Mathematical recreations and essays . perpendicular direction ( to leeward) shall be as large aspossible; and I will assume for the moment that the formerof these resistances may be neglected, and that the latter isso large as to render motion in that direction impossible. Now, as the boat moves forward, the pressure of the airon the front of the sail will tend to stop the motion. As * OziJ,nam, 1803 edition, vol. iii, pp. 359, 367; 1840 edition, pp. 510, 543. CH. V] MECHANICAL RECKEATiONS 99 long as its component normal to the sail is less than thepressure of the wind behind the sail and
Mathematical recreations and essays . perpendicular direction ( to leeward) shall be as large aspossible; and I will assume for the moment that the formerof these resistances may be neglected, and that the latter isso large as to render motion in that direction impossible. Now, as the boat moves forward, the pressure of the airon the front of the sail will tend to stop the motion. As * OziJ,nam, 1803 edition, vol. iii, pp. 359, 367; 1840 edition, pp. 510, 543. CH. V] MECHANICAL RECKEATiONS 99 long as its component normal to the sail is less than thepressure of the wind behind the sail and normal to it, theresultant of the two will be a force behind the sail and normalto it which tends to drive the boat forwards. But as thevelocity of the boat increases, a time will arrive when thepressure of the wind is only just able to balance the resistingforce which is caused by the sail moving throMgh the air. Thevelocity of the boat will not increase beyond this, and themotion will be then what mathematicians describe as In the accompanying figure, let BAR represent the keelof a boat, B being the bow, and let SAL represent the that the wind is blowing in the direction WA witha velocity u; and that this direction makes an angle d withthe keel, angle WAR = 6. Suppose that the sail is set soas to make an angle a with the keel, angle BAS =^ a, andtherefore angle WAL = ^ + a. Suppose finally that v is thevelocity of the boat in the direction AB. I have already shown that the solution of the problemdepends on the relative directions and velocities of the windand the boat; hence to find the result reduce the boat to restby impressing on it a velocity v in the direction BA. Theresultant velocity of v parallel to BA and of u parallel to WAwill be parallel to SL, if v*sina = usin (6-{- a); and in this casethe resultant pressure perpendicular to the sail vanishes. Thus, for steady motion we have v sin a â u sin (0 + a).Hence, whenever sin (^ + a) >
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