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The pressure on an object in a fluid varies with the depth of that part of the object in the fluid.
B=(P b – P t)A = (ρ fluidgh)A = ρ fluidgV
P b=pressure at bottom
P t=pressure at top
A=area of bottom face
ρ fluid=fluid density
V=volume of fluid displaced by object
(formula from pg. 428, Serway and Jewett)
"The fraction of the volume of a floating object that is below the fluid surface is equal to the ratio of the density of the object to that of the fluid."(p.429, Serway and Jewett)
V fluid/Vobj = ρ obj/ρ fluid
Vobj=volume of the object
ρ obj=density of the object
Buoyancy of the craft is created by the shape of the hull, but also with buoyant materials in specific places. Air tanks, buoyancy bags, and polystyrene blocks are all used to add buoyancy to a boat.
The figure below shows how the buoyant material should be distributed and the effects if it is not.
figure from The Handbook of Sailing
The distrubution of buoyancy is key to having the boat float properly.
Bernoulli's principle is that the air moving past a foil, an object that has one curved side and one flat side, will take longer to move past the curved side than the flat side of the foil. This will cause the flat side to have higher air pressure and to exert a force on the object. The force cause a planes wing to lift and a sail to push a boat. "With the wind pushing on one side of the sails and the water pushing on the other side of the centerboard, the boat moves forward." (p. 35, Dellenbaugh)
The angle at which sailing is important. A 45 degree angle to the wind is the most effective angle.
Wind is what propels a sailing ship so weather has a large impact on the craft. Certain weather conditions are not suitable for sailing or specific crafts.
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Wind is caused by the movement of air due to warming caused by radiation. The sun warms the air. Warm air rises and cool air falls causing a circulation of air in the atmosphere. The radiation from the sun also warms the ocean and the land. The land looses its heat slower than the ocean does and therefore stays warmer longer. An offshore breeze caused by the warm air moving out to take the place the cooler out at sea. "A breeze that's blowing from the shore onto the water (such as a high-pressure wind) is generally oscillating. As you get closer to shore, the wind is puffier and shiftier and the water is smoother."(pg.183, Dellenbaugh)
One of these forces that the water has on the boat is drag. The boat must push through the water moving the water in front of it out of its way. "As the boat picks up speed, she creates waves, and these rather than the surface friction becomes the major part of the drag at higher speeds." (pg.7, Brewer) Sailing ships hull heel, an "athwartship inclination of the vessel" (pg. 208, Brewer),when they are moving faster, which increases drag on the ship. Most of the time the ship is also tipped slightly to the side instead of completely perpendicular to the water. This is due to the angle at which the boat is sailed into the wind ane the force the wind has on the ship. This difference in angle from the vertical also causes more drag on the ship.
Water has the another effect of determining the maximum speed of a ship. "When a boat which does not plane moves, it creates two waves which become further apart the faster the boat moves. At a certain speed, the distance between the wavecrests is close to the waterline length of the boat and the two crests are situated near the ends of the waterline shape of the boat." (pg. 327, Bond)
Now that you now how the boat stays afloat and is propelled through the water you need to be able to maneuver it. Vectors are used in manuevering a sailing ship. Vectors are described by both a magnitude and a direction. In the case of a ship, it is the speed of the ship and the direction the ship is going.
Sailing directly into the wind is difficult if not impossible. The wind is needed to propel the ship forward but a wind directly on the front of the ship will not be caught by the sail. The most efficient angle at which to be sailing into the wind is a 45 degree angle. At times, your destination will be in the same direction that the wind is coming from. To handle this, you will need to tack. Tacking is sailing back and forth at an angle to your destination, instead of taking the direct route to that destination.
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Experienced Sailor, 1995, Alfred A. Knopf, New York
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Dellenbaugh, David and Brad Dellenbaugh, Small Boat
Sailing: A Complete Guide, 1990, Sports Illustrated, New York
Dent, Nicholas, How To Sail: a practical course in boat
handling, 1978, Orbis Publishing Limited, London
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