
direct measurements on a real boat, he has to rely
on empirical data and simpli!yingassumptions for engineering calculations. In addition, a finite element model requires another highly critical decision, that regarding model support and other boundary conditions. Sailing
boats can be thought of as hollow beams on elastic foundation. However, the determination
of this kind of support is a complex matter and leads engineers to make additional simplifying assumptions, regarding model support.
In the sequence, the various steps required for a sailboat FEM analysis are presented,
from model creation to results interpretation, including hardware and software requirements.
*
+
Figure 1 The International 470 Class Dinghy
easily adapted to any other boat type. The 470 is a two-person boat, with a length of 4.70 m
and is currently being used in the Olympic Games (see Figure 1).
For maximum efficiency, a 486 or Pentium PC is needed, while the installed RAM and hard disk capacity dictate the size of the model that can be processed. More RAM allows the
manipulation of larger system matrices and provides higher processing speeds, while larger
hard disks provide more temporary storage space, thus permitting the analysis of larger
models. It is possible to use less RAM but some specific models, especially for non-linear analysis, may require more hard disk space. As far as the required software is concerned, although it is possible to create personal FEM analysis codes, it is recommended to obtain a commercially available package meeting the analysis requirements. Generally, these offer a
variety of options, allowing numerous element types and thousands of elements in each model, while they are usually more user-friendly than the in-house developed software. Some
packages include complete CAD software, along with specialized pre- and post-processors. With these modules, one can transform a drawing to a finite element model with a few key
strokes, as well as view graphically the results of the analysis on the screen.
In the present case, a FEM package from Algor Inc. was used [9]. It includes a CAD module, a surface generating program, various decoders for automatic input file generation,
static and dynamic linear/non-linear processors, and composite and buckling analysis
processors. The first step in the analysis procedure involves drawing the model using the
CAD program. For the boat hull, it is better to use the surface generator capabilities and then transfer the drawing to the CAD module. Of course, it is possible to import a drawing
constructed by another program, if needed. The loading and boundary conditions are subsequently applied. Then, the appropriate decoder creates the FE model input file from the
drawing and the respective FE processor is employed. Finally, the post-processing module is used for the presentation and interpretation of the obtained results.
In order to create a computer model of the 470 dinghy, a set of the current class rules
and lines plans was used [10]. The 470 is controlled by a set of tight rules that limit the external shape of the hull, the materials used in its construction, and the sail and mast
dimensions. The intention of these rules is that the boats shall be as alike as possible in all
respects affecting speed and ease of handling, in order that racing success shall depend mainly
on the skill of the crew. In fact, the current edition of the rules, introduced in 1993, pose
several restrictions in hull construction, eliminating most of the loopholes present in previous
editions which enabled the construction of specialized boats. Thus, the optimization of this
type of sailboats is no longer possible as it is now illegal to alter the stiffener arrangement, but
the 470 remains one of the best boats for structural analysis and reinforcing arrangements evaluation. It is rather lightly built but severely loaded and, in the past, this usually led to
rapid deterioration of hull strength and stifThess. In fact, the class rules intention is to increase the average 470 life span. Thus, besides the evaluation of various alternative stiffener arrangements, a verification of the rules efficiency can be also made here.
STRUCTURAL MODELING
Before creating a FE model, certain decisions must be taken by the designer on the type of
elements to be used for the various parts of the model, the loads to be imposed on the model,
its support and, finally, the use of possible axes or planes of symmetry. Sailboat hull models
usually combine plate or shell, orthotropic or laminated elements with beam and possibly 3-D
solid elements. Mast models can be constructed either with beam and cable, or shell and
cable, elements, depending on the purpose of the model. Finally, keels can be modeled using 3-D solid elements, while "sandwich" or orthotropic plates or shells can be employed for thin centreboards and rudders.
The 470 hull-deck model was created using the surface generator module of the FEM
package. Data input can be accomplished with a digitizer directly from the plans, or by using
the keyboard for offset points input. The latter procedurewas used in the present case study.
Numerous hull and deck stations are drawn on screen as B-Splines and then, hull and deck
surfaces are generated as NURBS surfaces, defined by the respective curves. Using the
surface-surface intersection tool, the various bulkhead-defining curves are produced and the 3-D surface model is generated with a simple command that, after selecting the appropriate
curves, creates quadrilateral or triangular NURBS patches. Powerful rendering tools are used
next for surface verification. If an existing design is modeled, then careful data input almost always creates fair surfaces, but if a new design is tried, there are a few surface-fairing tools
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Figure 2 Complete 470 Hull Mesh
available. Once the designer is convinced that the model is "correct", he proceeds to the final
step, the meshing of the patches. Both local and global mesh density can be controlled with
simple command parameters, which means that once the surface patches are ready, the
designer can create a meshed model as fine or as coarse as required within a few seconds.
Figure 2 shows the complete 470 hull mesh generated in the present case.
There is a very important factor affecting the mesh of a model, namely the material
actually used in the structure under investigation. Isotropic materials like metals are modeled
easily, since there is no difference in their rnechnical properties along different axes. On the
other hand, orthotropic and generally laminated materials possess different properties depending on the material axis concerned. In most cases, these are the materials used for
sailboat construction [11], thus great care must be taken to carefully orient each element local
coordinate system to coincide with the actual principal material axes. For laminates made of alternating mat and woven roving layers, homogeneous orthotropic plate or shell elements
can be used with reliable results as far as displacements are. concerned but, if stress contours
are to be obtained and/or if sandwich laminates or unidirectional and other special layers are
to be implemented, composite laminated elements must be employed.
The. meshed hull-deck model is then. transferred to the CAD module of the FEM
package, where the final adjustments are made. before the decoding stage. Plate or shell
elements of different materials are assigned to different groups, while line color defines the respective element thickness. Finally, boundary conditions and loads
are applied to the
appropriate nodes or elements and the plate or shell hull/deck skin model is ready for decoding, thus providing the analysis input file for that portion of the structure.
The various stiffeners are modeled with beam elements, so a different specialized
module is employed for input file preparation. Then the plate or shell and beam models are combined into the final boat model using a special utility program. Different beam models
were used for testing various stiffener arrangements, and modified plate or shell models were employed for testing modified materials or variable skin thickness. There are certain areas in the model where 3-D solid elements may be employed; inside the keelson, under the mast step and at the fore and aft edges of the centreboard case, solid wood is used as reinforcement and 3-D solid elements can be used to simulate this. It is also possible to use plate or shell
elements for the stiffeners, since they are usually of the top-hat type, but this leads to a very
complex, large and inflexible model if the complete boat is concerned. Thus, this may be done
for small parts of the boat only, if and where detailed analysis is desired; for example, in
stiffener intersections or special construction details such as hull and deck joints.
The mast can be modeled with beam elements for the mast tube and cable elements
(tension truss) for the rigging. This is a coarse model, suitable for global buckling analysis or for the calculation of reaction forces, which can then be used as load input to the hull model.
If detailed mast analysis is desired, plate or shell elements must be used for the mast tube instead of beams. In this way, local buckling analysis can be performed and highly stressed
areas can be clearly shown, while the bending characteristics of different mast sections can be also checked in more detail. There is a very important point that must be observed here: mast
models have to be geometrically non-linear, while hull models can be linear. The geometric non-linearity of the mast model is due to the large displacements observed, especially when
the mast spreaders are not perpendicular to the mast but angled aft. Pre-tensioned rigging and time-depended loads are also better simulated in non-linear models.
Having reached the final decisions concerning the model geometry and the element types, the focus sets on the loading conditions of the model. In sailing conditions, dynamic wind forces are carried to the hull through the sails and mast, in addition to rig pre-tension,
hydrostatic pressure on the immersed areas of the hull and impact pressures on the bow, loads due to dynamic lift of the centreboard, and point loads from certain fittings and the two crew
members. The 470 is usually sailed with a highly pre-tensioned rig for performance reasons
and although certain deck areas are also highly stressed from the crew, stresses due to the rig
tension have been the major problem so far, directly affecting the racing performance of the boats. Thus, in this paper a typical case is analyzed, showing the effects of high rig loads. In practice these are achieved by tensioning the jib halyard which acts as a forestay. By taking into account only these loads which are symmetric about the center plane of the hull, only a
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model is required because the loads are not symmetric and torsion is also experienced. In the
present case, the forestay and shrouds are in tension, while the loads at the mast step are
compressive. A tension load of 2400 N on the forestay is applied on the beam mast model and the calculated shroud and mast step reactions are used as input to the hull model. This tension load is probably the safe maximum amount used in 470s and that is why, it was used here. The
mast was assumed to be choked-restricted in the fore-aft direction at mast gate level, so the
respective reactiOn is also added there. All loads are added as forces on the respective nodes. The last decision to be taken is on the support of the model. The main factor affecting it is the purpose of the analysis. If the objective is to make comparisons among different
stiffener arrangements, a simplified approach can be taken. Keeping that in mind, the boat here is simulated with fully tensioned rig but standing on a trailer that supports it on two
points along the centerline.
RESULTS AND DISCUSSION
The goal in the structural optimization of a racing sailboat is the achievement of a rigid
platform for the mast, strong enough and at the same time as light as possible. In order to
compare the stiffness and rigidity of the various evaluation schemes, certain criteria should be established. The mast stands on the mast step, the shrouds connect to the hull chainplates and
the forestay is attached to the stem fitting. The 'relative displacements of these points - step, stem and chainplates - determine the rigidity of such a platform. Obviously, it is desirable to create a hull that, under load, keeps these displacements to a minimum. For every "case",
calculations of these displacements are made. The fairness of the deformed hull shape can be also checked visually on the displaced model; the presence of large, bumps and hollows on a racing hull should be avoided at all costs. In addition, the element stress level's are checked to confirm that they do not exceed the strength limits of the respective materials. In fact, stresses
should be much lower than the ultimate strength values, because in reality not only are there more loads to be considered, but fabrication defects may also lower the material properties. The key here is the avoidance of stress concentration areas and the reduction of stress levels
to the minimum possible amount. Finally, total weight, center of gravity and mass moment of inertia calculations provide vital information to the designer:: all One-Design classes prescribe minimum hull weights and sometimes they require additional "hull swinging" tests to
determine the weight distribution of their' boats. If a boat is found, underweight or having lighter ends than allowed, then corrector weights are added, sometimes located at points
causing performance problems. Weight calculatiOns reveal such possibilities and so remedying
actions can be taken before boat measurement, while in the case of an overweight boat, the
In order to perform a comparative structural analysis of a sailboat, a hull with a basic
structural arrangement should be created first. This is the "standard" boat which will serve as a benchmark for all tests. Every other idea should be tested against this in an effort to improve it. Subsequent design cycles may be done based on another "standard" hull, Which should be the best case of the previous cycle. In this way, continuous improvements are achieved, whereas at the same time a pattern showing the effectiveness of certain ideas is
steadily set. Experience gained from such an approach is helpful if another similar boat type is
to be analyzed, as it saves time and effort by eliminating certain ideas that havenot been
proven effective enough.
In the present case, a half 470 hull is modeled using 3638 plate/shell orthotropjc
elements of variable thickness and mechanical properties. Forty-one (41) wooden 3-D solid
elements are used in certain points inside the keelson and in the centreboard case. Finally, 941 beam elements simulate the various hat-type stiffeners that reinforce the hull and deck skins.
It must be noted that these beams must be offset to their centroid coordinates in order to be
accurately modeled. This can be done automatically in the beam pre-processor module, but it proves difficult in the case of ring frames, where each element needs different offset values. In
reality, the program internally moves the beam nodes to their centroid coordinates and then uses quasi-rigid, very stiff beams to connect them with the plate nodes. Thus, instead of
specifying offsets, additional stiff beams are used there in the same manner that the program should have done it. However, in order to avoid solution difficultiesby specifying excessive beam stifThess, a simple reinforced surface is analyzed first and the calculated rigid beam
values are then used in the boat model. The mast model is made by using 220 non-linear beam and cable elements. Since the problem incorporates large displacements, the updated Langrangian formulation is used for the mast problem.
Model post-processing is done with the respective module of the FEM package, where
nodal displacements and element stresses are graphically presented. Figure 3 presents the
initial and deformed shape of the mast obtained from the large displacement analysis, whereas Figures 4 and 5 show examples of the stress contours obtained on the top and bottom side of the hull, respectively. For hull stiiThess evaluation, the displacements of the mast and shroud
bearing nodes in each case are taken and used in themast model as prescribed displacements varying with time. The case that keeps the mast closer to its initial position is the one that
provides the stiffer hull. The mass properties processor provides only three numbers for each
model: total weight, coordinates of the center of gravity and mass moment of inertia about any point we chose. After calculating the center of gravity, a second run provides the mass
moment of inertia about this point. Division of this inertia by the hull weight gives the radius
of gyration which, along with the hull weight, can be directly compared to the current rule
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Figure 3 Initial and Deformed Configurations of the Mast Model
Tensor 3 .Ee+DE 2.9e+OE 2.3e4-t15 1 .le+DE 1.De+OE -.e4CS -B .e-f CS -1 .e+EI -2.e+Cb -2.e-fCB -3.E+flE -'1.e+O
Tensor 3.Ee+O . 2.9e+D . 2.2e+OB 1.le+05 1.Oe+U LL9e+Q -2.e#O -O.e+05 -1.E+O -2.e+O -2.e+OE -3.e-fOE _Lle+OE
Figure 5 Longitudinal Stresses on the Bottom Side of the Hull
CONCLUSIONS
A FEM analysis can provide vast amount of information to the designer, that otherwise would
be available only after the construction and evaluation of a real boat. The latter process is very costly and time-consuming, while the finite element method is faster and more reliable
because it does not take into account possible material imperfections or faults in the
construction technique that may degrade the quality and mechanical properties of a laminate.
Thus, while a real boat may suffer from an initial problem of this kind, ruining the overall performance evaluation process, a finite element model, by assuming perfect materials and
production techniques, can directly rate the structure, provided that no serious mistakes have
been made during modeling. The aforementioned facts imply, of course, that very careful
material selection and as perfect as possible boat construction processes are needed for a boat to behave in reality as predicted in the computer analysis. It must be also noted that additional factors also exist affecting the performance of a racing boat. If they are not taken into
account, they can render all the above calculations useless. For instance, the advantages
gained by having a rigid hull can be quickly negated by not using the best shrouds available.
The hull would not deflect too much, but the shrouds would stretch instead, ruining the mast
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[21 Atkinson, P., "On the Structural Response of a Mast-Sail System," In RJNA
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[21 ALGOR iNC., Finite Element Analysis Reference Manuals, 1994. International 470 Class Rules, International YachtRacing Union, 1993.
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