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# Physics Of Sailing [BETTER]

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.

## Physics of Sailing

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.

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.

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.[4]

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.[5] 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.[4]

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.

At a stable angle of heel (for a sailboat) and a steady speed, aerodynamic and hydrodynamic forces are in balance. Integrated over the sailing craft, the total aerodynamic force (FT) is located at the centre of effort (CE), which is a function of the design and adjustment of the sails on a sailing craft. Similarly, the total hydrodynamic force (Fl) is located at the centre of lateral resistance (CLR), which is a function of the design of the hull and its underwater appendages (keel, rudder, foils, etc.). These two forces act in opposition to one another with Fl a reaction to FT.[8]

Whereas ice boats and land-sailing craft resist lateral forces with their wide stance and high-friction contact with the surface, sailboats travel through water, which provides limited resistance to side forces. In a sailboat, side forces are resisted in two ways:[8]

All sailing craft reach a constant forward speed (VB) for a given wind speed (VT) and point of sail, when the forward driving force (FR) equals the forward resisting force (Rl).[8] For an ice boat, the dominant forward resisting force is aerodynamic, since the coefficient of friction on smooth ice is as low as 0.02. Accordingly, high-performance ice boats are streamlined to minimize aerodynamic drag.[5]

The approximate locus of net aerodynamic force on a craft with a single sail is the centre of effort (CE ) at the geometric centre of the sail. Filled with wind, the sail has a roughly spherical polygon shape and if the shape is stable, then the location of centre of effort is stable. On sailing craft with multiple sails, the position of centre of effort varies with the sail plan. Sail trim or airfoil profile, boat trim and point of sail also affect CE.[6][9] On a given sail, the net aerodynamic force on the sail is located approximately at the maximum draught intersecting the camber of the sail and passing through a plane intersecting the centre of effort, normal to the leading edge (luff), roughly perpendicular to the chord of the sail (a straight line between the leading edge (luff)and the trailing edge (leech)). Net aerodynamic force with respect to the air stream is usually considered in reference to the direction of the apparent wind (VA) over the surface plane (ocean, land or ice) and is decomposed into lift (L), perpendicular with VA, and drag (D), in line with VA. For windsurfers, lift component vertical to the surface plane is important, because in strong winds windsurfer sails are leaned into the wind to create a vertical lifting component ( FVERT) that reduces drag on the board (hull) through the water.[10] Note that FVERT acts downwards for boats heeling away from the wind, but is negligible under normal conditions.

Forward resistance comprises the types of drag that impede a sailboat's speed through water (or an ice boat's speed over the surface) include components of parasitic drag, consisting primarily of form drag, which arises because of the shape of the hull, and skin friction, which arises from the friction of the water (for boats) or air (for ice boats and land sailing craft) against the "skin" of the hull that is moving through it. Displacement vessels are also subject to wave resistance from the energy that goes into displacing water into waves and that is limited by hull speed, which is a function of waterline length, Wheeled vehicles' forward speed is subject to rolling friction and ice boats are subject to kinetic or sliding friction. Parasitic drag in water or air increases with the square of speed (VB2 or VA2, respectively);[11][12] rolling friction increases linearly with velocity;[13] whereas kinetic friction is normally a constant,[14] but on ice may become reduced with speed as it transitions to lubricated friction with melting.[5]

Lateral force is a reaction supplied by the underwater shape of a sailboat, the blades of an ice boat and the wheels of a land sailing craft. Sailboats rely on keels, centerboards, and other underwater foils, including rudders, that provide lift in the lateral direction, to provide hydrodynamic lateral force (PLAT) to offset the lateral force component acting on the sail (FLAT) and minimize leeway.[8] Such foils provide hydrodynamic lift and, for keels, ballast to offset heeling. They incorporate a wide variety of design considerations.[23]

Sails come in a wide variety of configurations that are designed to match the capabilities of the sailing craft to be powered by them. They are designed to stay within the limitations of a craft's stability and power requirements, which are functions of hull (for boats) or chassis (for land craft) design. Sails derive power from wind that varies in time and with height above the surface. In order to do so, they are designed to adjust to the wind force for various points of sail. Both their design and method for control include means to match their lift and drag capabilities to the available apparent wind, by changing surface area, angle of attack, and curvature.

So, for a given windspeed and Hsu's recommended value of p = 0.126, one can expect G = 1.5 (a 10-knot wind might gust up to 15 knots). This, combined with changes in wind direction suggest the degree to which a sailing craft must adjust to wind gusts on a given course.

A sailing craft's motive system comprises one or more sails, supported by spars and rigging, that derive power from the wind and induce reactive force from the underbody of a sailboat or the running gear of an ice boat or land craft. Depending on the angle of attack of a set of sails with respect to the apparent wind, each sail is providing motive force to the sailing craft either from lift-dominant attached flow or drag-dominant separated flow. Additionally, sails may interact with one another to create forces that are different from the sum of the individual contributions each sail, when used alone. 041b061a72