*Chapter 20
The hull of a racing yacht*

The functions of the hull of a racing yacht have been listed in chapter 2. It is clear that the several requirements of the hull cannot all be satisfied and that the design of the hull will be a compromise. Let us look at the several factors in turn.

The hull of a model racing yacht can easily be made strong enough to withstand any of the forces that are likely to be exerted on it without a severe weight penalty. However those who race yachts at the highest levels take the view that a light hull is at an advantage over a heavy one. If nothing else the light boat will have a marginally greater acceleration in the same wind. However, even with modern composite materials like carbon fibre, it becomes very difficult to provide adequate strength in a very thin shell. Such hulls have a short racing life. If a lightweight hull is the aim it becomes important to understand the character of the forces that may be exerted on it. Those forces exerted on a hull arise in different ways but they can be divided into externally applied forces and internal forces.

The obvious external force is exerted on the hull by the water when it is sailing and any hull that can withstand the forces exerted by the rigging is most unlikely to fail as a result of forces exerted by the water. However some skippers or their helpers are not averse to dropping or throwing their yachts into the water to launch them. In most yachts there is a weak region around the junction of the fin and the hull and the impact forces produced by such launches can be severe enough to cause cracking in this region. The hull must be strong enough to withstand boat-to-boat collisions in racing and also with obstructions. These exert localised forces that are not easily resisted by very thin hulls. Model yachts go out of control for various reasons and have to be recovered and then they must be strong enough to be handled by a person in a rowing boat.

The rig is mounted on the hull and this means that the hull must resist all the forces that are exerted on it by the rig. If the yacht has a Bermuda rig the shrouds, the fore stay and the back-stay are each attached at one end to the mast and to the hull at the other as shown in Figure 16-1. They combine to exert a force on the mast tending to push it through the bottom of the hull. This necessitates some internal structure such as that in Figure 16-2. This frame is the internal equivalent of the shrouds and cross trees and puts all the forces in equilibrium without any of them passing through the hull. However, the hull will still be subjected to bending by the forces in the fore stay and the back-stay. This bending can be a problem for a thin hull[1] but the effects of bending are usually quite obvious as wrinkling of the hull. The resistance to bending may be impaired if too much of the deck is removed to save weight. Taken to the limit the hull would have the same resistance to bending as plastic guttering.

The hull will also have to have adequate strength to withstand the forces exerted on it by the heavy bulb mounted on the end of the fin that is effectively a long lever. These forces are probably not severe when the boat is being raced because the boat can move in the water to accommodate forces as they are applied. It is different when the boat is being handled because it is often held by its fin and carried against the wind fully rigged. Then large forces are transmitted through the hull. If the fin box is joined to the mast structure the forces can be carried from the sails to the fin without forces being transmitted through the hull. This is particularly important for a yacht fitted with a swing rig where there are no stays and the mast becomes a cantilever just like the fin.

When the design of the hull is being considered the class rules may have an influence on the weight and strength. For instance the popular One Metre boat can only be made of wood or glass fibre and there is a minimum weight for the rigged boat and a maximum for the fin and bulb. These weights give the builder the option of a quite substantial hull without excessive weight or a very light hull with ballast. Those who take the second option choose to put the ballast at the lowest point in the hull and so improve the static stability. As we shall see (page 100) it is not possible to make a substantial improvement in static stability with weight which is moved just an inch or two downwards in the hull.

Club racers probably need to balance out durability and lightness. In your author's view one should aim to build to the minimum weight and not aim to use ballast. The improvement in stability is just too small to be justified when it is set against the use of the weight to make the hull more resistant to wear and tear.

Let us start with floating. The hulls of model yachts have a variety of shapes that stem from the priorities that designers place on different requirements of the design. One designer may think that it is more important to have very fine bows to cut through waves and another may prefer a much fuller bow to give buoyancy when the boat is being driven hard. Some designers favour a slender hull and others favour a very wide hull. Whatever the ultimate design may be there are certain flotation requirements to be satisfied for every attitude that the hull may take.

In Chapter 3 we have met the physical concepts that are involved when a body floats at rest. We know that the hull will sink into the water until the weight of water displaced by the hull is equal to the weight of the yacht.[2] This means that slender hulls must sink deeper than hulls with a wide beam. This is shown in Figure 20-1 where the areas below the waterline of the two shapes are equal.

When the hull is under way and is producing bow waves and stern waves and other waves in between, the weight of the displaced volume must still equal the weight of the yacht. If the water level drops amidships the hull must drop as well to immerse the bow and stern more deeply to restore the buoyancy. The hull will heel in response to transverse forces from the sailing rig to alter the shape of the displaced volume in a different way. The shape of the displaced volume will always be changing and it is not something that we can design for. Nevertheless we have to settle the dimensions of the hull in some way.

We need to have some starting point and designers do as they have always done and envisage an attitude for the hull when it is floating at rest in still water and give the hull a water line. For a yacht to float at its intended water line the volume below the waterline must be such that, if it were to be water, it would equal the weight of the yacht. At one time it was an extremely tedious job to find the volume of water displaced by the hull when upright and a second equally tedious calculation was needed to find the centre of buoyancy. It need not be so tedious now. We have seen in Chapter 6 that all devices moving through a fluid should have shapes that are free from sudden changes of curvature. The best way to achieve this is to use mathematical expressions for all the shapes and this suits computational methods. Then finding the displaced volume and the centre of buoyancy becomes easy as does finding the distance between the metacentre and the centre of buoyancy and finding the area of the wetted surface for resistance calculations.

* *

*Stability*

It is obvious to any casual observer that Marbleheads have developed to have extraordinarily deep keels. This development has not been driven by a desire to improve the performance of the fin but by the desire to reduce the beam of the hull. (See Picture 20-2). It is to be expected that the reduction in beam will reduce the stability given to the hull by its shape and, to compensate for this, the bulb is lowered in order to lower the centre of gravity of the yacht. Such a development is not possible for metre boats and A boats because both are restricted for draught. However the desire to make finer hulls is universal at the time of writing. It would make sense to have an idea how the stability is affected by a change in beam.

The first thing to recognise is that even
with a thin hull the model racing yacht is quite strong when compared with a
conventional ship and we can increase the stability as much as we like within
the inevitable compromises of design. Let us look at the relative positions of
the centre of gravity, the centre of buoyancy and the metacentre of a model
yacht. These are shown in Figure 20-3. Now we see that the metacentric
height MG = BG + BM*. *In order to
increase MG* *we must increase either
BG* *or* *BM or both.

We have an expression for BM*. *It is BM=I/V where I is the second
moment of area of the water plane section of the hull about the centre line and
V is the displaced volume of the yacht. We need to interpret this for a model
yacht.

Most readers will know that plans for model
yachts give a side view and plan view of the hull and cross sections of the
hull at regular intervals. A water line will also be given and a horizontal
section of the hull at the water line can be drawn. It would look like
Figure 20-4. In that figure a small area dA has been defined between two
transverse lines and two lines parallel to the axis of the hull. The second
moment of this small area about the axis is dA x^{2 }and the second
moment of area of the whole water plane section about the axis, which is
denoted I, is the sum of the second moments of all the small areas which make
up the section. The evaluation of this seems to be quite formidable but in fact
the second moment of area of the narrow strip between the two transverse lines
is given as b.d^{3}/12. This gives us a way of finding a good value for
I because the area can be divided into somewhat wider strips and the values of* *d measured so that values of b.d^{3}/12
for all the strips can be summed to give I.

It also tells
us that I increases with the cube of the beam and this is quite important. For
example the designed weight of all metre boats is the minimum required by the
rules. This means that the design value of V*
*is the same for all designs of metre boats. It follows that the component
of stability BM* *is greater for
designs with wide beams. We can put a figure to this by observing that if the
beam of a hull is reduced by 20% the component of stability due to the hull,
BM, is reduced by about 50%. This only has significance if the contribution of
the hull to stability is also significant. This means that we must make an
attempt to find out the relative magnitude of the contributions to stability
made by the keel weight and by the hull for typical yachts.

It is not difficult to estimate a likely position for the centre of buoyancy because hulls only sink a few inches into the water. It is easy to locate the centre of gravity of the whole yacht with its tallest suit[3] and from these two points find a fairly good value for BG. Then, if MG is a measure of the stability BM tells us how much is due to the hull and BG how much is due to lowering the centre of gravity.

The finding of the second moment of area may be troublesome but it is possible to measure the metacentric height of a yacht. The method depends on the balance of forces as shown in Diagram 20-5. There a couple that is applied to the mast is balanced by a couple produced by the weight acting through the centre of gravity and the upthrust (equal to the weight) acting through the metacentre

To carry out a test first wait for calm conditions. Fit the tallest rig and sheet it in. Prevent the sails from moving by the judicious use of masking tape. Turn the filter pump off in your fish pond and float the boat. Attach a tether to the mast just above the deck and secure the tether to the pond surround. Fix a deck pulley or the like to your step ladder and attach a line to another point high on the mast so that the line runs horizontally to the pulley and prepare to hang a weight on its free end. Attach a small weight, about ½ ounce, to the line to take up the slack in the system. Now add about a ¼ pound to the line to make the yacht heel and measure the travel of the line, ie the distance x. Measure the distance between the line and the tether. Weigh the yacht and find out the position of its centre of gravity by balancing it on its fin on a rod of some sort. When this has been done we can calculate the metacentric height.

Let the weight of the yacht be W and that of small weight be w. Then:-

W times the distance between lines of action of the weight and the upthrust = w.y

The distance between lines of action of the weight and the upthrust = x/y.MG.

From this W.x.MG/y = w.y
and MG = (w/W).(y^{2}/x)

For a Metre boat W = 9 lb, w = 0.25 lb, x=7.25² and y = 44² from which MG= 7.5²

The centre of gravity was 4.2² down the fin from the bottom of the boat. The depth of immersion was about 2² so, allowing for B to be about 1.3² above the bottom, the distance from B to G was about 5.5². From this BM = 2². We can now see that the contribution to the static stability that can be attributed to the hull is about 27% the rest being attributable to the low centre of gravity. This means that reducing the beam by 20%[4] would reduce the static stability by about 13 %. This reduction is of a magnitude that cannot just be ignored and a balance has to be struck between low wave making drag and stability.

Similar measurements for a Marblehead with a fin of 18.5² including the bulb gave a metacentric height of 13.5² of which BG =10.5² and BM = 3². Once again the lowering of the centre of gravity is the most important factor in the static stability. If this is the case we need to have some idea of how to assess any proposed way of lowering the centre of gravity.

Figure 20-6 shows a yacht of weight W
balanced on a knife-edge. Suppose that a component of the rigging weighing w is
moved nearer to the knife edge by a distance x. The yacht will have to be moved
on the knife-edge to restore the balance. The question is how far must it be
moved? The answer is _{} and this is the
movement of the centre of gravity resulting from the lowering of the weight.

Let us put some useful figures to this. Suppose that the weight of the boat is 12 pounds and that a battery weighing 5 ounces and 4.5 inches long can either be mounted on end in the hull or laid flat on the bottom of the hull. The effect is to move the centre of gravity of the battery by about 2 inches. Putting these numbers in the expression above shows that the centre of gravity of the yacht would be lowered by 0.052 inches. The effect of this on the static stability will depend on the metacentric height. For a typical Marblehead this will be about 12 inches. So the change in static stability is about 0.4%. It is hard to see many opportunities for such changes in the weight distribution on a yacht and it is equally hard to be certain that such a change is detectable. Suppose now that it was thought to be desirable to fit a burgee to the mast head. The burgee might weigh 0.5 ounce and be at a height of 84 inches. By the same argument the centre of gravity of the yacht is raised by about 0.2 inches and the static stability is reduced by nearly 2%. This tells us that reducing the weight of the rig by a very small amount it more useful than making a light hull only to add ballast to achieve a similar result to that given above for a battery.[5]

Some stability is given to the boat as a result of its movement through the water. The asymmetrical wave pattern tends to keep the yacht upright but the effect is very small. We have seen that the fin tends to overturn the yacht and the rudder will have a small effect depending on what it is doing. However the bows can be flared to provide an effect on the fore-and-aft stability by lifting the bows against the force on the sails acting some way up the mast. The working of flared bows is not straightforward because they only work when the boat is moving and water is being thrown off sideways by the flare. Before that can happen the boat must pick up speed. Picking up speed involves acceleration and acceleration is the result of a force acting at the centre of gravity. The accelerating force is provided by the sails which is, unfortunately, a long way above the centre of gravity. The result is that the yacht is subjected to a moment tending to turn it over forwards as well as the accelerating force. The hull may have enough buoyancy forwards to provide a resisting moment by the lowering of its bow and the raising of its stern which may well happen if the acceleration is not too great. Then as the speed increases the flared bow can take over. However, if the acceleration is applied suddenly as in a gust of wind the flare will not be working and the buoyancy will not be sufficient to prevent the yacht “diving”.

There is another method of providing a measure of dynamic stability using the shape of the hull. It is used in “skiffs”. In heavy weather the yacht will heel more than usual and have to push its bow through waves or wavelets and this increases the effect of the bow in steering the yacht. At the same time the heeling lifts the stern and in doing so gives the yacht a bow down attitude. This means that the centre line of the yacht is higher at the stern than the bow and, as a result, the angle of the fin changes and it may well produce a force which tends to right the yacht whereas a normal hull always has a force on the fin tending to overturn the yacht. This would make the skiff a good boat in heavy weather but not necessarily in lighter conditions.

*Leeway and turning*

In this text I have referred to the way that the Cutty Sark is steered and how it resists transverse forces produced by the sails. I have also shown how a fin and rudder can act together to do the same thing. There is no reason to suppose that the introduction of the fin working with a submerged rudder completely replaced the effect of leeway on the hull or the action of the hull during turning. In practice we should expect both the hull and the fin to resist the transverse forces. Our problem is that we have no idea of the relative magnitudes of the contributions made by the hull and the fin. This problem is difficult to analyse because the angle of the leeway is so small.

It is claimed that a hull with a wide beam is more easily turned than a hull of the same length with a narrow beam. This seems to be borne out in practice. Cutty Sark despite being a clipper ship designed for sustained high-speed sailing was also a cargo boat and is quite full at the bow with a significant angle of the bow at the stem. This full bow produces a bow wave that lifts up in front of the hull and offers a large resistance to motion. By comparison a modern fighting ship has very fine bows with a very small angle at the stem. It produces a wave that lifts to its greatest height at a significant distance from the stem to give a much lower resistance to motion that is, of course, the reason for the fine bow. The very fact that the fine bows give lower resistance to motion also means that a smaller transverse force can be exerted on the bow to help with leeway and turning. For the designers of model yachts a decision to use fine bows is also a decision to reduce the contribution made by the hull to turning and to impose an increased duty on the fin. Picture 20-2 shows clearly the fairly flat surface at the bow that has to be pushed through the water sideways when the hull is turning. See also Diagram 18-10 that shows the direction of the bow when a yacht is turning.

*The shape of the hull.*

There is a formidable body of text on the design of full sized hulls but it is not readily transferable for use with model hulls because of the difference in the ratio of the average height of the surface waves to hull length. All the methods are attempts to get round the basic problem that a hull is too complex a device for us to design it from any rigorously applied science. Consequently the shape of the hull is the outcome of some process that has gone on in the designer’s mind. The possibilities are endless and no one knows the definitive shape for a hull. We use an evolutionary process that one might expect to converge gradually to the best design just as the small four-door car is converging to one design. However there is an extra factor in the design of model yachts that prevents one design from being the outcome of the process. All family cars are designed for use on ordinary roads that are fairly standard but model yachts sail on the surface of lakes where conditions vary with the size of the lake and with the surroundings as we have seen in Chapter 4. It seems that no single design is best for all the conditions that may be encountered. As a result there is a wide variety of designs each of which is best suited to a particular combination of wind and wave.

The problem facing the club racer
is that of making a choice from the designs available. Unfortunately the
assessment of the performance of a yacht involves the skill of the skipper and
we may find that two hulls of widely different design occupy first and second
places in world championships. The only thing for a club racer to do is to
start by deciding where he is going to race, that is, on his home water where
the conditions are known, or at many venues. If the decision is to race at home
the design of yachts used by those who win there regularly is the best guide.
If the decision is to race on many lakes then one must assess carefully the *overall* performance of various designs
taking into account the ability of those racing the yachts before making a
choice. It is a help if the important features of suitable designs can be
recognised and this is the aim of this section of the chapter.

If we are to look at hull design we must start by recognising that the hull must be designed to satisfy the rules of the class in which it is to be raced. This leads to designs that, broadly, can be divided into two categories, one where the hulls are restricted for overall length and the other where there is a restriction on the length of the water line. They are quite different in appearance because hulls conforming to a restriction on the water line length can have overhangs fore and aft. This chapter has set out the several requirements to be met and for either category the shape of each hull depends on the priorities placed on each requirement by the designer and how the designer thinks that some desired overall behaviour can be achieved.

Before we can look objectively at existing designs of hulls it helps to have a basic design to alter to achieve some different behaviour. I have chosen a shape based on simple geometrical figures for a length-restricted hull like the Marblehead shown in Pictures 10-2 and 10-3. The shape is drawn in Figure 20-7. The deck plan is made up of two arcs of circles for the gunwales and a flat transom. The side elevation is another arc with a blend at the stem. Four cross-sections are shown, the two aft sections are arcs of circles, the next is an arc blended to suit the beam and the forward section is part of the blend to the stem to give a “V” shaped bow. We might start by assessing this design. This means assessing the compromise between the need to minimise the wetted area for very light wind conditions when the drag is mainly due to friction and the need to have low resistance to wave making in heavy weather. The shape that has the least wetted area for a given displacement is a semi-circle but only if it is fully submerged and it is clear that while most of this hull is semi-circular it is only partly submerged. This could be improved but we must consider wave making. When the yacht moves in a typical wind, bow and stern waves form and the level in between drops. The bow and stern will both become submerged and then we need the volume provided above the static waterline to keep the yacht afloat. The bows are “V” shaped and they part the water as is shown in Figure 2-5 and in Picture 7-3. The "V" gives a substantial volume above the static waterline at the bow which can be submerged to resist the moment tending to overturn the boat forwards in a gust. That same volume has a side area which makes an angle to form a flare when the yacht heels to give good steering and reduce the force on the fin. The shape near to the stem has little side area to resist turning. The hull is a good compromise for general use.

Now we can consider possible changes. The first change is to the shape of a hull where the class rules permit overhangs. Typical changes are shown as dotted lines in Figure 20-8. The bows are clearly finer which will reduce the wave-making resistance. The run aft is unchanged. The overhangs also give more volume to be submerged as the speed increases and the bow and stern waves form. The crests of these waves can be farther apart than they can be for the original hull and so give the potential for a higher top speed. The extra volume added at the bow will reduce “diving” to only the most severe conditions. These changes are all improvements and they go to show the severe disadvantages of having a restriction on overall length.

Pictures 20-9, 10, and 11 show such a hull and it is easy to see in the deck plan how the bow and stern have been made sharper by effectively drawing tangents to the original radii. Picture 20-11 shows the length of the overhangs when the boat is afloat and moving slowly.

Let us now look at changes that do not involve a change in length. We have seen above that fine bows will reduce the resistance to motion caused by wave making and this leads to a desire to reduce the angle at the stem. The obvious change to make is to reduce the beam by using a larger radius for the gunwales. This is shown in Figure 20-12 and in a real boat in Picture 20-13. The reduction in beam affects static stability of course and the section of the hull will have to change to restore the displacement. A change to the deeper shape in Figure 20-12 will lead to a new side elevation which has been shown as another arc but meeting a lengthened stem at the static water line at a point. The run aft is not as good as it was before the change and the flow is more vulnerable to the disturbance caused by the rudder. The longer stem restores the volume forward but will be immersed as soon as the bow wave starts to form. This changes the pattern of the bow wave that may or may not be an improvement. The developed form of this bow is shown in Picture 20-2.

The next possible change is to change the deck profile to move the maximum beam aft to retain the static stability. This is shown in Figure 20-14 and in Picture 20-15. The side elevation need not be changed unduly but the sections aft will lead to sharper curves at the stern. This general concept is used quite frequently in full sized racing yachts. It seems likely that the rig and the fin will need to be moved aft to restore balance with the hull.

The final version of this type of change is the “skiff” which has a plan shape that is more or less triangular. It is shown below in Picture 20-16, 17 and 18

[1] This was demonstrated in the Americas Cup races in 1995 by the Australian boat which broke in half and sank in about a minute.

[2] When estimating the displaced volume one must not overlook the volume displaced by the fin, the rudder and the bulb which typically, for a metre boat, may together contribute about 0.7 lb, two thirds of which comes from the displacement of the bulb.

[3] The centre of gravity moves down the fin for smaller suits so the metacentric height is least for the top suit.

[4] For One Metre boats there is a limit for the depth of submergence of the hull which may limit reductions in beam.

[5] It is instructive to find the positions of the centre of gravity of a Marblehead when it is fitted with each of its suits of sails.