List of contents
Why bother?
Appraisal of the wing-sail and the soft sail
Application of the rigid wing to a model yacht
The wing/stabiliser system
The wing-sailed yacht at various points of sailing
Running
2.6 The model wing-sailed yacht
Why bother?
When I had come to understand the soft sail there was an obvious gap in the application of aerodynamic devices to driving a yacht. There was the whole range of angles of attack from 0° to about 35°. The only device that seems even half suited to operate in this gap is the rigid wing. I had seen wing-sails in operation on a catamaran coming up the Thames at Gravesend and knowing the problems of driving a boat with soft sails I did not think that the wings on this cat stood any chance at all of operating as aerofoils. If they were working at all it was in a deep stall mode. I was not impressed. Ever since the last war wing sails have popped up with great promise but little achievement. I thought that it was time to look more closely at the rigid wing to see just why it was not succeeding.
I built my first wing sailer 40 years ago. It was built on a catamaran hull with a wing that was fairly free to rotate and was controlled by a control vane fitted behind the wing. In those days radio control equipment was not very good 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.
In the intervening period 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 and I am well kitted out to test the outcome in a model.
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.
Appraisal of the wing-sail and the soft sail.
The soft sail is well known. Its characteristic feature is that it is made from fabric that, physically, is capable of being rolled. Such a sail can flap and it depends on an array of ropes and spars and the wind to give it shape. (The fully-battened sail that is effectively a single-surface aerofoil is rigid and is not dependent on the wind to give it shape is used only where the sail can be switched from tack to tack by the sailor.) I have already explained in section 1 of this site that soft sails operate in a permanently stalled condition. In this respect they operate in a quite different aerodynamic regime to the wing-sail, which operates as a normal wing and is not stalled.
The wing-sail is literally a wing without twist and having an aerofoil section. Figure 1 shows my wing sailer reaching 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.
If we are to compare the way that soft sails and wings operate we need to turn to aerodynamic data. In Section 1.1 of the web site I argue for my graph of the coefficients of lift and drag for a soft sail plotted against angle of attack. I reproduce it here as figure 2.
In
order to create that graph I had to define the angle of attack for a sail and
it is shown in figure 3.
The soft sail does not fill until it has an angle of attack of about 35° so there is no graph for angles between 0° and 35°.
By comparison the rigid wing can work for angles of attack from 0° to 90° when, of course, it is fully stalled. The symmetrical section can work properly (ie un-stalled) over a range of angles of attack from 0° to 15° as an absolute maximum. It follows that we need accurate data for this range of angles. The best source is the NACA.
The data published by the NACA is derived from wind tunnel tests of the highest standard. The chord of the models that were tested was about the same of the wing of a high performance glider so these are really tests on full-sized wing-sections and not the small sections that might be used on a model. We should note that these are tests in two-dimensional flow and not in three dimensions as would be the case for a real wing. Nevertheless the data will be sufficient for the design of a model yacht.
The section that I have found to be most satisfactory is NACA 0012-64. It is shown in figure 4. Clearly it is symmetrical and the 12% thickness gives a useful radius in the first 15% behind the nose that improves the stalling characteristics. In tunnel testing the angle of attack for a symmetrical section is measured between the axis of symmetry and the direction of the undisturbed flow. This would be the centre line of the tunnel. It is shown in figure 5. Figure 6 gives the graph of coefficient of lift versus angle of attack. (The coefficient of lift is explained in section 1 of this website on page 2 of section 1.1)
We must first note that the slope of the graph of coefficient of lift against angle of attack is pretty much the same for all aerofoils. It passes through 0.8 and 8°. It is the maximum value of the coefficient of lift that changes with the section. NACA give data for three different values of Reynolds number for each test section and one for the section with the first 8% 0f the upper surface artificially roughened to promote breakaway of the flow as might be caused by dead insects on the wing of a glider. This roughening is much more severe than would be produced by normal manufacturing methods for full-sized aeroplanes. The plots for the un-roughened section are the three upper ones and the graph for the roughened section is the lower one. A model-sized wing will not be troubled with dead insects but it will not be made to the high standards of the NACA test sections. It also operates at low Reynolds numbers. I have to decide where the curve for a model wing might fit on this graph. The roughened test model stalls at about 9° and the three standard sections at about 15° and moreover they are closely grouped. I think that the model wing will stall somewhere between 10° and 12° and experience with the actual yacht where the wing is set at 8° suggests that there is a useful margin between 8° and the stall. So I shall suppose that the model wing with its NACA 0012-64 section stalls at about 11° with a coefficient of lift of about 1.1°. So, unlike the soft sail, the range of angle of attack for which the rigid wing can operate most effectively is only 11°. Should it stall, the lift on the wing will suddenly drop. It is a decidedly unpleasant characteristic for an engineering device and led to many deaths during the evolution of the aeroplane.
However the wing-sail can operate when it is deeply stalled so we really need a graph of coefficient of lift versus angle of attack for the range from 0° to 90°
Figure 7 shows what I think is a good approximation to the actual graph. Certainly this is what it feels like when sailing the yacht[1]. It may not be accurate but it cannot be wholly wrong. It follows that we could work a wing-sail over a wide range of angles of attack, say from 0° to 50°[2] and for the range from about 6° to 30° the lift per square foot will be greater than that of a soft sail. By way of comparison the soft sail does not fill until its angle of attack is 30° or more and so it is always stalled. It works from about 35° to 90°.
In Figure 2 the red-hatched area representing the possible relationship for a sail is just part of figure 7
Clearly there is an incentive here to explore the application of the wing-sail to a model yacht.
Application of the rigid wing to a model 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 I have learnt over the years that the idea of our yachts operating in a steady wind is false. I devoted the whole of section 1.7 to gusting and veering so I do not need to repeat it here. It is a serious problem for all devices that are extracting energy from a 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 our wing is going to stall at about 11° we stand no chance of responding by radio control to changes in wind direction 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 model or a full-sized wing sailer for that matter. However, if the wind in which the yacht can be sailed approaches without serious obstruction for a mile or two, there will be few small eddies and not much gusting and veering.[3] Then, the wing-sailed model yacht becomes viable. Such conditions occur on the boating lake at Maldon on a useful number of days each year and it is within my range. 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.
It becomes clear that the design is for a wing-sail that can only be made to drive a yacht in a steady wind.
I learnt some things from my first wing-sailer. First the wing-sail requires a hull with some weight to it. 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. The evolution of the computer-controlled transmitter has provided exponential shaping of the response of the wing servo and this might be used to advantage.
When I started to think about it again I started from scratch and considered a whole range of possible designs but in the end, decided that my first idea was best. It is to use a wing in combination with a control vane just like an aeroplane. I explained this mechanism in my book on sailing model yachts. Here is the extract.
The wing/stabiliser system
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 18-3
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[4]
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 18-4. 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.
We could use this system on a yacht. It would be a version of a swing rig. There would be no gravitational force corresponding to the weight of the aeroplane. 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. 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. The mast in its socket and swinging on ball bearings would replace the pivots. If the control vane were to be set with zero angle to the wind the rig would generating no lift and simply weathercock to follow any wind shifts. If now the control vane were to be set at say 5° (There is no reason for the choice except that it is a suitable starting angle) the rig would still weathercock so that the vane lines up with the wind and, in doing so, set the wing at 5° to the wind. The wing would then produce a force that might be used to drive a boat. Setting the control vane out to the other side by the same angle of 5° can reverse 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. If mounted on ball races it can respond to slow-ish changes in wind direction. It is then a wing-sail.
The wing-sail will also be required to drive the yacht downwind, that is, to run. I agonised over this for a long time but in the end, decided to set the control vane at 40°, deeply stall the wing, and just use the drag to drive the boat. It works well but this decision prevented me from exploring the use of greater angles.
The wing-sail can be mounted on a normal racing hull complete with fin and bulb and balanced rudder.
The wing-sailed yacht at various points of sailing
Suppose that the control vane is set at 8° for beating and reaching. The whole rig will swing
until the control vane is in line with the true wind if the yacht is stationary
or with the relative wind if the yacht is moving. Within these limits, whatever
course the yacht may follow, the wing-sail will make the same angle of attack
to the relative wind. If we are to understand this yacht we need to know how
well this rig might drive the yacht at any of these various courses.
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 wind. The forces are shown in figure 12 where the drag has been taken to be 1/10 of the lift.
The drag on the model sail is difficult to predict directly because the NACA data is for their high quality test models and not a model wing with its inferior surface. One can make a reasoned estimate by considering ratios of lift to drag for existing devices. The highest ratios of lift to drag are about 60 to 1 for not just the wings but for the whole of a high performance glider made from composite materials to great accuracy. For a wooden glider this ratio might be 30 to 1. For light aeroplanes with their low aspect ratio wings the lift to drag ratio for the whole aeroplane will be much lower at 10 to 1. The whole model wing-sail might have a ratio of say 15 to 1. It is very efficient compared to a sailing rig with soft sails with its stalled sails and its spars, ropes and wires.
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 assumed but the effect of this ratio can be found by quite straightforward calculation using a maths package.
I
have shown in figure 13 the wing-sail in operation. The control vane is set at
8° and
as a result the wing makes 8°
to the relative wind. 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. This force will depend on the square of the relative wind that
in turn depends on the course and speed of the yacht. If I take the speed to be
constant and the true wind to be constant calculations showing how the force
available to drive the yacht varies with course and with the ratio of lift to
drag become possible.
Figure 14 shows the diagram on which the calculations are based. I have shown the yacht making an arbitrary course at q to the true wind. This has been combined vectorially to give the relative wind at a to the true wind. The wing is shown at 8° to the relative wind and the coefficient of the wing at this angle is known at 0.8. The result is a lift at right angles to the relative wind and a 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 q the force can be calculated.
Figure
15 is the outcome of these calculations. It is for a wing sail of 2.65 square
feet set at 8°
in a true wind of 12 knots and a boat speed of 2 knots. The force in pounds is
plotted in polar coordinates for four lift/drag ratios of 12, 6, 3, and 1.5 to
1.
The red graph for 12 to 1 shows that the wing sail has the potential to get much closer to the wind than a soft sail. The drive looks to be zero at 15° but, at 22°, it is about 0.5 pounds. This is a good characteristic. The drive is close to a maximum between 45° and 90° and tails away to 0.5 again by 140° and at 180° there is no drive. Running before the wind with the control vane at 8° is not possible.
The black graph is for a ratio of 1.5 to 1, which is not possible with a well-made wing but might be possible if the wing is fitted with spoilers that are deployed. It shows us that, if we can contrive some drag, the yacht can run downwind.
I have already said that I have used a stalled wing for running but there is a choice of angle for the control vane to decide how deeply the wing is stalled. If the calculations for the drive when the wing is un-stalled are repeated for a stalled wing, the two graphs can be combined to find a good overall graph for beating, reaching and running.
Running
The physics of the wing-sailed yacht suggests
that it is a viable proposition. We now need to look at the radio control
system.
I have used two different set-ups on the wing. The second came out of writing-up this model for my web site. I will describe the first set-up and then the second which is much better. Figure 8 shows the general arrangement of the wing for both set-ups. It fits on to a hull for a metre boat. A carbon-fibre tube is built into the wing and is fitted with races as shown in figure 9. This bearing assembly works in a tube that replaces the mast socket. The receiver for the wing is built into the bottom of the wing and the battery is in the extension forwards at the foot of the sail to act as a balance weight. The wing is 48² long with an 8² chord and the control vane is 15² long with a 5² chord with an arm between the axes of the pivots of 13².
I
first used it with the servo hook up for the control vane shown in figure 10.
The servo is a mini-servo with its normal arm connected via a stranded wire to
a horn on the control vane. There is a matching horn on the other side for an
elastic band to get rid of slack and give a “spring” return. The control vane
operates in one of five positions, centre, +8°, +50°,-8° and -50°. No
other positions were thought to be necessary.
A gate was needed on the transmitter so that these
positions could be found with confidence. Figure 11 shows the gate on the
transmitter with the stick in the 8° position to the right. The left hand notch gives 8° left and taking the stick to either end point gives
50° for running. Obviously
both the 8° and the 50° settings must be found accurately and the
exponential function and the ATV have been adjusted to give these positions.
It was all very simple.
There
is a decision on how to set up the transmitter. The rudder is on whichever
stick is normally used. It is convenient to use the other stick to control the
vane. One direction can control the large angle and the other the small angle.
Then there are four required positions. They are up centre, down centre left
centre and right centre. I found that I could not rely on the spring return to
keep the stick centred when applying the small angle. Any movement of the stick
produced a large unwanted change in angle. I had to fit a gate to find the four
positions accurately as shown in figure 16. It seemed to me that it was best to
fit the running stick to the up down direction and use the left right direction
for beating and reaching. This permitted the vane to be set for beating on the
port tack when the stick is to the left.