Section 3 The Bermuda rig


The Bermuda rig

The most common adaptation of the single sail in order to improve its performance upwind is to split the area of the single sail between two sails as in the Bermuda rig. The two sails are the mainsail aft of the mast and the jib forward of the mast and attached in some way to the foredeck. The two sails then become a rig and the two sails work together to improve the overall performance of the sailing craft when it is beating. In order to see how this occurs we must go back to figure 16 of section 1 and look at the flow pattern in figure 50.

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Fig 50

I have already drawn attention to the fact that the single sail diverts the flow ahead of it to leeward. This is evident in figures 16a and 16b and is made clear in figure 49 that has its origin in Prandtl. In figure 50 I have drawn a circle in the diverted flow and, in this circle, the flow is orderly and diverted to leeward. I have drawn the centre line of the hull of a yacht in the position relative to the sail that it would have if the yacht were to be beating. The diverted flow obviously goes over the foredeck. This means that it is practical to erect a second sail on this deck to operate in this region of diverted flow. The diversion of the flow over the mainsail in this region ranges up to about 28° and, if a sail were to be set in this position, it will further divert the flow just as the main does and tilt the force exerted on the small sail forwards into a direction that will drive the yacht. That sail could be set at some even greater angle to the apparent wind than the main sail, work in just the same way, and produce a force that has a useful component in the direction of motion of the boat.


I do not think that we can guess at angles for the jib or at flow patterns over the combination of two sails. When I was writing my book on model yachts I made and used a Hele-Shaw rig to get some idea of flow patterns. The resulting pictures are on this web site but I bring them across to this section with the text in red.




Extract from "The RC Racing Yacht Explained"


The Bermuda rig in the Hele-Shaw  equipment

It seems that the Hele-Shaw rig offers us a cheap way of looking at the flow pattern round two sails working together as in a Bermuda rig. The rig will tell us where to expect a breakdown in flow but not what that breakdown would look like. Perhaps its value should be taken to lie in the understanding of the flow so that the process of learning to set up a sailing rig is shortened. With the warning that we must not expect too much from this equipment we can go on to simulate the flow over the sails of a Bermuda rig when it is beating close to the wind.


We need an experimental plan. I suggested in chapter 8 that one might consider the fore sail as working in a different apparent wind to the main sail. In truth the two sails share a flow pattern and the idea is too simple. We are trying to decide how the fore sail can best be set relative to the main sail so that it produces a useful force to drive the yacht. We do know that the boom of the fore sail on a model yacht must be able to swing past the mast so that sets one limit. We also know that the swivel point for the fore sail boom will be on the centre line of the deck and that, most frequently, the swivel is attached to the boom at about a quarter of its length from the tack. So it makes sense to let the centre line of the yacht make 32.5° to the undisturbed flow, put the model of the main sail on the centre line, and then set the fore sail model at angles of, say, 10°, 15°, 20°, 25°, 30°, and 35° which should cover the likely range of angles.


The following photographs were taken with a digital camera to facilitate their inclusion in the text. I could not avoid the shadowy outline of the photographer as the rig is an outdoor exercise and the plates must be horizontal. Perhaps I should have used non- reflecting glass.


Now we have to assess these pictures to find out what we can from them. As it happens one flow line passes through the gap between the sails in every picture. In 9-8b there is a sharp kink in this line near to the mast and the flow over the main sail is greatly altered from when it is operating as a single sail. The flow over the luff of the fore sail is going to lead to a serious break down of flow.


In Picture 9-6l this flow line has lost its kink and two other flow lines also pass through the gap. One of these lines has come from under the main sail and the other has come from over the fore sail. The sharp deflection of the one going round the mast is not at all desirable. The shape of the one going under the fore sail suggests that it could easily break away near to the luff.


This leads us to look in the middle of our chosen range for a better pattern. Before doing so we should recall that we are not just looking for a large force on the fore sail, it must also have a large component in the forward direction. Furthermore we would like to have this force without a vigorously eddying wake to add to the drag.


Insert to this extract. When you look at these pictures from the Hele-Shaw rig note that the flow lines that go under the "sails" are all well defined but those that go over the "sails" are feathery. Where they are feathery the flow is having difficulty making a change in direction and they occupy spaces where the flow would break down.

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Picture 9-6b Close-up of 9-6a

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Picture 9-6a Fore sail set at 10°


















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Picture 9-6d Close-up of 9-6c

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Picture 9-6c Fore sail set at 15°


















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Picture 9-6f Close-up of 9-6e

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Picture 9-6e Fore sail set at 20°















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Picture 9-6h Close-up of 9-6g

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Picture 9-6g Fore sail at 25°


















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Picture 9-6k Close-up of 9-6j

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Picture 9-6j Fore sail set at 30°


















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Picture 9-6m Close-up of 9-6l

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Picture 9-6l Fore sail set at 35°















Study of the pictures suggests that the two best flow patterns are those for 20° and 25°. In both cases the presence of the main sail is diverting the flow smoothly upwards into the concave side of the fore sail and the flow over the convex side of the fore sail may be such that the flow does not break away. The flow over the main sail is not much different from that of the sail acting alone. There is still a kink in the common flow line but that is to be expected. In the 30° and the 35° pictures the flow into the fore sail is changing to require an unlikely bend upwards and the flow round the main sail also requires a new rapid change in direction.


It seems that it is best if the fore sail makes an angle of between 20° and 25° to the centre line of the yacht.[1]


Having come this far with the Hele-Shaw rig it is evident that we could form an opinion on the possibility of producing an even better flow pattern by letting the main sail make a small angle with the centre line. I have taken pictures with fore sail at 25° and the main sail at 5° and 10°.


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Picture 9-7b Fore sail at 25° Main at 10°

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Picture 9-7a Fore sail at 25° Main at 5°
















The change does not improve the flow over the fore sail and the only way to re-establish the flow is to reduce the angle of the fore sail. That is not what is wanted.


The reader will have his own view of the success of the Hele-Shaw equipment as a cheap way of seeing how fluid flows over the sails of a Bermuda rig. I think that most readers will have a better idea of the characteristics of the flow and may be better placed to experiment.


The Hele-Shaw rig has given us only a two-dimensional flow and now we must think about the sails in three dimensions.


There is no way to predict the best place for the jib sail although it could be found by trial. In practice there are constraints. The jib can have its luff on the forestay or it can be attached at its foot to a boom swivelling on a fixture on the foredeck. In the latter case the swivel cannot be more than about ¼ back from the luff or the jib will not change tack automatically. I will put a jib on the foredeck as if it were to be set on a boom and swivel. Then I can attempt to draw a flow pattern that fits with the laws of physics. In order to do so I have to represent the jib and I have let the length of the jib boom be about 60% of the length of the main boom and let it swivel at its quarter point. I know from previous work that the jib needs to be set at between 20° and 25° to the centre line of the hull. When endeavouring to construct a flow pattern that would not be contrary to physics, I found that 20° was not large enough but 22.5° would do. I used that angle and constructed the flow pattern in figure 27. I retained the flow pattern over the jib but, in accordance with the telltales, showed a flow line over the lee surface of the sail. I have no way of knowing what goes on in the hatched area and did not guess. The effect of the jib is to divert flow even further to leeward to flow over the jib. The air, as it flows over the jib, behaves exactly as it does over the single soft sail. Now there are two wakes but they join to form one wide diffuse wake in which the eddies break into smaller eddies.


It is clear that the jib gives two improvements. One is that the force that it produces in a more useful direction and the other is the likely reduction in drag of the main sail.


Had the jib been a Genoa the suppression of the breakaway of flow on the lee side of the main would have extended further along the main further enhancing these improvements.


This extract is sufficient for a flow pattern to be drawn for a beating yacht. It is figure 51.

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Fig 51

If you follow the rules for drawing flow patterns the area of high pressure on the windward side of the jib is inevitable.







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Fig 52
It is now possible to draw a diagram showing the forces on the two sails when beating. In order to do so I have supposed that the area of the jib is one half the area of the main, that is, the whole sail area is shared 1/3 to the jib and 2/3 to the main.


I have used the sinusoidal models for lift and drag taking the values from figure 29 to get coefficients of lift and drag and supposed that the value of  would be the same for both sails and then the forces would be proportional to .


If the yacht follows a course at 30º to the apparent wind and the chord of the main is along the centre line the angle of attack of the main is also 30º. The flow over the jib is complex but I used a notional apparent wind at 12º to the real apparent wind. The 12 º is a mean angle taken for the circle in figure 50. The jib is set at 22º to the centre-line as suggested from the Hele-Shaw rig. The important outcome is that the main produces a tiny force in line with the course to drive the yacht and the jib, despite having a much smaller net force on it, produces a much larger force along the course to drive the yacht. This is what is needed.


This raises the question of what happens to the jib between beating and running. There is no doubt that, when running, the main sail will be at an angle between say 80º and 90º and one might expect the jib to be at the same sort of angle. It follows that the jib must progressively lose the 22º difference between it and the main sail. It is possible to show this on a diagram that is figure 52. The sails are normally both to leeward but when the yacht is running there is an obvious advantage in having the sails out to opposite sides.

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Fig 53
This shows how the Bermuda rig is used to drive a yacht but we really need to know how the force produced by the two sails to drive the yacht varies with the course. We already have a graph of driving force to some scale versus angle between the course and the apparent wind in section 1. It is figure 42.


It is clear from figure 50 that the introduction of the jib alters the flow pattern over the main and it is impossible to predict the exact effect that this might have on the forces on the two sails. However it is not unreasonable to use the figures for figure 42 to plot new graphs for two smaller sails and take account of the different position of the jib to the apparent wind.

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Fig 54

These two graphs are shown in green for the jib and blue for the main. When they are added the result is in red. This means very little until we have the graph for the single sail for comparison. This is the graph in blue and we see immediately that the Bermuda rig is much better when sailing close to the wind but is not quite as good as the single sail when reaching and broad reaching.


Clearly the splitting of the sail into a main and a jib has increased the drive when close hauled by rather more than 25%. This can be used to go faster when close hauled or to increase the distance made good against the wind on a course of about 45º.


Application of the Bermuda rig.

The jib sail seems to have appeared first on square rigged vessels in an attempt to give them more manoeuvrability when sailing in estuaries. The jib was found to pull out of all proportion to its size and it became normal to set two or three jibs as part of the full suit of sails on three masts. Those jib sails must have worked in a flow of air that has been diverted by the square sails just like the flow round a tall building.




[1] This does not match the angle at which the fore sail boom is normally set but it does match the angle of the sail at a point about half way up the luff. We will return to this.