- 



SAIL 



SAILINGS. 



osed to be known, the 

 t be found. If x M D 



. the ratio of A' to A" being IU| 

 nine of E K D, that it, the ship's lee-way, mi 

 45* and the ratio of A" to A' be assumed to be a 13 to I, the lee- 

 way wiU be found tobeWffjandifmDa 80', the lee-way will be 

 20 <'. Rot experiment alone can determine this element, lor, with 

 equal rclocitiw and equal quantitiea of nil, it varies in difleront ships ; 

 and, in the aune aUip, with the Telocity, and the deposition and 

 quantity of the ail 



x v reprcMOt the Telocity of the M\> in the direction it r. ; then 

 H H the diagonal of the parallelogram w N, will represent the efficient 

 y ofUie wind in that direction, w u being the true direction of 

 the Telocity; and letting fall on YZ the perpendicular cz, this last 

 line will represent the velocity perpendicularly to the nail. Therefore 

 the force of the wind in thu Amman will be proportional to wl'; 

 then drawing <t<t parallel to M B, to meet * Q drawn through z perpen- 

 dicularly to M E and w Q, we have x r g equal to the complement of 

 1MB, and consequently r z 1 being resolved in the direction M E or ir q, 

 becomei i- coa. z r Q, or tr x sin. z >i E. But w z varie* an sin. 

 ^ r M z ; therefore the force of the wind to impel the ahip in the 

 direction M E U proportional to sin'. tent ain. ZMK; and the force of 

 impuUe being proportional to the aquare of tlie velocity produced by 

 it, it follows that tli- velocity of the i-hip will vary with sin. ir M / N ' 

 in. z M E. Now making the differential of thin expreaaion equal t 

 considering r M E a* con-tint and z u E as v.iriable, it will be found 

 that thin product U a maximum when /_ tc x E U BO divided that tm. 

 ic MI : tan. z M E : : 2 : 1 . or that sin. ( ir M z - /. u E) - } ain. tea K. 



In Maclurin'i ' Fluxions' (art. 912) there ia given an investigation of 

 the angle w 11 z, between the true direction of the wind and the plane 

 of the sail, when the Telocity of the ship's motion in M K is a maximum. 

 The general expression is complex, but wheu the direction of the wind 

 is perpendicular to the ship's course we have tan. w M z = 



s j -2 + " ^ | + | ; v' being the velocity of the ship and v that 



of the wind. 



Therefore, if the Telocity of the ship were very small, we should 

 have tan. w M z = v 2 nearly, or w M z 54 44' nearly. But, on 

 nuking v' equal to |, 4, and ^ of v, we obtain for Z.v>*z the several 

 corresponding values 61 27', 68 26', and 66 58'. It may be observed 

 .lino that, if both ^ z u E and v are given, the Telocity of the bhip will 

 be a maximum when the angle w z is a right angle, or when the sails 

 are perpendicular to the true direction of the wind. 



In the same work (art. SI 17) there is given the investigation of an 

 equation from which may be determined the angle z M K. between the 

 plane of the sail and the line of the ship's motion when the velocity is 

 a maximum ; and from that equation it is inferred (art. 919) that, if 

 the wind is perpendicular to the sail, the velocity is the greatest 

 (pmvidr.l tin- velocity of the ship before the wind be not leas than 

 one-third of the velocity of the wind) when sin. z M E : radius : : 



(v 1)^ : 1-5874; the velocity of the hip Iwing expressed by 

 unity, and v, the true velocity of the wind, by a multiple of that 

 - may also be inferred from the same equation, that if 

 the velocity of "the wiud be such as to cause the velocity of the 

 ship to be greater than one-third of itself, the ship will sail faster 

 when the course is oblique to the wiud than when coincident with 



The force of the wind, which is denoted by r. A. to U J sin.*, ir M z sin. 

 x M E, being made equal to r'. A', v'' (which will express the resistance 

 of the water, if A' represent the area of the immersed section of the 

 ahip perpendicularly to u E), the value of v', the velocity of the ship, 

 might from thence be obtained ; and from the expression of th.it 

 value it may be seen that, while the other terms remain the some, the 

 y of the ship varies with the relative velocity of the wind 

 and ship, with the sine of its inclination to the plane of the sail, 

 and with the square root of the area of the sail. Hence also, when 

 the Telocity of the wind and both the area and position of the sail 

 arc constant, the velocity of the ship varies with sin. u z ; that 

 it, with the sine of the angle made by the apparent direction of the 

 wind with the plane of the sail. It may be inferred from the 

 general equation, that, by sufficiently increasing A and the angle 

 tcnz, the Telocity (\') of the ship may be made to exceed Kill, which 

 ia that of the wind. 



If it were required to find the course of the ship and the position of 

 the sails, so that the ship might recede most rapidly from any point of 

 danger, as from a lee-coast situated, for example, in the position 

 indicated by v'r", at right angles to MM. the direction of the wind; 

 we must imagine M r to be drawn parallel to M' r', that is, 

 dicular to v M. Then, the Telocity of the ship in the direction M K 

 being represented by sin. VMS y sin. Z M E, let this velocity be 

 resolved into the direction perpendicular to Mr; that U, let it be 

 multiplied by sin. r. M p : the ship will recede most rapidly from u' i' 

 when the expreanou tin. WMZ. sin. EMPVsuiZMlis a maximum. 

 On making the differential of this expression equal to zero, we shall 

 find that the velocity perpendicularly to M r is the greatest when 

 ^ ic u I- is divided *> that the tangents of the angles v u z, z u K, and 

 K M P are to one another as the numbers 2, 1, and 2. If the velocity 

 of the ship I * very small, we shall have \r 11 K, or its equal z M r, = 

 54* 44' nearly; and ^ irM z = 36 10' nearly. And since receding at 



right angles from a line u' r', when that line is perpendicular to the 

 direction of the wind, is an advance towards the wiud ; it follows that 

 the above value of ton/ will indicate the position which the sail 

 should have with respect to the wind, in order that the ship may get 

 to wmdw.iid with the greatest possible Telocity. If th. 



P be taken into consideration, the angles w M K and ir M / will, tut 

 I* modified by the relation between the velocities of the ship 

 and wind. 



the lee-way, which a ship always makes when her soils are 

 oblique to the direction of the wind, destroys the equality of the 

 reaction of the water which would take place on the t-.vo I... us it her 

 movement were in the direction of her keel, and gives rise to an excess 

 of pressure against the lee-bow ; it follows that in these cii 

 the ship's head is constantly forced to windward, and that the tendency 

 of the ship to turn on the axis of the rotation is so much greater as 

 the bows are more acute. To oppose, in some measure, thu ten- 

 the quantity of sail in front of the centre of rotation, is greater than 

 that which is behind it ; but, notwithstanding such dis|>ositioii, it 

 always requires some movement of the rudder to complete the counter- 

 action. 



SAI L-M AK IXC. The canvas used for sails is a very stout material, 

 woven in Kngland or Scotland from Hussion hemp, and purchased in 

 the form of rolls called Mt, each bolt containing about 40 va 

 canvas 24 inches wide. There, are six or seven different qual 

 this canvas, according to the size and position of the sail to I , made ; 

 and each quality has a [articular number attached to it, and must 

 have a certain weight per square foot. Thus, in the Koyal > 

 bolt of No. 1 canvas, containing 38 yards, must weigh 44 llw. ; whereas 

 No. 7 weighs only about half as much: the intermediate nu 

 having intermediate weights. 



As the canvas is only two feet wide, many breadths are required to 

 form a large sail The mainsail of an East Indian inn contains nearly 

 700 yards of canvas; while the whole suit of sails for such a ship 

 requires as much as 9000 yards. As the sails vary much in shape, 

 considerable tact is required in cutting up the canvas so as to 

 waste. The art of the sail maker consists not only in seaming up thu 

 numerous breadths, so as to give the requisite dimensions to ti 

 but also in strengthening the Kail by .-vwing rope to its edges. The 

 seaming and sewing are effected with large three-sided 

 seven or eight different kinds, which are threaded with sowing twine 

 having from 200 to 400 fathoms to the Ib. The skeins of twine 

 previous to being used are dipped into a trough, containing melted tir, 

 grease, and oil, which is afterwards dried. The sail-maker has a 

 thumb-stall and a palm-thimble, for protecting his right hand. His 

 stitches have a regulated degree of closeness, on which his rate of 

 payment in part depends ; there are usually about 100 stitches in a 

 yard. The overlapping of the breadths is an inch or an inch and a 

 half. Besides the seaming, sundry small pieces of canvas are stitched 

 to the sail to strengthen it in various directions ; and the edge-rone or 

 bolt-rope is sewn on with great firmness. So skilfully is the canvas 

 marked out and cut up by a master sail-maker, that in the 9000 yards 

 for the forty sails of a large ship, there will not be more than tl 

 four yards actually wasted. 



The patented ill 1844 by Mr. Archibald Trail are mad.- 



in the usual manner, but are subsequently strengthened by sewing 

 to their surface a number of canvas bands about an inch > 

 with cords woven in them, such bands being secured at their end* 

 into the bolt-ropes, or cords forming the boundaries of tli. 

 and carried diagonally across the surface of the sail at an an 

 45 with the seams, and at a distance of about three feet from 

 other. Two sets of bands are used, crossing the sail in opposite 

 directions, one set being attached oil each side of the canvas. l!y 

 this simple contrivance the strain is so equalised as to render tearing 

 less probable than with on ordinary sail; while, if any injury be 

 inflicted, the rent is confined within the narrow limita of one of the 

 diamond-shaped comportments into which the Bail is divided by the 

 protecting land-. 



SAILINGS; or THE SAILINGS. The various modes'in which the 

 calculations of a ship's true course are conducted, have already, mid. r 

 the : head K i AT SKA, been referred to individually, as 



forming part of a seaman's "day's work," or dead reckin,in ; / as it is 

 called ; distinctive of such portions of his work as depend on ol 

 tion of the heavenly bodies. In this article it is proposed to review 

 the peculiarities of the soilings with reference to the great pi 

 .>f tli.- accurate navigation of the surface of a sphere. 



i the word NAVIGATION the subject has been treated rather as 

 th.' pi-ai-lice of a general system ; and its details hovo been partly re- 

 ferred to under the terms COM > 



LOXOITI UK AND LATITUDE, &c. It remains then to treat of the. 

 relative values of the various means of estimating a ship's true position 

 by means of certain operations called " sailings. " 



In considering first the nature of the most simple lot -in of naviga- 

 tion, namely, plane sailing, but which is only available for 

 spaces on the earth's surface and in low latitudes, the following dia- 

 gram will assist. 



Suppose for example, a ship bound to a jmrt bearing true N.AV., 

 distance 80 miles or knots. Her average general velocity to be 8 

 knots per hour. A W.N.W current to be setting at i! 



