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.
Overview 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.
Language of velocity and force + Nomenclature Term described Vector Scalar Variables relating to speed True wind velocity and speed VT VT Boat velocity and speed VB VB Apparent wind velocity and speed VA VA Variables relating to force Lift on sail L L Drag on sail D D Total Aerodynamic Force on sail FT FT Driving force component FR FR Lateral component FLAT FLAT Other variables and constants Apparent wind angle α
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.
Components of force: lift vs. drag and driving vs. lateral force
Lift on a sail (L), acting as an airfoil, occurs in a direction perpendicular to the incident airstream (the apparent wind velocity, VA, 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 (VA). 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.Klaus Weltner A comparison of explanations of the aerodynamic lifting force Am. J. Phys. 55(1), January 1987 pg 52
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.
Lift and drag are components of the total aerodynamic force on sail (FT). Since the forces on the sail are resisted by forces in the water (for a boat) or on the traveled surface (for an ice boat or land sailing craft), their corresponding forces can also be decomposed from total aerodynamic force into driving force (FR) and lateral force (FLAT). Driving force overcomes resistance to forward motion. Lateral force is met by lateral resistance from a keel, blade or wheel, but also creates a heeling force.
Effect of points of sail on forces
Apparent wind (VA) is the air velocity acting upon the leading edge of the most forward sail or as experienced by instrumentation or crew on a moving sailing craft. It is the vector sum of true wind velocity and the apparent wind component resulting from boat velocity (VA = −VB + VT). In nautical terminology, wind speeds are normally expressed in knots and wind angles in degrees. The craft's point of sail affects its velocity (VB) for a given true wind velocity (VT). Conventional sailing craft cannot derive power from the wind in a "no-go" zone that is approximately 40° to 50° away from the true wind, depending on the craft. Likewise, the directly downwind speed of all conventional sailing craft is limited to the true wind speed. Effect of apparent wind on sailing craft at three points of sail Boat velocity (in black) generates an equal and opposite apparent wind component (not shown), which adds to the true wind to become apparent wind.
Sailing craft A is close-hauled. Sailing craft B is on a beam reach. Sailing craft C is on a broad reach.
A sailboat's speed through the water is limited by the resistance that results from hull drag in the water. Sail boats on foils are much less limited. Ice boats typically have the least resistance to forward motion of any sailing craft. Craft with the higher forward resistance achieve lower forward velocities for a given wind velocity than ice boats, which can travel at speeds several multiples of the true wind speed. Consequently, a sailboat experiences a wider range of apparent wind angles than does an ice boat, whose speed is typically great enough to have the apparent wind coming from a few degrees to one side of its course, necessitating sailing with the sail sheeted in for most points of sail. On conventional sail boats, the sails are set to create lift for those points of sail where it's possible to align the leading edge of the sail with the apparent wind.
For a sailboat, point of sail affects lateral force significantly. The higher the boat points to the wind under sail, the stronger the lateral force, which requires resistance from a keel or other underwater foils, including daggerboard, centerboard, skeg and rudder. Lateral force also induces heeling in a sailboat, which requires resistance by weight of ballast from the crew or the boat itself and by the shape of the boat, especially with a catamaran. As the boat points off the wind, lateral force and the forces required to resist it become less important. On ice boats, lateral forces are countered by the lateral resistance of the blades on ice and their distance apart, which generally prevents heeling.
Forces on sailing craft
+ Nomenclature Term described Vector Scalar Variables relating to forces on sails Centre of effort CE Apparent wind angle from course over ground β Angle of attack on jib αj Angle of attack on main αm Heel angle θ Heel force FH FH Vertical aerodynamic force FVERT FVERT Vertical moment arm h Variables relating to forces on hulls Centre of Lateral resistance CLR Centre of buoyancy CB Centre of gravity CG Leeway angle λ Total hydrodynamic force on hull Fl Fl Hydrodynamic lift Pl Pl Hydrodynamic lateral force PLAT PLAT Hydrodynamic resistance Rl Rl Hydrostatic displacement weight W W Buoyancy force Δ Δ Horizontal moment arm b
Each sailing craft is a system that mobilizes wind force through its sails—supported by spars and rigging—which provide motive power and reactive force from the underbody of a sailboat—including the keel, centerboard, rudder or other underwater foils—or the running gear of an ice boat or land craft, which allows it to be kept on a course. Without the ability to mobilize reactive forces in directions different from the wind direction, a craft would simply be adrift before the wind.
Accordingly, motive and heeling forces on sailing craft are either components of or reactions to the total aerodynamic force (FT) on sails, which is a function of apparent wind velocity (VA) and varies with point of sail. The forward driving force (FR) component contributes to boat velocity (VB), which is, itself, a determinant of apparent wind velocity. Absent lateral reactive forces to FT from a keel (in water), a skate runner (on ice) or a wheel (on land), a craft would only be able to move downwind and the sail would not be able to develop lift.