Articles about Aerodynamics

Advances in sail aerodynamics
Sail aerodynamics - part two
Sail Dynamic Simulation
Streamlines & swirls
WindTunnel Movies
Sails shape & aerodynamics
The Quest for the Perfect Shape
Note on the effect of side bend
Anatomy of a Mini-Transat
Mini boat - Maxi challenge
Mini boat - Maxi challenge
470 Aerodynamics
Lifting bows with foresails
Telling tales ...
The scientific Finn
Wind tunnel images

The Quest for the Perfect Shape

The quest for the Perfect Shape

Have you ever wondered that while text books describe in detail how sail shape can be adjusted through various trim lines - cunningham, outhaul, boom vang, backstay, runners etc. - they never tell you what the best shape is - what shape to strive after with all those trim lines? The reason for this is quite simple: There is no such thing as the best sail shape - there are countless different "best" shapes, depending on the wind, waves, boat type & size, even weather & air temperature.

Furthermore, for a given sail the shape varies from the foot to the top, and the fast shape of a mainsail is different from that of a jib which is different from that of a #1 genoa, not to mention a spinnaker. However, it is possible to give some general guidelines about the fastest shapes - we attempt to do it in what follows.

The wind's law of the 2nd power

Why can't we do away with one best shape of sails? The principal reason for this lies in the nature of wind power itself: The pressure that the wind exerts onto the sails & the rig of a sailing boat depends on the 2nd power of the [apparent] wind speed. Double the wind speed from say 5 knots to 10 knots, and the pressure (force) on the sails is quadrupled. Increase the wind from 5 to 15 knots and the pressure is nine times bigger - to 20 knots, and a force 16 times as big will be heeling your boat over. In the Southern Ocean, the Whitbread sixties frequently sail in winds of 60 knots - the pressure on the rig then is 144 times more than in the light airs of the doldrums. No wonder you have to do something with your sails, to cope from 5 to 20 or 30 knots of wind.

Meanwhile, the controls we have on the sails only work in a linear manner: Flatten your sails to half, from say 12% depth to 6% (flatter than this is hard to get) and the force is halved. The same goes for the angle angle of attack: Narrow the apparent wind angle the boat is sailing from 32 degrees in light winds to 16 degrees in a stiff breeze, and the heeling force is again halved. In the mean time, the wind pressure follows its merciless square law.

Luckily, the heeling moment is more important a factor in the sailboat equation than the sail force per se. The heeling moment of the sails is opposed to the righting moment of the boat, provided by the keel and/or the crew weight. To keep heeling moment under control, we can pull some special tricks. Twisting off the sails in their upper part (often called feathering), where they influence the heeling moment most, is very efficient and helps to keep things under control. Finally, when nothing else works, we resort to changing the headsail and even reefing.

The design wind

Most boats are designed so that they get powered up in 10 to 12 knots of true wind. This wind force, where the boat is sailing at its optimum heel and nearly maximum upwind speed is often called the design wind. Below and up to the design wind we want the sails to be powerful, to provide as much forward drive as possible, and we are not concerned with the heeling moment. Once the design wind is attained, the heeling moment to drive ratio becomes more and more important, and we try to maximize drive, with the heeling moment constrained to its maximum value. This calls for a very different sail shape in the lightest zephyrs from those of a stiff breeze.

Think one

To understand sail shape it is useful to visualize the mainsail and the jib as a single "wing" (airfoil) with a slot in the middle. The slot between the main and the headsail makes it possible to adjust the power of the rig, to cope with the huge variation in sail force described earlier. In light winds, a narrow slot ÓgluesÓ the airflow onto the leeward side of the mainsail, preventing flow separation. This is enhanced by the overlap of the headsail. You can sheet the mainsail closer to the boat centerline and even over it, effectively increasing the camber of the main + jib combination.

In a breeze, opening the slot allows to spill the wind and to depower the rig. As the slot widens up, more air flows through it and less is bent to the lee of the headsail, or goes over the mainsail. The slot works like a safety valve. With an open slot the mainsail can be sheeted further outboard, effectively reducing the camber of the ÓwingÓ, and at the same time also diminishing its angle of attack. Thus the two-sail rig with a separate mainsail & headsail allows for much better power control than a single sail cat-rig.

While looking at mainsail-foresail together as a wing, you can distinguish three areas, looking up from the deck:

  1. The part of the foresail below the boom level. This part does not enjoy the beneficial "lift" from the mainsail.

  2. The part up from the boom level to the hounds (where the forestay attaches to the mast). In this part the jib benefits of the main behind it, while the main is being backwinded. However, the presence of the jib is not all detrimental to the main, as it helps prevent flow separation on its leeward side.

  3. The part of the mainsail above the hounds (on a fractional rig). The main is no longer under the influence of the jib while at the same time it starts to get narrow. There is also a pronounced "dent" in the profile where the forestay turns into the top of the mast.

The airflow is different in these three parts and this influences the sail shape as well.

The perfect shape - the mainsail

While it s important to remember that the main and the jib are just two different parts of one and the same airfoil, itŐs easier to describe them in detail by to looking at them separately. The two sails perform a very different task so itŐs only natural that they should be quite different in shape too. The mainsail is closer to us so itŐs shape is more familiar:l

The correct cross section of the mainsail resembles the arc of a circle which is more or less flattened in its rear part. The maximum depth is close to the middle of the sail. Vertically, the relative depth increases from the boom up, especially in lighter winds.

In light winds, we want a full main and the fullness can be further forward behind the mast. The fullness allows to sheet the boom close to the boat's centerline and gives power. Looking vertically up the sail, the foot is fairly full, the mid part is deeper and the top is deepest. The lower and more triangular the sailplan, the more pronounced the difference in fullness between the lower and the upper part should be. The leech of the sail is fairly straight with little twist, exept in lightest zephyrs.

As the breeze builds up and the boat starts to attain its design wind, you want to start to flatten the sail as a whole and especially in the upper part, to keep heeling moment under control. The top gets flatter than the mid-part, and the entry gets finer as the maximum flow moves towards the middle and even aft of it. The flatter main can be sheeted further outboard without excessive backwinding. In the overlap area, the want to flatten the front of the main as much as possible to minimize backwind. At the same time, twist is gradually increasing.

The same applies for the top of the sail above the hounds: The most efficient way to control heeling moment is to let the sail twist off. Simultaneously, you want to flatten the top as much as possible - you end up in a partly inverted shape with the maximum depth well aft of the middle. In strong winds, the whole front part of the mainsail can be inverted (backwinding), so that only the roach( the batten area) is filled all the time. By the time even the roach starts flapping it's time to change into a smaller headsail or reef.

The headsail

The shape of the headsail will vary much less than that of the mainsail in different winds, if we ignore changing it entirely into another sail. One reason is that attached to the forestay, the headsail cannot be nearly as readily trimmed as the mainsail supported by a bendy mast and the boom. Another reason is the role of the headsail as the "leading edge" of the sailplan forming one airfoil: the foresail stays put while the main acts like a flap or aileron behind it, regulating the power.

This does not mean we would not want a different jib for light and heavy air. The basic shape of the jib is very different from that of the main. Looking at the cross section, the entry is much rounder. Maximum flow is further forward, about 40% from the luff (or even closer), and from mid-chord back a jib or a genoa should be perfectly flat with a clean exit, especially in its lower part with overlap.

The headsail needs to be much more twisted than the main, for the leech to follow up the surface of the sail behind it. The more overlap, the more twist is required. When the distance from the leech of the genoa to the mainsail is even all the way from the boom to the hounds, the slot is said to be even. This is a good setting for medium winds. When the distance from the leech of the genoa to the mainsail is getting smaller as we approach the hounds, the slot is closing. This brings power in light winds. When the slot gets wider towards the top, it is said to be open and allows to spill power in heavy air.

In light winds, you want a headsail with a round entry with lots of fullness to allow sailing at wide angles to the apparent wind. The top of the sail should be very full, up to 20%. As the breeze builds up, ideally you want to flatten the sail in front & in the upper part. This can be done to some extent by tightening the forestay by different means, but often the opposite is true: the forestay sags more, an the headsail gets fuller. In small boats and one-designs, you move the jib lead back. This tightens the foot to keep the lower part flat and opens the upper leech to depower & allow sheeting the main further outboard. On a big boat, you switch to initially a genoa with less overlap and finally to a jib.

The big picture

In the animated drawings on the right, we are looking separately at cross sections of both the main and the jib at different heights. However, even more important to the performance of the sailboat than the sails' cross sections is the shape of their leech, the twist. One might go as far as to say that cross section is only a means to "place" the leech into a desired location in space. What lies in between the luff and the leech, wrinkles, creases or inverted curves, is of little consequence as long as the leech of the sail (the twist) is correct. Severe wrinkles in front of the battens may be detrimental, in the extent that they affect the shape of the leech (which may be falling off or hooking in).

This is especially true for the mainsail, whose airflow is more or less spilled by the mast in front of it. We would want the front part of the genoa or a jib to be as smooth as possible, as there may be a possibility for some laminar flow on either side of it. However, shape is more important than smoothness, so in light air it pays to ease the halyard to wrinkle or scallop the luff, making the sail fuller. Even for the headsail, wrinkles in the leech area or a small hook are of little consequence.

To get the big picture, consider the sail to start at the luff of the genoa and to end in the leech of the mainsail.

Appendix: Every picture tells a story

A picture can tell more than a thousand words - the appendix consists of a picture gallery of sails with comments (will open in a new window).

Print Printer friendly version. Will print out nicer than this 2-column display-version.

Heeling Force
5 knots 10 knots 15 knots 20 knots

Move cursor over the buttons to pick a wind speed. See how dramatically the heeling force goes up as wind increases.

Forces & Moments

Sail forces & moments

The heeling moment is caused on one hand by the sail heeling force acting in the center of pressure of the sails, and on the other hand the side force developed by the keel, the rudder and the underwater hull. This couple trying to overturn the boat is balanced by another couple, the righting moment, caused by the buoyancy of the boat and the weight of the keel and the hiking crew (these forces are not shown).

While the heeling force grows in a quadratic manner with wind speed, the heeling is best controlled by feathering the sails (twisting the head off) and flattening them especially in the upper part. This lowers the aerodynamic center of effort, making it possible to keep the boat upright.

To get a feel about the actual forces & moments, see SailPowerCalc.

Defining a sail

Think One

The mainsail and the jib can be seen as a single ÓwingÓ (airfoil) with a slot in the middle. This "wing" can be divided in three areas with different flow characteristics:

  1. The part of the foresail below the boom level.

  2. The part up from the boom level to the hounds (where the forestay attaches to the mast)

  3. The part of the mainsail above the hounds (only on a fractional rig).

Looking at a cross section, the profile starts at the jib luff and ends at the mainsail leech. The chord is the straight line between these two, and the twist of the airfoil as a whole is referred to this line. The camber is between the fictive curve and the chord line, and can be adjusted by letting the mainsail traveler out (less camber) or pulling it in (more camber).

There are "discontinuities" in the sailplan at the junctions of the three areas: a discontinuity in the chord and the twist where the mainsail starts (I & II), and also discontinuities in the "quarter chord line" (gray dashed line). The quarter chord line is an important aerodynamic factor, as it determines the sweep within each area.

At the hounds, there is a discontinuity (dent) in the leading edge : increasing rake and bending the topmast back smoothes out this discontinuity. Sails, looked as a wing, are complex creature: Very highly cambered, much twisted, with discontinuities, a sharp leading edge and a slot in the middle - much more complicated than a 747 wing with all its flaps and ailerons.

Defining a sail

Defining a sail

The shape of a sail section is defined with sufficient accuracy by two percentages and three angles: the camber, expressed in percentage of the local sail chord (width, 12%), the position of the max. camber, similarly expressed in percentage of the local sail chord (47%), the twist expressed in degrees relative to the sail foot chord (10 degrees), the entry angle (32 degrees) and the exit angle (17 degrees), as defined in the illustration.

To define the geometry of a complete sail, we usually take three sections, at 25% - 50% - 75% heights, and the foot section plus the headboard. We also need to know the sheeting angle between the centerline of the boat and the foot chord of the sail, and the mast bend or forestay sag, to be able to fully describe one setting of the sail.

Heeling Force
Light air
Medium wind
Heavy air

Move cursor over the buttons to simulate sail shape for a wind range (helicopter view from the lee).

The figures are indicative, but show you the trend upwind from light to heavy air. The real "best" shape varies from boat to boat: Light, modern, fast and big boats in general tend to have flatter sails than old, heavy, and small boats.

To see how the sheeting of the main & jib influence sail forces & airflow, take a look at SailTrimSim (will open in a new window).