The Rig of the “UCA” - Finite Element Analysis

University of Applied Sciences Kiel Yacht Research Unit

Prof. Dr.-Ing. Guenter Grabe

Guenter.Grabe@FH-Kiel.de 1. Introduction Results of global Finite Element Analysis (FEA) computations of the “UCA” rig are presented in this report. They are performed within the scope of a research project from the German Ministry of Education and Research (BMBF) called: “Development of Procedures for the Dimensioning of Rigs from Modern Sailing Yachts”. The aim of the computations is to simulate the behaviour of the rig in three different conditions:

- dock tune, pretension of the standing rigging - sailing close hauled with up to 30 degrees of heel - sailing on a broad reach with spinnaker.

The maxi racer “UCA” was designed by judel/vrolijk & co Yacht Design & Engineering in Bremerhaven. The 85’-racer is a yacht designed for racing the DCNA-Challenge in June 2003 and IMS-racing in the Mediterranean.

The “UCA” was built by the Shipyard Knieriem in Kiel and launched after only 7 month of work in the year 2002 in time for the “hanseboot” boat show in Hamburg.

Figure 1 Sail plan

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

The rig was produced by Nordic Mast in Aabenraa, Denmark according to the sail plan from judel/vrolijk and a spread sheet supplied by Applied Engineering Services (AES) in Auckland, New Zealand. Nordic Mast developed the detailed engineering for the carbon rig.

The rig was certified by the Germanische Lloyd in Hamburg [ 1 ].

2. Description of the “UCA” rig and the FEA models The “UCA” has a top-fractional rig like the rig of a Volvo Ocean racer of the race in the years 2001/2002. Differences are the five spreaders instead of four and that the spreaders are not in line but are raked aft 22 degrees. The “UCA” rig is larger than a Volvo Ocean Racer rig. The main measurements are:

I = 30.700 m

P = 32.250 m J = 9.500 m E = 12.000 m

The rig of the “UCA” is very slim. The staying base of thI divided by the staying base is 13.2. The rig is made outof elasticity for the mast tube is 110 kN/mm². The standi Two FEA models are built up. The first FEA model is fosecond FEA model is for sailing on a broad reach (apparfinite element models are illustrated in Figures 2 and 3.

The global FEA models of the rig are constructed with band the spinnaker pole. Nonlinear link elements with therigging. Only the forestay is made out of a beam elementelements are used for the goose neck of the boom and thmodelled. But a spring at the chain plate of the forestay s

Figure 2 FEA model for dock tune and sailing close h

main sail = 240 m²100 % genoa = 140 m² spinnaker = 600 m²

e vertical shrouds is 2.334 m. The relation of the length of high tensile and high modulus carbon. The modulus ng rigging is out of rod. Figure 1 shows the sail plan.

r the case of dock tune and sailing close hauled. The ent wind angle (AWA) = 135°). The geometries of the

eam elements for the mast tube, the spreaders, the boom ability to fall slack are chosen for most of the standing to make visible the sag of the forestay. Bearing

e spinnaker pole. The hull of the “UCA” is not imulates the hull stiffness.

auled

- 2 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

Figure 3 FEA model for sailing on a broad reach, AWA: 135°

The computations for the load cases dock tune and sailing close hauled consider large displacements (geometrical nonlinearity). The computations for the load case downwind are performed with small displacements.

The FEA program is ANSYS 6.1. The computations are performed on a PC.

- 3 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

3. Dock Tune The rig is pre tensioned in the FEA by initial strains of the standing rigging. The size of the initial strains is computed according to a chosen percentage of the breaking strength of the different rods. Table 1 shows the pretensioning of the single shrouds and the forestay.

Table 1 Pretensioning of the standing rigging

D Length Breaking strength

Chosen % of breaking strength Pretension force Initial strain

Shortening of shrouds and

forestay

D1 16,76 7,408 267813 15 40172 0,00104 7,71

D2 12,70 5,868 169713 14 23760 0,00107 6,29

D3 12,70 6,005 169713 14 23760 0,00107 6,44

D4 12,70 5,556 169713 14 23760 0,00107 5,95

D5 14,27 4,990 213858 14 29940 0,00107 5,34

D6 12,70 4,432 169713 29 49217 0,00222 9,84

V1 22,23 7,475 513063 29 148788 0,00219 16,37

V2 19,51 5,831 401229 29 116356 0,00222 12,97

V3 17,91 6,121 338445 29 98149 0,00223 13,63

V4 16,76 5,804 267813 29 77666 0,00201 11,68

V5 12,70 5,274 169713 29 49217 0,00222 11,71

Forestay 17,91 31,982 338445 15 50767 0,00115 36,83 mm m N N mm

The rig of the “UCA” is pre tensioned with a hydraulic mast jack. The typical procedure for adjusting the pretensions in the rigging is performed in six steps:

1. the cap shrouds and the forestay are tensioned, all diagonals are slack 2. additional the D1’s 3. additional the D2’s 4. additional the D3’s 5. additional the D4’s 6. additional the D5’s

For every step the hydraulic pressure is controlled and the turnbuckles are adjusted until the computed mast compressions are achieved. Figure 4 shows the tension and the compression forces and also the mast bending curve of the rig after step 6. The forces in Newton [N] are made visible with contours and colours. The width of the contour is proportional to the force. The mast bending curve is shown with vectors in meter [m]. The length of the vectors and the colour correspond with the deformation in three dimensions. The length of the vectors is in an enlarged scale to make the small deformations visible. The mast bending curve is made plain by a black line.

Table 2 lists mast foot compression forces for the steps 1, 2 and 6. In the second column are the values computed with FEA. Chris Mitchell from Applied Engineering Services (AES) in Auckland, New Zealand computed also the compression forces in the mast foot (column 3). He used a spread sheet. The values from the FEA and from AES spread sheet are compared with each other in the third and fourth columns.

Table 2 Mast foot compression forces

FEA AES Difference % difference Cap’s only 126915 160678 -33763 -26.6 Cap’s, D1 212554 225061 -12507 -5.9 Cap’s, all D’s 343841 339308 4533 1.3 N N N

- 4 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

[N]

[m]

Figure 4 Mast bending, tension and compression forces, all shrouds and the forestay are tensioned

- 5 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

The compression forces are about the same for the final step. But the mast compressions for the first step differ with 26.6 % very much. The reason for this is that the spread sheet computation can’t take into account large displacements. All diagonals are not tensioned in the first step. The mast bends forward caused by the compression forces of the spreaders. The mast compression is smaller when the mast bends than when the mast is a straight line. The mast bending is reduced when the D1’s are tensioned in the second step. In the last step the mast bending is even smaller and the mast foot compressions from FEA and AES are about the same. The comparison shows the importance of applying large deformation effects in FEA for rigs.

4. Sailing close hauled

Sailing close hauled is for a rig with a good aft rigging like on the “UCA” the critical load case. Most of the computations are performed at a standard heeling angle of 30 degrees. Results are deformations like bending curves of the mast and forces, bending moments and torque in the rig. Also stresses are computed.

In addition to the standard 30° heeling angle other heeling angles are also computed. The heeling angle was increased from 0° (dock tune) in steps of 5° as high as possible.

All computations are performed considering large displacements (geometrical non linearity).

4.1 Heeling at 30 degrees

A load model for rigs sailing upwind and downwind is developed in the BMBF research project [2, 3] on the base of real size measurements and a FEA of the rig of the sailing research yacht “DYNA” from the Technical University of Berlin. The load model is applied on the Rig of the “UCA”.

The loading of the rig for the close hauled case is simulated on the base of the righting moment of the “UCA” at 30 degrees of heel. The apparent wind angle (AWA) is defined to be 30 degrees. The size of the righting moment at 30 degrees of heel is 46,900 kgm. With full main and 100 % genoa the necessary wind speed to heel the “UCA” 30 degrees is 13.3 m/s or 26 knots. The load model for the close hauled load case gives single forces and uniform loads. The single forces act in the three directions of a Cartesian coordinate system at different points like sheave axles of the sails, the boom tip and the goose neck. The uniform loads act on the forestay and the mast tube.

Figure 5 shows an overview like for the dock tune case about the mast bending curve, the tension and the compression forces for a heel of 30 degrees. The largest deformation is in the mast top with 717 mm. In the case of dock tune it was only 70 mm. The sag of the forestay is 156 mm (137 mm aft and 74 mm leeward). That is a very small value. It is only 0.5 % of the forestay length. The tension in the forestay is 141090 N (14,4 t). The mast compression force rises from 343841 N (dock tune) to 498876 N or about 50 t. The leeward rigging is slack above the third spreader. V3, V4 and the diagonals D4, D5, D6 are without tension.

More deformations are visualised in figures 6, 7 and 8. All deformations are in scale with the rig dimensions. The mast bending in figure 6 looking from the side is visible but small. Figure 7 shows a view looking from above the mast top down to the deck. The whole mast is twisted a little bit clock wise. Figure 8 shows the sag of the forestay.

Figure 9 shows torque in the rig. The torque rises stepwise from the mast top down to the mast foot. Every spreader and every diagonal on port and starboard side change the torque. The spreaders push and the diagonals pull. Above the third spreader the leeward rigging is slack. There is only small torque. Bending moments for the mast can be seen in figure 10. The largest bending moments are at the height of the forestay connection to the mast. The leech of the main sails pulls aft. The backstay is not tensioned. The step in the bending moment is caused by the tension force of the forestay pulling at the lever from the neutral axis from the mast to the forestay tang and the halyard pulling at the lever of the halyard sheave.

Figure 13 shows von Mises stress in the mast tube and the main boom. The von Mises stress is computed for a homogeneous and isotropic material. Carbon is strongly inhomogeneous and anisotropic. The computed von Mises stress values can only give an idea of the distribution and the size of the real stress in the carbon.

The largest stress computed after the formula of von Mises is at the backside of the mast at the height of the forestay tang. At that point the bending stress and the compression stress are added. The von Mises stress is there up to 200 N/mm².

- 6 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

[N]

[m]

Figure 5 Deformations, tension and compression forces, close hauled, AWA 30°, heel 30°

- 7 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

Figure 6 Deformed shape looking from the side, mast bending, close hauled, AWA 30°, heel 30°

[m]

Figure 7 Deformed shape looking down from the top to the deck, sag of forestay and distortion of mast with

spreaders close hauled, AWA 30°, heel 30°

- 8 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

Figure 8 Deformed shape, sag of forestay, close hauled, AWA 30°, heel 30°

[Nm]

Figure 9 Torque, close hauled, AWA 30°, heel 30°

- 9 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

[Nm]

Figure 10 bending moments, close hauled, AWA 30°, heel 30°

[N/m²]

Figure 11 Stress von Mises, close hauled, AWA 30°, heel 30°

- 10 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

4.2 Heeling from 5 to 32 degrees

Figure 12 shows tension and compression forces for a range of heeling angles between 0° and 30°. The heeling angle 0° belongs to the dock tune. The forces of the sails rise with the heeling angles and the corresponding righting moments and wind speeds. The windward shrouds are tensioned more and the leeward shrouds become less tensioned. At 15° heel the leeward shroud D5 starts to fall slack. A larger pretension in the D5 would keep the tension in the D5 up to higher heeling angles. It would also reduce the bending of the mast in panel 5. The rising mast bending reduces the pretension in the shrouds for the spreaders are swept aft. At 30° heel V3, V4, D4, D5 and D6 fall slack. The heeling angle for the falling slack of the leeward shrouds depends also on the tension force of the runner. The tension force of the runner is adjusted by initial strain. It is 15.1 kN at the heeling angle of 30°. The runner pulls the rig aft. That reduces the pretension in the shrouds still more. Table 3 shows important data for the different heeling angles up to 32°. The righting moment is assumed to rise approximately linear with the heeling angle.

Table 3 Data for a range of heeling angles from 0° to 32 °

heeling angle

Righting moment

AWS force in mast panel 1

force in forestay

displacement in mast top

shrouds falling slack

0 0 0.0 343.8 33.3 70 --- 5 7,817 5.4 393.4 104.6 370 ---

10 15,633 7.7 407.8 111.7 418 --- 15 23,450 9.4 423.4 118.9 472 D5 20 31,267 10.9 441.3 126.2 531 D5 25 39,083 12.2 460.6 133.5 595 D5 30 46,900 13.3 498.8 140.9 717 V3, V4, D4, D5, D6 32 50,027 13.7 533.1 143.6 823 V3, V4, D4, D5, D7

° kgm m/s kN kN mm

All computations are performed with the consideration of large displacements (geometrical nonlinearity). The computations don’t converge any more when heeling angles are larger than 32° of heel.

The forces of the sails are computed in the load model depending on the righting moment. The computation of the sail loads in the load model assume, that both sails also the main sail are still full standing in spite of the rising mast bending. In reality this will not be the case. The mainsail forces will become smaller and the fore sail forces will become larger. This results in less bending of the mast and more tensioned leeward shrouds. That stabilises the rig again and the rig will keep standing up to higher heeling angles.

- 11 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

F

0° 5° 10° 15°

20° 25° 30°

[N]

igure 12 Tension and compression forces, dock tune heel 0°, close hauled, heel from 5° to 30°

- 12 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

5. Sailing on a broad reach

The downwind load case is not as critical as the close hauled load case for the “UCA” mast has a good aft rigging. The FEA computations for the downwind load case consider small displacements only. It was tried to take into account large displacements but there are still numerical instabilities and the computations do not always converge.

The “UCA” has different gennakers up to 599 m² but no symmetrical spinnaker. The developed load model for downwind sailing is based on the symmetrical spinnaker of the “DYNA”. In the computations a configuration of full main sail and a fictive symmetrical spinnaker with 600 m² is considered. The chosen apparent wind angle (AWA) is 135 degrees (broad reach). The loading of the rig for the downwind case is simulated on the base of the defined apparent wind angle and a chosen apparent wind speed (AWS). It is always difficult to define a sound AWS for downwind sailing. The chosen AWS is 10 m/s or about 20 knots. 20 knots AWS is quite much for the 600 m² spinnaker. The load model for rigs sailing downwind with a spinnaker is explained in detail in [3].

Figure 13 shows the deformed shape, figure 14 the deformations, tension and compression forces. The maximal mast deformation is with 272 mm much smaller than sailing close hauled. Most of the deformations are to leeward and not aft. The main boom and the spinnaker pole move upwards a little bit. The compression force in the mast reaches 382 kN. The tension force on the windward V1 is 172 kN. No part of the standing rigging is falling slack.

Torque in the mast tube is shown in figure 15. The boom and the pole distort the mast anti clock wise. The rotating direction of the torque changes at the goose neck. The maximal torque is with 7387 Nm larger than sailing close hauled (4361 Nm). The torque will be still bigger considering large displacements.

Figure 16 visualises von Mises stress. The von Mises stress is smaller when sailing on a broad reach than when sailing close hauled. Hot spots are on the front side of the mast. Here the spinnaker pole pushes into the mast. That leads to compression stress that is super positioned with the mast compression stress. The stress level is with 50 N/mm² smaller than sailing close hauled (200 N/mm²).

All computations are performed for an AWS of 10 m/s. The wind speed can rise in a sudden gust by a factor of 1.5 or more. That raises the sail forces by a factor of 2.25 or more. The rig will be loaded much more in the case of a sudden gust than computed here.

Figure 13 Deformed shape looking down from the top to the deck, broad reach, AWA 135°, AWS 10 m/s

- 13 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

[N]

[m]

[N]

Figure 14 Deformations, tension and compression forces, broad reach, AWA 135°, AWS 10 m/s

- 14 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

[Nm]

Figure 15 torque, broad reach, AWA 135°, AWS 10 m/s

[N/m²]

Figure 16 von Mises stress, broad reach, AWA 135°, AWS 10 m/s

- 15 -

The Rig of the „UCA“ Yacht Research Unit, University of Applied Sciences Kiel

- 16 -

6. Conclusions A finite element analysis is performed for the rig of the “UCA”. Three steady state load cases are computed:

- Dock tune - Sailing close hauled - Sailing on a broad reach.

All three computed load cases are steady state load cases. There are also unsteady loads. E.g. inertia forces caused by movements in a sea way like pitching when sailing close hauled enhance the steady state loading of the rig. Also peak loads occurring when a spinnaker after having lost the wind fills itself up again with a “bang” are neglected in the performed computations.

A tall rig like that of the “UCA” is a very complex structure. A lot of effects can be considered today applying FEA for rigs. But there are still some imponderables in known - and also until today - unknown effects. The human factor in tuning the rig and the sails depending on wind and waves plays an important part. FEA is only an endeavour to simulate the real world of

the rig of the “UCA”.

7. References

[ 1 ] Germanischer Lloyd: Rules for Classification and Construction, Ship Technology, Special Equipment,

Guidelines for Design and Construction of Large Modern Yacht Rigs, 2002 [ 2 ] Grabe, G., The Rig of the Research Yacht “DYNA” – Measurement of Forces and FEA, HP-Yacht,

Auckland, 2002 [ 3 ] Grabe, G., Downwind Load Model for Rigs of modern Sailing Yachts for Use in FEA, 16th Chesapeake

Sailing Yacht Symposium, Annapolis, Maryland, 2003