Section 2 The Bermuda Rig

 

The Bermuda rig

The most common adaptation of the single sail in order to improve its performance 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 26

 

 

 

 

 

 

 

 

 

 

 

 

 

I drew attention to the fact that the single sail diverts the flow ahead of it to leeward. In order to make this clear I have added lines representing the undisturbed flow. I have enclosed, in a circle, the region where 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 is about 10° 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 will add it to figure 26.

 

There are two sorts of foresail, the jib sail and the Genoa. I will start with the jib sail. Telltales attached to the jib and the main sail suggest that, when the yacht is beating, the presence of the jib will alter the flow over the main. It appears to prevent the flow breaking away from the luff where the curvature of the flow is greatest and the flow, at least near to the leeward surface of the sail appears to remain attached. Telltales also show that the flow over the upper part of the main sail where there is no jib breaks away to give eddying flow as does the flow over the jib.

 

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.

 

Now I need some diagram to show how this adaptation actually improves the way that the boat sails.

 

In order to draw figure 28 I have supposed that the area of the single sail is apportioned as 2/3 to the main and 1/3 to the jib. I have used the same expression for the drive as before for the main but reduced to 2/3. I have let the angle of the jib, when sheeted in, lead the main by 22.5° which is the angle for which the flow pattern was drawn. For the jib I modified the expression to take account of the change of the spatial relationship of the two sails as both sheet out to 90°. There are drive graphs for the two sails taken separately and for them acting together. For reference there is the drive graph for the single sail.

 

I have drawn a dotted line in black to indicate the approximate course at which the sail will collapse and therefore the closest course to the wind. 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 45°. There is a disadvantage in that the drive is lower when broad reaching and running. As racing courses are usually set to have legs of beating, reaching and running and a spinnaker is set for running, this is the preferred arrangement.

 

However what we really want to know is how the speed of the yacht varies with the course. A polar plot of this is called a polar performance diagram. I drew my drive plot for a constant speed but I can use the speed versus resistance graph to convert driving force to speed. This is shown in figure 29.

 

In Figure 29 I have shown the drive plot in blue for the Bermuda rig and, because I cannot find a way of completing the computation using my maths package, I have plotted the graph of speed in red using figure 21 to some arbitrary scale.

 

The graph is valid for the arc from about 35° to about 130° after which the rig is fixed relative to the hull and is changing to wind “jamming”.

 

This is as far as this computation can be taken. I had in mind that this would be one stage in an iterative process of perhaps three stages each with a better boat speed but clearly the boat speed for the range of courses for which the computation is valid is almost constant so there is no need. However there is a need to compare the outcome with the polar performance diagrams for real yachts.

 

 

In figure 30 I have plotted my calculated curve in black with the invalid part in chain dots. The two red curves are for a 12 metre yacht at true wind speeds of 20 and 12 knots. The blue curve is for a 35 foot boat in 15 knots and the green curve is for a windjammer[1] in 15 knots. The effect of the drag from the rigging and the poor performance of the sails is very clear.

 

My curve is to no particular scale but I have placed it in a suitable position for a 25 foot boat. It is clear that it has the same general shape as the other boats with of course the exception of the angles between 130° and 180°. It is based on a two dimensional model and the lift and drag curves that I constructed. It all appears to have worked.

 

However I must consider the effect of the third dimension.

 

It is possible to draw a diagram showing the forces on the main and jib for a yacht beating to windward. The usual position of the main for beating is for the boom to be along the centre line of the hull. Of course the sail will have a twist but, for this diagram, I will ignore it. Then the hull can be set at 37.5° to the apparent wind. In my flow pattern for two sails I let the jib make 22.5° to the main and I will do this again. The lift and drag on the main can be drawn at right angles to, and in line with, the apparent wind. To my knowledge there is no convention for dealing with the angle of attack of a sail working in the influence of a following sail. Sailors will know that both the sails will be set so that when beating as close to the wind as possible they are just fluttering at their leeches. Presumably they have the same angle of attack to the air flowing over them. I shall use the same values of the coefficients of lift and drag for both sails, and suppose that there is a notional apparent wind for the jib that is 22.5° forward of the main apparent wind. In figure 31 the drags are in blue, the lifts in red, the two forces on the sails in black and the components of these forces along the course in green. It is immediately obvious that the driving force produced by the jib is greater than that produced by the main despite the difference in area. This explains the success of the Bermuda rig.

 

However this diagram is really for a two-dimensional sail in air that is flowing in an orderly, steady manner and not for a real sail in a real wind. I have to consider what the consequences are. The starting point must be to recognise that, in the diagram above for a yacht beating up to the wind the driving forces on the sails are much dependent on the actual values of the lift and drag. In both cases, if the drag should increase and/or the lift decrease, the driving forces will drop away very quickly. This performance of these sails is vulnerable to the vagaries of the wind, the design of the sails and the compromises that are inherent in the mechanical arrangements of the rig eg the balance of the boat.

 

I pointed out on page 1 that the speed of the wind increases with height and that the vigorous eddying at low levels decays with height. The change in average speed means that the sail operates in an apparent wind that changes in speed and direction with height. Fortunately the twist in the sails, that is inevitable because of the mechanical arrangement, is in the direction required to match the “twist” in the apparent wind but, if the sail is to be twisted to match the apparent wind, the required twist will vary with wind speed. The twist in a sail is not always controllable especially but some sail arrangements[2] permit a good match between the twist in the sail and the twist in the apparent wind. Nevertheless it takes us away from the simple two-dimensional sail in my diagram and will adversely affect the net values of the lift and drag.

 

I have noted that the effect of the two vortices that are generated at the head and foot of every sail can be reduced very considerably by designing sails to have a high aspect ratio. But this is not always an option and many sails have to be of low aspect ratio and these sails will have a much-reduced lift at all points of sailing and have an increased drag. This is reflected in the performance of cruising yachts when compared with racing yachts.

 

If we go back to figure 31 it becomes obvious that, if the drag increases and the lift is reduced for both sails, the driving force from the main will go to nothing and then negative leaving the jib to overcome the negative force from the main and drive the boat. At some point it becomes necessary to bear away and beat at a greater angle to the true wind.

 

All this suggests that the wing sail will have even greater difficulty coping with these conditions.

 

There is one more factor to be taken into account and that is what aerodynamics people call parasite drag. In the discussion above I have been listing effects of what I called “the vagaries of the wind, the design of the sails and the compromises that are inherent in the mechanical arrangements of the rig”. These serve to reduce the driving force. This force is being created to drive the yacht but before it can do so it must overcome wind drag on parts other than the sails like halyards, cross trees, stays, hulls above the waterline, people and so on. All these things produce parasite drag and they should be minimised. Their combined effect is reflected in how close the yacht can sail to the wind. The lower the parasite drag the closer the yacht can beat to the wind.

 

Endnote

I said in the introduction that an understanding of the applied physics of sailing is useful. Now I have given my version of this physics and I find it hard to imagine that there is another version that fits in with accepted science. So I need to explain how it can be useful.