Aerodynamics of Sails and Implications on Performance and Stability of Sailing Vessels

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. All airfoils 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 (est. 1738) states that the pressure depends on the speed of a fluid - the lower the speed the higher the pressure, and vice versa. At low speeds, asymmetrical wings are much more efficient than symmetrical ones and are designed (by nature and then by humans) in such a way that their upper surface is cambered (airflow wise) and the lower surface relatively flat. When a wing is set under a small angle of attack, the airflow above the wing speeds up dramatically in relation to the flow below the wing, creating a suction zone at the upper side and a pressure zone at the lower side. This pressure difference is what keeps birds and nonpowered 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 centerline, depending on the point of sailing. The vessel's keel and rudder actually break the total aerodynamic force into its driving (parallel to the centerline) 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. Larger the sail, larger the drive - inevitably penalized with a stronger heeling moment. This in turn necessitates wider hulls and heavier ballasts to make vessels more stable and safe, and their sailing rigs as vertical as possible to avoid dissipating of the aerodynamic force. Ironically, heavier hulls with more wetted surface are slower, need larger sails...and the story goes on.

Can we 'reverse the spiral'? Traditionally, the problem of sailboat stability has been treated at the level of hull, improving various (multi)hull shapes, keels, ballasts, outriggers. For keel-less boats, beach cats and light craft, the main stabilizing method has been the crew balancing.

But let us move from this low level and go higher, to the root of the problem - to 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 60:1! Why is this so?

Wings are designed according to the science of aerodynamics and numerous catalogues (NACA, Goetingen, RAF, Wortmann, Eppler, Quabeck, Clark ...) with hundreds of efficient wing sections, each of them described by the amount of camber, the thickness, the position of maximum thickness, the leading edge radius and the coefficients of lift and drag. Wings of nonpowered, low speed aircraft (could be compared to sailrigs) have very high aspect ratios (the ratio between the span and the average chord of the wing) of up to 30:1 that significantly reduce the induced drag.

On the contrary, a traditional single ply sailrig doesn't have any 'aerodynamic' thickness and its leading edge (mast, even a 'wing' mast) is disproportionally 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 3:1 and 6:1. Such a sail generates much smaller aerodynamic lift force 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 centerline (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 membrane 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 moment (see diagrams 1 and 2).

This is something very important that somehow eludes most designers and sailors, in spite of their customary familiarity with the name and work of C.A. (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."

Does increased heeling moment of a sailing vessel decreases the vessel's stability? If two identical hulls were rigged with different sails of different aerodynamic properties, and sailed the same course in the same conditions, one heeled 20 degrees and another 40 degrees, which one is more probable to capsize or to get rolled by a breaking wave? Answers to these questions seem obvious, or at least should be, but even if one would dare to ask such a weird question, who could possibly give the answer? In spite of routine stability calculations including determination of the maximum heeling moment, the sail yacht stability is measured and expressed through its Range of Stability. It basically pertains to a capsized keelboat which is supposed to return to upright (eventually), if not heeled beyond certain angle. In fact, this ability has nothing to do with sail aerodynamics, but with the vessel's buoyancy, ballast, center of gravity and righting arm. How is this kind of 'stability' measured for dinghies and beach cats? Perhaps by number of crew righting the boat?

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.

Some experts claim that the driving force FD of a wingsail is twice the larger than that of a conventional sail of the same size, with twice the smaller heeling force FH. Essentially, the 33rd America's Cup has proved far superior wingsail performance, and made history. From now on, the AC design teams will continue to "toil over hot computers to get that extra hundredth of a knot", but this time on new multihull platforms rigged with wingsails (AC45 and AC72).
One might rightfully ask why regular boats and yachts would simply not be rigged with wings instead of Bermudian sails, if they are that superior?

There are at least two reasons that make this difficult:

First, 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). Contrary to this, sailboats tack and gybe, receiving wind from either the port or the starboard side. That means that a wing sail has to be adjustable (i.e. flexible) in order to provide an optimal, 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 U.S. patent No.3, 332, 383 mechanically solved variability of a wing sail camber, but such a sail would probably weigh hundreds of kilos (the BMW Oracle's wing weighs 3.5 tons!) 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 fulfill 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. 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 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 into The Millennium Race, had two freestanding masts over 40m high!). Combined with wingsails, they bring sailing to a quite amazing perspective Wingsails do not care which direction the wind is blowing from. When in neutral position, a wingsail will feather. When set under a proper angle of attack, it will start producing an aerodynamic force (see diagram 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 light craft are actually much easier to rig with freestanding rigs, both technically and practically, either on shore or on the water.

Happy sailing!