Chapter 8       How a yacht beats to windward

 

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Diagram 8-1

Tacking

We need to start with an observation that anyone can check. It is that a competitive yacht will tack through nearly a right angle when it changes its course from beating as closely as it can to the wind on one tack to beating as closely as it can on the other tack. Moreover this angle does not seem to change with wind speed.

 

Diagram 8-1 shows the course of a yacht changing from beating up to the wind on the starboard tack to beating up on the port tack. In order to draw it I have had to choose an angle between the two courses. I have already said that this is nearly a right angle and so I have drawn it at 85°. This means that the yacht is taken to be pointing up at 42.5°. No one should suppose that I am claiming to know the angle to an accuracy of 0.5°, only that the yacht tacks through 85° and 42.5° is a half of 85°.

 

Apparent wind

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  Diagram 8-2
Let us now turn our attention to the yacht when it is pointing at 42.5°. If we can put practical values to the wind speed and to the speed of the yacht we can draw a diagram to find the speed and direction of the apparent wind.

 

Model racing yachts usually have three or more rigs that can be fitted to suit the wind conditions. At this stage, let us consider only the rig with the largest area. We will be aware that the rig will probably be effective up to a wind speed of about 15 mph. Within this range of wind speed it will be most effective up to about 10 mph, at which speed it will drive the yacht at almost its maximum speed. In the range of 10 mph to 15 mph the yacht will heel excessively, be troublesome to control, probably respond badly to gusts but will not be noticeably faster. The rig probably works best at a wind speed of 10 mph.

 

Now we must choose a realistic speed for the yacht when it is pointing as close to the wind as it can. A yacht which is well set up may well move at about two thirds of its critical speed. This depends on the length of the hull and so we must choose a length. Perhaps the length of a Marblehead can be regarded as typical. This length is 50² and for this length the critical speed is 3.15 mph. For our purposes it will be acceptable to regard the yacht speed as 2 mph. This is in accordance with experience that tells us that a beating yacht will move at a slow walking pace.

 

These two speeds combine to produce a speed of the wind relative to the yacht. This is what the sailors of full sized yachts call the apparent wind for the obvious reason that this is the direction from which the wind appears to come. We can draw a diagram to show the course of the yacht relative to the true wind and add to it the speed and direction of the apparent wind.

 

Diagram 8-2 is drawn to scale and the apparent wind turns out to have a speed if 11.6 mph at an angle of nearly 7° to the true wind. In the diagram the arrowheads for the true wind and the apparent wind have been drawn a little way from of the apex of the triangle for clarity.

 

Leeway

Now we must deal with another aspect of beating. This is the leeway. There can be no question that there is a net transverse force on the rig when the yacht is beating. The yacht heels in response to this force. The transverse force is resisted by the fin and rudder acting together. The fin acts in the same way as an aerofoil. It is a hydrofoil. In order to generate a force the fin must have an angle of attack and the only way for this to be created is for the hull of the yacht to be skewed relative to the course. As a result the hull appears to be moving forwards and sideways. The sideways movement is the leeway.

 

It is one thing to know that there is leeway but quite another to put a value to it. I first thought that I could see the leeway in the two bow waves generated by a boat but this turned out to be wrong. The asymmetry of the bow waves caused by the heeling masks the true leeway. In the tests described in Chapter 7 I could see no asymmetry in the wake when it was going ahead. The leeway is small and my best estimate is 3° and I will use it for the yacht when beating close to the wind.[1] With this information we can draw our next diagram.

 

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  Figure 8-3

Vector diagram for the beating  yacht

In Diagram 8-3 the true wind and the apparent wind are shown, as is the course of the yacht when beating up to the wind. The fore and aft axis of the yacht has been drawn at an angle of 3°. Inspection of the angles involved shows clearly that the angle between the apparent wind and the axis of the yacht is 32.5°. The magnitude of this angle has far reaching implications for those wishing to understand the behaviour of model racing yachts.

 

In order to see why, we must now show the sails on the deck plan of the yacht. If we are to do this we must know fairly accurately where they will be set for the yacht to point as high as it can. I need to draw on common experience. We must all know within a very few degrees where the main boom will be for beating up closely to the wind. It will be between zero and 5° to the centre line of the yacht.[2] Of course knowing the position of the boom does not necessarily tell us anything about the rest of the sail because the sail will inevitably be twisted. However it is the only certain angle and I will add the boom to the deck plan of the yacht and a curve representing the foot of the sail as in Diagram 8-4.

 

Angle of attack of the main sail

It is interesting to see that the apparent wind seems to be aligned with the luff of the sail but do not read too much into this because things will not turn out to be so simple. The real message from this diagram comes from the re-orientation of the Text Box:  
  Diagram 8-4
diagram to represent such a sail in a wind tunnel with the apparent wind coincident with the axis of the tunnel as in Diagram 8-5.

 

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 Composite picture 8-6
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  Diagram 8-5
I have drawn the appropriate Diagram 8-5 and taken the opportunity to use the terminology of aerodynamics. The apparent wind becomes the free stream and the angle between the apparent wind and the main boom becomes the angle of attack. Now we can see why all this was necessary. The angle of attack is 32.5°. It follows that we shall have to find out how a soft sail behaves at this angle of attack. The answers will not be found in aerodynamics because a soft sail is so different from an aerofoil. Nevertheless we can make some use of the flow pattern round an aerofoil at a high angle of attack. I have a picture of the flow round an aerofoil at an angle of attack of about 30°. It has been taken from a picture of smoke lines round a model in a wind tunnel. In the original the lines were very feint in the regions where the velocity is high. I have retraced the flow pattern to show these lines clearly to give Composite picture 8-6. The most obvious feature is the total breakaway of the flow over the upper surface. Now all of the mathematical analysis of aerofoils is restricted to cases where the flow does not break away and remains in contact with the upper surface. At this high angle of attack the outcome of these analyses does not apply. As aerofoils stall at about 12° and no efficient aerofoil would be worked at 32.5°[3] all the practical and theoretical data that is available for aerofoils has little relevance for sails.

 

The best data for soft sails that I can find is for the sail of a 12 foot yacht measured directly by suitably tethering it in a steady wind. It is given in the Table 8-7 below.

 

Table 8-7

Angle of attack

CL

CD

CL/CD

20°

1.0

0.13

7.7

25°

1.34

0.2

6.7

30°

1.5

0.36

4.2

40°

1.27

0.53

2.4

The data is such that the values of CL/CD should be regarded as having an accuracy no better than +/- 10%. If we are to use these figures as a guide to the performance of model sails we must think of higher values of CD for somewhat lower values of CL and consequently considerably lower values of CL/CD. By aeronautical or engineering standards these are dreadfully low values and we must conclude that sails are very inefficient.

 

Forces on sails

However, we are trying to find out how a yacht generates the forces needed to beat to windward and so far all we have is the main sail lying along the axis of the yacht and making an angle of attack in excess of 30°. We know that we do not need a large forward force to drive the yacht but it is not at all clear that the sail will produce a force having any component in the forward direction. We have to make an attempt to put at least a direction to the force exerted on the sail even if we cannot give it a magnitude.

 

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Figure 8-6

We must go back to the aerofoil in the wind tunnel. The wind tunnel is a device that is designed to let us look at the performance of the wing of an aeroplane when it is stationary and the air is moving. The lift and drag are directly useful when considering aeroplanes because the lift is what we want and the drag is what we have to overcome to get the lift. When dealing with yachts the wind tunnel is by no means as simple to use because the yacht sails in a different direction to the apparent wind. What we want to know is the force generated by the sails in the direction of motion of the yacht not the force in the direction of the apparent wind. This means that we have to rework any data on the lift and drag on sails when it is given relative to the apparent wind. In Figure 8-6 a sail is drawn with an angle of attack of 32.5° to the apparent wind and the course of the yacht is drawn at 3° to allow for leeway. For one value of lift (at right angles to the apparent wind) several different drags are shown corresponding to ratios of CL/CD of 4, 3, 2 and 1. A typical triangle is drawn for the CL/CD of 4 with all the forces marked. For each ratio the resulting force on the sail is drawn. Each of these forces will have a component in line with the course of the yacht and another across the course. The components in the direction of the course have been drawn for all four ratios of CL/CD. For CL/CD = 4 the component is of significant size and in the desired direction but when, CL/CD = 1, the component is also of significant size but in the wrong direction. The changeover comes when CL/CD = 1.4.

 

This figure shows that the main sail of a full sized yacht will make a major contribution to the drive but, for a model yacht, where the ratio of CL/CD could easily be less than 2, the size of the contribution from the main sail is critically dependent on the drag. The chances are that the main sail of a model yacht does not drive the yacht at all.

 

It was necessary to check this practically. I persuaded a fellow yachtsman to sail his A boat with it set up as he would use it for racing so that we could have an idea of how it normally performed. Then we removed the fore sail. The yacht would not point close to wind at all when sheeted in normally. The sail had considerable twist and when this was removed the performance improved to the extent that the boat would beat but it was painfully slow and it could not move quickly enough to pass through head to wind. Tacking involved gybing and as far as I could tell the angle between courses was still about 90°. Clearly the main sail was not making a major contribution to progress. When the yacht was allowed to bear away slightly and the sail was sheeted out slightly there was a significant increase in speed. The yacht sailed quite well at other points of sailing.

 

This suggests that when a yacht is pointing up close to the wind the net force on the main sail will be nearly at right angles to the boom and possibly acting slightly forwards. In order to make progress we must choose a realistic direction for the force and I will show it at right angles to the boom.

 

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Picture 8-8
By implication the main sail does not provide the drive to the yacht when it is beating up into wind and so the drive must come in some way as a result of fitting a fore sail. This means that we must find some mechanism that makes this possible. For this we can go back to our aerofoil as in Picture 8-8 and study the flow pattern.

 

The region that now interests us is in the top left hand corner. I have added more lines to the picture of the flow pattern round the aerofoil. The horizontal ones represent the direction of the undisturbed flow and the centre line of the aerofoil has been added. This line has been extended into the region ahead of the aerofoil. The flow pattern in this region would look to be much the same for an aerofoil, for a flat plate or for a sail. The thing to recognise is that the main sail has deflected the flow ahead of it upwards. This means that, if another sail were to be mounted in this region the flow would approach it at an angle that, depending on the position of the sail, would be in the range of 7° to 15°. The apparent wind for the new sail would be at an angle to the apparent wind for the main sail. This new sail can be set at say 32.5° to its apparent wind and then it would produce a force which acts forwards by between 7° to 15° and this will drive the yacht. It would suit our purposes if it turns out to be the larger angle.

 

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  Diagram 8-9
It is now desirable to put this on another diagram. Diagram 8-9 has been drawn for an apparent wind for the fore sail at 15° to that for the main sail. It looks much like the way that a model yacht would be set up for racing. The angle of attack for the fore sail relative to its apparent wind is 32.5°. No attempt has been made to estimate the force exerted on the fore sail. It will be smaller than the force on the main sail because the area is much smaller but, as we have seen, only a small force is required to produce a very useful speed.

 

The obvious next question is why not bear away a little, sheet out a little and increase the drive? Sailors of full sized yachts do. However in model yacht racing courses are very much shorter in terms of say the number of boat lengths and being able to beat close to the wind and make fewer tacks is more likely to win races than bearing away, gaining speed, and making more tacks.

 

This chapter has shown us that the Bermuda rig is more complicated than seems to be the case at first sight. The idea of a different apparent wind for the fore sail is attractive but in truth there must be some best position for the fore sail which gives the greatest forward component to drive the yacht. This may not correspond to the greatest force on the sail because the best angle is equally important. The best position may require the luff to be a long way to windward and the swivel to be close to the mast to get the fore sail “wrapped round” the mast in the swiftly moving air just ahead of the mast. These ideas are just speculative unless we can find some way to look at flow patterns. I have attempted this and the outcome is the subject of the next chapter.



[1] Others when estimating this angle have used values as large as 10°. I think that this value is too high because the lift generated by a fin will suddenly drop at an angle of about 12° and there is too little margin for good yacht control. In fact the area of the fin is chosen partly to give satisfactory control of the yacht and partly because of its mechanical function in supporting the lead bulb. The result is a fin area that is adequate at angles of attack of just a few degrees.

[2] Some claim that this figure should be 10° but all I can say is that I have never seen anyone use this angle.

[3] One application of a simple curved blade used at a high angle of attack is that of the so-called aerofoils on a grand prix racing car. These must give high drag as well as a down force but they probably respond less to “turbulence” than a proper aerofoil would.