Bernoulli’s Principle of sailing ship

Bernoulli’s Principle: Bernoulli’s Principle states that for an inviscid flow, an increase in the speed of the fluid occurs at the same time as a decrease in pressure or a decrease in the fluid's potential energy. This can be derived from the principle of conservation of energy. This states that in a steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Meaning, if pressure increases in one area, it must decrease in another in order to maintain that constant overall sum. Fluid particles (like in a liquid or a gas) are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.

Inviscid: In fluid dynamics there are problems that are easily solved by using the simplifying assumption of an ideal fluid that has no viscosity. The flow of a fluid that is assumed to have no viscosity is called inviscid flow. The flow of fluids with low values of viscosity agrees closely with inviscid flow everywhere except close to the fluid boundary where the boundary layer plays a significant role.

Viscosity: the resistance of a fluid (liquid or gas). In everyday terms, viscosity is “thickness.” Thus, Bernoulli’s principle is effectively applied to water and air (which have a low viscosity and are assumed in calculations to be “inviscid,” but could not be used to navigate a sea of honey.

Lift force: A fluid or gas flowing past the surface of a body exerts a surface force on it. Lift is defined to be the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is defined to be the component of the surface force parallel to the flow direction.

Airfoil: An airfoil is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section.

Math

Bernoulli developed his principle from his observations on liquids, and his equation is applicable only to incompressible fluids, and compressible fluids at very low speeds (perhaps up to 1/3 of the sound speed in the fluid). It is possible to use the fundamental principles of physics to develop similar equations applicable to compressible fluids, like air. In engineering situations, elevations are generally small compared to the size of the Earth, and the time scales of fluid flow are small enough to consider the equation of state as adiabatic, meaning there is no heat transfer with the environment to take into account.

Tacking

Tacking or coming about is a sailing maneuver by which a sailing vessel turns its bow (the front of the boat) through the wind so that the direction from which the wind blows changes from one side to the other. For example, if a vessel is sailing on a starboard (right side of the boat) tack with the wind blowing from the right side and tacks, it will end up on a port (left side of the boat) tack with the wind blowing from the left side. See the image below; the red arrow indicates the wind direction. In practice, the sails are set at angle of 45° to the wind for conventional sailboats and the tacking course is kept as short as possible before a new tack is set in.

Thus when a ship is tacking, it is moving both upwind and across the wind.

Diagram: Tacking from starboard tack to port tack. ① on starboard tack, ② turning to windward (towards the wind) to begin the tacking maneuver or "preparing to come about",③ headed into the wind where momentum carries the vessel forward,④ powering up on the new port tack by sheeting in the mainsail,[F1]⑤ on port tack.

Faster than the wind? Due to Bernoulli’s Principle, how the force of the wind acts on the sails to create a higher pressure on the front of the sail than the pressure inside the sails, boats sailing at 45 degree angles into the wind can actually sail at a faster speed than the wind.

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