the round shape was the best downwind. The effect of the bulb is a bit uncertain. As we have seen in Fig 6.11 the large radius may help the flow pass the tip and move up 011 the other side, but this does not happen for all bulbs. A way to avoid this is to put a small riblet at maximum draft, thereby promoting separation of the vortex. Disadvantages of the bulb are that the wetted area increases greatly and that some interference drag is created in the corners between the bulb and the keel. These negative aspects may, however, be well compensated by the large increase in stability. Whether or not the total effect is positive depends 011 the stability of the hull itself. For instance, the America's Cup class yachts would not be able to carry their huge sail area without a very large bulb. The bulbs of this class have been the subject of extensive optimization studies, where the shape and fairing to the keel have been perfected. It should be remembered that heavy weights far from the total centre of gravity increases the gyradius, and have a negative effect on the performance of the yacht in a seaway.
Advanced planform In this section we will describe some more advanced concepts used design recently in the keel planform design for racing yachts. In most cases a relatively detailed knowledge of the flow around the hull and keel is required, and this calls for tank testing or Computational Fluid Dynamics (CFD) methods, not normally available to the amateur designer. It may, however, still be of interest to understand the principles behind the different concepts. A similar presentation will be made in connection with section design.
Winged keels The most spectacular development in planform design in recent years is the keel wing used on many 12 metre yachts in the 1980s. This technique is slowly making its way into cruising. The basic idea is to increase the effective aspect ratio of the keel without making it deeper, and thereby reduce the induced resistance. Alternatively, the keel could be made shallower for a given resistance, an attractive option for cruising yachts.
The idea of manipulating the tip flow with some kind of device is not new. Even in the 1940s experiments were made with end plates on keels at the Davidson Laboratory in New York. By putting a plate perpendicular to the keel plane at the tip, the overflow from the pressure to the suction side was reduced, and the effective aspect ratio increased. However, this was only at the expense of a large increase in viscous resistance due to the plates, so the total effect was unfavourable. It was not until the late 1960s that more effective devices with a streamlined wing shape were wind-tunnel tested by the aerodynamicist S O Ridder, and used on racing yachts. The real breakthrough came after the victory of the Australian 12 metre Australia II in the 1983 America's Cup races.
If the tip device is to reduce the overflow it obviously has to have an angle of attack relative to the local flow direction. A device following the local streamlines would not alter the direction of the flow. With this in mind it is easy to understand why the simple plates did not work. A
flat plate at an angle of attack produces a large drag, because the flow separates at the leading edge. It is therefore necessary to use well designed foils with a minimum of viscous resistance to obtain a net positive result. Since the foils will not be aligned with the flow a lift force will develop. On the leeward side of the keel the flow is directed downwards and the wing generates a downward force. The opposite is true on the windward side, where the force points upwardjs. If the foil is effective enough both forces may have a component forwards." The wing then pulls the yacht along. Fig 6.12 demonstrates that this occurs only if the drag is small enough relative to the lift. If this condition is not satisfied the wings will generate a drag force. It should now be apparent why the proper design of the wings is of the utmost importance.
Fig 6.12 Keel wing force on windward side
Another way of looking at the effect of the wings is to consider the trailing vorticity left behind the keel. Without the wings a strong vortex is formed near the tip due to the overflow. The wing takes advantage of the vortical energy and reduces it, so that less is left in the wake, thereby reducing resistance. It should be pointed out that new vortices (of less strength) are now left behind the tips of the wings, where some overflow occurs.
Points to consider in the design of keel wings are:
root chord • cant angle span • junction angle taper ® junction fairing twist • section characteristics longitudinal position at keel tip
In the early days of keel wing design, attempts were made to exploit the lowering of the centre of gravity of the yacht made possible by fattening the wings. Therefore, the weight of the wings could have been added to the list above, but in modern designs it has been realized that it is better to put this weight in the lower part of the keel or in a bulb, used in connection with the wings.
As to the root chord, there is a trade-olT between frictional and induced resistance. In a frictionless fluid the root of the wing should be as large as the tip of the keel in order to avoid discontinuities in the load carried over from the keel to the wins. Such discontinuities mean shed vorticity and hence induced resistance. On the other hand, to minimize wetted surface and friction the chord should be as short as possible.
A similar situation exists for the span. In principle, the vortices shed at the wing tips are smaller for large spans, but the wetted surface is larger. Another important aspect of span size is the variation in local How direction along the span. The larger the span the stronger the variation. In the inner part of the wing the flow is mostly governed by the displacement of the hull, while further out the flow direction is determined by the waves. Obviously, heel angle and speed will alter these conditions. It is thus more complicated to design large span wings.
The taper and twist of the sections determine the loading and shedding of vorticity spanwise, and have to be optimized together.
If the chord of the wing root is smaller than that of the keel tip, the position of the wing along the tip has to be considered. A forward position may be advantageous, since this part of the keel carries the largest load. On the other hand, the wing has been shown to have a very positive effect 011 the keel lift/drag characteristics when using the trim tab, if it is positioned below the tab. This speaks in favour of an aft position.
The cant angle has caused some debate in the yachting literature. This is the angle between the wing viewed from behind and the horizontal (hull upright). In our explanation above, the wings get their loading from the keel, due to the overflow from the pressure to the suction side. This is likely to be the major effect, but when the yacht heels and yaws the leeway itself causes an angle of attack 011 the wings, in such a way that the leeward wing becomes more heavily loaded, and the windward wing carries a reduced load. For instance, if the hull heels 45° and the cant angle is 45° the leeward wing will be vertical and exposed to the full leeway angle. The other wing will be horizontal and more lightly loaded. In this situation the largest vortex will be shed at the tip of the leeward wing which is at a draft that is probably larger than the nominal one. This is certainly an advantage. O11 the other hand, it is advantageous to equalize the vortices from the two wing tips, as will be explained below, and also, in fact, to spread them apart as much as possible. These latter effects speak in favour of small cant aneles.
The junction angle is defined as the angle of the wing root relative to the horizontal, viewed from the side. This has to be adjusted, as well as the angle of all sections, to the local flow direction. A common practice is to carry out the adjustment for the upright condition (where the wings are not needed) in such a way that the drag of the wings is minimized. In the early days of the winged keels this was accomplished by measuring the force on the wing and adjusting its angle in the towing tank to obtain minimum wing drag. The disadvantage of this approach is that the effect of the variation in the spanwise direction is not accounted for. It is now possible to compute the flow direction locally, and to unload each section of the wing by proper twisting.
At the junction between the keel and the wing a vortex is normally created. This vortex gives rise to a resistance component. The same phenomenon, in fact, occurs also in the junction between the keel and the hull. To alleviate the problem a special fairing, called a fillet, may be introduced. The classic design of the fillet is to start .at the leading edge and increase the radius along the intersection backwards to the trailing edge, where the fairing radius should be of the order of the (largest) boundary layer thickness. In the keel/hull junction the hull boundary layer is normally a few centimetres, for a 40 footer like the YD-40 around 5 cm. In the keel/wing junction the keel boundary layer is thinner, and a radius of about 1 cm seems appropriate. It is very important that the fillet is tapered off smoothly behind the trailing edge. Other ideas for fillet design have been suggested recently, but they do not seem to work at an angle of attack, and are therefore of little use in yacht design.
Considering all the trade-offs and the detailed knowledge of the flow required, it is very unlikely that other than experienced fluid dynamicists can design effective wings. If wings are just added without the above considerations, the chances that they will have a negative effect, rather than a positive one, are quite high.
Inverse taper Inverse taper, or taper ratios larger than one, were investigated by the
Australia II team in the early 1980s, even before they decided to go for the winged keel. This taper, in itself, caused an increase in performance, but not as large as in combination with the wings. The reason why inverse taper may be advantageous for a very heavy yacht like a 12 metre (apart from the obvious stability improvement) is that the deep hull will carry a substantial part of the side force, ie the keel plus the hull must be considered a wing, albeit with a very strange planform and with a huge thickness in the upper part.
The load distribution for two taper ratios larger than one is shown in Fig 6.13. Obviously, it is very different from the optimum elliptical distribution from the tip of the keel to the waterline. A particularly harmful feature is the rapid drop in load at the junction between the keel and the hull, where much vorticity is shed. A way to alleviate this problem is to reduce the keel chord at the intersection with the hull, thereby reducing the difference between the keel and the hull loadings. As can be seen in the figure the smaller chord for the larger taper gives a somewhat smoother load distribution, and hence smaller vorticitv and induced resistance.
Another important effect of the inverse taper is that the load will be moved away from the water surface, which may have a positive effect on the wave resistance. This advantage is, of course, even larger if wings are added.
An important condition for the use of inverse taper is that the hull is deep. For modern fin-keel yachts the hulls are shallow and act more or
Fig 6.13 Side force distribution - inverse taper
less as a flat wall attached to the top of the keel, as we have seen above. The simple theory presented in Fig 6.5 may be used for designs without wings. If wings are added, the load distribution will be completely changed, and a more complicated optimization procedure is required.
Forward rudders In the America's Cup races of 1987 the American yacht USA featured
(canard wings) a radical underwater design, where the two normal tasks of the keel (to lower the centre of gravity and to produce a side force), were split on different devices. The ballast was put into a large bulb, kept in position below the hull by a streamlined strut, and the side force production was left for a forward and an aft rudder.
The effect of splitting the side force between two surfaces may be investigated using biplane theory. The principle is straightforward: by reducing the lift on each one of the surfaces, keeping the span unchanged, the sum of the induced resistances becomes smaller than for one surface alone. This is so because, as we have seen in the lifting line theory, the induced resistance is proportional to the lift squared. If there were no interference between the two surfaces, splitting the lift into two halves would result in a resistance of each surface of only one quarter of the original one, ie the total resistance would be halved.
Unfortunately, the interference effects cannot be ignored, unless the trailing vortex systems are several span lengths apart. There is thus no point in putting the aft wing in the wake of the forward one. The vortex systems would then coincide and co-operate to generate the same resistance as if there had been only one wing. If the wings, or lifting surfaces, are put side by side, there is a gain. For instance, on sailing catamarans the two centreboards are several span lengths apart and may be considered independent.
At first glance, the forward and aft rudder configuration may seem a useless idea, since the rudders are located behind one another. However,
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