Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
Figures 1 and 2 show the wind tunnel model, the vortex lattice and the calculated pressure distribution. The WTT conditions are shown in Table 2.
Table 2: WTT sailing conditions. Sheeting angles
Apparent Wind Angle (AWA) Jib
Top Gradient Wind Speed (TGWS) wind velocity measured at 1 m high
12°
Mainsail 0.5° 21°
8.2 m/s
It is important to note that the wind tunnel tests were carried out in an Apparent Wind Speed (AWS) that varies with the height in order to simulate a realistic wind gradient. The aerodynamic analysis should therefore consider the effect of the wind gradient. As a wind gradient invalidates the irrotational assumption the wind speed is kept uniform, still is reduced in order to obtain the same heeling moment on the sailplan, as measured in the WTT: this wind speed is called the Equivalent Uniform Wind Speed (EUWS). Thus, the results in Tables 3 and 4 are related to two different wind speeds. The wind tunnel test AWS is the maximum speed measured in the wind tunnel (Top Gradient Wind Speed). The AWS of the MVLM is the EUWS, producing the same heeling moment on the sailplan [6].
Tables 3 and 4 show the results of the validation study. Wind tunnel tests reveal very little difference between the two sailplans. This validation study has concluded that, on the basis of the heeling moment as a control parameter, the MVLM:
Slightly underestimates the height of the Centre of Effort (CE) by 15% at most. This difference is due to the fact that the aerodynamic analysis carried out in the implemented MVLM considers the uniform wind flow and therefore the sails develop higher pressure forces in the lower part with respect the forces developed by the sails in the gradient wind flow in the wind tunnel.
Slightly overestimates the total aerodynamic force in a range not higher than 20%. This discrepancy can be explained by the fact that the CE calculated with the MVLM is lower and a bigger force is needed to achieve the same heeling moment to calculate the EUWS with a smaller arm.
Estimates a total force direction in a range not higher than 5 degrees aft. This discrepancy is believed to be due to inaccuracies in
the geometrical data
measurement taken from the pictures: in particular the entry angle and twist. This variation in the direction of the totals force explains the differences in the thrust (overestimated).
Overall the results of the validation considered satisfactory.
exercise are (underestimated) and side force
Table 3: Square top mainsail: WTT vs. MVLM results. Method
WTT 8.2 m/s 74° MVLM 6.4 m/s 12.1
Table 4: Pin head mainsail: WTT vs. MVLM results. Method
WTT 8.2 m/s 74° MVLM 7.4 m/s 15.5
+13% 78° 4° aft
3.2 SAILS STRUCTURAL ANALYSIS The structural
0.47
AWS Force [N] Force angle CEz [m] 11.6
0.50 +4% 79° 5° aft 0.47 -5%
AWS Force [N] Force angle CEz [m] 13.8
0.54 - 13%
deformation and stress distribution of the rig-sail system by using a non-linear
analysis consist of computing the finite element method where
geometric non-linearities are taken into account and material properties are linear [7]. The approach is well suited for problems involved where large displacements are encountered, while the material is expected to work within the linear region of the stress-strain function; no yielding is modelled. Since a non-linear problem is solved, Newton-Raphson’s method is used to find the deformed equilibrium state given a load perturbation. A linear relation between strain and displacement
is
assumed: this approximation is certainly verified when displacements are small within each load iteration by a suitable choice of the load perturbation (load step). For a detailed description of the numerical approach to the membrane element modelling, wrinkling and validation method refer to Malpede-Baraldi [2].
Two finite element types are considered: a membrane element modelling the sail and a beam element modelling the battens. Geometrically non-linear analysis is required for both elements: large displacements and buckling of battens are expected. The rotational degrees of freedom of the beam elements are introduced in the linear system discretizing the sail and battens, while the stiffness relative to the linear displacement degrees of freedom is simply added to the existing membrane nodes. This approach implies a one to one interface between the membrane mesh and the beam mesh. The approximation does not take into account the sliding contact between sail and inner nodes of the batten. The approach used may be described as a unified approach for the modelling of the sail, rig and battens.
4. RIG STRUCTURAL ANALYSIS
The element stiffness matrix, KE, is based on beam- column theory in order to account for stress stiffening and softening in the presence of axial load. Beam-column equations with bending about two axes and torsion are employed to generate the element stiffness and solved with the finite difference method in order to generate the various stiffness contributions of each finite element. In this fashion, the effect of member displacement upon
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©2011: The Royal Institution of Naval Architects
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