Why a sail is not a wing

 

Introduction

I have wrestled with the problem of explaining why a sail is not a wing for far too long. However if the recognition that there is a problem had not been there I would not have found the answer.

 

From my first contact with model racing yachts I had no confidence at all in claims that the sails were really wings with attached flow on the leeward side. It seemed to me to be impossible especially as Ludwig Prandtl showed what happened to an aerofoil at similar angles of attack. Yet I had seen photographs of sails with telltales lying flat against the lee surface. Other observations puzzled me. Soft sails do not stall as they would if they were to be wings. They just go on interacting with the wind to produce a force that changes smoothly as the angle of attack increases up to 90. How does that happen? Eventually I realised that telltales cannot tell us whether the flow is attached or detached and could start to try to understand what actually happens.

 

I had other allied problems. Wind-powered corn mills and wind-powered water pumps use sweeps that are very definitely not wings nor are they fan blades although they are twisted but, in their final form, were lattices made from square section timbers to house flat louvres so that the area of the sweeps could be changed. One might dismiss these as having been superseded and no longer of any interest but they made flour, and hence bread, possible for people everywhere and at the very least we should be able to explain how they worked. Outback wind-powered water pumps use 16 blades made of sheet metal. They are still being made all over the world in sizes up to 20 feet diameter. How does it come about that wind turbines use only three blades? In putting this question I am not saying that one is wrong but wondering whether there are some engineering reasons that could permit both to be right. The small pump on my filtering system for my fish pond uses 35 watts. It maintains a significant flow through a pre-filter, that is often clogged, and through the main filter. My main vacuum cleaner is rated at 1,600 watts. This is 2 horsepower! It picks up dust and filters it into a bag! If it were not so very noisy it could be used as a very expensive fan heater. I now know that this collection of devices share their mode of operation with that of a sail.

 

From the science angle to this I had another question. The NACA tested large models of whole families of aerofoils made to a very high standard indeed. What they did was tell us the "upper" limits of performance of these aerofoils in the expectation that aerofoils made to some lower standard would not achieve these limiting figures. This appears to be correct but, as most practical aerofoils do not achieve the standards of those tested by the NACA, we are left with little data about the behaviour of real aerofoils. What we do know is that, at any instant, there are thousands of aeroplanes flying quite efficiently all over the world. So what is so special about wings?

 

I have explained about aerofoils in chapter 19 of my text book on this website. The first part between the Introduction and the section headed Shapes of Aerofoils is almost wholly prose and diagrams with no mathematics. It is readable.

 

Aerofoils and wings

The upshot of the text from my book is that an object that has a plan form like a wing, and is inclined to a steady flow of fluid so that it produces a lift, can only be regarded as an aerofoil if the flow over the upper surface follows that surface without breaking away to become detached. Then both the lower and the upper surfaces contribute to the lift. In what seems like a large bonus, the drag on the aerofoil is almost unbelievably low. In order for the flow to be attached and for us to get this extraordinary performance the whole cross-section of the object must be carefully shaped especially at the leading edge and for the first 20% or so of the length of the object front to back. That shaping involves having a suitable nose radius and a suitable profile for this first 20% and smooth continuous curves for the rest. The need for a nose radius leads to other consequences. The radius could, in principle, be zero but that would destroy the section as an aerofoil because the flow could never get round the sharp edge to become attached. So the nose must have a finite but, as it turns out, not very large radius and then, if the radius is to be blended into the curve over the first part of the profile, the aerofoil must have thickness. In fact the most useful sections have thicknesses of around 12% of the chord. There is no other device that does not conform to these requirements that gives anywhere near the same performance. This has profound consequences for sails.

 

If the object has a cross-section that is an aerofoil the lift will increase with the angle of attack until, at some value of the angle of attack between about 8 and 16 the lift will quickly, or possibly suddenly, decrease and the object is said to stall. It is the process of detachment of the flow from the upper surface. In almost all applications of aerofoils the stall sets some limit to the useful range of angle and may be catastrophic as it could be for airliners with high-set stabilisers (T tails) which most of them have[1]. The angle at which the stall occurs depends on the shape of the aerofoil but is also affected by the accuracy of the profile and its surface finish. Even so, for aerofoils, the coefficient of lift increases with angle of attack at the same rate of 0.1 per degree for all aerofoils made to ordinary manufacturing standards, and this slope is the same as that for aerofoils made to the highest standards that we can achieve.

 

The aerofoil, when made into a practical wing, can give ratios of lift to drag up to 50, quite routinely, when the very best can have ratios of 140, but this high ratio is very vulnerable to disturbance caused, say, by insect debris or rain or ice. The performance is very easily disrupted.

 

So wings are special and they must be looked after carefully if they are to produce their astonishing performance. The Airbus A 380 can fly non-stop a distance of 7,000 miles carrying between 500 and 800 passengers. Just looking at the A380 it is evident that the four engines must be a small fraction of the all up weight and, if power output of engines is related to size, the drag of such a large aeroplane must be very low and the ability of the wing to lift must be very good.

 

If a wing stalls at an angle to the direction of flow of between say 8 and 16 one must ask what happens when the direction of flow changes more or less cyclically through angles that are often more than 16 as it does in the natural wind. The short answer is that the wing operates some of the time as an aerofoil and some of the time it is stalled and the flow over the upper surface is detached. This is probably the case for wind turbines that have problems that stem from the sheer size of the rotor and the low speed of the wind.

 

The fact is that we also use many devices that are always stalled. This is the case for the windmill, the wind-pump, almost all fans, most centrifugal pumps and, amongst others, sails.

 

Sails

Text Box:  
Fig 1
Figure 1 shows the sailing rig on a super-yacht. The yacht is beating and is being driven by the jib and the overlapping Genoa working together and working with the main sheet and the mizzen. The main and mizzen have been trimmed to be flat and sheeted in to and become devices that do not contribute to the driving of the yacht but become obstructions round which the air must flow. This diverts the air ahead of the main to flow over the curved jib to produce a force with a very significant component in the direction that the yacht is moving.

 

Here we have a very clever mechanism in the form of a sailing rig that allows a yacht to make way at a very useful speed against the wind and it just comprises four sheets of fabric some spars and some wire bracing albeit a bit on the special side. However an essential part of that mechanism is under the water and it is a wing of symmetrical section made to high standard that, for a very small drag and at a very small angle of attack, can resist the sideways force exerted on the sailing rig. This angle of attack is achieved by the hull making a small angle to the course.

 

Any discussion of sails must, I think, start with a statement about what is normally classed as a sail. What we are talking about is a shaped piece of fabric with appropriate seams and hems with reinforcements as required. It will have fittings to allow it to be mounted on some form of framework using ropes to give it some desired shape. Without these fittings and the framework the sail cannot function at all so, strictly, the structure that gives the sail its shape is part of a sailing rig and any resistance to flow caused by this structure is part of the unavoidable drag and must be attributed to the sail. In the model world the fabric part of a sailing rig must be capable of being rolled and I have no doubt that the same applies to full sized sailing, if only for stowing and transport. I know that in some racing classes the fabric part of the rig not only conforms to this rule but the sail must also be made by an approved sail maker.

 

If the sails shown in figure 1 are normal sails it follows that there is no design of sail made from one thickness of fabric that can satisfy any of the requirements for it to have an aerofoil section and therefore be a wing and have the low drag that is the great advantage of wings. All sails work with detached flow. They are not wings. For reasons that evade me most regard this as a disadvantage and pretend that the sail is a wing. In my view no one should underestimate the importance of the fact that soft sails with detached flow on the leeward side do not undergo anything comparable to an aerodynamic stall but change their net force progressively as the angle to the relative wind changes from being as close to the wind as they will operate up to running before the wind. Couple this with the facility to alter the area of the sail to match the strength of the wind and we have a very versatile device to power our sailing vessels. In my view this characteristic of sails made sailing the oceans possible as long ago as 2,000 or even 3,000 years. Just imagine trying to sail in an open boat on which the sail suddenly lost its drive or, more alarmingly, suddenly regained it. This is what would happen as a result of veering and backing if the sail were to have behaved like a wing. Of course, if the sail is not a wing, it cannot have the very low drag that aerofoils have when they are operating at their low angles of attack. Fortunately the drag of a sail and its associated rigging, even on a square rigged ship, never needs to be so great that it can prevent a very useful force being created by interaction between the sail and the wind. The sail belongs with windmill sweeps but has been developed to make much better use of the wind for the specific purpose of driving boats and it probably belongs with the outback pump.

 

In my "Physics of sailing" on this site I showed that the lowest angle of attack to the apparent wind will occur when beating as close to the wind as possible and a typical figure is between 20 and 25. There may be some conditions where there can be a lower angle but even this lower angle exceeds the angle at which the very best aerofoils stall. I know that there are those who claim some esoteric property of a sail that lets it have attached flow at this angle of attack but this must be wishful thinking and wishful thinking leads to long trains of fallacious "logic".

 

There is one thing that I think comes from wings and that is the shape of the camber. Before the Wright Brothers made their epic contribution to flight by designing, building and learning to fly the first practical aeroplane, the few wings that had been built were either flat or curved to an arc of a circle. The Wright's found that it was better to have a wing with its maximum offset from the line joining the leading and trailing edges at about 40% back from the leading edge. The Wright Brothers' wing section was thin but subsequently many very useful aerofoils have been designed by plotting a symmetrical aerofoil section about such a line so giving the aerofoil thickness. That same curve has been shown to be best for sails as well. There is good reason for this.

 

Text Box:  
Fig 2
Figure 2 is from Arvel Gentry who says that it was obtained in a water tunnel. It appears to be a rigid, curved plate set at 20. This picture is, in fact, the negative of Gentry's picture. It is important to look at the flow upstream of the plate. The plate is clearly an obstruction to the flow and the pressure on the plate rises as a consequence. That rise in pressure acts in all directions including upstream. This diverts the approach flow upwards as we see the picture and when the flow reaches the plate it is divided into two flows. The shape that best matches the natural curve of the flow over the underside is not a circular arc but a camber line with the maximum offset at 40%. It is the shape of the very attractive jib and Genoa on the yacht in figure 1. With a uniform plate like this the flow over the upper surface is detached.

 

Wings and sails generate a force by diverting a flow of air "downwards" and this is evident from the Gentry picture. Any shape that is essentially a plate making an angle to the flow will produce a similar diversion even if it is as angular with protruding spars as a sweep on a windmill. The diversion causes a continuous change in momentum in a direction at right angles to the flow to produce lift. That diversion is made most efficiently, that is with the lowest drag, when the plate or sail has smooth curves and is free from excrescences.

 

If a sail always works with detached flow it must always produce an eddying wake. I have been accustomed to watching eddies being formed and then shed as water in rivers flows round bridge piers and, even in small rivers, the eddies may persist for 20 or more metres beyond the pier. I rather expected sails to do the same thing because it is a matter of observation that sails do, in fact, produce a swirling wake. The picture due to Gentry says that this is not the whole story. Somehow four eddies form over the leeward side of the sail and are not shed. We need to find a mechanism to account for that. The first thing that must be accepted is that the eddies in Gentry's picture could not be stationary relative to the sail and persist unless energy is continuously imparted to them. That energy must come from the flow surrounding the eddies. We need more information.

 

Figure 3 is a picture of a symmetrical aerofoil at high angle of attack in a wind tunnel and is genuine with the exception that the original tended to lose definition where the speed of flow was high and the lines have been hardened. It tells us nothing about the flow in the white space but it is very clear that the flow over the aerofoil flows into that black area where there must be a mixing process in which energy is exchanged. This is where the energy goes into the eddies and the unlikely looking gap between the flow lines where the black area tails off tells us that something special occurs there.

 

Gentry's picture is not good enough to analyse. We need something better. Figure 4 is in Prandtl's book. It is for an asymmetrical aerofoil section and it has the same set of four eddies as Gentry's picture. These two flows are of the same character and if we can explain Prandtl's picture the result will transfer to Gentry's

 

Prandtl's picture is more conveniently used if it is in negative. It is figure 5. We can now see the eddies. There are four eddies A, B, C and D trapped by a fifth one F. Prandtl does not show all of the fifth one but Gentry does so we can be confident that it is an eddy. The flow pattern is consistent with eddies rotating in the directions that I have shown. Their presence bends the flow lines that that flow above the four eddies and then sweep off into the free stream to contain the larger wake. It is the flow that separates from the lower surface that sustains eddy F to trap eddies A to E. It is inevitable that the velocities of the air over the nose will be high and as it flows round the pattern of eddies the velocity of the free stream over them will get progressively slower. The flow under the aerofoil will accelerate as it flows towards the trailing edge. As a result the air in eddy F is acted on by a large shearing force at the bottom and a much smaller, opposing, shearing force at the top. Eddy F must rotate anti-clockwise. Eddy A has a shearing force on it at the top and another with eddy F to its right, is subject to a drag when it is in contact with the aerofoil that tends to slow it down. Inevitably it will rotate clockwise. This all leads to a path for flow over D and C, under B, over A and then down to come into contact with the flow from under the aerofoil. These two paths transfer energy to the eddies to keep them rotating and the air that entered at the top is extracted at the leech or trailing edge as is appropriate. There is another less complex path up and over D to A to go down to the mixing region between F and the flow under the section.

 

If this interpretation of the flow pattern is accepted it will also fit with Gentry's picture and the inclination of Gentry's eddy F is seen to be due to the different angle at which the flow of the underside leaves the underside of the sail when compared with the aerofoil.

 

This flow pattern appears to be stable.

 

There is no constraint on the flow beyond eddy F and presumably eddies will be shed in some sequence to form a typical eddying wake.

 

The interesting region in the flow pattern is on the upper face just before the trailing edge. The lower of the two paths through the eddies appears to have a sort of hook away from the trailing edge and then back again to enter the mixing region. This situation must be associated with a rise in pressure to arrest the downward flow of the air. If this were to be a sail this rise in pressure will oppose whatever pressure is exerted on the sail from the underside. It could lead to there being no net force on the sail at that point and the sail flutter. This can be observed.

 

Pro rata, the wake in Gentry's picture is not as wide as that in Prandtl's picture because of the difference in the angles of attack. Nevertheless these two pictures are part of a whole family of such pictures that would come from a progressive change in angle of attack.

We can see how the flow pattern must change from figure 6 which is my attempt to show how the changes take place. It may not be accurate but I do not think that it gives an incorrect impression. Looking at these flow patterns in conjunction with the pictures from Gentry and Prandtl it is reasonable to infer that there is some order on the eddy pattern in the wake. We can see that the wake widens as the angle of attack increases and that the two mixing regions change in strength to become more or less equal at 90 As the angle of attack increases the small eddies just aft of the luff that are evident in Prandtl's and Gentry's picture have more space to develop and ultimately the wake will be dominated by two counter rotating eddies and probably two small ones. It seems to me that there can be no doubt that there is order in the wake at all angles of attack and that order is brought about by the presence of the mixing region at the leech.

 

All this raises the question of whether this information can be utilised in sail setting for best performance. I do not know but I do know that it is all part of a much wider question of the behaviour of all the devices that operate with detached flow including wings.

 

(Should you care to read the rest of this article keep in mind that I have never sailed and have no direct experience of sailing. I am just looking at a mechanical system as an engineer and deciding where I would start if I had to use it.)

 

It is not uncommon for someone to buy a new yacht and expect to rig it, put it in the water and set off. Luckily the wind driven vessel is very forgiving and with only a modicum of common sense it is possible to do this and get about on say a lake and return to the starting point without having any clear idea of how the sails work or how to set them for the best.

 

But what is this would-be sailor trying to do? He has bought a yacht that will have parts under the water to resist sideways movement and to steer and a sailing rig comprising one or more sails to make it go. The sails are made of cloth to a design that has much more "can do" about it than science. This is inevitable in the absence of any agreed science but we have a sort of pseudo-science that is often quoted. The main sail will be attached to a mast in some way with some means of keeping the luff taut and have a cringle (eyelet) at the clew to attach it to the boom if there is one. Forces have to be carried from these fixings through the sail and the sail maker reinforces the corners and uses the seams to carry these forces through the sail. He also uses the seams to give the sail a belly. This is achieved by making the edges of panels of the sails that are to be sewn together not quite straight. Clearly I am describing a craft not a science. However, once a sail is found to be acceptable modern production methods allow the sail to be copied very accurately. I understand the 220,000 copies of the Laser dinghy have been made so at least this number of sails have been made. Accurate copying is essential. Then every competitor in a Laser has to meet the same challenge.

 

Experienced racers expect to work at the trim of their sails continuously in order to make their boat go as fast as it can. One can see the problem for say a sailor who is racing in a dinghy. He will be trying to make his dinghy go as fast as possible in whatever the conditions may be. In order to do this he will have to hang out to windward to try to balance out the force on the sail that tends to overturn the dinghy to leeward. In this position he must also move his body fore and aft to maximise the boat speed over the waves. He will need to steer whatever he deems to be the best course and be aware of his position. On top of this the outhaul, the downhaul, the sheet, and the kicking strap must all be adjusted continuously. This is a serious workload and it takes a long time for a sailor to become really proficient to the point where boat handling is almost automatic and he can concentrate on racing. On larger yachts several people make up the crew and these jobs can be shared out under the overall control of the skipper. Crew members often concentrate on sail trimming and they have an important role because the rig is the engine of the yacht and they are the engine management system.

 

The object of the sailing rig is to produce the maximum force to drive the yacht along its intended course and we must remember that this force is just a component of the force on the rig. The magnitude of this component depends on the magnitude of the force on the rig and on the angle of the force to the course. (This is hard enough to work out on paper let alone mentally when racing.) It is likely that the best combination of force and angle does not coincide with the maximum force on the rig. So just maximising the force on the rig is not enough.

 

So how can this component force be maximised? No one really knows and herein lies part of the attraction of sailing. Everyone can try to learn how to trim the sail or sails of a sailing rig. So what is the problem? The answer is that we do not know how because there are too many variables involved and we must work with the natural wind with no reliable instruments to help us. Sailors make use of every cue that they can find. They have a simple weather vane fitted to the mast head of large yachts and to the lower mast of dinghies to gauge the direction of the relative wind. They try to set the shape of the sail or sails to give the best shape for the angle between the course and the relative wind. This shape is in the mind's eye and is continually being updated.

 

Trying to adjust the several controls of the sail whilst dealing with all the other problems to achieve this ill-defined goal is very difficult unless there are indicators of success. The obvious indicator of success is speed through the water but we have no natural ability to gauge that. Another indicator that is very simple is speed relative to other competitors in identical boats but that, for a dinghy at least, is tangled up with the action of the sailor in utilising the waves to advantage. On a large boat with several crew the instantaneous speed is not so dependent on the precise positions of the crew members and then there is sufficient manpower for a GPS device to be used to give speed.

 

It is only necessary to look at sailing vessels under way to see that sails are set in all sorts of shapes but there is a remarkable uniformity of shape in class racing.

 

Text Box:  
Fig 7
Authors of sailing guides seem to be quite confident that telltales can be used to detect what is going on over a sail when it is driving a boat. Non-sequiturs include the claim that the telltale can be used to detect changes from attached flow to detached flow. This ignores two facts, the first is that the flow is never attached and the second is that the telltale is simply not good enough a device to do this even if there were to be a change from attached to detached flow. It is a crude device as shown in figure 7 but it is simple and if it can be used to some advantage then so much the better. We need to know what it can do. It works by responding to the drag imposed on it by air flowing past the fluff. Its most likely reaction is the become straight when it can indicate the mean direction of flow. It gets into difficulties when the flow is curved or simply unstable and it is then difficult to decide what it is doing from its appearance.

 

The eddies that are attached to the lee side of the sail must move about as the angle of attack changes with the backing and veering of the natural wind. Furthermore the two pictures from Prandtl and Gentry and my flow patterns show that the shapes of these eddies change with angle of attack. It may be that pairs of telltales on opposite sides of the sail and viewed through the sail will indicate something useful to the sailor over some small range of angle of attack but it is hard to see how rather indefinite instructions on where to fit the tell tales can make this transferable between sailors.

 

There are two possible places for fitting streamers, as distinct from tell tales, to the rig. The obvious place is the leech where a streamer will be influenced by the interaction between the flows coming off the two sides of the sail and its behaviour when the sail is set to best advantage noted. The other is in the space between the main and the Genoa where the must be a junction between the smooth flow over the windward side of the Genoa and the eddying flow over the main.

 

It is all very interesting.

 

Ivor Bittle January 2012

 



[1] Airliners are fitted with stick pushers to avoid this problem.