force when the keel is canted relative to the upright case both with and without the forward rudder.
The same test setup was used that led to the results displayed in Figure 8 and the results are displayed in Figure 9.
When the keel is canted sideways, the loss of side force should in theory be equal for both cases if there were no interaction effects, but this is not reflected in the two experimental curves. The results indicate that the difference is due to the changing interference between the forward rudder and the canting keel. When the keel is swung sideways from zero to twenty degrees for example, the side force drops less when the forward rudder is fitted. The same is true for higher canting angles.
This situation could be explained by the downwash effect of the forward rudder, reducing the angle of attack of the canting strut, which is less significant at higher canting angles. This way the angle of attack would slowly increase compared to the zero canting angle case, generating a greater total lift and thus side force.
Looking back at Figure 7 it can be seen that the two curves seem to diverge at the higher canting keel angles. They both level off, but with the forward rudder the curve levels off more. This trend could also be explained by downwash effects. A relative increase in the angle of attack of the canting strut at higher canting angles when a forward rudder is fitted increases the lift and thus the induced resistance.
4.5 INTERRELATION OF RESISTANCE AND SIDE FORCE
In this section the effects of the canting keel and forward rudder on resistance, side force and heave motion, which have so far been discussed separately, will be considered in combination. To compare different appendage setups the effective draft principle (equation (6)) has been used together with total resistance versus side force squared plots.
The effective draft ratio for a test where the speed of the upright yacht was fixed (Fn = 0.364), the leeway angle constant (4 degrees) and the forward rudder fitted, is given below. The maximum draft (T = Tcb + Tck) is constant and equals 0.334m. For the calculation of the effective draft, equation (6) can be rewritten as:
Te
R V cos SF
2 I 2 2 (10)
in which RI is the induced resistance calculated by subtracting the upright resistance from the measured total resistance.
Te/Tmax[m]
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
0 0,000 10,000 20,000 30,000 40,000 CK angle[°]
Figure 10: Variation of effective draft to maximum draft as a function of canting keel angle.
When the keel is canted up to forty degrees, the induced resistance for a given amount of produced side force is lower than in the upright case. Canting the keel to higher angles shows an adverse effect. At higher canting angles the assumed external force reduces the side force significantly and the reduction of induced resistance levels off, as discussed previously. Thus, for this model sailing at Fn = 0.365 and with four degrees leeway, a canting angle greater than forty degrees, leads to a significantly sub-optimal performance.
The optimal CK angle can thus be calculated for any particular yacht and sailing condition.
4.6 SIDE FORCE PRODUCTION BY THE TWO RUDDERS ONLY
A major benefit of the forward rudder configuration is that the lift production is independent of leeway. The biplane theory has been used to calculate the optimal load distribution between the rudders in the absence of the canting keel using equation (5). The conventional keel case, plotted on the RT-SF² graph for the purposes of comparison, has been calculated by generating all the required side force through leeway, and leaving the rudders unturned. It should be kept in mind that the drag for an equal amount of side force is higher for a real monoplane because splitting the lift over more than one appendage reduces the induced resistance.
The total resistance obtained for the different configurations is shown in Figure 11.
The results indicate that the worst way of producing the side force is with a fixed keel or monoplane. The slope of the curve on the RT-SF² curve and hence the induced resistance are comparatively high. For low side forces, in light winds for example, sailing at zero leeway with the entire load produced by the forward appendage would clearly be the best choice.
The figure also shows that the total resistance remains constant for increasing forward rudder angle. This interesting result indicates
that viscous interaction effects between the appendages play a significant role B-46 ©2007: Royal Institution of Naval Architects 50,000 60,000 70,000
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