Sail shape & Aerodynamics

Out of popular demand, we give some aerodynamic background for the sail shapes described in "The Quest for the Perfect Shape". This is by no means a complete treatise of sail aerodynamics - we are merely scratching the surface - but should shed some light on why sails look the way they do.

The light air case

In light air, a sailboat will almost always go faster if sail lift can be increased. As long as there is no significant flow separation, drag increases as the square of the lift. As lift continues to increase, drag rises even more rapidly until we reach maximum lift and the sails start to stall. Until near maximum lift, sail drive will increase and the boat speed ditto, in spite of the quickly rising drag and the related heeling force. This is because in light air the heeling force (or moment) is not an issue, at least up to very high values of the side force, when the induced drag of the underwater hull gets excessive.

So, in light air we need to look for shapes that maximize lift:

• round headsail entry to allow for large angle of attack
• maximum overlap to allow bringing the boom to the centerline and over, inducing lots of camber into the sailplan looked as a whole
• maximum fullness of both sails separately
• possibly a rounded leech of mainsail to increase rear loading
• twist as needed to prevent stalling

The headsail enjoys a beneficial lift from the mainsail behind it - after all, it is sailing in the "safe leeward position". To prevent flow separation on the leeward side, we want a round, full entry. For best performance in light airs, boats need to sail low and fast, at large apparent wind angles.

Overlap helps to maximize lift in two ways. Firstly, the genoa benefits as its leech is in the high speed airflow on the leeward side of the main. The highly accelerated airflow on the leeward side of the headsail, creating most of the suction that drives the boat, does not need to decelerate to apparent wind speed at the leech of the genoa. Instead, deceleration will happen gradually over the leech of the main.

Ironically, the overlapping genoa leech benefits the main at the same time: it prevents the airflow from accelerating too much over the forward part of the mainsail. Consequently, the airflow does not have to slow down as much as it approaches the mainsail leech, and is not as prone to separate. Separation is caused by the deceleration of the flow, and the flow has to decelerate close to apparent wind speed at the leech of the mainsail (the trailing edge of the wing as one), unless it separates already earlier.

Camber (fullness) will increase lift, but up to a limit: as the airflow on the leeward side accelerates to more than twice the apparent wind speed, it will stop to a halt at the windward side, or even start to flow against the wind, and lift will be decreased. This happens in practice at around 20% depth.

Rear loading, achieved by curving the mainsail leech, may increase the lift a touch more by adding to the positive pressure on the windward side of the sail. Care must be taken that separation will not be increased too much on the leeward side - leech tell tails are a good indicator.

Twist is used to regulate the size of the flow separation areas. Maximum lift (and drive) is achieved with significant areas of separated flow, but there is a limit to it. The flow separation is controlled by the amount of twist. Due to their triangular shape, sails are "tip stallers": separation always starts at the head spreading down along the leech.

Here's the reason: as the angle of attack is increased (the boat bears off or you sheet in), the narrower top part of the sail is progressively more and more loaded (per unit area) than the lower, wider part of the sail. This is nature's attempt to minimize the harmful lift induced drag, by spreading the loading more evenly over the sailplan.

By virtue of their triangular planform, sails twist the airflow in front of and over them as much as 30-40 degrees (!) up along the luff. In the lower part, the sail is headed (effective wind angle is decreased), while towards the head the effective angle increases rapidly (see sketch).

The end result is flow separation starting at the top, while the actual mechanism of this massive bending of the airflow lies in the trailing edge vortices and the strong tip vortice shed at the leech of the sail, at high lift connected with large apparent wind angles (see illustration of the airplane on the right).

This is why in light airs we want sails that are flatter down low (less loading per unit area) and get fuller towards the head (more loading per unit area). A more even vertical distribution of loading means less induced drag and more drive - the famous elliptical loading being ideal but not achievable with triangular sails. The deeper profile fits better for the twisted flow, but you also want to move the maximum camber forward towards the top, further increasing the entry angle, to ensure a smooth flow without separation bubbles at the luff.

Wind gradient

Wind is slowed down close to the sea surface because of friction: windspeed is usually several knots more at the mast top than at the deck level. When this wind speed gradient is combined to the boatspeed, we also experience a twist in the apparent wind in the order of 5 degrees or so (close hauled - downwind the twist can be double as much).

The increase in the apparent wind speed and the wind angle both contribute to loading more the upper part of the sail plan, rendering the triangular sailplan more efficient than it would be in uniform flow.

The case for heavy air

When we reach the design wind and more, maximum lift and the associated flow separation ceases to be an issue. Instead, the heeling moment starts to dominate the performance of the sailboat. We saw in the Quest for the Perfect Shape that drag not only reduces the driving force of the sails, but also increases the heeling force. Therefore, minimizing drag and maximizing the lift to drag ratio become important.

Flattening and twisting the top part of the sails helps keeping heeling moment under control. So does the (often undervalued) triangular shape of the sails: As the helmsman starts to pinch to prevent excessive heeling, the sails are set at a narrower at angle to the wind. The opposite of what was discussed in the light wind case occurs. The upper part of the sails is unloaded, and the effective angle of attack is more even from foot to head. With the reduced lift coefficient the leech vortices are less powerful than in light air, and the sails do not twist the wind nearly as much as before.

This is a property of the triangular planform (side view) of the bermudan sails, something that the hip elliptical leech sails do not enjoy. The sails automatically adjust their loading when the apparent wind angle changes so that the sailboat can cope with a larger wind range more easily.

To avoid backwinding, we want to flatten especially the mainsail in its front part. The feathered top of the sail needs to be even flatter, moving the point of maximum draft towards the leech.

In extreme conditions, it is advantageous to allow the top "reverse" completely a part of the time, providing a negative heeling force (lift to windward), supporting the boat with a large lever. This allows to produce much more lift down low and you end up with more drive for a given heeling moment. However, before the sail starts to backwind you want to flatten it as much as possible. Backwinding not only pushes the boat back but also tends to increase weather helm, usually a problem in heavy air.