Science Article

Sailing began many thousands of years ago, when some innovative primitive held up a skin to catch the wind and found that he could escape in this way the labour of paddling whenever the wind was fair. When the wind was not fair he accepted that he still had to paddle. As the centuries rolled by, sail-powered ships were developed for fishing, for trade, and for military might. The skin held up to catch the wind was replaced by woven sails. These ships were reasonably efficient for downwind and crosswind sailing but dreadfully slow when they had to sail against the wind.Because they had to sail in narrow waterways where they had no option but to sail against the wind for much of the time, smaller boats of different kinds appeared: the Arab dhows of the Red Sea and the Bristol Channel cutters in England were the first boats to display good windward sailing ability.

Nowadays, modern sailboats can routinely sail against the wind and can, in some cases, be faster than the wind. From the day engines appeared on boats, sailing has progressively become an activity people do for fun: it has become a game where an understanding of the involved physics proves extremely useful.

Guillaume Florent
Former Schlumberger IT Engineer

Sail parts and terminology

How Sails Work

A boat is moved in a windward direction by using forces that are created on each side of the sail. This total force is a combination of a positive (pushing) force on the windward side and a negative (pulling) force on the leeward side, both acting in the same direction. Though you wouldn't think so, the pulling force is actually the stronger of the two.

In 1738 the scientist Daniel Bernoulli discovered that an increase in air flow velocity in relation to the surrounding free air stream causes a decrease in pressure where the faster flow occurs. This is what happens on the leeward side of the sail - the air speeds up and creates a low-pressure area behind the sail.

Why does the air speed up? Air, like water, is a fluid. When the wind meets and is divided by the sail, some of it sticks to the convex (leeward) side and hitches a ride. In order for the "unstuck" air just above it to move past the sail, it has to bend outward toward the flow of air unaffected by the sail. But this free air stream tends to maintain its straight flow and acts as a kind of barrier. The combination of the free air stream and the curve of the sail creates a narrow channel through which the initial volume of air has to travel. Since it can't compress itself, this air has to speed up to squeeze through the channel. This is why the velocity of flow increases on the convex side of the sail.

^{Virtual Lab}Click here for a demonstration of the Bernoulli principle.

The Bernoulli principle acting on an umbrella

Once this happens, Bernoulli's theory takes effect. The increased air flow in the narrow channel is faster than the surrounding air, and the pressure decreases in this faster flowing area. This creates a chain reaction. As new air approaches the leading edge of the sail and splits, more of it flows to the leeward side - air flow is attracted to low pressure areas and repulsed by high pressure areas. Now an even larger mass of air must travel faster to squeeze through the channel caused by the convex sail and the free air flow, causing an even lower air pressure. This continues to build until the maximum speed is achieved for the existing wind condition, and a maximum low-pressure area is created on the lee side. Note that the air flow increases only until it reaches the deepest point of the curved shape (the chord depth). Up to this point the air is converging and speeding up. Beyond this point the air diverges and slows down until is again the speed of the surrounding air.

^{Virtual Lab}Click here to see how this works.

Laminar air flow around a sail (optimal angle between sail and wind)

In the meantime, just the opposite is happening on the windward side of the sail. As more air travels to the leeward side there is less air on the windward side to travel through the expanded space between the concave side of the sail and the free air stream. As this air flow spreads out it slows down to a speed less than the surrounding air, creating an increase in pressure.

Now that we know about these potential forces, how do we actually develop them in order to move our boat? We need to create an ideal relationship between the sail and the wind that will allow the wind to both speed up and flow along the convex curve of the sail. One part of this relationship between sail and wind is called the angle of attack. Picture a sail pointing straight at the wind. The air will split evenly to each side - the sail sags instead of filling to a curved shape, the air does not speed up to form a low pressure area on the lee side, and there is no movement of the boat. But if the sail is angled to the wind to just the right degree, the sail suddenly fills and the aerodynamic forces develop.

^{Virtual Lab}Click here to see the forces developing on a sail.

Forces developed by a sail in laminar flow

The angle of attack must be very precise. If the angle remains too close to the wind the front of the sail "luffs" or flaps. If it's angled too wide the flow lines along the curve of the sail detach and rejoin the surrounding air. This separation creates a "stall zone" of whirling air that causes a decrease in speed and an increase in pressure. Because a sail's curvature will always cause the aft end of the sail to be at a greater angle to the wind than the leading edge, the air at the leech is unable to follow the curve and returns its direction to that of the surrounding free air. Ideally, separation shouldn't start until the airflow reaches the leech. But as a sail's angle of attack widens, this point of separation gradually moves forward and leaves everything behind it a stall zone.

One would think that a boat could only move in the direction that the wind was blowing - that is, downwind. But a triangular sail allows a boat to move toward the wind (windward). To understand how this movement is accomplished, we first need to identify some of the parts of a sail.

^{Virtual Lab}Click here to see the influence of the angle of attack.

Influence of the angle of attack

The leading edge of a sail is called the luff; it's positioned at the front of the boat. The trailing edge at the back is called the leech. An imaginary horizontal line from luff to leech is called the chord. The amount of curvature in a sail is called the draft, and the perpendicular measurement from the chord to the point of maximum draft is called chord depth. The side of the sail that the air fills to create a concave curve is called the windward side. The side that is blown outward to create a convex shape is called the leeward side. We'll return to these terms as we proceed.

You can see that, along with having the correct angle of attack to allow air to pass smoothly onto it, the other important factor in the wind to sail relationship is that the sail must have the correct curvature so the air attaches all the way aft. If the curve is too slight the air flow will not bend out, and there will be no squeezing effect that increases the speed. If the curve is too deep the flow cannot remain attached. Therefore, separation can occur from too much curvature as well as from too wide an angle of attack.

So now we know how pressures on the sail are developed in theory and in practice. But how do these pressures move a boat forward? Let's take a closer look.

At sea level air pressure is 10 tons per square meter. When the air flow on the leeward side of the sail is increased, you recall that air pressure decreases. Suppose it decreases by 20 kilograms per square meter. Likewise, air pressure on the windward side increases - let's say by 10 kilograms per square meter (remember, the pulling pressure is stronger than the pushing pressure). And even though the leeward pressure is negative and the windward is positive, they both work in the same direction. So now we have a total of 30 kilograms per square meter. Multiply that by a 10 square meter sail and we've created a total force of 300 kilograms on the sail.

Each point of the sail has different pressures working on it. The strongest force is at chord depth, where the curve of the sail is the deepest. This is where air flows fastest and pressure drops most. Force weakens as it moves to the rear and separates. The direction of these forces changes also. At every point in the sail the force is perpendicular to the sail's surface. The strong forces in the forward part of the sail are also in the most forward direction. In the middle of the sail the force changes to a sideways, or heeling, direction. In the rear part of the sail the force grows still weaker as wind speed decreases, and causes backward or drag direction.

^{Virtual Lab}Click here to steer your boat upwind.

Forces acting on a boat sailing upwind

Each force on a sail can be calculated to determine the relative strength of its forward, heel and drag components on either side. Since the forward forces are also the strongest, the total force acting upon the sail is in a slightly forward, but mostly sideways, direction. Increasing the power of a sail to gain more forward drive also results in a much greater increase in the heeling force. So how does one move forward into the wind when the greatest force is to the side? This involves the angle of attack of the sail to the wind, and the resistance of the boat to the other fluid involved here: water.

The direction of the total force is nearly perpendicular to the sail's chord. When a sail's chord is parallel to the boat's centerline, the main force is almost completely to the side. But if the sail is angled a bit so the sail force is in a slightly more forward direction, the boat itself moves forward at once. Why? The centerline, or keel, of the boat acts against the water in a manner similar to that of the sail against the wind. The keel produces a force that opposes the heeling force of the sail - it keeps the boat from simply going in the direction of the sail force. And although total sail force is always to the side when sailing into the wind, a proper angle of attack will move the boat forward.

The farther the sail is angled from the centerline of the hull, the more the force points forward rather than to the side. Combine that slight adjustment in forward force with the opposition of water to air, and we have a boat shooting windward because it is now the course of least resistance.