# Principles of Yacht Design

like a cod. but very slender. The Cn should be less than 0.5 and the j p

LCB should be positioned in front of the midship section. This would be a good design were it not for the wave resistance. As will be seen later, bluff forebodies tend to increase the waves, while in fact bluff afterbodies tend to decrease them. A thick stern boundary layer (on a bluff afterbody) makes the hull appear longer than it really is, and this effect is even more pronounced if separation occurs. Some designers have therefore produced very bluff sterns with some separation, just to decrease the wave resistance. This is not likely to pay off, however, unless there are important gains, from a measuring point of view in a rating rule. Obviously, the stern design, as well as Cp and LCB, must be optimized considering the speed for which the yacht is designed (ic for which wind conditions it is optimized). The higher the speed the more important the wave resistance and the bluffer the stern. Optimum values of Cp and LCB will be given later, in the discussion of wave resistance.

While the frictional resistance is set mainly by the wetted surface, the viscous pressure resistance depends 011 the shape of the hull. This is also the case for the wave resistance, and both appear due to pressure imbalances, so it is very common to lump both together into one component: the residuary resistance. We will not give any formula here for the viscous pressure resistance itself, but follow general practice and give the formula only for the residuary resistance. This will be presented later. In Fig 5.4 we have simply assumed that the viscous pressure resistance is 10% of the friction, which is a reasonable figure.

Roughness The third component of the viscous resistance, due to surface roughness, might not be too important from a design point of view, but it is certainly of interest for the practising yachtsman, and should, therefore, be discussed.

According to a large number of experiments with flows over rough surfaces, the effect of roughness disappears if the roughness elements are embedded in the viscous sublayer, introduced above. There is thus a limit, below which the surface may be considered smooth from a resistance point of view: khydraulically smooth' in fluid mechanics terminology. We have already noted that the thickness of the viscous sublayer is very small, normally of the order of 0.1 mm. Let us look at this in more detail, using the boundary layer calculation for the 7.6 m traditional yacht as an example. In Fig 5.10 the thickness of the viscous sublayer, ie the permissible roughness height, is given for three different speeds. One branch of the curves represents the hull, while the other is for the keel. At the forward end of the hull the boundary layer is laminar and. although the theories for this part are less well developed, it is safe to assume, as has been done in the figure, that the permissible roughness in this region is the same as in the most forward part of the turbulent boundary layer.

Several observations may be made concerning Fig 5.10. First, there is a strong dependence on speed: secondly, there is an increase in the permissible roughness aftwards. Thirdly, the increase is not as large on Fig 5.10 Permissible the keel as on the hull near the stern. We may also note that the most roughness. Traditional strict requirement is 0.03 mm, or 30 um for the highest speed on the vacllt forward half of the hull. To get a feeling for this small value we may note that a sandpaper of number 400 has a grain size of 25 jum. This does not mean that the surface should be sanded with this paper. A considerably rougher one would yield the required smoothness, since the grooves left after the paper are much smaller than the grains.

There is a very simple relation which can be used for estimating the permissible roughness on the forward part of the hull. This relation is given in numerical and graphical form in Fig 5.11. Note that the roughness is given in microns and that it is inversely proportional to the speed.

An appropriate question now is how much the viscous resistance is increased if the requirement for a hydraulically smooth surface is not met. To answer this, we may return again to the calculations for the traditional yacht. In Fig 5.12 the increase in viscous resistance for varying roughness heights and speeds is given. It is seen that the increase is considerable, particularly at higher speeds. Fig 5.12 was computed based on measurements for flat plates, where the surface was densely covered with sand grains. This is not the case for a sailing yacht, so the values given must be considered as an upper limit. In any case, it is obvious that roughness heights above the limit for a hydraulically smooth surface cannot be tolerated for racing yachts. It Fig 5.11 Estimation of the permissible roughness at different speeds

Fig 5.12 Increase in viscous resistance due to roughness - traditional yacht should be pointed out that barnacle growth results in much larger increases in resistance than indicated here. Two or even threefold increases in the viscous resistance have been noted for densely packed barnacles, several millimetres in height.

The YD-40 has a maximum speed of about 8.5 knots, ie slightly more than 4 m/s. According to Fig 5.11 the permissible roughness is

7 knots knots Increase [X]

7 knots knots

Roughness height />/

then about 20,u. Normally, a brush-painted surface has grooves 50 lOOu in height, so there is a significant resistance increase as compared to the hydraulically smooth surface. In Fig 5.4 the roughness component is 10% of the friction and the speed is 6.8 knots. This is reasonable, judging from Fig 5.12, where the 7 knot curve yields 8-23% increase for heights between 50 and 100u. As pointed out above this is probably somewhat high for normal roughness types. The fact that the curves of the figure are for a different hull is not too important, since the speed is the most significant factor.

Wave resistance, basic We will now turn to the second major resistance component of Fig 5.4:

concepts wave resistance. Like the viscous resistance it could be split into sub components. but they are of interest only under certain conditions, for instance when the bow wave breaks or is transformed into spray. We will ncglcct these phenomena here. As in the case of viscous resistance we will start by introducing some basic concepts.

If one throws a stone into a pond, circular, concentric waves originate from the point where the stone hits the surface. If one were to throw several stones in a row along a straight line the circular waves would interfere with one another and create a wave system very similar to that far behind a yacht. This is a system with well-delined properties, called the Kelvin wave system, and is due to a travelling point disturbance on the water surface. The same system is found far behind large ships, and in fact behind all objects moving along the surface. The reason why the same system is created is that if the waves have travelled a sufficiently large distance, and occupy a large area compared to the dimensions of the object, the latter may always be considered as a point. For instance, if a ship moving in calm water is viewed from an aeroplane, the ship itself is very small as compared with the area covered by the wave system, and the latter has the typical Kelvin structure. Fig 5.13 is an illustration of this phenomenon. It may be seen that two types of waves

Fig 5.1 3 The Kelvin wave system  