becomes increasingly significant. The contribution of the different components of resistance to the total resistance is one of the issues that has been considered. Swinging the keel sideways gives rise to a vertical lift component. The influence of this component on the viscous resistance and the wave resistance has also been investigated. The addition of the forward rudder introduces further levels of complexity as interaction effects between it and the canting keel come into play. The effect of this third appendage on the resistance, vertical lift and side force characteristics has also been closely examined.
2. BACKGROUND THEORY 2.1 THE LOSS OF SIDE FORCE
When sailing at constant speed in a given direction all the forces acting on the yacht are in equilibrium. The driving force
produced by the sails balances the
resistance, and the aerodynamic lateral force is balanced by a hydrodynamic side force. The latter is provided by the canoe body and appendages.
In order to develop a lift force from a symmetrical keel, which plays the major role in the side force production of a conventional keel and rudder configuration, a leeway angle is needed. The analogy with aeronautical theory is direct and the keel, rudder and canoe body can be thought of as wings which need a given angle of attack (the leeway angle) to produce a corresponding lift or side force.
When a canting keel is installed the situation becomes more complex. By canting the keel, the lateral projected area is reduced which has a negative effect on the side force production because part of the total lift is now directed vertically. The situation is illustrated in Figure 1.
2.2 THE CALM COMPONENTS
WATER
RESISTANCE
The total calm water resistance of a sailing yacht can be written as:
R R R R R T W V H
RV : viscous resistance RW : wave resistance RH : heel resistance RI : induced resistance
These components and their relevance to the appendage configuration to be analysed are now examined in more detail.
2.2(a) The viscous resistance
The viscous resistance is made up of frictional drag and the resistance caused by the pressure imbalance between the fore- and after body (3D-effect) due to viscous effects such as boundary layer development and flow separation.
The viscous
major components, one associated with the canoe body, and the second
RkC V A
(1 ) 2 vf ws
1 2
resistance can be subdivided into two with the
appendages. For both
components the viscous resistance can be determined using:
(1)
where Cf is the frictional resistance coefficient of the body or appendage, determined from the ITTC ’57 extrapolation line and k is the form factor, accounting for velocity augmentation and the other viscous effects apart from friction. The viscous resistance can be calculated for the hull and the appendages separately using the appropriate form factors.
When the keel is canted sideways and a leeway angle is adopted, a vertical lift component is produced (figure 1). This vertical lifting reduces the wetted surface of the hull and thus the viscous, the wave making and total resistance (equation (1)).
Figure 1: Force components acting on canting keel
In the configuration analysed in this paper, the loss of side force is compensated for by the forward rudder.
When sailing at a realistic leeway angle (4°) and canting the keel sideways, the effect of interaction between the different appendages on their viscous resistance has been assumed to be negligible compared to the influence of other drag components. This simplification appears to be borne out from the results of a CFD analysis carried out by McKee [3], who looked at 2D horizontal slices of the flow around a canting keel configuration. However, when a zero leeway angle is adopted, the effect of an increased angle of attack of the forward rudder on the
I
B-40
©2007: Royal Institution of Naval Architects
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