Chapter 18        The rudder

 

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Figure 18-1

A yacht is raced by continually adjusting both the sheeting of the rig and the rudder. Normally the aim is to have the greatest forward drive from the sails as the priority and then to adjust the rudder to hold the course for which the sails have been set. It is evident that this is not always possible and that the sails may have to be eased in order to maintain directional control. In this chapter we must look at the way that the rudder acts with the fin to help the hull to maintain the desired course of the yacht and then to think about its design.

 

The underwater parts of a modern yacht are shown on Figure 18-1 (the bulb has been omitted) but at one time yachts sailed without a fin. It is important to see how this was achieved.

 

A good example of successful sailing vessels that had no fin or keel of any sort is the Thames barge. Hundreds of these were built with weights up to 300 tons and they were capable of working all round the British Isles and to the Mediterranean on a simple hull using only a rudder and one of two quite small lee boards for directional control. If we can decide how such vessels were steered we can go on to see how the addition of a fin might have improved the control.

 

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Picture 18-2 Aft end of Cutty Sark

The directional control of a yacht

The course of most vessels is made up of stretches of sailing in a straight line linked by changes from one line to the next in turns of a suitable radius. In order to sail a straight course the sails are set and then the rudder position adjusted to both minimise the leeway and to balance any tendency to turn produced by the sails. During a change of course the rudder causes the hull to follow a curved path to the new course when the sails are trimmed again and the rudder set to a new position. The rudder on a Thames barge and for that matter on much larger sailing ships and on rowing skiffs is hung on the aft end of the boat on pintle bearings and the hull is shaped to let the water “run” aft and over the rudder. Picture 18-2 shows the rudder of the Cutty Sark and also the way that the hull is shaped to let the water run on to the rudder which is so small that it cannot be the force on the rudder itself that causes the turning. Directional control is achieved mainly by the increase in the pressure on the hull forward of the rudder on the side of the hull to which the rudder is turned and a corresponding lowering of pressure on the other side.

 

Let us consider the process of turning to change course and straight sailing separately. If we take the turning first we must recognise from mechanics that for any object to follow a curved path a force acting towards the centre of the arc must be exerted on the object. This is the centripetal force. Now a vessel is made to follow a curved path by turning the rudder towards the centre of the curve and thereby producing a force acting outwards partly on the rudder and partly on the hull. This is the opposite of what is required. It follows that in some way the hull, being the only other surface involved, must generate sufficient force to overcome this outward force and provide the centripetal force.

 

There is only one possible mechanism; the hull must move with leeway, that is, to move forwards and sideways simultaneously. The sideways movement will cause a cross flow under the hull which, when combined with the forward movement, will produce a corkscrew flow pattern. This will be accompanied by a heaping up of water on the forward side of the hull on the outside of the turn and a reduction of level on the inside of the turn. The difference of level will produce different forces on the two sides of the hull and the net effect is the required force towards the centre. Of course the rearrangement of the flow will not be simple but the main evidence will be in the asymmetrical appearance of the bow wave and of the wake. Figure 2-5 shows us such a wake. The asymmetrical bow wave will produce a local force at the bows that, when combined with the force from the rudder, continuously turns the vessel. This mechanism must operate whether the vessel is power driven or sail driven and regardless of other mechanisms such as a keel or a deep fin. If the force is great enough to steer a sailing barge it will make a significant contribution to the steering of a racing yacht even when it is fitted with a fin.

 

Now let us look at sailing a straight course. Suppose that the barge is reaching. Then the sails produce a transverse force, a forward force and, no matter how well the sails may be trimmed, a residual system of forces that tend to turn the yacht[1]. For the sails to be effective the transverse force must be resisted. The mechanism is the same as for changing course but now the hull follows a straight course with the fore and aft axis of the hull turned through a quite small angle to windward. This generates the required transverse force.

 

The Thames barge and all the other vessels depending on the combination of asymmetrical flow over the hull and a rudder for control of the course did not sail very well into the wind. It took a long time for yachts to evolve to having a deep fin and a bulb and a separate rudder. The deep keel came first but with internal ballast. A few intrepid designers then fitted the ballast outside as an integral part of the keel and with the rudder hung from the keel so that, when the rudder was on centre, it was faired into the keel. The change to having a separate rudder came next although it was not an all-moving rudder and, once that had occurred, the step to the use of a very deep fin and a bulb and a separate all-moving rudder was not great. The changes allow a modern yacht to point up to  the wind to less than 45° compared with 55° for a sailing yacht in say 1930. This is a very large improvement and it means that we need to understand how a fin and rudder work. On the face of things it seems that the fin has replaced the hull in steering the yacht but it seems much more likely that the hull and the fin both respond to the rudder and jointly steer the yacht.[2]

 

Figure 18-1 above showed the essential underwater parts of a model yacht ie the hull, the fin and the rudder. All the forces that were present for the sailing barge are present for the racing yacht but now there is a relatively large, fixed, vertical surface, the fin, to work under the water with the rudder. The rudder is no longer hanging on the back of the boat but is wholly submerged and it rotates about an axis that is more or less vertical. The axis of rotation is near the middle of the rudder so that any force on it acts just behind the axis of rotation and little effort is required to operate it. This is because the rudder is no longer required to act with the after part of the hull to change the course but to act with the fin. A consequence is that the hull now requires no significant depth aft nor does it need to be shaped to make the water run aft for the rudder to operate. The yacht hull is a different shape aft to that of a sailing barge.

 

If we suppose that both the fin and the hull are used to control the course there is no reason to suppose that they share the task equally. It is more likely that the fin normally dominates but that, in some circumstances, the effect of the hull may be adequate. We cannot hope to sort out the contribution made by each system but in order to design a fin we must know how the fin and rudder work together on their own.

 

 

The wing/stabiliser system

The fin is clearly a small wing working under water. Aeroplane wings do not work unaided but as one element in a wing/stabiliser combination. This is the arrangement used almost universally on aeroplanes. In the same way the fin works with the rudder. This means that we can look at the information available in aeronautics for an explanation of the mode of operation of the wing/stabiliser system and then use as it a guide to the operation of a fin and rudder. However we must consider the case of a wing and stabiliser with symmetrical sections because the fin and the rudder have to produce a force in both directions and so must be symmetrical.

 

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Figure 18-3 Model in tunnel
Figure 18-3 shows a model of a wing and stabiliser in the working section of a wind tunnel. The wing is of parallel chord and is pivoted[3] at its tips in the sides of the tunnel. A rod, acting as a fuselage, is fixed to the wing to support the stabiliser at one end and a balance weight at the other. Provision is made for the adjustment of the angle that the stabiliser makes with the axis of the rod.

 

Let us start with the stabiliser aligned with the rod. When the tunnel is running neither of the two surfaces experiences a vertical force although both are subject to a skin drag. Our interest starts when the stabiliser is set at a small angle of just a few degrees to the rod.

 

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Figure 18-4

The immediate effect is to produce a force on the stabiliser that deflects the stabiliser downward and tilts the wing to give it an angle of attack. This movement brings two forces and two moments into existence. The aerodynamic force on the wing is exerted directly on the pivots. As we have seen in chapter 6 this force is usually regarded as the combination of a lift and a drag and it is inclined towards the trailing edge. As we have also seen, a moment about the pivot will also be exerted on the wing. These will both change with the angle of attack. A similar force and a moment of smaller magnitude will be exerted on the stabiliser. The final position adopted by the model is shown in Figure 18-4. In this position the wing and stabiliser are in equilibrium with the stabiliser providing an upward force to balance out the combined moments on the wing and on itself and to do this it must make an angle of attack (probably smaller) in the same direction as that of the wing. The net force exerted by the two aerodynamic surfaces will be exerted on the pivots. It must be evident that this system permits the control of the angle of attack of the wing, and therefore the force exerted on it, by adjusting the angle that the stabiliser makes with the fuselage.

 

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Figure 18-5

Before we can carry this over to a yacht we must see what happens to the wing/stabiliser combination when another force is applied to this model at some point other than the pivot. Two suitable points A and B are indicated in the wind tunnel diagram. Let us start with a force applied at point A. The final position is shown in Figure 18-5. The wing is shown in the same position as before but now the stabiliser has to provide a much greater upward force to balance the combined moments on the wing, its own moment, and the moment about the pivot caused by the added force at A. The angle of attack of the stabiliser must be increased. In Figure 18-5 it is shown with just about the maximum angle it can have without stalling.

 

If now we consider the case of a force exerted downwards at B the outcome is shown in Figure 18-6 where the wing is again in the same position. Here the force required at the stabiliser acts downwards mainly to balance the force at B. The stabiliser now has to have a “negative” angle of Text Box:  
Figure 18-6

attack and, in the equilibrium position, the force and moment it generates balances the force and moment on the wing and the moment exerted about the pivots by the force at B.

 

We need to know what happens when the point of application of the added force is too far from the pivots. Suppose that the position of A were to be moved backwards progressively. The angle of attack of the stabiliser would have to be increased and eventually the angle would exceed the stalling angle. Then the front of the wing would rise and the system would enter a state from which recovery is impossible. In the case of B, the progressive movement forwards would require an increasingly negative angle of attack until the stabiliser stalls and again there would be no recovery[4].

 

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Figure 18-7

The fin and rudder system

Clearly, if we choose to use aerofoil sections for the fin and rudder, they will operate in just the same way as a wing and stabiliser even if they have different names. Then the behaviour of the wing and stabiliser derived from the model in a wind tunnel is directly transferable to the same system working in water. The first thing to recognise is that the rudder will work best if it does not have to cope with forces like those at A and B for the wing and stabiliser. We want the forces on our yacht to be as well balanced as we can get them so that the rudder can be used mainly for controlling the course. This means that the mast and the fin must be set in the best position relative to each other and, bearing in mind the effect of leeway on the hull, to the hull.

 

Figure 18-7 shows a yacht with its sails sheeted in and on it are shown the points of action of the net force on the rig and of the net force on the combination of the fin and the rudder. The forces both have components in all three directions but for this point of sailing the forces are substantially transverse. For one metre boats the positions have been found one way or another and most boats are set up with the mast about 19² from the stem and, for vertical fins, the leading edge at the top is about 1²+ behind the mast. Then, as shown in Figure 18-7 the points of action of the forces on the sails and the fin are nearly in line. The moment caused by this want of alignment will be balanced by the turning force on the hull due to leeway or by the rudder.

 

Now we can try to find out what is required from the rudder at all points of sailing. There are really four conditions to be considered. They are for beating, reaching and running and for turning from one course to another. Let us take them in the sequence above.

 

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 we can see easily when the yacht is pointing too high because either the flow over the fore sail breaks down or the yacht slows or both.

 

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Figure 18-8

Now we must decide how we would like the boat to be set up. The best position will offer the least drag. We must have leeway and this will be the greatest for any point of sailing. We know that it will be about 3° and the drag produced by the fin is unavoidable. If we look at Figure 18-4 we can see that what we really want is the rudder to make no angle of attack (least drag) and yet still control the angle of the fin to augment the transverse force produced by the hull. It is not possible. The sails, the fin and the hull must somehow produce a resultant combination of forces and moments to keep the fin at the correct angle so that the rudder can be offset slightly to align it with the flow. When this has been achieved the boat is “balanced”. (Figure 18-8.) It is doubtful whether this can be achieved even for a constant wind speed and we must set up in the expectation that some rudder action will be necessary. Most would opt for the yacht to luff gently to windward with no rudder offset and use the rudder to correct this and in doing so line up the rudder very closely to the position of least drag.

 

Setting up for balance may be a protracted process and means that, if the yacht is a new design, at least the mast must be moveable.

 

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Figure 18-9

Now we can consider the other points of sailing. The boat will be set up for pointing and we must now find out how the change in course affects the balance. What we would like is for there to be no change in the moment of the force on the sails about the mast. We can look at the sailing diagrams in Chapters 11 and 14 to see how the force on the rig and its line of action changes with a change in course. We can usefully think of the moment as the force times its distance from the mast. Then, for the swing rig, the moment decreases as the course changes from pointing to running simply because the force decreases and, for the ordinary rig, the line of action of the force moves very considerably and we must expect serious imbalance unless some system of “jib-twitching” is used. The implication is that rudder action will be needed in each case with the consequent additional drag.

 

Before we think about turning to change course we should look at the problem of broaching because it influences our choice of area for the rudder. A yacht that  is running before the wind is likely to encounter gusts which suddenly increase the forces on the sails and upset the balance of forces which has been achieved by rudder action. Figure 18-9 shows a yacht running before the wind and the rudder turned through 9° (just short of stalling) to generate a force to resist the forces produced by the sails. There is probably a small force on the fin. If the forces on the sails suddenly increase the yacht will turn to port, the angle of attack of the rudder will increase and the rudder will stall. Then the force produced by the rudder will be insufficient to prevent the sails from turning the yacht further to port and out of control. This will give the fin an angle of attack and the fin will lift to port. The yacht will slow as its kinetic energy is used to lift the bulb and the yacht will go on heeling until its kinetic energy drops sufficiently for the bulb to drop again as the lift dies. The whole sequence is violent and is called broaching.

 

Changing course

A model racing yacht is required to change course for several reasons. At the start of a race the dominant need is for the yacht to be very manoeuvrable. When it rounds a mark the need is to do so in an arc of small radius to minimise the space between the yacht and the mark and to do so with the minimum loss of boat speed. Penalty turns require the yacht to make a 360° degree turn in the shortest time and come out with good boat speed.

Turning is not just a matter for rudder control; it requires the use of the sheeting control as well so that the sails are driving all round the turn. The sails have to go through all the settings that they would for sailing a triangle in the short time available for a turn. This is only possible if the sail winch can move quickly enough to match the rate of turning of the yacht. If the yacht can turn quickly and the winch responds only slowly the turns will be made largely at the expense of boat speed. We need to look at the forces on a yacht as its follows a curved path.

 

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Diagram 18-10 

Before we can do so we have to get some idea of the normal turning radius of a model yacht because this will permit us to estimate the angle which the rudder must make. A turning radius of 3 feet seems to be possible for all classes of yacht. We have already seen in this chapter that, for a yacht to follow a curved path, there must be a net inward force. When a yacht is turning each part of it follows a different circular path as is shown for the stem, the fin and the rudder in Diagram 18-10. The instantaneous directions are tangential to the paths. Suppose the fin to move in an arc that is 3 feet in radius. The centreline of the hull must make an angle with the tangent to this arc so that it points inwards to give the fin an angle of attack. It has been shown as 3° that is a practical angle. The fin then produces the essential centripetal force and any other force that is needed. The bow of the yacht follows an arc as shown and clearly the bow is continuously turning inwards which upsets the bow wave to increase its size on the inside of the turn and decrease it on the outside of the turn so causing an outward force. The rudder must now generate a force to overcome the force at the bows caused by the turning and keep the fin at the correct angle of attack. It must be turned relative to the hull until it makes an angle of attack to its instantaneous direction and produce the force shown.

 

For a turning circle of 3 feet shown in Diagram 18-10 and an angle of attack of 5° the offset of the rudder is about 34° which is much larger than is likely to be used in sailing between marks. For this turning circle the force on the rudder has a large component acting backwards which is not at all what is wanted. If the turning circle is reduced the angle of the rudder must increase, the outward component of force must be greater and as a result the backwards force be much greater even if the rudder does not stall. There is clearly a compromise to be made here between maximum throw of the rudder, the resulting turning circle and the drag caused by the rudder. It seems that throws of about 35° are enough for turning at marks but, if reduction in boat speed during the countdown to a start is acceptable, a larger throw may be used but it calls for careful stick control.

We cannot just leave this turning because there is a transition between sailing a straight course and the yacht turning steadily. The transition could be initiated by moving the rudder directly to its final position. This would give the rudder an instantaneous angle of attack of more than 30° which would cause the rudder to stall giving a transverse force and a large drag. The drag will slow the boat and the transverse force will start the turn and eventually the steady condition will be reached at the expense of boat speed. However if the rudder is applied more gradually the  transition will take much the same time but will not cause the rudder to stall and the speed of the yacht will not drop so much. The response of the yacht will also improve if the weight at bow and stern is kept to a minimum and the overhangs be no longer than is essential.

In dealing with turning we have not mentioned the effect of the sails. One of the difficult manœuvres in sailing that makes a great demand on the fin and rudder is the rounding of a buoy from a running leg. The yacht will approach with the sails fully sheeted out and possibly both on the same side. This produces a force tending to turn the yacht away from the sails and turning can only be prevented by use of the rudder and the fin. If the sails are on the same side of the yacht as the mark so that the yacht will gybe as it rounds the mark the rudder will already be producing a force towards the outside of the impending turn. Initiating the turn by using extra rudder may in fact cause the rudder to stall and control to be lost. If the turn starts successfully and the boat gybes the sails will suddenly add to the inward force required from the fin which may stall. In either case the yacht may well blow away out of control. If this sequence of events is to be avoided the cause of them must be understood so that, at least, sudden changes in rudder position to excessive angles are avoided and sail changes are made in anticipation of the manoeuvre to come.

 

Design of the rudder

We have reached the stage where we can consider the design of the rudder. All the evidence suggests that we should look for a section that stalls at a high angle of attack and when it stalls does so gently. Sections with about 10% thickness and with the maximum thickness at 40% or 50% of the chord come closest to having these characteristics. The rudder will work better in every way if it operates at low angles of attack and this can only be achieved by using a generous area and by making that area work effectively.

 

The choice of a shape is not so clear-cut as it is for the fin. It seems to me that rudders are all variations of one of the two designs shown in Pictures 18-11[5] and 18-12. To an aerodynamicist  18-11 would appear to be equivalent to one wing of a pair butted up to a fuselage and 18-12 to be equivalent to a pair of wings joined at one tip to a fuselage. The aspect ratio of 18-11 is about 5.3 and for 18-12 is about 3.4. Rudder 18-11 will generate one vortex and rudder 18-12 will try to generate two. Graphs 6-10 and 6-11 tell us that potentially rudder 18-11 will have the better performance.

 

However the upper ends of both rudders work quite close to the surface. If rudder 18-11 is used at high angles of attack and a large heel it is possible for the surface of the water to be depressed behind the rudder to ingest air. It is possible that rudder 18-12 is designed to avoid this. It is hard to decide whether this effect is of any significance but it does mean that a rudder on a yacht operates in a different environment to the stabilising surfaces used on aeroplanes that have to do the same job. To this extent the choice of shape may not be made solely on aspect ratio.

 

Typically the areas of rudders vary from about 20% to 33% of the area of the fin.



[1] It has been found that it is best to rig the boat so that it tends to turn into wind.

[2]In Chapter 20 I have suggested that, for some points of sailing, the forces exerted on the hull are sufficient to steer the yacht and the fin may be used for improving the stability.

 

[3] The use of pivots ensures that the model can move only in two dimensions but it also introduces a simplification when compared with an aeroplane. For an aerofoil moving freely in the air the pressure forces on the aerofoil reduce to a single force and a couple. The point of application of the force and its magnitude and that of the couple vary with the angle of attack. The use of pivots permits us to locate the force at the expense of changing the couple to a moment about the pivot.

[4] This obviously has significance for aeroplanes but we should recognise that an aeroplane flies freely and the simplification which was introduced by using the pivots on the model no longer applies. For aeroplanes the added force corresponds to the weight of the aeroplane. It would seem to be desirable to arrange for the weight to act at a point which requires no angle of attack for the stabiliser and therefore the least drag. However, in practice, the weight is usually arranged to act in front of the lift because this gives good response to disturbance caused by gusts and the added drag is accepted.

 

[5] In aircraft practice the shapes of the stabilising surfaces are like 18-11 and they have not changed in 60 years during which the search for improved performance has been unrelenting. The only change that I can see is that used on the Dornier feeder liner where the leading edge of the outer third of the surface is raked back. This is claimed to have advantage. So, in order to get away from the simple rectangle, one might choose to rake back the leading edge of the rudder instead of using a radius.