wave resistance of the yacht was therefore assumed to be negligible for any further resistance calculations.
4.2 SIDE FORCE LOSS WITH A CANTED KEEL
The model was towed with six different canting keel angles, including zero degrees, at a fixed speed (Fn = 0.364) and with the forward rudder removed. Zero heeling and a four degree leeway angle were adopted.
The theoretical side force reduction for a canted keel can be determined as a fraction of the side force produced by the non - canted keel alone (figure 1):
SFtheory
SF onCKCK angle SF onCKCK0 _
_ cos(
CK angle SF onCK
_ _ CK0 ) 1
To be able to compare the experimental values with the theory, the measured change of side force is also represented by a percentage value:
SFexp
SF totalCK angle SF totalCK SF totalCK
_ _
_ 0
0 (9)
Thus, the experimental loss of side force is expressed as a percentage of the total side force instead of the side force on the non-canted keel alone in the theoretical case. The reason for this is that during the experiment only the total side force could be measured.
When the values for both curves are compared in the Figure 5, one must be aware that the theoretical loss is thus relatively overestimated (SF_on_CK < SF_total at same speed and leeway angle).
Change in SF[%]
-70,000 -60,000 -50,000 -40,000 -30,000 -20,000 -10,000 0,000
0,000 10,000 20,000 30,000 40,000 50,000 60,000 70,000 (8)
The trim was measured for all the different CK angles and was found to remain almost between 0.29° and 0.36°).
constant
Hence, the influence of the trim on the angle of attack and the produced side force was neglected. The result
from Figure 5 can now be considered
together with the findings from the previous section, where the vertical force was found to be negative or low at slow speeds. The results indicate external vertical force acting downwards on the canting keel, reducing the vertical lift and the side force.
This adverse effect could be explained by a relative flow around the hull having a vertical downward component due to the negative pressure at the keel’s windward side.
4.3 RESISTANCE CHANGE WITH A CANTED KEEL
The total resistance change at a four degree leeway angle between a zero and forty degree CK angle at several speeds is given in Figure 6. The model was towed without heel for this test and the forward rudder was installed for both cases and set at 0° relative to the centreline of the yacht.
Change in RT[%]
-9,000 -8,000 -7,000 -6,000 -5,000 -4,000 -3,000 -2,000 -1,000 0,000
0,200 0,250 0,300 0,350 0,400 0,450
(ranged
Fn[-]
Figure 6: Change in total resistance for change of forty degree canting keel angle as a percentage of the total resistance for the vertical keel as a function of Fn
Theoretical Experimental
CK angle[°]
Figure 5: Change in side force as a function of the canting keel angle
Even with the theoretical loss being overestimated, the experimental values on the graph are still higher than theory predicted. This means that the side force is reduced more than theoretically expected.
B-44
When the keel is canted sideways from zero to forty degrees, the heel and induced resistance are the only varying components. As before, for the same reasons, the viscous resistance change due to varying appendage interaction has been neglected at four degrees leeway. The heel resistance is augmented due to the bulb which is brought closer to the surface, as explained in the previous section. The induced drag is changed in two different ways. Bringing the low pressure zone at the windward side of the keel closer to the free surface changes the wave pattern of the free surface. The “free surface” induced drag is thus increased. On the other hand, the interaction of the trailing vortices is reduced due to a greater gap when the keel is canted. The
©2007: Royal Institution of Naval Architects
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