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www.sname.org/sname/mt April 2013 of a yacht given a true wind direction and a true wind speed. VPPs solve the equations of motion for the yacht and are used to study a yachtÂs performance throughout the range of true wind angles and speeds in which the yacht will sail. VPPs are used to determine in what conditions the boat becomes overpowered. Generally the maximum loading a yacht will see occurs when the sails are producing a heeling moment equal to the maxi- mum righting moment of the yacht. From these VPP studies, maximum loading conditions are established and used for input into the coupled CFD-FEA analysis. Once the apparent wind speed and angle have been set for a load analysis, a RANS CFD calculation is performed to solve for the aerodynamic forces on the sails and other structures. RANS CFD models yield surface pressures and frictional shear forces on all the surfaces as well as the detailed ow patterns in the vol- ume of air surrounding the boat. Post processing RANS results from maximum loading runs can give the designer valuable information about ow conditions producing the maximum loads. e results can show details of the ow such as when the sails are stalled, when unsteady wakes and vortices are pres- ent, and how various components interact aerodynamically. ere are many RANS codes used for the analysis of sails and rigs. We mainly use Fluent, but CFX, Star CCM+, and OpenFOAM are often used. ere are a number of proprietarty RANS codes in use as well. e surface forces are then transferred to the FEA model across the surfaces. e surfaces serve as the interface between the uid volume forces solved for in the CFD model and the solid stresses and displacements solved for in the FEA model. Because the CFD and FEA models have separate meshes, the surface forces from the CFD analysis must be interpolated to the FEA grids. is procedure works well but a slight loss in forces can occur. Proper denition of all included faces in the model is an important part of both the CFD and FEA analysis setup. Nonlinear FEA simulations Many of the exible structures used in yachts such as sails, masts, mandrels, and cables behave nonlinearly when loads are applied. erefore, non-linear FEA codes must be used to ana- lyze them. Non-linear FEA codes iteratively solve for structural displacements, enabling the loads to change as the geometry deforms. Capturing this behavior is important for the mem- brane calculations on sails, the reaction of cables that can go slack when no load is applied, and the bending of masts, booms, and furling mandrels. ere are two types of reaction loads that are important to the sailing load analysis of yachts. e rst is the membrane loads in the sails that are used by sail designers to engineer the sails. e second is the reaction loads that the sails impart to the rigs that are used by the yacht designers to engineer the hard- ware to which the sails attach. Membrane loads are modeled using nonlinear shell FEA elements. Sails are constructed from layers of woven material or laminate cloths made with load bearing bers sandwiched between sheets of plastic lm and reinforcing bers. Depending on how detailed a load analysis is being performed, the sail material can be dened either isotropically or by oriented layers of orthotropic material dened by the structure of the mate- rial and how it is arranged in the sail. Patches, battens, corner, and edge attachments are added to the models as needed by the analysis. When detailed analysis is performed on the sails, it is important to resolve nonlinear behavior such as folding and load realignment. Sail designers use the membrane load- ing information to select materials and also to help determine the panel and ber layouts in the fabric. Maps of stress paths in the sails that come from the FEA models are used to minimize the needed ber weight and costs in laminate sails by aligning bers with load paths. e second type of reaction loads important to sailing load analysis is the reaction loads placed on the rig by the sails. For initial design studies, sail corner and edge loads can be used as input into rig component FEA models. For nal design, the reaction of the sails and rig can be solved for together in one model that captures the details of the sail-structure interaction. One common use for rig load analysis is to accurately dene the maximum load sheeting and sail setup conguration. e RANS CFD surface and shear force contours.