Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
As the maximum displacement evaluated on both sails is approximately 1% of the relative luff length (as shown in Table 8) it has been decided to verify the flying sail shape and final loads by carrying out the aeroelastic analysis (Figure 6). Tables 9 and 10 show the results obtained when the equilibrium on the flying sail shape has been reached.
Table 9: Equilibrium Jib CP
CDrive CSide η
1.84 0.45 1.81 0.25
-13% -13% -12%
aerodynamic results and
comparison with results obtained in the first aerodynamic analysis (Table 6)
Mainsail
1.44 0.21 1.40
= 0.15
-15% -13% -15% =
Table 10: Equilibrium structural results and comparison with results obtained in the first structural analysis (Table 8)
Jib
δmax σmax
Clew 0.21 m
104 MPa 8.0 kN
Halyard 8.6 kN Tack
2.1 kN obtained
-9% =
-5% =
Mainsail
0.22 m 85 MPa 11.9 kN 11.4 kN
-15% =
-7% =
+31% 2.2 kN +47%
Comparing the results of the aeroelastic analysis with the one
from the aerodynamic and structural
analysis, it is interesting to note that the calculated flying sail shape is equally efficient. In fact, both sails develop a lower drive and side force than the ones calculated in the first aerodynamic analysis; still the efficiency (η) is the same. Since the aerodynamic pressure on the flying sail shape resulting from the aeroelastic analysis is lower than the pressure on the design sail shape (computed in the aerodynamic analysis), the maximum displacement decreases. The maximum stress is found on the head of both sails, directly related to the halyard load applied. As the halyard load is, in this case, considered constant through the aeroelastic iterations, the maximum stress does not differ. Distribution of wind pressure and stress on the sailplan resulting from the aeroelastic analysis are very similar to the ones calculated in the aerodynamic and structural analysis phases; see Figures 4 and 5.
The sail loads evaluated with the aeroelastic analysis are then transferred onto the rig to perform the sailing rig analysis. Sections, pre-stress and material properties are set prior to start the structural analysis; in particular, the following inputs are required:
Spars thickness or, alternatively, section area, second moment of area and polar moment of inertia of area
Stays and shrouds diameters Stiffness modulus and density of each material Tuning strains or pre tension on shrouds and stays Mast step vertical and longitudinal displacement
©2011: The Royal Institution of Naval Architects
Once the FEM of the rig has been set, aeroelastic sailing loads, weight loads and tuning loads are applied step by step in the non-linear analysis, in order to compute the sailing rig shape and the sailing loads on chainplates, mast step and collar. The mast tube section is considered elliptical (longitudinal diameter is 28 cm, transversal diameter is 14 cm) and the rigging assumed solid circular rod. Sections,
pre-stress and material properties are
reported in Table 11. Due to its instability, the boom is not considered in the FEM. Nonetheless, the loads on the gooseneck and on the vang are computed directly on the basis of the clew load of the mainsail and the sheet position.
Table 11: Rig elements section, tuning and material properties
Mast and spreaders
Panel 1 Panel 2 Panel 3 Panel 4
Spreaders Rigging
D1 V1
Thickness (mm)
6 8 8 6 2
Diameter (mm)
10 12
8 8
Tuning (mm)
-
(kg/m3) 1500
ρ E
(GPa) 75
Tuning (mm)
-2.5 25
D2 8 0 V2 D3
Forestay 10
15 15 0
Backstay 6 190 2550 225
The resultant rig weight is 218 kg and its centre of mass is placed at 11.5 m high, 48% of the mast height (24 m). In the undeformed configuration, the mast is initially straight and the mast step is fixed about torsion and lateral bending. Then, the mast
step is moved 4 cm
backward. Figure 7 shows the deformed rig shape obtained under the weight, tuning and sailing loads. The deformation is magnified by a factor of 4 for displaying purposes.
In order to evaluate the influence of sailing loads, a dock tuning analysis has been performed. This analysis takes into account only tuning and weight loads. Tables 12 and 13 present the results for both cases: dock tuning and sailing analyses.
Table 12: Mast bend and forestay sag. Dock tuning
Mast bend Forestay sag
(kg/m3) 7889
ρ
E
(GPa) 180
Sailing
1.25% @ 55% 1.48% ↑ @ 60% -
1.70% @ 46%
B-123
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62