237 



SAIL. 



SAIL. 



238 



may, by means of the braces, be placed obliquely to the keel. The 

 sails which are attached to the ship's stays, and the sails of boats or 

 email vessels, are generally in a vertical plane passing through the 

 keel ; a certain degree of obliquity to that plane may, however, be 

 given to them at their lower extremities if necessary. Sails are 

 strengthened by ropes, called bolt-ropes, sewn along their edges in order 

 to prevent them from being easily torn by the action of the wind. 



When ii vessel is in still water, the pressure of the wind against the 

 sails overcomes its inertia, and motion takes place in some direction. 

 The motion goes on increasing by the accelerative power of the wind ; 

 but at the end of a certain time the resistance in an opposite direction, 

 both of the air against the sails and hull of the ship, and of the water 

 against the latter, becoming equal to the accelerative power of the 

 wind, the ship acquires a terminal or uniform velocity, and in this 

 state (neglecting the resistance of the air) there may be said to be an 

 equilibrium between the pressure of the wind against the sails and of 

 the water against the vessel. 



The principal problem connected with the motion of vessels on the 

 water has for its object the determination of the relation between the 

 velocities of the wind and of the vessel ; and its solution consists in 

 finding algebraic expressions for those pressures, and making them 

 equal to one another. But many practical difficulties present them- 

 selves in investigating that relation ; for the pressure of the wind is 

 modified by the form which the sail assumes when acted upon, by the 

 obliquity of the wind's direction to the general plane of the sail, and 

 by the interference of one sail with another, by which interference the 

 wind may be partly intercepted, or currents may be produced in 

 directions different from the general direction of the wind. The 

 resistance of the water is also greatly modified by the form of the 

 ship's hull, and by the direction of its motion with respect to the line 

 of the keel. These difficulties cannot be removed; therefore the 

 results of mathematical researches concerning the motion of ships can 

 only be considered as very remote approximations to the rules which 

 I guide the practice of the seaman. And in order to simplify 

 the problem, it is necessary to suppose that the ship is furnished with 

 only one sail, whose area is such that the action of the wind upon it 

 may be equivalent to the efficient action of the wind upon all the sails. 

 The centre relieve, as it is called by foreign writers, or the centre of 

 piessmo or effort, must also be supposed to be at the centre of gravity 

 of the sail. That part of the ship's surface which is resisted by the 

 water must moreover be represented by a plane surface whose area is 

 such that this resistance shall be equivalent to the efficient action of 

 the water on the ship. 



The pressure of the air perpendicularly against a plane surface equal 

 to one square foot is usually estimated at ^lb. avoirdupois, the surface 

 pressrd being at rest, and the wind moving with a velocity equal to 

 one foot per second, or about 0-68 mile per hour ; also the resistance 

 of water against a like surface and moving with an equal velocity is 

 estimated at l'51b. The pressure or resistance, by the laws of hydro- 

 dynamics, varies with the square of the velocity; and, from the reso- 

 lution of forces, it may be shown [AKRODTXAMICS] that the <'' 

 force with which a fluid strikes a plane surface obliquely, when 

 estimated in a direction perpendicular to the plane, varies with the 

 square of the sine of the inclination to the plane. This, how 

 only an approximation for practical purposes, its insufficiency arising 

 ant of allowance for the accumulation of force depending on 

 the shape or curved surface of the sail ; and, from the experiments ol 

 Bossnt, D'Alembert, and Condorcet, it appears to bold good only for 

 inclinations between 60 and 90*. The experiments of Smeaton 

 indicate that the pressures vary nearly with the sine of the inclination 

 when the latter is between 60* and 60 ; at greater inclination* tin 

 pressure 'a some fractional power of the sine, and at very small incli- 

 nations it approaches nearly to the square. But the following formula 

 of braeaton gives the effective velocity very nearly as 



= T tin i < 



From the experiments of Dr. Mutton it is found that at inclination.* 

 between 60* and 90* the pressures vary nearly as the sines of the 

 inclinations. 



In determining the pressure of a fluid against the surface, which is 

 in motion, it roust be observed that, by the laws of the collision o:" 

 bodies, the efficient velocity of impulse is to be expressed not by thi 

 absolute, but by the relative Telocity of the impelling power. Hence 

 when the wind and ship are moving in the same direction, the effectin 

 velocity is the difference, and when they are moving in opposite 

 directions, it is the sum of their several velocities. It must also be 

 observed that the force of the wind and the reaction of the water are 

 to be considered as taking place in horizontal directions, and that tli 

 effective pressure of the wind on a flat sail is in a direction perpen 

 dicular to the plane of the sail, whatever be the position of the latte 

 and the direction of the wind. 



Now when a ship sails before the wind in still water, if we conside 

 the sail as a plane surface at right angles to the keel of the ship am" 



>f the wind ; representing the pressure of the air on 

 square foot, when the velocity is one foot per second, by r, and th 

 pressure of the water on a square foot with an equal velocity by v' 

 also potting T for the velocity of the wind, and v' for that of the ship 



oth being expressed in feet per second ; A for the area of the sail, and 

 ' for that of a vertical section through the immersed part of the ship 

 aken perpendicularly to the keel ; the equation of equilibrium will 

 vidently be 



A. p. (v v') 2 = A', p'. v' 2 ; 



and from this equation v' may be easily found. It follows from the 



same equation that, when the other terms are constant, varies 



v V 



ith V A, or the velocity of the wind in the sail is to the velocity of 

 he ship aa unity ia to the square root of the surface of the sail. _~ 



But while the plane of the sail ia supposed to be perpendicular to 

 he keel of the ship, let the direction, of the wind be oblique to both, 

 and let the force of impulse perpendicularly to the sail be proportional 

 .o the square of the sine of the inclination of the wind to the sail ; 

 hen, if K L be the keel, M the place of the mast, y z the position of the 

 ard, and w' M represent the direction and velocity of the wind, wo 

 hall have w' M. : sin.- w' ir c for the force of impulse with which a particle 

 f air acts on the sail. This value of the impulse is, however, correct 

 nly at the moment before the ship begins to move ; for, let the ship 

 advancing in the direction K. L with a velocity such that the sail 

 moves parallel to itself from M to R, while a particle of air would move 

 Torn w' to M if the sbip were at rest, it will be evident now that a 



flag at M, which, when the ship is at rest, would have its plane in the 

 direction W'M produced, being carried by the motion of the ship from 

 M towards L, would be acted on by the particles of air coming against 

 it, as if it were resisted by forces parallel to M K aud tending from K 

 towards M ; therefore the forces parallel to W'M and it M being i 

 tively proportional to those lines, the flag will by the composition of 

 forces take the direction W'M, the diagonal of the parallelogram W'H. 

 This is the efficient direction of the wind, and ita velocity may bo 

 represented by that diagonal, when that of the wind in its true 

 direction is represented by W'M: consequently the impulse of the wind 

 perpendicularly to the plane of the sail must be represented by r..v. 

 H/M*. sin. 1 K-'MC. By this impulse motion is produced in the ship in 

 the direction of its keel, and the whole expression may be made equal 

 to \'.r'.v'-, the former expression for the resistance of the water. 

 The values of W'M and of M R, that is, v and v', the absolute velocities 

 of the wind and ship, and also the angle L M w' being known, the value 

 of W'M may be computed. 



When the direction of the wind is not coincident with the line of 

 the ship's keel, its power to impel the ship forward will be increased 

 by placing the sail in some oblique position, as v /. In this case let 

 M c, perpendicular to Y z, represent the velocity with which, if not 

 resisted by the water, the ship would move by the action of the wind. 

 Then, by the resolution of motions, letting fall c D perpendicularly on 

 K L, M D and D c will represent the velocities in those directions ; and, 

 in the case of equilibrium between the actions of the wind and water, 

 the resistance of the latter against the side of the ship perpendicularly 

 to the keel will be to that against the bow, parallel to the keel, as c D 

 to D M, or as tang. / o M D to radius. Let A" be the area of a vertical 

 section through tho immersed part of the ship in the direction of the 

 keel, and A', as before, the area of the vertical section perpendicularly 

 to the keel ; also suppose that, in consequence of the reaction of tho 

 water, the ship's motion, instead of being in the direction MC, should 

 be in some other, as M K. Then, V representing the velocity of the 

 ship in this direction, and the resistance of the water being supposed 

 to be proportional to the square of the velocity and square of the sine 

 of the inclination, we have P'.A".V /J sin. 5 E M D for the resistance of the 

 water against the ship's side, and p'.A'.v' 3 cos. 5 EM a for the resistance 

 against the bows. Therefore 



tan. c M D : radius : : A" sin. 1 t: M i; : A' cos. : E M D ; 



