How do sails work?

Article by Paul Bogataj

Sails are wings that use the wind to generate a force to move a boat. The following explanation of how this occurs can help understand how to maximize the performance achieved from sails.

Sails are Flexible Wings
It is useful to recognize what a typical sail is. They are normally built from a flexible material in order to allow the sail to work with the wind on either side to allow tacking. This is a significant restriction that prevents many shapes from being built because they would not be able to support themselves in the wind. This leads to the traditional triangular planform of sails, since the material below has to hang from the material above, which eventually is reduced to a point at the top of the mast. So, the problem becomes how to build and operate a flexible sail in the wind to produce a substantial force component to move the boat.

As the restriction that sails support themselves is diminished (full battens and stiffer materials for example), sails can evolve to be more efficient. Their appearance then becomes more wing-like and less sail-like. Analyzing how a sail works as a wing is useful, not just for modern sails that look more like wings, but also for very traditional sails that, while they look like sails, operate very much like wings.

Velocity and Pressure
Flow accelerates over the top surface of an airfoil, either because it is at an angle to the flow, or because the top has more curvature than the bottom, or both. When a fluid (like air or water) is accelerated, the pressure that it imparts on an adjoining surface decreases. This lower pressure pulling upward on the upper surface of a wing produces lift.

Camber
If the thickness of an airfoil is ignored, it can be reduced to a thin curved line defining the camber. The shape of this camber line determines the amount of lift produced at a fixed angle of attack. Since a sail has essentially no thickness, it exists only as camber. The flow over the convex leeward side has reduced pressure (through accelerated flow) and the flow over the concave windward side has increased pressure (through decelerated flow). The difference in pressure across the sail holds the flexible sail into its cambered shape and produces force to pull the boat.

Upwash
An airfoil developing lift causes the flow approaching it to bend upward. This is because the lower pressure on top of the airfoil pulls air up toward it. This upward change in flow angle is called upwash.

Planform Effects
The planform of a wing is defined by the shape of the leading (front) and trailing (back) edges.

In addition to the upwash that an airfoil causes on itself due to the lower pressure on top influencing more air to flow over it, additional upwash occurs due to changes in the planform of the wing. This is because, just as the low pressure on top of the wing influences the air some distance upstream to move upward toward it, that low pressure also influences air a similar distance away in the spanwise direction to alter its direction. This causes variations in upwash along the span of the wing on adjacent sections.

Sweep
The sweep of a wing is defined as the angle between a line perpendicular to the flow and a line (called the quarter-chord) passing through the 25% chordwise (luff to leech) positions along the span. The 25% chordwise position is chosen because, typically, the load on a section can be thought of as being centered there. This is because an airfoil generates much more lift in its forward portion than it does aft, so using the quarter-chord line as a reference is a convenient manner to characterize the sweep of a wing.

Sweep has the effect of increasing the upwash on the outboard wing sections. As a wing is angled aft, flow over the outboard sections must pass by the low pressure on top of the wing sections immediately inboard and forward. The close proximity of that low pressure to the air just outboard causes the outboard flow to turn upward more, resulting in higher upwash on the outboard wing.

Taper
Taper is defined as the ratio of the chordlength of the tip divided by the chordlength of the root. For sails, where the head tapers to nearly a point, the taper is extreme (zero), resulting in a triangular planform.

A tapered wing has a much shorter tip section than root section. As the wing tapers, lift produced by the shorter outboard sections is less because they have less surface area to support lift. Since the outboard sections are smaller than the inboard sections, they are significantly influenced by the larger wing just inboard. Air approaching the outboard portion of the wing is deflected by the low pressure on top of the larger inboard wing that is still generating a large amount of lift only a short distance away. The close proximity of that low pressure to the outboard wing causes the flow to be pulled upward additionally over the outboard wing. Hence, the smaller outboard sections operate with higher upwash. This enhances the amount of lift that they produce but does not make up for their loss of area.

Flow Conditions in Earth's Boundary Layer
Identifying the flow conditions that sails operate in is very useful for understanding how they work. The wind blows over the surface of the earth and, as with any fluid flowing over a surface, has friction with it. This friction slows the air closest to the surface and through shear causes the air immediately above it to slow some, too. This effect continues upward until at some distance above the surface the air is all moving at a similar speed. This behavior is called the boundary layer. While it occurs at a very small scale in the water flowing along the surface of hulls and keels, it occurs at quite a large scale in the air flowing over the earth. This means that the true wind speed is increasing up the entire height of a mast.

Apparent Wind
Apparent wind is the wind velocity experienced by the sails on a moving boat. This is the wind speed and direction that can be directly measured (felt) from the boat while it is moving. It is a combination of the true wind and the wind generated by the motion of the boat. The figure shows how these two wind components are added to create the apparent wind.

Notice that the apparent wind vector at the bottom of the rig, where the true wind speed is slower, is shorter (slower) and angled from a more forward direction, than the apparent wind vector at the top of the rig, where the true wind speed is faster. The true wind is coming from a single direction in this example, but varies in speed with height due to the earth's boundary layer. This variation in true wind speed not only causes the variation of apparent wind speed with height, but also its variation in angle. This is because all of the mast and sail are moving at the same speed and in the same direction as the boat across the moving air. Since the wind solely due to the movement of the boat is identical at all heights, the apparent wind speed and direction resulting from its addition to different true wind speeds at various heights is different.

While in this example the true wind velocity only varied in strength with height, it is possible that a variation in true wind direction can occur with height. In that situation, each tack will experience different apparent wind twist than the other.

Twist
Since the flowfield that a sail experiences is twisted due to the movement of the boat through the earth's boundary layer, the sail needs to incorporate some twist in order to fly in that flowfield. The increase of apparent wind angle with height is a factor that influences a sail to fly in a twisted manner, where the top is angled more off-center from the boat than the bottom. Other factors affecting how much twist is appropriate are sweep and taper as they alter the amount of upwash along the span of the sail.

Isolated Sails
A mainsail by itself (cat rig) is tapered, but if the mast is close to vertical is actually swept forward. Recall that sweep is measured relative to the 25% chord line, which in the case of a tapered sail on an upright mast is angled forward. In this case, the forward sweep would have somewhat of a canceling effect on the increased upwash due to taper. The actual degree of upwash depends on the magnitudes of taper, sweep, and aspect ratio (height/width) of the sail. The sail still operates in the twisted flowfield caused by the boat moving through the earth's boundary layer, so an amount of twist would be appropriate. Raking the mast back increases sweep and will cause additional upwash on the top of the sail, necessitating more twist to the sail.

Genoas and jibs are very tapered and swept. Those two features, combined with the already twisted apparent wind, cause significant upwash toward the head of the sail.

Sails in Combination
Each sail by itself is much simpler than the combination of a foresail and mainsail as in the sloop rig. The sails are operating so close to each other that they both have significant interaction with the other. The most interesting feature of this is that the two sails together produce more force to pull the boat than the sum of their forces if they were each alone.

Earlier, upwash was identified as the increase in flow angle immediately upstream of a wing. There is also a corresponding change in angle, called downwash, just behind a wing, where the flow leaving the wing has been turned to an angle lower than the original flow. This is the cause of the well known "bad-air" that a boat just to windward and behind another boat experiences.

The mainsail of a sloop rig operates in the downwash of the forward sail, causing the flow angle approaching the mainsail to be significantly reduced from what it would be otherwise. This decreases the amount of force that the mainsail produces. The observed affect commonly referred to as "backwinding" is partially a result of downwash from the foresail, but is also due to the higher pressure on the windward side of the genoa being very close to the forward, leeward side of the mainsail, causing the flexible material of the mainsail to move away from that higher pressure.

The foresail of a sloop rig operates in the upwash of the mainsail. The wind as far upstream as the luff of a genoa is influenced by the upwash created by the mainsail. Hence, a jib or genoa in front of a mainsail has a higher flow angle than it otherwise would have by itself, causing an increase in the amount of force that the forward sail produces. So, while the mainsail is experiencing detrimental interference from the foresail, the foresail benefits from the interference of the mainsail. Notice that more air is directed around the curved leeward side of the foresail. This causes higher velocity (lower pressure) and more force. The net result is that the total force of the two-sail system is increased, with the foresail gaining more than the mainsail loses.

There is a converse affect to a windward boat receiving "bad air" (downwash) from a boat ahead and to leeward. A leeward boat gains additional upwash ("good-air"?) from a boat just to windward and slightly behind that acts like a lifting windshift until it moves ahead of the windward boat. This is the same phenomenon from which a foresail of a sloop rig benefits.

Another consequence of the difference in flow angles that the two sails experience in each others' presence is that the mainsail must be trimmed to a much closer angle with the boat's centerline than the foresail, which is able to be trimmed to a lead position well outboard. This angle represents the difference in upwash on the foresail and downwash on the mainsail due to each other.

Masthead Rig
On a masthead rig, where the forestay is attached to the top of the mast and both sails taper to basically zero chordlength at their heads in a similar fashion, the interference effects of the sails on each other are similar along the entire height of the mast. The mainsail ends up being rather tightly trimmed all the way up because of the genoa's downwash, and the genoa gains from favorable upwash all the way up.

Fractional Rig
A fractional rig has the more complicated characteristic that the top of foresail is not as high as the top of the mainsail. This means that the top of the foresail is very close to the front of the mainsail at a height where there is still an ample amount of chordlength in the mainsail. As the foresail luff approaches the mainsail luff, the upwash on the foresail due to the mainsail increases, because the low pressure behind the mainsail has more affect the closer the flow gets to it. This causes the top of the foresail to experience even more upwash and contributes to a fractional rig's foresail being trimmed more twisted than a masthead rig's foresail.

The top of the main on a fractional rig extends well above the foresail, leaving the upper portion of the mainsail free to experience the apparent wind without the downwash interference of the foresail. Apparent wind toward the top of the mast comes from a much higher angle, so the mainsail above the foresail experiences much higher wind angles than the lower portion of the mainsail where the genoa is causing substantial downwash. This change in flow angle with height on a mainsail is quite dramatic with a fractional rig and leads to trimming a fractional rig's mainsail with more twist than a masthead rig's mainsail.

Flow Angles
Reviewing all of the affects so far reveals that both sails experience increasing flow angle with height. The foresail operates in the twisted flow of the apparent wind, with upwash induced by itself due to taper and sweep, and in the upwash field of the mainsail. The mainsail is operating in the same twisted apparent wind, with additional upwash caused by its taper, but somewhat lessened by its forward sweep. It is also flying in the downwash field of the foresail, which is probably twisted because the foresail flies in a twisted fashion. This is particularly exaggerated with a fractional rig.

Sail Shape
With the flow directions established, it is now useful to consider the ramifications of sail shape. Previously, it was stated that a sail section exists solely as camber. Now it is interesting to explore the differences in camber that are possible and what would be most beneficial.

Since a sail is constructed of flexible material, its cambered shape is supported by the pressure difference that it generates. It follows that the leading edge entry angle of the sail must be reasonably aligned with the incoming flow angle. If the entry angle is too high the sail will luff, and if it is too low the sail will stall, since the flow would be required to turn an impossibly sharp corner around the luff. It is also apparent that the entry angle should increase with height to match the twisted flowfield. There are two remaining issues. Where should the trailing edge be, which defines the angle of attack at each height, thus twist? What path to take to get there, or what should the specific cambered shape of the sail be?

The trailing edge location in relation to the leading edge locations establishes the angle of attack of a particular section. Lift increases proportionally with angle of attack, so, since a sailboat is trying to extract as much force as possible from the wind (until overpowered into heeling too much), it would seem best to position the trailing edge (leech) as close to the boat's centerline as possible. This would achieve the highest angle of attack and hopefully the most lift, but unfortunately the ability to trim a sail to unlimited angles of attack is not possible.

Click here to continue...