Chapter 17     The fin

 

Introduction

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Figure 17-1

The course of a yacht is determined by the balance between all the forces acting on it. These forces are applied by the wind on the sails and by the water on the hull and on the fin and rudder. In this chapter, we will concentrate on the design of the fin. The only thing that the fin can do is generate a force which acts more or less at right angles to its centre line just like the lift of an aeroplane wing. We need such a transverse force to resist the transverse component of the combined force exerted on the sails. The fin also works with the rudder to control the course of the yacht and that will be the subject of the next chapter.

 

The fin is set along the centre line of the yacht and when  the yacht moves with leeway the fin moves through the water at an angle as shown in Figure 17-1. In the figure the leeway is the angle between the centre line of the yacht and the course sailed and this is shown as 3°. The fin would then be subjected to a force as shown in the figure.

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Picture 17-3 Fin and rudder of Marblehead

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Picture 17-2 Fin and rudder of A boat

The design of a fin will involve choosing a cross section for it, deciding its area, and its shape. A glance at Pictures 17-2 and 17-3 show the range of designs which are needed. The difference comes from the class rules that restrict the draught of an A boat but not that of a Marblehead. In addition the very fact of the existence of the fin gives a useful place to mount the lead bulb.

 

The section of the fin

We can start with the section of the fin. The best shape we know for the cross section of the fin and rudder is an aerofoil. This gives the lowest drag for a given lift when it is working normally, ie, not stalled. The data gathered by the NACA has been introduced and explained in Chapter 6. Now we want to make use of it. Before we start we must recognise that the data may not be directly transferable. Strictly data is only transferable between systems having the same value of Reynolds number. It is not necessary for us to understand this concept of Reynolds number only to know that our model yacht fins work at a value of Reynolds number which is about 20 times less than that at which the NACA models were tested. This means that we must be careful when we use data collected in wind tunnels. Fortunately the behaviour of the aerofoil as a lifting device is not much affected by the changes in Reynolds number that we encounter here, it is the drag that is most affected. At the lower Reynolds numbers at which the fins and rudders of model yacht operate the drag coefficients may be as much as twice that for the models tested by the NACA.

 

A few of the sections that are suitable for use for the fin and rudder of a yacht are shown in Figure 6-6. Their lift versus drag characteristics are shown in Graph 6-7. Two graphs are given for the NACA 0012-64 section. One is for a very smooth test model the other for a model with an artificially roughened surface that is thought to be typical of real sections. The two graphs show very clearly the effect of the surface finish in that the smooth model stalls at a value of CL that is just under 1.4 whereas the typical surface stalls at about 0.95. We must decide whether the surface finishes which can be achieved for model yachts will allow us to work with the high coefficients of lift in Graph 6-7.

 

Surface finish

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Picture 17-4

We have seen that the molecules of fluids (in our case air or water) are exceedingly tiny and have extraordinary motion. This molecular motion does not change because the fluid is flowing over an aerofoil but the fluid in the immediate vicinity of the surface forms minute swirls and eddies in response to variations in the shape of the surface. Picture 17-4 shows the surface of a new, plastic, spectacle lens magnified 20,000 times. This is an enormous magnification yet the “lumps” are still about 400 molecular diameters across. Viewed from a distance a large cross is evident. Even an optical quality surface is by no means smooth when viewed at the molecular level. The “lumps” will disturb the flow and so will the waviness. A new carbon fibre fin will feel very smooth to the touch but look at it through a jeweller’s eyepiece and the surface imperfections, especially scratches, are obvious.

 

There is a mass of data on the resistance to flow caused by friction at the surface of pipes and aerofoils. All this data supports the observation that large surfaces of a given texture offer less resistance per unit area than smaller surfaces of the same texture. In this context the surfaces of the fins and rudders of model yachts are small and we must regard our surfaces as being rough. It follows that, if we are to use aerofoil sections for these items, we should look towards the data for artificially roughened surfaces given in Graph 6-8. However we can easily reduce the performance and increase the drag by using fins and rudders with poor surface finish and inaccurate profiles.

 

Choice of section

The choice of a section for fins and rudders is not constrained to aerofoil shapes and some designers think that a flat plate with rounded leading and trailing edges is to be preferred. A flat plate used as a lifting surface is known to be very inefficient [1](the drag becomes large for a given lift). It is also accepted that aerofoils of small chord (3 inches or less) become inefficient to the point of being not much better than a flat plate. The fins of most yachts are wider than 3 inches except perhaps near to the bulb so most fins should have aerofoil shapes.

It follows that some appraisal of the data for the sections is needed. Before we do that we need to look at the variation of coefficient of drag with angle of attack for these artificially roughened sections. The graphs are given in Graph 17-5 and this just shows how complicated things are for these symmetrical sections. They are for the same basic section but with maximum thicknesses of 6%, 9% and 12%. Each curve has a value when the angle of attack is zero. This is the skin drag that probably does not change much with the angle of attack. The increase in coefficient of drag is the result of the change in the flow pattern to produce lift. The 6% section has the lowest coefficient of drag at zero angle of Text Box:  
Graph 17-5

attack but at 5° has the highest value and the coefficient is rising rapidly with increasing angle of attack. The 9% section has a marginally higher value of the coefficient of drag at zero angle of attack than the 6% section but mostly it has the lowest values at all other angles of attack. These figures suggest that 6% is too thin and that 9% is a good choice but there is still the question of validity. For the models tested by NACA the lift over drag ratios easily reach values of 60 to 1. Such values are now achieved on modern full-sized gliders. The sizes of section used on model yachts will not have these low values of coefficient of drag. We must expect figures up to ten times as great but the poor performance of the thin section by comparison with others is likely to be the same because it is mainly attributable to the small nose radius. The Text Box:  
Picture 17-6 Fin for A boat 7.5% thick section.

thin section reaches high drag before the stalling angle is reached. This all suggests that a thickness near to 9% is the best choice and most designers seem to use this value.

Selection is not limited to the three sections listed above. There are other sections having the maximum thickness further back and these may be useful to accommodate structure. The position of the maximum thickness in the range of about 30% to 50% of the chord makes no great difference to the performance at the chord lengths involved. Picture 17-6 shows a 7.5% section of an A boat fin. This section is NACA 0016-64 scaled down to 7.5%. It has its maximum thickness at 40% of the chord and is suitable to accommodate the carbon fibre mounting tube.

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Graph 17-7

If any symmetrical section of about 9% thickness is chosen we can usefully represent its behaviour as that shown in Graph 17-7. Here the coefficient of lift grows to 0.9 as the angle of attack increases to 9° and then remains at 0.9 as the angle of attack goes on increasing. A conservative figure for the lift over drag ratio for a fin is about 8 giving a coefficient of drag at 9° of about 0.11 but once the stall takes place the drag coefficient may well rise to a figure as great as 1.6 at angles of attack of 90°[2].

 

Area of fin

In Chapter 7 we decided that the most important point of sailing for a model yacht is pointing into wind and that it is essential to set up the rig to give the best performance to windward even at the expense of performance at other points of sailing. In some ways it is fortunate that this is the case because pointing is the only mode of sailing that can be found repeatedly with confidence. This is also the point of sailing where the transverse force on the sails is greatest so we must design the fin to have sufficient area to resist this force. In order to do so we must have a good idea of the magnitude of the transverse force on the sails

 

The forces acting on a yacht are shown in Figure 2-4. We can make use of this to experiment on, say, a Metre boat fitted with its top suit. If we float the yacht with a cord round the fin to prevent side ways movement and a cord round the mast to exert a horizontal pull we can make the yacht heel to a normal racing angle. If the cords correspond to the points of action of the force on the fin and the combined force on the sails the force in either cord will be the transverse force normally exerted on the rig. I did this and the force was about a pound and, at this angle of heel, did not seem to vary much as the heel changed.

 

We have an expression for the lift produced by an aerofoil. It is Lift = r .A (see Chapter 6). Before we can use this expression we need to sort out the units.

 

The symbol r stands for the density of water and, if we measure forces in pounds[3], speed in feet per second and the area in square feet, r will have the value 62.4/32.2. We have throughout taken the speed of the yacht when pointing to be about 2 mph or about 3 feet/second. Using this the value of ½ r  becomes equal to 8.7 and A = 1/(8.7.  ) square feet or =144/(8.7.  ) square inches. This reduces to 16.5/ .

 

So the area of the fin depends on the coefficient of lift. We could work our fin at the point of stalling where, at an angle of attack of 9°, the value of  is 0.9 and then the area would be 18 square inches. However we have to use this fin in conjunction with the rudder to steer the boat and the last thing we want is a stalled fin. So we must think of using a much larger fin working at a much lower angle of attack. Let us try 3°, the figure that I used for a typical leeway. For this angle the value of  is 0.3 and the area of the fin would be 55 square inches (The designer of the yacht provided a fin of 323 square cm ie 50 square inches.) or three times the minimum area. The ratio of the drag of the larger fin when producing the same force as the fin of minimum area is about 1.5 to 1 because of the lower coefficient of drag. These methods clearly produce areas that fit in with practice.

 

Shape of fin

We now have a suitable section and a suitable area and the next step is to decide on a shape. As we have seen the shape is to some extent dependent on the class rules but class rules cannot account for the wide variation of shape within a class. So let us try to set some guidelines for fin design. Let me list the several effects.

 

(i) We know that the fin produces a force that tends to upset the boat. (See Figure 2-4) and it would make sense to keep the point of action of the force on the fin as high as is possible.

 

(ii) The fin fits between the underside of the hull and the lead bulb. Both act as end plates to reduce the cross flow which we have seen on aeroplane wings and which leads designers to use high aspect ratios. A fin like the one shown in Picture 18-6 would not show any marked improvement if its aspect ratio could be increased.

 

(iii) It may be desirable to gain higher stability and therefore increase the ability to carry sail by lowering the lead bulb. This means that the fin must be longer and, if the area of the fin is not to be increased, the width must be reduced. This leads us into the grey area of small aerofoils with dubious performance. It also leads to fins that are liable to twist under load.

 

(iv) Some place importance on blending the fin into both the hull and the bulb. In aircraft practice the fairings between flying surfaces that meet at right angles are really quite small[4].

 

(v) Yachts normally sail in a heeled condition. This produces an asymmetrical bow wave as shown in Figure 2-5. Inevitably the different levels will produce a skewed flow under the hull to add to the other flow patterns and there may be a case for cutting the fin away near to the hull as in Picture 17-8.

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Picture 17-8

Taking these guidelines into account it would seem that fins should taper from top to bottom to raise the point of action. They should only be as long as is deemed to be essential and, for long fins, the problem of torsional stiffness must be addressed. A cutaway at the top may help. Beyond this it is hard to see any reason for any special shape except for eye appeal.

 

 

 



[1] The problem with small sections is unavoidable. The section must have a radius at the nose and as the chord becomes shorter this radius gets smaller. In order for the fluid to follow this nose radius an inward force is required. The pressure difference required to produce this force becomes progressively less likely to occur as the radius gets smaller and the flow breaks away. With a flat plate which must be thin breakaway occurs at the leading edge for all sizes.

[2] This is how the rudder we use to control the direction of our yachts behaves. It produces lift quite efficiently up to about 9° when it stalls and then goes on producing the same lift with increasing drag as the angle goes on increasing.

[3] If there is a preference for SI units then the force will be in newtons, the density will be 1000 kg/cubic metre, the speeds in metres/second and the area in square metres.

[4] Fairings of significant size are used where flying surfaces join say a round fuselage at an angle eg on high wing aeroplanes.