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SAILS AERODYNAMICS:

Figure 1

As sails can be regarded as wings, in principle, there is no difference in the way forces are generated by the flowing fluid and in the way shapes are designed by engineers. However, designing sails is much more complex than designing aircraft wings for a number of reasons. First, sail aerodynamic and hull hydrodynamic performances are inherently coupled. The sail thrust force has in fact to balance the hydrodynamic resistance generated by the interaction of the hull with the water flow, and the sail heeling force needs to be balanced by the hydrodynamic side force. The sailboat weight, together with the vertical component of the aerodynamic load, finally has to balance the buoyant forces, as it can be seen in the figure 1, which shows a schematic representation of the overall equilibrium of the sailboat in the plane perpendicular to the direction of motion. The heeling angle at equilibrium (i.e. at real sailing conditions) is thus a result which comes from the coupled solution of both the sail aerodynamic problem and the hull hydrodynamic problem, and depends upon the wind and sea conditions. Therefore it is generally not known in advance.
The second reason why sail design is more difficult than classical wing design is represented by the fact that, under the aerodynamic load, the mast bends and the sail fabrics strain. Clearly, different materials show different stressstrain relations and the deformations may be somehow limited by choosing suitable, more expensive, materials: industrial research and technological development are heading in that direction. In general however, such deformations determine a modification of the sail shape, which in turn determines a modification of the aerodynamic field and, as a consequence, the pressure load on the sails changes too, and so on and so forth. This is a socalled fluidstructure interaction problem which requires the coupled solution of both the sail aerodynamic and the sail structural problems. This is done generally with an iterative procedure where the aerodynamic and the structural problems are repeatedly solved one after the other until the changes between two successive iterations, both in the material deformation and in the aerodynamic load over the sails, become smaller than a predefined tolerance.
Finally, to make things even more complicated, while in classical wing aerodynamics the incoming flow is generally a uniform stream with constant intensity and direction, in sails aerodynamics this is not true any longer. The wind speed is not constant at different heights: close to the sea surface the wind is in fact slowed down by the viscous stresses (sea surface friction) which generate a boundary layer. The result is that the wind speed may vary by several knots along the mast, from the deck level to the mast tip. The figure 2 shows the vector composition of the true wind at four different heights along the mast with the velocity wind (i.e. the reversed sailboat velocity). The resulting apparent wind flowing over the boat rig shows an increasing intensity, moving upward along the mast, as well as a varying angle of attack at the sail leading edge. The schematic picture of the overall coupled problem of sailboat design is shown in the figure3.
We now turn our attention to the tools which are used by engineers to find a solution to problems of Applied Aerodynamics. The final goal is the determination of the wing shape, or of a sail shape eventually, capable of generating, for instance, the maximum thrust force under a number of known requirements, or the minimum heeling force, just to make a couple of examples. This is an optimisation problem because the shape that has to be determined will assure the optimal solution (maximum thrust or minimum heeling force) while satisfying a number of given requirements. To this end engineers use wind tunnel tests and computer simulations, which is a new branch of the computational sciences, called CFD after Computational Fluid Dynamics. CFD is devoted to the computer solution of the non linear system of the partial differential equations which govern the mechanics of fluids. Though such equations have been known since the 18th century, their practical use was limited by their complexity until the early 1980s when computers began achieving enough power to solve them with engineering accuracy.
Compared to wind tunnel measurements, CFD allows to drastically cut the time and the cost of the development: the design of new aircrafts, of new gas turbine blade rows, and of the new Formula 1 cars, just to make few examples, are almost fully studied and designed by CFD, with wind tunnel tests used for the final validation only. Moreover, wind tunnel measurements are affected by a number of side effects capable of contaminate the results, while CFD is not: for instance the presence of the tunnel walls which change to some extent the external flow conditions which occur in reality, and the need to experiment on a scaled, smaller, model that could be fit inside the wind tunnel test section.
Coming back to sail design business, today's detailed engineering studies are still only carried out by the Americas Cup consortia, though mostly via wind tunnel analysis and not yet, or not yet enough, via computer simulation. The reason why CFD has not entered yet into such a business is that sails aerodynamics is more difficult than wings aerodynamics or hull hydrodynamics. Even though it took time to CFD to show its capacity to be efficiently used for the accurate aerodynamic analysis of the wind flow over a pair of sails, CFD has now reached maturity and the right time for its extensive use in this field of application has finally come.
The need for wind tunnel tests to work on scaled models can be better understood by recalling here one of the most important parameters in fluid mechanics, the Reynolds number Re, which is defined as:
Re = ρLU / μ
where: L is a characteristic length scale (for instance the boat length), U is the average fluid velocity, ρ the fluid density and μ the viscosity coefficient. The Reynolds number represents the ratio between the inertia forces and the viscous forces acting on the body and it has the important property in fluid mechanics that all performance coefficients, such as the well known lift or drag coefficients of aeronautical applications, depend only on Re, i.e. C_{L}=f(Re), for any chosen geometrical design. The main goal of the aerodynamic analysis, either carried out by means of computer analysis or by wind tunnel tests, is the accurate determination of such performance coefficients. For example for a 45' sailboat moving in normal atmospheric conditions with an apparent wind speed of about 10 knots, the resulting Reynolds number would be of about 5x10^{6}. At such high values of the Reynolds number the curve of all performance coefficients is very close to be flat, i.e. all performance coefficients remain about constant with further increases of Re. By increasing the sailboat size to 90', provided that the sails design remains geometrically similar to the previous smaller case, and with the wind speed increased to 20 knots, than the Reynolds number would increase to 2x10^{7}, and very little would probably change in terms of non dimensional coefficients. The overall thrust force T would simply increase according to T=0,5C_{T} μU²A, due to the increase of the apparent wind U and of the overall sail surface area A, with a thrust coefficient C_{T} that remains almost constant.
Lets consider now what happens when one carries out experiments in wind tunnels. Even the biggest wind tunnels are limited by the dimension of their test sections, that in by no means can be big enough to accommodate a full scale model of sailboat. From the point of view of fluid mechanics, experimenting with a sail rig model some 10 to 20 times smaller than the real sail rig, would be equivalent to experimenting a smaller sail with the same wind speed, or to experimenting the full scale sail with a much weaker wind. In both cases the model Reynolds number would be lower than the real one by a factor 10 to 20. Computer simulation, as opposite, allows to make the fluid analysis always with the correct dimensions and conditions. However, thanks to the fact that real sailing conditions occur at very high values of the Reynolds number where its influence gets smaller and smaller, when a sail design is chosen, both the wind tunnel testing and the computer simulation keep their validity no matter what the sailboat size is.
A routinely use of CFD can help achieving the optimal design, saving time and resources. Different design options can be tested and eventually discarded in a matter of few days without resorting to constructing, sewing and trying them; different design options can also be quantitatively evaluated without resorting to subjective impressions which could result by testing sails in possible different wind and atmospheric conditions. Moreover, virtual experiments by computer simulation provide information of all thermofluid dynamic quantities at every location of the computational domain. For example, the figure 4 shows the surface pressure distribution on both the gennaker and the mainsail of a Volvo Ocean 60. The streamlines help understanding the flow structure in the vicinity of the sails. The figures 5, 6 and 7 show three cross sections at different heights of the jib and the mainsail of a Tornado catamaran: flow visualization of the computed results permits an extremely deep observation and investigation of all details of the flow field, both in two or threedimensional form, suggesting improvement and new design solutions.
Though the pictures show the enormous potential of computer simulation for the engineering design of more performing sails, a lot of Research & Development is going on in industries, research centres and universities in order to eliminate bottle necks from the whole computer process which includes pre and postprocessing with the actual numerical simulation in between. The figure 8 shows the output of the preprocessing phase, namely the creation of a suitable mesh for the computer simulation based on the use of finitedifference or finitevolume techniques.
More precisely, the figure shows a mesh of about 1 million points for the Volvo Ocean 60. It is needless to say that the quality of the mesh represents an important prerequisite for the quality of the computed results. Unfortunately, in case of complex geometrical arrangements of wings and sails, the achievement of a good quality mesh is a very difficult and time consuming task. This is the reason why R&D is looking for a sort of meshless numerical techniques such as the socalled "Immersed Boundary Technique".
The IBT consists of immerging the body on an underlying regular grid (a Cartesian mesh for instance) and then to add special extra terms to the equations, which should account for all the possible ways the body cuts the regular grid. To go into more details is beyond the object of the present article, however, if such a technique turns out to be an accurate method, than the long term objective of the simulation of a complete sailboat (which includes sail aerodynamics, hull hydrodynamics and fabric strain) will become reality in the very next future.