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As you know, upwind sails should function as efficient wings, developing the maximum lift with the minimum drag and heeling moment. This goal is achieved when the optimum spanwise circulation distribution is chosen and when the separation of the flow is minimized. These choices reflect the two main objectives of sail computations: the calculation of precise sail coefficients to feed the Velocity Prediction Program (VPP), and the determination of the optimum sail dimension and shape to aid the sail maker in the design of the sails.
Optimization of Upwind Sails
To determine the sail shape that maximizes the thrust for a given condition of wind speed and angle, an inverse 3D Vortex Lattice Method has been developed. The optimization procedure is based on a genetic algorithm (developed, as the whole software, by Ing. Mario Caponnetto), where the optimum is obtained adding successively random disturbances to an initially arbitrary shape. With this approach several different constraints can be added very easily. Sails can be optimized with or without the constraint of maximum heeling moment. Limiting values of the sectional lift coefficient can be included to prevent stall. The viscous drag (taking into account the separation of the flow behind the mast) is added at each section using 2D drag coefficients that have been previously calculated using Fluent (a Navier-Stokes flow solver) for different combinations of camber ratio and mast dimension. During the iteration procedure, unrealistic sail shapes can be discarded. Typical is the case of mainsails having an inverse camber in the upper part; theoretically this shape maximizes the thrust in strong wind conditions, but is obviously very difficult to trim. Using this code it is possible to obtain the complete polar diagram of the “best” sails in upwind conditions and their corresponding shapes.
Fig. 1 shows a sample case of how the optimum circulation distributions on the genoa and the mainsail change varying the wind speed.
In both cases a heeling moment of 30 t*m, corresponding to a heel angle of about 30 degrees for an IACC, has been imposed. In medium wind conditions (Aws=18 Kn) the main is very loaded, especially toward the head. As the apparent wind speed increases (Aws=30 Kn), the main must be unloaded at the tip, and in theory the circulation should be zero from the headboard to the top of the genoa. For the same sample case the corresponding twist angle and camber ratio are plotted in Fig. 2 and Fig. 3.
These results are in good agreement with the experience. In medium wind both the genoa and the main have relatively highly cambered sections. The twist of the main is large, but the boom is close to the centerline of the boat. In stronger wind the sails must be flattened, especially the main in the upper part, to lower the center of pressure. The head of the genoa must be still relatively fat to avoid separation. The twist of the main is reduced, but the angle of the boom is increased.
Given as input the dimensions of the sail plan (P, E, four main girths, headboard width, BAS, I, J, headsail foot length, mast longitudinal diameter, rake), the sailing conditions (heel angle, boat speed, true wind speed, true wind angle) and the heeling moment that must be developed (equal to the righting moment of the boat for the given heel angle), “Sailopt”, considering also the vertical wind shear and the water surface symmetry effect, gives as output:
Aerodynamic resulting forces and moments (driving force, heeling force, vertical force, heeling moment, yawing moment, pitching moment), extremely useful for the boat designer to design and position the appendages, to feed the VPP with very precise upwind aerodynamic coefficients and to compare the performance of different possible sail plans
3D optimum sail flying shape and sail trim, very useful for the boat designer to position the headsail tracks and the standing rigging, and for the sail designer to evaluate optimum camber and twist of each section of the upwind sails.
A lot of effort has been put in the validation of the software, and the good results achieved allow now to extensively trust the values given by “Sailopt” computations.
Here is an example of the comparison between “Sailopt” aerodynamic driving force and tank testing based IACC hydrodynamic drag, which should be equal in the VPP computed sailing points. As you can see in Fig. 4 the two values show very good agreement. |