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2.6 The wing-sailed yacht
This is just an article to go on my website. It replaces one that I wrote and up-loaded in 2005 that was really a design study for a model wing-sailed yacht. That design study did not depend on anyone else's explanation of wing sails but, in one crucial respect, I was short of experimental data. I did not know how an aerofoil behaved for angles of attack beyond the stall and up to 90°. Being an engineer I was able to work round that difficulty but some readers did not find this to their liking.
It is now 2013 and two things have happened. Reliable data on symmetrical sections has become available and the Greenbird land yacht has used the same system as I used to set a new world record at 126 mph and in doing so has shown in spectacular fashion that it works. This means that I can rework my original analysis for a full-sized wing and not for a model to make it general and give details of how it might be used for a model wing sailed yacht.
The second analysis is given in greater detail but it merely confirms the first analysis. It is in fact not an analysis of a yacht but of a wing being used as a sailing rig. That is of a wing rig.
It seems to be totally obvious that it would be better to use an aerofoil, that is a wing, to drive a yacht instead of the almost universal soft sail. After all wings are much more efficient than fabric sails. It does not turn out to be obvious at all. Supposing that all the mechanical difficulties of fitting a wing to a yacht can be overcome the characteristics of any aerofoil section that may be used for the wing lead directly to the need to set the wing at some angle to the relative wind that is around 8° to 10°, depending on the section, for most points of sailing. No one can do this with any system of sheeting to be adjusted manually. It follows that success depends on solving this problem as well as the more mundane problems of building a rig. This raises the question of what advantages might be expected if one were to use a rigid wing to drive a yacht.
Every vessel driven by the wind works very well when it is sailed across the wind but it has problems in going upwind and in going directly downwind. One must endeavour to find out whether a wing rig is better than soft sails for these two points of sailing.
When going directly downwind the sail or sails are set to be square-on to the wind and there is only drag to drive the boat and no aerodynamic force. This means that the force exerted on the sailing rig depends on the area of the rig and the difference between the speed of the wind and the speed of the boat. It follows that the force decays as the boat speed increases and sets a limit to the speed unless the area of the rig can be increased. This leads to the use of spinnakers etc on boats with soft sails and fortunately concave sails have greater drag than equivalent convex surfaces. The wing is not as good as a spinnaker when set to produce drag.
When any yacht attempts to beat upwind the angle between the relative wind and elements of the rig decreases as the heading gets closer to the wind until there is no net drive at all because the force produced by the sailing rig must first overcome the wind drag on the hull, the crew, the rigging and the like. There has always been an incentive to reduce the angle at which the drive becomes ineffective, that is to get closer to the wind and the improvements since the days of the square-rigged, wooden-hulled ships have mainly come from reducing wind drag. The wing sailed yacht clearly has an advantage in that its drag will be very low indeed if it can be operated like an aeroplane wing and it can get closer to the wind than any other rig.
So anyone who aims to use a full-sized wing-sail must balance out the advantages and disadvantages of wing-sails versus soft sails. The following is a list of relevant factors.
The potential advantage of the wing-sail comes from having an accurately made aerofoil section that has a properly designed leading edge, smooth curves and a good surface finish. Given this, the improvement over a sail comes from an increase in lift and from a very large reduction in drag. It is a design challenge to make a tall, light wing with a good profile and an ongoing challenge to maintain the original surface finish.
The performance of the wing-sail is potentially better than that of soft sails. However the good aerodynamic performance of aerofoils is only for a range of angles of attack to the relative wind of 0º to about 10º and the ordinary wind-shifts are greater than this.
The wing-sailed boat will need the same under-water parts as a boat with soft sails to resist transverse forces and to give stability and this means that the wing-sail must be light.
There can be no question that sailing boats spend most of their time in store in the open. Soft sails can be rolled and stored indoors and the remaining hardware is reasonably resistant, but not impervious, to wind, rain and sun. A rigid wing-sail is not so easily stored or transported.
If the wing-sail is superior to the soft sail for most points of sailing one might think of using a smaller area for the wing-sail. However, when running, the drag produced by a wing-sail is, area for area, lower than that for a soft sail. One can envisage the use of spinnakers with wing-sails.
In truth the balance is in favour of soft sails unless the aim is to set speed records for land yachts.
This short article is not about the design of a wing-sailed yacht but about the way in which a wing can be made and used to drive a yacht. All sorts of cut-and-try designs have been seen but the success of the Greenbird land-yacht in setting a world speed record of 126 mph in 30 knots of wind has shown a very practical way to use the wing on a yacht and it is hard to see how it might be improved. Fortunately the action of the Greenbird wing is easily understood.
I give the theory of that sailing rig in section 1 and go on to give the design of a model using the same rig in section 2.
Figure 1 is of the holder of the world land speed record at 126 mph in a wind gusting from 30 to 50 mph (13 to 22 m/s). The yacht is driven by a rigid wing that is free to rotate about a vertical axis and it is controlled by the green stabiliser attached to the wing on a boom that also extends forward of the wing to carry a balance weight. The stabiliser, that is just like the stabiliser of an aeroplane, has a moving control surface like the elevator of an aeroplane. The elevator is controlled by the pilot and sets the angle of attack of the wing to the relative velocity of the wind. The relative velocity is, of course, the vector sum of the wind speed and the yacht speed.
The provision for the wing to rotate under control of the stabiliser also lets the wing respond automatically to the swinging of the wind that is inevitable if the wind is gusting.
The control surface is operated through a radio link so the wing that can be seen here is the whole sailing rig. I want to explain how it works. This depends fundamentally on the behaviour of aerofoils and this has to be extracted from empirical data gathered in wind tunnels.
Greenbird is designed to reach on the port tack only and therefore could use a wing of asymmetrical section but most probably uses a symmetrical section. "Ordinary" wing-sailed yachts must be able to sail on either tack at any point of sailing and can only be understood in the light of the performance of aerofoils of symmetrical section. This data is obtained by testing in wind tunnels. The net force exerted on a test model of a given aerofoil section when set at an angle of attack to the airflow cannot be measured directly and instead the lift and the drag are measured. The lift is the component of the force exerted on the model at right angles to the undisturbed airflow and the drag is the component in line with the flow. In order to store the experimental data the lift is expressed as and the drag is expressed as where are the coefficients of lift and drag and is the density of air, is the velocity of the air and the plan area of the model.
For use with aeroplanes it is usual to test up to angles of attack of about 20° but wing sails may operate at high angles of attack for running and we need more data than that for aeroplanes.
(When I first wrote this article I did not have data for such sections for angles of attack in excess of about 18º. Since then the use of aerofoils for the blades of wind-powered turbines has led to data being available on the internet.)
The following data comes from Aerospaceweb from Sandia National Labs report SAND 80-2114 giving lift and drag coefficients for NACA 0015 shown in figure 1 for angles of attack from 0º to 180º. (They were interested in vertical axis wind turbines.) They tested seven sections including NACA 0015 which is shown in figure 4. It is clearly a proper aerofoil and will exhibit a normal stall but it will also have a graph of coefficient of lift versus angle of attack on into the stalled flow region. They gave their results in two graphs of coefficient of lift versus angle of attack in figure 2 and of coefficient of drag versus angle of attack in figure 3.
This data can be re-plotted for our range of 90º.
The two plots are in figures 5 and 6. Figure 5 is taken directly from the original graph but figure 6 has been re-plotted because the original data is too indistinct. This data is for the NACA 0015 for values of Reynolds number between whereas for a model sail the value might be about .
We have other relevant information. All well-made aerofoils have the same graph of coefficient of lift for the range of angle of attack from 0º to at least 8º and the divergence from there until the stall is reached depends partly on the value of Reynolds number and mainly on the camber of the aerofoil. What we have is typical of symmetrical sections. We shall not be interested in the stall but we may choose to use the aerofoil at high angles of attack when we shall need the rest of the graph although that appears to be more or less the same for all values of Reynolds number and indeed for most sections.
The value of a coefficient of drag cannot exceed 2. We may use this wing at angles of attack of about 70º where the value of the coefficient of drag is not much less than 2. The important information in this graph is the presence of a region of very low values of the coefficient of drag from about 0º to about 12º. It is called the drag bucket. I have added the plot of the coefficient of lift for this section and the useful range of coefficient of lift coincides with this region of low drag. This is the range of angles of attack that one must use for a wing sail to take advantage of the aerofoil to drive a yacht.
It is tempting to proceed by imagining that the wing-sail is working in a steady wind and studying the mechanics of the sail. However yachts do not operate in steady wind and I devoted the whole of section 8 in book 1.3 to gusting and veering so I do not need to repeat it here. It is a serious problem for all devices that are using the natural wind, not least wind-turbines. It will affect the wing-sailed yacht. If the yacht is sailed in a wind that might veer through more than 20° and the wing is going to stall at about 11° we stand no chance of responding to changes in wind direction by sheeting if we are to keep the sail working in its narrow band of 11° and, unless a very accurate and fast automatic control system can be devised, it is pointless building a wing-sailed yacht. Fortunately there is a simple system that works tolerably well that can be used.
Aeroplane wings do not work unaided but as one element in a wing/stabiliser combination. This is the arrangement used almost universally on aeroplanes. Here we must consider the case of a wing and control vane with symmetrical sections because then our wing has to produce a force in both directions and so must be symmetrical.
Figure 7 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 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 to make the model pivot freely. 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.
The immediate effect is to produce a force on the stabiliser that deflects the stabiliser downwards 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. 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 8. 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.
This system is used on a wing-sailed yacht. It is very obviously the system used on Greenbird . As we have seen the wing is mounted vertically on a freely-moving bearing and has a stabiliser just like the aeroplane. The word stabiliser has its roots in its function on an aeroplane and in the context of a wing sail is not now well named so I shall call it a control vane, that is, a surface that lines up with the air flow like a weather vane. There would be no gravitational force corresponding to the weight of the aeroplane. Instead the force generated by the wing would be resisted fore-and-aft by the water acting directly on the hull and by the fin acting across the beam. When the control vane is set with zero angle to the wind the rig generates no lift and simply weathercocks to follow any wind shifts. If now the control vane were to be set at say 8° (This is a practical value in the light of the aerofoil data.) the rig would still weathercock to follow wind shifts but the vane lines up with the instantaneous direction of the wind and, in doing so, sets the wing at 8° to the relative wind. The wing will then produce a force that can be used to drive the yacht. Setting the control vane out to the other side by the same angle of 8° reverses the angle of attack of the wing so that the yacht can tack.
This simple system of a wing and control vane is quite capable of producing a force to drive a yacht and is simple to switch to change tacks. However the vane is behind the wing and it would seem that any change in the direction of the wind will be exerted on the wing before the vane but changes do not occur suddenly. Instead the whole flow pattern changes in an orderly way just like a rising tide and this simple system may, in fact, work quite well. We have to accept this system anyway because there is no obvious way of detecting the direction of the wind ahead of the wing to control the vane by some electrically powered automatic control system.
If we accept that the vane can be set at +/- 8° and that sailing down wind can be achieved by tacking, every feasible point of sailing is possible without any control other than rudder. However, it may be desirable to run before the wind instead of tacking, when a second setting of the wing-sail using the vane will be required. We need to understand how this all works.
We have to sort out a way of looking at this wing-sail first. The wing-sail as a whole exists to interact with the wind to produce a force that can be used to drive a yacht. None of its parts are there for any other purpose and none can be discarded. The interaction between the wind and the wing alone produces a force on the wing. This is usually derived from the lift measured at right angles to the relative wind and the drag measured in the direction of the relative wind. The forces are shown in figure 9 where the drag has been taken to be 1/10 of the lift.
It is quite possible to calculate the force on the wing-sail at any point of sailing if a ratio of lift to drag is chosen and then the effect of this ratio can be found by quite straightforward calculation using a maths package.
I have shown in figure 10 the wing-sail in operation. The control vane is set at , the desired angle of attack of the wing, and as a result, the stabiliser moves to become aligned with the relative wind and then the wing also has an angle of attack of . The force on the wing is the sum of two other forces, the lift acting at right angles to the relative wind and the drag in line with the relative wind. The freedom of the wing to rotate ensures that this diagram will be the same for all points of sailing. All that will change is the angle of the wing relative to the yacht and the speed of the relative wind as the course changes. The force on the wing will depend on the square of the speed of the relative wind.
This now leads to another diagram showing the component of the force on the wing that is available to drive the yacht.
Figure 11 shows the way that the wing produces a force that has a component in the direction of the course of the yacht. This force will overcome wind drag on the hull and drive the yacht. The component at right angles to the course will be exerted transversely on the hull and be resisted by the fin moving through the water. I have shown the yacht making a course at to the true wind. This has been combined vectorially to give the relative wind at to the true wind. The wing is shown at to the relative wind.
Diagrams like this one can be drawn for any direction that yacht might sail and the speed of the relative wind will change with the course and the force will change with the square of the relative wind. The component to drive the yacht will change with the force and with angle . If we knew values for the coefficient of lift and the coefficient of dag we could calculate the magnitude of the component in line with the course and show how it changes with .
Wings such as those that might be used on a wing-sailed yacht will not all be made to a high standard. Some will have a high aspect ratio, that is be long and narrow, and some will have low aspect ratio. The aspect ratio and the build quality affect the values of the coefficients.
Usually the data given for aerofoils is derived for models that, in effect, have infinite aspect ratio. Then the coefficient of lift is numerically equal to about one tenth of the angle of attack in degrees. Symmetrical sections usually stall at about 12° and to allow for fluctuations in wind speeds a practical angle of attack to set as a maximum is about 8°. It would not be unreasonable to expect to have a value for the coefficient of lift of 0.8. It is the coefficient of drag that varies with the aspect ratio and with build quality. As a result the ratio of lift/drag is the most convenient parameter to use and, if we equate lift/drag and , we can put , where is the lift/drag ratio and will depend on the quality of the wing.
We need an idea of the range of lift/drag ratios. One can make a reasoned estimate by considering ratios of lift to drag for existing devices. The highest ratio of lift to drag for a high aspect ratio wing is about 100 to 1. It will be achieved on a high performance glider made from composite materials to great accuracy. For wing of a wooden glider made to a good standard this ratio might be 50 to 1. The wing of a wing-sailed yacht made to the exacting standards for record-breaking might be up in the 90's but for home-builts 30 might be a good figure. It could be much lower.
These figures are very high when compared with a soft sail but this is the price to be paid to get them to work with such tight limits on the angle of attack.
For models, wings made from wood and fabric might have a ratio of say 15 to 1.
For my purposes here the precise value of lift/drag is not important. I want to show how it affects the drive produced by a wing on a yacht.
I will show the way to make the calculations and give the graphs that come from them using a mathematics package. The calculations come directly from the diagram in figure 11.
Let the true wind be denoted and the speed of the yacht . The course of the yacht is the variable and we have that the course makes the angle to the true wind. If we put typical values to we can plot the relative wind speed against .
Using figure we can see that the speed of the relative wind is given by Pythagoras:-
This can be evaluated for suitable values of . Suppose that the true wind has a speed of 20 knots. The yacht speed will depend on the angle of the course to the true wind and on the way that the resistance to motion of the hull varies with speed. It is sufficient for my purpose to let the yacht speed be constant at 6 knots.
I have plotted the result in figure 12 where the speed of the relative wind is in red and the angle between the relative wind and the true wind is in blue. It is what one might expect.
Now the lift and the drag on the wing can be found for any course from the speed of the relative wind and the coefficients of lift and drag. However we do need an area for the wing. Suppose that square feet (28 square metres).
Then the lift is given by where the density of air is 0.0765 pound/cubic foot and 32.2 is g in feet/sec/sec. must be in feet/second and in square feet. The drag will be and of the coefficient of lift of the wing at this angle is taken to be 0.8 the result is a lift at right angles to the relative wind and a drag, that depends on the value of lift/drag, in line with the relative wind. These two combine to give the force on the wing. This force can be resolved into two components at right angles, one in line with the course and the other across the yacht. For any value of the force can be calculated.
We can start with the lift and drag. Figure 13 gives the lift, the drag and the force on the wing which is the vector sum of the lift and drag. It is for a lift/drag ratio of 12 which is low but was chosen so that the traces are discernable. The others lie between the black and red graphs.
Now we have to find an expression for the component of the force on the wing in the direction of the course. We need the angle between the lift that is at right angles to the relative wind and the force. That will be . Then the force makes an angle of with the true wind. The component of this force in line with the course will make an angle of to the force. Then the component driving the yacht will be :-
the force on the wing × .
This can be plotted but it makes sense use a polar plot because we now have a force that varies with the course and is in line with the course.
This plot in figure 14 is for a true wind of 20 knots, a fixed yacht speed of 6 knots and a lift/drag ratio of 30. It is also for a wing area of 300 square feet and an angle of attack of 8°.
The decision to treat the yacht speed as constant will affect the courses between 0° and 30° and 135° to 180° most. The graph shows that the wing can generate a driving force when the yacht sails close to the wind but the down-wind performance is impaired. It produces the greatest driving force at a course at about 75° to the true wind.
However the wing is not easy to construct to high standard nor is it easy to maintain this standard and it follows that we really need to know how the lift/drag ratio affects this plot.
I have repeated graph figure 14 for four different lift/drag ratios of 5, 10, 20 and 40 to give figure 15. The red trace is for and the black for . The wing can produce a force to drive the yacht at angles to the true wind greater than about 15° which is much better than a sailing rig with soft sails when beating. The greatest driving force produced is about 300 pounds at around 75° which is exactly what was required for setting speed records. However the down-wind performance is inferior to that of a rig with soft sails which is to be expected. It looks as though making progress down wind by sailing and tacking is not really very satisfactory and one must ask whether the sail can be set at some new angle where the wing is stalled angle give better speed down-wind.
This raises the question of how to run before the wind with a wing-sailed yacht.
It is clear that there is a range of courses from about 120° to 180° where the wing-sail should be set to operate with the wing working in the stalled condition. We have data from Aerospaceweb for wings of symmetrical section and Aerospaceweb say that the data is accurate for the seven symmetrical sections that they tested. In fact it seems that their data applies to any wing that has a practical profile. We can look for a new range of lift/drag ratio for angles of attack from say 50° to 90°. At 50° the ratio is about 0.8 and at 70° is 0.4. Supposing that the vane could be set to have an angle of attack of 70° there is nothing in the mathematical modelling to prevent this lift/drag ratio of 0.4 being fed in to produce a diagram that matches figure°15.
I built my first wing-sailed yacht around 1970. It was built on a commercial catamaran hull with a wing, built to model aeroplane standards, that was fairly free to rotate and was controlled by a vane fitted behind the wing. In those days radio control equipment was not reliable and was quite heavy. I used two sets, one in the hull and one in the wing both on the same frequency but using different channels. At that time I did not understand the physics of the yacht and, to my shame, saw no need to do so. It was designed intuitively. I tried it on a lake surrounded by trees and it was not really successful. The main stumbling block was that the catamaran hull was too light to carry the yacht round a tack. This effectively prevented me from exploring its performance even if I had known what to look for. I shelved it until two or three years ago.
By 2000 I had learnt about sailing with soft sails and come to understand gusting and veering (See section 1.7 of this website.) and, on the way, I had analysed the wing/stabiliser system used on aeroplanes. There was nothing to prevent me from analysing the application of a rigid wing to driving a yacht of any size and I am well kitted out to test the outcome in a model.
I did not look for an existing analysis but resolved to find out how it worked for myself. However the analysis of an awkward thing like a yacht takes me a long time because of the number of variables involved. I write a record of my thoughts and it turns into a sort of diary with halts in it where I cannot see the way forward. Then, after a while, the variables get into some sort of order of importance and I make another step forward. I quite enjoy doing it. But the real pleasure comes when the analysis is finished, the model is constructed and it performs on the lake. Then I can watch my physics at work and it is very rewarding when it turns out to be correct. In this first analysis I was short of experimental data and used the methods of engineering to get round the problems. I put the analysis on the web and it attracted some unspecified criticism that might have been to my use of an engineering approach instead of a scientific approach.
My wing-sail design was literally a wing without twist and having an aerofoil section. Figure 19 shows it beating across the lake. It has a wing of uniform section and, despite the widely held belief that such a wing, when used on a yacht, must have a cambered cross-section, its symmetrical section is quite satisfactory. In the picture the water is choppy but the wake is discernable. It is going well.
Usable conditions occur on the boating lake at Maldon on a fair number of days each year and it is within my range of travel. Had this not been so I would not have bothered to build the yacht. That would have been a pity because this has been a rewarding exercise.
In my view a model maker must choose a design for any yacht to suit conditions where the model will be sailed. Mostly models are sailed on lakes that are either wholly or partially surrounded by trees and/or houses although some lucky modellers have open water with open land all round it. Using the methods of section 1 a rewarding model of a wing sailed yacht can be made for use on open water but not, I think, for lakes with obstructions that disturb the wind.
The problem with sailing a model in a confused wind is that the size of the eddies in the disturbance is small and not much larger than a model. The simple control vane cannot respond quickly enough to changes in wind direction and speed. Then, having been designed to work at an angle of attack of, say, 8° it could suddenly change to 0° or just as easily to 20° when the wing will stall. Neither of those cases matter but, when the control vane re-establishes control of the wing and the wing becomes "un-stalled", the force on the wing can double instantly. In this case the hull, with its built-in system of stability both side-to-side and fore-and-aft, responds quite violently. It must not capsize or pitch-pole
Now for best performance the wing should have a high aspect ratio, in other words, be tall. Multi-hull designs tend to pitch-pole or even to capsize for want of dead weight in the fins and are not first choice for sailing in a confused wind. Then one must think in terms of a conventional mono-hull with a fin and lead.
I learnt some things from my first wing-sailed yacht. First the wing-sail requires a hull with some weight to it just to make a tack reliably. Second the wing, if it is to be successful, must swing very freely, on ball races as the nearest we have to frictionless bearings. Radio equipment is now much lighter and the resolution of the servos is now much better that it was 40 years ago. The evolution of the computer-controlled transmitter has made setting up much easier especially the throw adjustment. I chose to use a hull for a one metre yacht that I had to hand and build a wing-rig for it.
I needed a well-made bearing assembly if this design was to work properly. The hull was fitted with a mast tube of 16 mm bore That would accommodate ball races from the odd races box to run on a piece of 12 mm carbon fibre tubing. That carbon tubing was fitted snugly into the wing between the main spars. It can be removed if necessary.
Figure 20 shows the bearings etc. and figure 21 shows the assembly. The cover is made of ptfe. The large race has an insert to make it fit on to the 12 mm tube and a brass carrier that fits snugly on the outer race and a collar that fits into the mast tube. The cover is just a cover to keep out water. The wing rests on top of the cover to form a seal. The small race is held between a brass insert that is glued into the carbon fibre tube and a clamping washer that is profiled to grip the inner race and clear the outer. A sleeve fits tightly on the outer race and fits smoothly in the mast tube. It is shown in figure 22.
Figure 23 shows the assembly in the wing and the wing in figure 24.
I reasoned that, as the force exerted on the wing rig is probably twice that exerted on a sailing rig of the same area, the wing could be half that of the top suit of a one metre yacht. I made it of constant chord with a NACA 0012-64 section. It is 48 inches long and of 8 inch chord. The control vane is 15² long with a 5² chord with an arm between the axes of the pivots of 13².
I made the wing in the normal way. The wing rib is shown in figure 24. Note the use of laminated main spars that can be tapered to the tip. It is essential to make the nose and the first 40% as well as is possible.
The control vane is also symmetrical with an NACA 0012-64 section. It is covered with 1/32" balsa. It is mounted on two outriggers that are stuck to the wing and pivoted on 1/8" rod at 40% of the chord from the leading edge. Again the first 40% needs to be well made.
In order to operate it I made the gate shown in figure 25 where the stick is in the position for giving the vane an angle of attack of 8°. When the stick is lifted a little and moved to the next notch the vane had to go to 50°. This was only possible using the exponential facility. The control vane operates in one of five positions, centre, +8°, +50°,-8° and -50°. No other positions were thought to be necessary.
It was all very simple.
Since I made this wing rig I have done a lot of work to my text book on the various uses of aerofoils and my understanding has improved. I have also been forced to change to a lake where the wind is always confused. I have been thinking of ways to sail on such a lake. The rigid wing with its automatic control might be an answer.
It seems to me that two things are needed if the rigid wing is to be used. The first is to go deliberately into the stalled condition to get away from the violent reaction to abrupt stalling and recovery. The second is to find a good angle of attack to get the best lift/drag ratio to give a useful drive. It is about 20°.
I think that if the wing were to be designed to have detached flow at every angle of attack, in other words to be permanently stalled, and the control vane be designed as an aerofoil it might be possible to use a multi-hull to advantage if the wing is set to about 20°. If then the wing is of low aspect ratio with end plates to offset this disadvantage by suppressing span-wise flow, the pitch-poling can be avoided without the use of heavy bulbs on the fin.
It has all been worthwhile.
Ivor Bittle January 2013
 The use of pivots ensures that the test 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