induced resistance associated with vortex generation is thus decreasing.


Because the trend in figure 6 is negative for the whole speed range, the results indicate that the induced resistance


reduction due to the trailing vortex separation is the most significant effect. 4.4 INFLUENCE OF THE FORWARD RUDDER


To investigate what happens to the induced resistance when the keel is canted to higher angles the upright model was towed at a fixed four degrees leeway angle, at a fixed speed, with varying canting keel angle.


By subtracting the upright resistance (total resistance with zero heeling, leeway and canting keel angle) from the measured total resistance, the induced resistance can be calculated for this specific speed (bearing in mind that the induced resistance has been defined as the resistance components associated with the production of lift).


For this theory to be valid, the increase in heel resistance, due to the keel being closer to the free surface, has to be neglected. This is reasonable on the basis of Figure 6, which shows that for a forty degree canting angle


the change in induced


components are dominant. The results calculation are shown in Figure 7.


resistance of


It is clear that the induced resistance is reducing with increasing canting keel angle. The total lift produced by the canting keel strut and thus the induced resistance due to vortex generation remains constant when the keel is canted. This could not be the reason for the drag reduction.


RI[N]


0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800


0,000 10,000 20,000


with FR no FR


this


Change in


heave[mm]


It is interesting to examine Figure 8 for the upright model at four degrees leeway with different canting keel angles with and without forward rudder at a fixed speed (Fn=0,364). When the forward rudder was fitted, it was set at 0° relative to the centreline of the yacht.


All the values of the change in heave relative to the upright case are higher without the forward rudder installed than with it. These results indicate that a forward rudder generates


Examination of Figure 7, shows that the curve levels off from a certain canting angle onwards. This effect could be explained by the increase of the “free surface” induced resistance when the low pressure system is brought closer to the free surface at higher canting angles.


a vertical force acting


downwards. Because the canting keel is working in the forward rudder’s downwash, the angle of attack of the flow on the canting strut is reduced. This results in a smaller total lift on this appendage.


-0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8


Experimental withFR Experimental noFR


0,000 10,000 20,000 30,000 40,000 50,000 60,000 70,000 CK angle[°]


Figure 8: Effect of forward rudder on vertical displacement as a function of the canting keel angle.


30,000 40,000 50,000 60,000 70,000 CK angle[°]


Figure 7: Variation of induced resistance as a function of the canting keel angle.


Because the trend is also negative without the forward rudder attached, downwash effects between the forward appendage and the keel can’t be the reason either. One explanation for the negative trends is the increasing vertical distance between the trailing vortices with increasing canting keel angle. The resulting drag reduction is much more significant than the increase in “free surface” induced drag due to bringing the keel to higher angles.


Change in SF[N]


-6,000 -5,000 -4,000 -3,000 -2,000 -1,000 0,000


0,000 10,000 20,000 30,000 40,000 50,000 60,000 70,000


with FR no FR


CK angle[°]


Figure 9: Change in side force as a function of canting keel angle


Because the canting keel is the only generator of upward lift, the forward rudder has a negative effect on the heave motion.


To analyse the interaction effects of the forward rudder in more detail it is useful to plot the reduction of side


©2007: Royal Institution of Naval Architects B-45


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