at zero leeway. When the aft rudder works in the wake of the forward rudder its resistance is seen to decrease.


In reality there will always be a need for a force on the aft rudder to balance the yaw moment produced by the wind forces on the sails. In this circumstance, the optimal load distribution is not adopted and the induced resistance will increase, as shown in figure 11, with aft rudder at 5 degrees and varying forward rudder angles.


0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000


0.000 50.000


leeway angle and to get more trailing vortex separation when three appendages are fitted. For practical purposes, a trade off should be made between sailing at a higher leeway angle with less drag, and sailing with a more optimal course, and hence additional resistance at a smaller drift angle.


hull at 2,4 and 6° LW


FR at dif ferent angles, no LW AR at 5°,FR at dif ferent angles, no LW hull at 2°LW and opt imal load distribut ion hull at 4°LW and opt imal load distribut ion


100.000 150.000 SF²[N²] Figure 11: RT-SF² curves for the different configurations in the absence of the canting keel.


Once the forward rudder is stalling it becomes harder to choose the


optimal configuration because the


differences in resistance for a given side force are rather small. Nevertheless the results indicate that for high side force values the four degree leeway with optimal rudder loading case would be the best option.


For more moderate lift forces the two degree leeway with optimally distributed loading case and the zero leeway with non- optimal seem to be in close concurrency.


loading distribution case


4.7 SIDE FORCE PRODUCTION BY THE TWO RUDDERS AND CANTING KEEL


In the final configuration considered, the canting keel was reintroduced and canted sideways


over


degrees to represent a more realistic sailing condition. With this third appendage, the biplane theory is assumed to be still applicable, although errors will be introduced due to extra interference effects.


The results show that there is a significant drag reduction for an equal amount of side force produced when


the rudders are inclined, compared to the


conventional keel setup. There is also a significant induced drag reduction when the triplane is compared with the biplane case. This is due to the distribution of the total lift over three instead of two appendages.


It can also be seen that the difference between the 2° and 4° leeway case is now more distinct than in the biplane case. The results show that from a pure resistance point of view it is better to choose a greater


forty


When the keel is swung to higher angles at a realistic drift angle, the side force and vertical lift force are found to decrease more rapidly than might be expected from


theoretical considerations. This could be


explained by a downward acting force generated by the relative flow around the hull due to the negative pressure at the keel’s windward side.


The hydrodynamic characteristics of the canting keel and forward rudder configuration, with respect to the side force and resistance generated, are such that there is an optimal canting keel angle for a given speed and leeway angle.


The addition of a forward rudder to the canting keel configuration introduces severe interaction effects. The downwash of the forward appendage causes a reduction of the angle of attack of the appendages downstream. This interference effect between the forward rudder and canting keel is reduced with increasing canting keel angle.


Applying the theoretical optimal load distribution on the two rudders in the absence of a canting keel,


200.000 250.000


0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500


0.000


hull at 2,4 and 6°LW (triplane) hull at 2°LW and optimal load distribution hull at 4°LW and optimal load distribution hull at 2,4 and 6°LW (biplane)


50.000 100.000 150.000 200.000 250.000 300.000 350.000 SF²[N²] Figure 12: RT-SF² curves CONCLUSIONS for the different


configurations with the canting keel included. 5.


A number of conclusions relating to the hydrodynamic performance of a canting keel in the presence of a forward rudder can be drawn from the data generated by the experiments, set in the context of biplane theory and using the effective draft concept.


Sailing at a realistic leeway angle and forward speed and canting the keel sideways reduces the induced and total resistance.


©2007: Royal Institution of Naval Architects


B-47


RT[N]


RT[N]


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