Forces on sails

Forces on sails result from movement of air that interacts with sails and gives them motive power for sailing craft, including sailing ships, sailboats, windsurfers, ice boats, and sail-powered land vehicles. Similar principles in a rotating frame of reference apply to windmill sails and wind turbine blades, which are also wind-driven. They are differentiated from forces on wings, and propeller blades, the actions of which are not adjusted to the wind. Kites also power certain sailing craft, but do not employ a mast to support the airfoil and are beyond the scope of this article.

Forces on sails depend on wind speed and direction and the speed and direction of the craft. The direction that the craft is traveling with respect to the "true wind" (the wind direction and speed over the surface) is called the point of sail. The speed of the craft at a given point of sail contributes to the "apparent wind"—the wind speed and direction as measured on the moving craft. The apparent wind on the sail creates a total aerodynamic force, which may be resolved into drag—the force component in the direction of the apparent wind—and lift—the force component normal (90°) to the apparent wind. Depending on the alignment of the sail with the apparent wind, lift or drag may be the predominant propulsive component. Total aerodynamic force also resolves into a forward, propulsive, driving force—resisted by the medium through or over which the craft is passing (e.g. through water, air, or over ice, sand)—and a lateral force, resisted by the underwater foils, ice runners, or wheels of the sailing craft.

For apparent wind angles aligned with the entry point of the sail, the sail acts as an airfoil and lift is the predominant component of propulsion. For apparent wind angles behind the sail, lift diminishes and drag increases as the predominant component of propulsion. For a given true wind velocity over the surface, a sail can propel a craft to a higher speed, on points of sail when the entry point of the sail is aligned with the apparent wind, than it can with the entry point not aligned, because of a combination of the diminished force from airflow around the sail and the diminished apparent wind from the velocity of the craft. Because of limitations on speed through the water, displacement sailboats generally derive power from sails generating lift on points of sail that include close-hauled through broad reach (approximately 40° to 135° off the wind). Because of low friction over the surface and high speeds over the ice that create high apparent wind speeds for most points of sail, iceboats can derive power from lift further off the wind than displacement boats.

Various mathematical models address lift and drag by taking into account the density of air, coefficients of lift and drag that result from the shape and area of the sail, and the speed and direction of the apparent wind, among other factors. This knowledge is applied to the design of sails in such a manner that sailors can adjust sails to the strength and direction of the apparent wind in order to provide motive power to sailing craft.

The combination of a sailing craft's speed and direction with respect to the wind, together with wind strength, generate an apparent wind velocity. When the craft is aligned in a direction where the sail can be adjusted to align with its leading edge parallel to the apparent wind, the sail acts as an airfoil to generate lift in a direction perpendicular to the apparent wind. A component of this lift pushes the craft crosswise to its course, which is resisted by a sailboat's keel, an ice boat's blades or a land-sailing craft's wheels. An important component of lift is directed forward in the direction of travel and propels the craft.

To understand forces and velocities, discussed here, one must understand what is meant by a "vector" and a "scalar." Velocity (V), denoted as boldface in this article, is an example of a vector, because it implies both direction and speed. The corresponding speed (V ), denoted as italics in this article is a scalar value. Likewise, a force vector, F, denotes direction and strength, whereas its corresponding scalar (F ) denotes strength alone. Graphically, each vector is represented with an arrow that shows direction and a length that shows speed or strength. Vectors of consistent units (e.g. V in m/s or F in N) may be added and subtracted, graphically, by positioning tips and tails of the arrows, representing the input variables and drawing the resulting derived vector.

Lift on a sail (L), acting as an airfoil, occurs in a direction perpendicular to the incident airstream (the apparent wind velocity, V_A, for the head sail) and is a result of pressure differences between the windward and leeward surfaces and depends on angle of attack, sail shape, air density, and speed of the apparent wind. Pressure differences result from the normal force per unit area on the sail from the air passing around it. The lift force results from the average pressure on the windward surface of the sail being higher than the average pressure on the leeward side. These pressure differences arise in conjunction with the curved air flow. As air follows a curved path along the windward side of a sail, there is a pressure gradient perpendicular to the flow direction with lower pressure on the outside of the curve and higher pressure on the inside. To generate lift, a sail must present an "angle of attack" (α) between the chord line of the sail and the apparent wind velocity (V_A). Angle of attack is a function of both the craft's point of sail and how the sail is adjusted with respect to the apparent wind.

As the lift generated by a sail increases, so does lift-induced drag, which together with parasitic drag constitutes total drag, (D). This occurs when the angle of attack increases with sail trim or change of course to cause the lift coefficient to increase up to the point of aerodynamic stall, so does the lift-induced drag coefficient. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasitic drag, increases due to the formation of separated flow on the surface of the sail. Sails with the apparent wind behind them (especially going downwind) operate in a stalled condition.