Chapter 11        The real flow over a Bermuda rig

In chapter 7 we set aside the problem of the true shape of the two sails and looked only at the positions of the booms. Clearly the real sails are complicated in shape; they have a more or less triangular plan form and they are twisted and curved. The Hele-Shaw equipment has given us an idea of the way that the air flows over a sailing rig but we need some genuine evidence for the real flow pattern. We all have access to real sails and it seems to be obvious that some system of tell tales might be used to make the flow visible. I decided to follow this line of experiment but before doing so it seemed to me to be worth trying to predict the general character of the flow.

Vortices and breakaway

We have already seen in chapter 6 that an aeroplane wing produces two vortices that rotate in opposite directions. These vortices look to be the same size even if they are of opposite rotation. The aeroplane really has just one wing made up of two equal halves. The aeroplane wing is flying at a low angle of attack and produces a thin eddying wake.

The yacht using a Bermuda rig has two sails, both of which are operating at high angle of attack, and I have suggested from the Hele-Shaw rig that a thick eddying wake will form behind each sail. The forces that create the vortices behind an aeroplane wing are also present on a sail. We have high pressure on the windward side and low pressure on the leeward side. The forces exerted by these pressures act up and down the sail and cause the flow to divert towards the top and the bottom just as the forces divert the flow span wise on the wing. But our sail is not made up of two equal halves; we have something close to a triangle. Where, for the sail, does the flow divide to create two vortices? In the words of a scientist the division takes place so that the angular momentum in the two vortices is the same. We have to decide what is meant.

Any little bit of the air flowing over the sail ends up following a curved path like the paths in Picture 6-1. This bit of air has mass and its angular momentum is just this mass multiplied by the its radius and its angular speed (like revs per minute). Now the final speed with which it turns depends on where it passes over the sail. At the top the sail is narrow and it acts on the air for only a short time and the air ends up turning slowly. At the bottom the sail acts on the air for a relatively long time and the air ends up turning quickly. The flow will split so that the sum of all the small amounts of angular momentum is the same for both vortices. As a result the vortex at the top will be made up of most of the air turning slowly and the vortex forming at the bottom will contain much less air turning quickly. Effectively the upper vortex will be much larger than the lower one. We might expect to find the flow over the foot of the sail moving diagonally downwards on the windward side and more nearly horizontally at the top.

In Chapter 4 I described the character of the flow of air in a typical open space and that is quoted here. “For much of the time the wind veers through about 10° either side of the mean direction in a random way and then, much less frequently, changes in direction of 45°occur”. Our Hele-Shaw pictures were for steady flow and it seemed to be unlikely that there would ever be attached flow over the leeward face of the sail at an angle of attack in excess of 30°. This veering of the wind may affect this.

Practical testing

I decided to make an attempt to see the flow pattern over the sails by putting tell tales on one side of the sails of a swing rig. Tell tales made of audio tape using can easily be attached to a sail using double sided adhesive tape. At first I thought that I could get someone to control the yacht so that I could take some pictures. This was not practical. I turned to setting up the rig in a stand

Photographs of swing rig under test

in a field where the approach flow was as nearly uninterrupted as possible. This was not as easy as it sounds and I had to travel over 50 miles to the best site that I could think of[1]. One might argue that testing in a wind flowing over grass is not the same as in a wind blowing over water. It seems to me that testing over water is nearly impossible because of the need for the approach flow to be uninterrupted and the inevitability of the generation of waves on the water. Then there is the sheer physical problem of setting up for testing to be solved. One must do what is possible.

I used the arrangement is shown in Picture 11-1 and I think that it worked well. It is no more than a wooden stand with a wooden socket for the rig fixed to the ground with tent pegs. I used a Dwyer anemometer to make an assessment of wind speed and a suitably sized windsock to assess the way the wind veered.

On the first visit the wind speed was about 8 mph, the wind veered about 10° either way and the vertical change in wind speed was from about 7 mph just above the ground to about 8 mph over most of the rig. I think that these are typical wind conditions and I do not think that they would be much different over water. The mixing of the air near to the ground caused by the grass would be similar to the mixing over water caused by waves and wavelets.

The rig was set up just as it had been used for racing and the twist is shown in Picture 11-2. The rig was tethered so that the fore sail was just on the point of fluttering. With the side with the tell-tales facing to windward the flow was very much as expected and it seemed to fluctuate between the patterns shown in Pictures 11-1, 11-2 and 11-3. Note the way that the flow dives down to go under the foot of the sail. I did check with the rig held horizontally at arms length and the tell-tales still dived down so it was not caused by gravity on the tell tales. There was a consistent instability of the flow over the main sail just behind the mast near to the upper fixing for the fore stay. Subsequent inspection showed that there is a joint in the mast at this point and a slightly larger gap between the mast and the luff.

Then the rig was changed to the other tack so that the tell-tales were on the lee side of the sails. The flow clearly fluctuated from being orderly to totally broken down and sometimes having part orderly and part disorderly flow. This is shown in Picture 11-4 where the flow is attached, Picture 11-5 where the flow is detached over the fore sail and over the top of the main sail and in Picture 11-6 where it is detached over both sails. I found this surprising at first but when I reflected on the fact that the angle of attack was varying from about 20° to about 40° it became more understandable[2]. Nevertheless an angle of attack of 20° is still large by aerofoil standards and must indicate that, in the right conditions, the single curved surface of a soft sail is capable of working to this large angle and probably right up to 30°. I did not see any evidence of sudden changes of load on the mast. Overall I felt that the field tests supported the Hele-Shaw rig and the deductions from physics etc.

I returned to the test site to test the rig when it was set square to the wind as if it were running because it seemed to me that attempts to improve downwind performance were doomed to fail if the flow had no sort of pattern. In anticipation of the possibility that the upstream flow might be regular in some way I attached six long tell-tales to a string that could be stretched across the flow upstream of the rig. The flow was just chaotic with no discernible pattern and, as far as I could see, no repetition. Pictures 11-7 and 11-8 show the flow seen from upstream. The string is at the level of the lower sail number on the main sail and three long tell-tales are evident in 11-7.

I reset the rig for beating with the tell tales on the windward side and just watched it for about a half hour. The tell tales on the fore sail were attached quite close to the luff. Sometimes they flipped forwards and round to the lee side of the sail. We can see why from Picture 9-4c and Picture 9-8b and 9-8d. Picture 9-4c shows how the flow over an aerofoil at high angles of attack splits well behind the leading edge some to go up and over the aerofoil and the rest to go under. Pictures 9-8b and 9-8d show that this could happen for a sail as well and the practical tests show that this is the case. A small reduction in the angle of attack stopped this behaviour. Presumably it is best not to have this reverse flow at the luff but it would not be wise to be dogmatic.

As a postscript to this testing I think that just seeing the rig working up close is informative if only to see how it works mechanically. One look at the luff of the fore sail separating from the fore stay like washing pegged on a clothes line is enough to make the case for using a pocket luff.

[1] It is virtually impossible to find a site on the ground where the wind is undisturbed. Any obstruction upstream of the test site will produce the same wake in the air near to the ground as we have seen in Picture 5-6. This will spread in just the same way and just a few trees or bushes a long way upstream may well be materially affecting the flow.

[2] I questioned two former sailors of full sized racing yachts and they said that this veering is normal and that its effect on the sailing rig can easily be felt in the rudder. They also said that the regular switching from attached to detached flow could be detected with tell tales and that it was the job of the winch men to watch these tell tales and to keep adjusting the sheeting to get the best from the rig. It was claimed that the helmsman could detect a wind-shift by a change in the “rhythm” of the rudder.