The Aerodynamics Of Sails And The Implications On Performance And Stability Of Kayaks
The aim of this article is to turn the attention of sailing minded kayakers and canoeists (and sailors in general as well) to certain irrefutable, scientific facts about the aerodynamic efficiency of sails; to give them a starting point for their own research of this utterly important matter; and to convince them that a well designed sail guarantees pleasant and safe sailing without the need of transforming their light craft into trimarans.
Upwind sails are devices for generating horizontal aerodynamic force. In aviation terms this force is known as the Lift force and the name of the generator of the aerodynamic lift is the Wing. Common names for such devices are airfoils and airprofiles and they work on the same principle called the Bernoulli principle.
Essentially, the generated lift force is a result of different pressures on the lower and upper sides of a wing, or the windward and leeward sides of a sail. The Bernoulli principle (1738) states that the pressure depends on the speed of a fluid – the lower the speed the higher the pressure, and vice versa. Wings are designed (by nature and then by humans) in such a way that their upper surface is cambered (airflow wise), thus longer than the lower surface. As a result, the airspeed above the wing is higher than below the wing, the pressure below the wing is higher than above it, and this pressure difference is what keeps birds and non-powered aircraft (paragliders, hang gliders, sailplanes) as well as subsonic and supersonic planes in the air.
The same process develops when a sail is set under a proper angle of incidence to the wind. If the sail is vertical, the resulting force will be horizontal and not necessarily parallel to the vessel’s longitudinal axis – depending on the angle between the axis and the sail. The vessel’s keel and rudder actually decompose the total aerodynamic force into its driving (parallel to the axis) and heeling (perpendicular to it) components. The ratio between these components should obviously be as high as possible and this is what makes a sailboat design a piece of art.
Sails that are too small cannot produce sufficient driving force. Large sail areas produce excessive heeling which in turn necessitates a wider hull and a heavier ballast to make the vessel more stable and safe, and its sailing rig as vertical as possible to avoid dissipation of the aerodynamic force as well.
Unfortunately, heavier hulls with a more wetted surface are slower, need larger sails… and the story goes on.
Traditionally, the problem of sailboat stability has been treated at the level of the hull. Light craft (kayaks and canoes), by their nature, are very light and narrow/streamlined. No ballasts, no wide beams, no righting arms to counter heeling forces – and they cannot even be balanced by the crew. Outriggers seem to be the only solution.
But let us move from this low level and go higher, to the root of the problem – to the sails again.
The above-mentioned Drive/Heel ratio (D/H) is variable and depends on the point of sailing. However, there is a characteristic value for each sail that clearly determines the D/H ratio at a given point of sailing, and it is called (borrowed from the aviation terminology again) the Lift/Drag ratio (L/D).
This ratio goes from 5:1 in modest sails to 10:1 in America’s Cup sail rigs.
Now comes the strange part: the L/D ratio in wings of some sailplanes goes up to 50:1! Why is this so?
Wings are designed according to the science of aerodynamics and numerous catalogues (NACA, Goetingen, RAF, Wortmann, Eppler, Quabeck, Clark, etc) with hundreds of efficient wing sections, each of them described by their amount of camber, the thickness, the position of maximum thickness, the leading edge radius and the coefficients of lift and drag.
Wings of non-powered, low speed aircraft (could be compared to sail rigs) have very high aspect ratios (the ratio between the span and the average chord of the wing) of up to 40:1 that significantly reduce the induced drag.
On the contrary, a traditional single ply sail rig doesn’t have any ‘aerodynamic’ thickness and its leading edge (mast, even a ‘wing’ mast) is disproportionately thicker than the foil itself, creating a lot of turbulence just behind it.
The position of maximum camber is much further aft from its leading edge, their aspect ratios being usually between 4:1 and 6:1. Such a sail generates much smaller aerodynamic lift force (small coefficient of lift) per unit of sail area than an ‘ideal’ sail and needs to be much larger than the ideal one in order to produce the same driving force (from now on I’ll call an ‘ideal’ sail a wing sail because there is simply no such design that is better than a design of the wing). A larger sail in turn increases the friction drag component. Because it is single ply, it must be trimmed closer to the centreline (the angle of attack of the wind has to be bigger to avoid ‘luffing’) which increases the form drag. We can see that all of the aspects of drag are inevitably higher for a conventional sail than for a wing sail – so is their sum total. The aerodynamic drag is usually thought to be a nuisance that only decreases the speed of moving through a surrounding fluid, but for sailboats it is also responsible for the heeling momentum (see Figures 1 and 2).
Figure 1 – a conventional rig
Figure 2 – a wing sail
This is something very important that somehow eludes most designers and sailors (including specialists from WUMTIA – Wolfson Unit for Marine Technologies and Industrial Aerodynamics in Southampton, UK), in spite of their customary familiarity with the name and work of CA (Tony) Marchaj, who in his Sailing Theory and Practice wrote, “We can conclude immediately from either pair of these equations that the drag not only lowers the driving force FR, but also increases the harmful healing force FH.”
The total aerodynamic force FT, as a vector, is determined by its magnitude and direction. Ideally, this direction would be the same as that of the vessel (even theoretically impossible, except at a certain broad reaching angle) – practically, the force is being rotated back toward the stern and the major factors that contribute to this are: the angle of attack at which the sail works, the positions of maximum camber and thickness, and the total drag. A wing sail is absolutely superior to a conventional sail in all of these points and its total force direction is much closer to the bow. It should be beared in mind that the drive force FD is the total force FT times the cosine of an angle between the FT and the centreline (ideally, when this angle is zero, FD=FT; in the same time the heeling force FH, which is FT times the sine of this angle, would be zero). It is no wonder that some authors claim that the driving force FD of a wing sail is 250% larger than that of a conventional sail, with twice the smaller heeling force FH. Yet, America’s Cup design teams “toil over hot computers to get that extra hundredth of a knot”.
One might ask why a boat wouldn’t simply be rigged with a wing instead of a Bermudian sail if it is that superior?
There are at least two reasons that make this difficult. First of all, one can always tell which side of a wing is the upper side and which is the lower side (except for some special purpose symmetrical wings). On the contrary, sailboats tack and gybe, receiving the wind from either the port or starboard side. That means that a wing sail has to be adjustable (i.e. flexible) in order to provide an asymmetrical aerodynamic shape on either tack.
Secondly, a wing sail has to be light, much lighter than aircraft wings.
Increasing the weight aloft can easily annul the aerodynamic superiority of a wing sail, or even render it unusable.
For instance, the US patents No 3, 332 and 383 mechanically solved variability of a wing sail camber, but such a sail (small size, as for kayaks) would probably weigh hundreds of kilos and a ripple would be enough to flip it over.
The search for a soft, light, simple and foldable wing sail has not been fruitful until recently. Now there are a couple of designs that fulfil the requirements mentioned above. Between the two sailcloth panels there is either a lateral or a longitudinal light structure that maintains the thickness of the sail while giving it a near optimum asymmetrical aerodynamic shape, depending on which side of the sail is being exposed to the wind. Details about technical/structural solutions for these sails would go beyond the scope of this article.
Now a few words on downwind sailing: if traditional upwind sails are conventional, traditional downwind sails are pre-conventional. That is how sailing started and how upwind sails were derived from downwind sails. Downwind sails as we know them work on a different, much simpler principle than Bernoulli’s one. The resistance of a large sail area spread out before the wind (basically the form drag) is much higher than the resistance between a hull underneath and the water. The end result is running before the wind.
There is an interesting development here. An airfoil under a proper angle of attack to the wind (10-20 degrees, Bernoulli effect) will produce an aerodynamic force roughly twice the resistance force produced when the same airfoil is placed at a right angle to the wind (conventional downwind sailing). Why isn’t this effect utilized in downwind sailing?
First, rigging wires (stays) don’t allow booms to travel beyond 90 degrees – at this point the boom would hit a stay.
Secondly, long and heavy booms, if they could pass the beam point when they rotate toward the bow (like freestanding 360 degrees rotational masts), could be difficult to haul back. Freestanding (unstayed) masts have been a reality for some time, thanks to technological advancements (the Team Philips catamaran, the British entry in the Jules Verne Around the World Trophy, had two freestanding masts over 40 m high!). Combined with wing sails, they bring sailing to a quite amazing perspective.
Figure 3 – a wing sail downwind
Wing sails do not care which direction the wind is blowing from. When in neutral position, a wing sail will align with the wind, like a flag. When set under a proper angle of attack, it will start producing an aerodynamic force (see Figure 3). It is only up to a sailor to use this force for propelling the sailing vessel in a preferred direction.
The only difference between upwind and downwind sailing from this standpoint is that the aerodynamic drag slows down upwind sailing and speeds up downwind sailing – yet the sailor might easily be unaware of this effect.
Even tacking and ‘gybing’ are substantially identical operations.
Stayed rigs on large boats and yachts still have some merits, but kayaks and canoes are actually much easier to rig with freestanding rigs than with stayed rigs both technically and practically, either on shore or in the water.
Mladen can be contacted at:
Wing Sails Co (Canada)
phone/fax: + 1 604 669 0757