Forces on sails

Similar principles in a rotating frame of reference apply to windmill sails and wind turbine blades, which are also wind-driven.

Kites also power certain sailing craft, but do not employ a mast to support the airfoil and are beyond the scope of this article.

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 behind the sail, lift diminishes and drag increases as the predominant component of propulsion.

Pressure differences result from the normal force per unit area on the sail from the air passing around it.

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.

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.

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.).

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.

The three dimensional vector relationship for net aerodynamic force with respect to apparent wind (VA) is:[8] Likewise, net aerodynamic force may be decomposed into the three translational directions with respect to a boat's course over the surface: surge (forward/astern), sway (starboard/port—relevant to leeway), and heave (up/down).

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.

[15] Sailing hydrofoils also substantially reduce forward friction with an underwater foil that lifts the vessel free of the water.

[16] Sailing craft with low forward resistance can achieve high velocities with respect to the wind velocity:[17] 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.

[8] In stasis, heeling moment from the wind and righting moment from the boat's heel force (FH ) and its opposing hydrodynamic lift force on hull (Fl ), separated by a distance (h = "heeling arm"), versus its hydrostatic displacement weight (W ) and its opposing buoyancy force (Δ), separated by a distance (b = "righting arm") are in balance:[8] Sails come in a wide variety of configurations that are designed to match the capabilities of the sailing craft to be powered by them.

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.

Fossati presents polar diagrams that relate coefficients of lift and drag for different angles of attack[8] based on the work of Gustave Eiffel, who pioneered wind tunnel experiments on airfoils, which he published in 1910.

[30] They show that, as aspect ratio decreases, maximum lift shifts further towards increased drag (rightwards in the diagram).

If the lift and drag coefficients (CL and CD) for a sail at a specified angle of attack are known, then the lift (L) and drag (D) forces produced can be determined, using the following equations, which vary as the square of apparent wind speed (VA ):[31][32] Garrett demonstrates how those diagrams translate into lift and drag, for a given sail, on different points of sail, in diagrams similar to these:[33] In these diagrams the direction of travel changes with respect to the apparent wind (VA), which is constant for the purpose of illustration.

Constant VA in these examples means that either VT or VB varies with point of sail; this allows the same polar diagram to be used for comparison with the same conversion of coefficients into units of force (in this case Newtons).

Displacement sailboats exhibit a change in what course has the best velocity made good (VMG), depending on windspeed.

Arvel Gentry demonstrated in his series of articles published in "Best of sail trim" published in 1977 (and later reported and republished in summary in 1981) that the genoa and the mainsail interact in a symbiotic manner, owing to the circulation of air between them slowing down in the gap between the two sails (contrary to traditional explanations), which prevents separation of flow along the mainsail.

Likewise, the presence of the mainsail causes the stagnation line on the jib to be shifted aft and allows the boat to point closer to the wind, owing to higher leeward velocities of the air over both sails.

The total length around the outside has also increased and the difference in air speed between windward and leeward sides of the two sails is greater, resulting in more lift.

The use of battens allows a sail have an arc of material on the leech, beyond a line drawn from the head to the clew, called the roach.

This formula demonstrates that a sail's induced drag coefficient decreases with increased aspect ratio.

[41] Staysails and sails attached to a mast (e.g. a mainsail) have different, but similar controls to achieve draft depth and position.

On a staysail, tightening the luff with the halyard helps flatten the sail and adjusts the position of maximum draft.

[44] Traditional displacement sailboats may at times have optimum VMG courses close to downwind; for these the dominant force on sails is from drag.

Often simplifying assumptions are employed when making design calculations, including: a flat travel surface—water, ice or land, constant wind velocity and unchanging sail adjustment.