## Principles of Yacht Design

possible, and in the following we will explain how this may be accomplished.

Since the pressure and suction forces are much larger in the front part of the wing, the centre of effort of the resulting force is located in the forward part. In fact, it may be shown theoretically that the centre of effort is at one quarter of the distance from nose to tail for a symmetric section in a two-dimensional frictionless fluid. The lower part of Fig 6.2 shows a diagram, where the pressure is plotted in the more normal way, ie with the pressure on the vertical scale and the position along the section on the horizontal scale. Note, however, that negative pressures arc plotted upwards. In this way the upper side of the wing corresponds to the upper part of the diagram, and conversely for the lower side. The distance between the upper and lower curves is representative of the vertical force being generated at that position, and the total vertical force is proportional to the area between the two curves.

Real wings are not, of course, infinitely long, nor are they mounted between the walls of a tunnel. They therefore have free ends in the flow, and that creates some new phenomena. This is the three-dimensional case.

In Fig 6.3 a keel is shown from the side (a) and from behind (b). Since the pressure is higher on the leeward side of the keel than on the windward side, the flow will tend to move around the tip from the leeward to the windward side. This creates a downward motion on the leeward side, gradually increasing from zero at the root to a maximum at the tip. A corresponding motion upwards is created to windward. Streamlines on the two sides of the keel therefore have different directions, and when they meet at the trailing edge vortices are created. Fig 6.3 Force and vortex This is particularly so at the tip, where a strong vortex is left behind the distribution on a wing keel. Sometimes, when the yacht heels strongly this vortex can be seen,

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a) Side view b) Rear view c) Force distribution d) Ellipse

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