RUDDER. 



its diftance from the top, or to its depth under water. The 

 back, or inner part of it, which joins to the ftern-poft, is 

 diminifhed into the farm of a wedge through its whole 

 length* fo as that the rudder may be the more eafily turned 

 from one fide to the other, where it makes an obtufe angle 

 with the keel. The hinges, which are bolted round the 

 ftern-polt to the after-extremity of the (hip, are called 

 googings, and are fumifhed with a large hole on the after-part 

 of the item-poll. The other parts of the hinges, which are 

 bolted to the back of thi_- rudder, are called pintles, being 

 ftrong cylindrical pins, which enter into the googings, and 

 reft upon them. The length and thicknefs of the rudder are 

 nearly equal to thofe of the itern-pott. The rudder is 

 turned upon its hinges, by means of a long bar of timber, 

 called the tiller, which enters nearly in an horizontal direc- 

 tion into the fhip, palling under the upper or middle deck 

 tranfom ; and its operation is diredted by the tiller-rope, 

 which in large veffels is wound about a wheel. (See 

 Tiller.) The power of the rudder is reducible to that of 

 the lever, and the oblique aftion of the water upon it is to 

 be determined by the refolution of forces. 



In order to explain the aftion of the rudder on the fhip, 

 it fhould be coniidered that if, inflead of leaving the rudder 

 exactly in a right line with the keel, fo as to be a kind of 

 prolongation of it, it be turned to one fide or the other, as 

 BD (Plate IV. Navigation, Jig. 4.), it receives an imme- 

 diate impulfe from the water, which glides along the (hip's 

 bottom, in running aft from A to B ; and this fluid impels 

 it towards the oppofite fide, while it continues in that fitua- 

 tion, fo that the Item, to which the rudder is confined, re- 

 ceives the fame movement ; and the (hip receiving an impulfe 

 fideways, her ftern turns accordingly from B to b, on any 

 point whatever C, while her head pafles from A to a. It 

 muft be obterved, that the water lh-ikes the rudder ob- 

 liquely, and only with that part of its motion which adts ac- 

 cording to the fine ot incidence, in impelling it in the direc- 

 tion N P, with a force which depends not only on the rapi- 

 dity of failing, but alfo on the greatnefs of the fine of inci- 

 dence ; a force which is confequently in the compound ratio 

 of the fquare of the greater or leis velocity of the fhip's 

 motion, and of the fquare of the larger or fmaller fine of 

 incidence, which depends upon various circumftances. So 

 that, if the veflel runs three or four times more fwiftly, the 

 abfolute fhock of the water upon the rudder will be nine or 

 fixteen times (tronger under the fame angle of incidence, and 

 will be augmented in a greater proportion, if the fine of in- 

 cidence be increafed. This impuliion, or, what is the fame, 

 the power of the helm, is always very feeble, when it is 

 compared with the whole weight of the veflel ; but it adts 

 with a very long arm of a lever, which occafions it to work 

 very advantagcotifly in turning the fhip ; tor the helm is 

 fixed at a very j^reat diftance from the centre of gravity G, 

 as well as from the point C, upon which the fhip is lup- 

 pofed to turn, with refpedl to the point of percuffion B : 

 and if the direction P N ot the impreflion of the water upon 

 the rudder be prolonged, it is evident that it will pafs per- 

 pendicularly at the point*R, will.' 1 'litre 

 of gravity G ; therefore the abfolute effort of the water is 

 very powerful. It is not therefore furprifinr, that this 

 machine imprefTes the fhip with n CO 

 movement, by forcing the ftern from B to b, and 

 from A to a, and even much farther, when the velocity of 

 the fhip is preferred ; becaufe the effort of the helm always 

 keeps pace with the rapidity of the fhip'-; way. 



Amongft all the obliquities which may be given to the 

 rudder, there is one fituation which is more favourable than 



any of the others, to make it produce with more rapidity 

 the effedt of turning the fhip, in order to change her courfe. 

 To be convinced of this, we have only to confider that, if 

 the obtufe angle A BD (Jig. 4.) were to be leflened, the 

 impulfe of the water on the rudder would augment, at the 

 fame time that it would more oppofe the failing of the (hip, 

 fince the angle of incidence would be more open, and would 

 prelent a greater turface to the fhock of the water, by op- 

 pofing its paflacrc more perpendicularly : but then the direc- 

 tion N P of the effort of the helm upon the fhip would pafs 

 at a fmaller diftance from the centre of gravity G towards 

 R, and would lefs approach the perpendicular N L ; ac- 

 cording to which, it is abfolutely necefl'ary that the power 

 fhould act with greater effedt to turn the (hip. Therefore, 

 it is evident, that, if the obtufe angle A B D were too much 

 leflened, the greater fhock of the water could not counter- 

 balance the lois occafioned by the diftance between the di- 

 rection NP and NL, or by the great obliquity which 

 would be given to the fame direction N P of the abfolute 

 effort of the helm with the keel A B. If, on the other 

 hand, the angle A B D were made more obtufe, the direc- 

 tion N P of the effort of the rudder would become more ad- 

 vantageous to turn the (hip, fince it would approach more 

 the perpendicular N L, and fince the prolongation of N P 

 would augment G R, by palling at a greater diftance from 

 the centre of gravity G. But the rudder would then be 

 (truck too obliquely ; for the angle of incidence would be 

 more acute ; fo that it would only prefent a fmall part of 

 its breadth to the fhock of the water, and would of courfe 

 receive but a faint impulfion. All this proves that the 

 greateft diftance G R from the centre of gravity G will 

 not counterbalance the too great obliquity of the fhock of 

 the water. Whence it mult be concluded, that when the 

 water ftrikes the rudder too obliquely, or too perpendi- 

 cularly, a great deal of the impulfion, or of the eftedt it 

 fhould produce, is loft. Therefore, between thefe two ex- 

 tremes, there is a middle pofition, which muft be the mod 

 favourable. 



The diagonal N P of the redtangle IL (Jig. 4.) rcpre- 

 fents the abfolute direction of the effort of the water upon 

 the rudder : N I expreffes the portion of this effort which 

 oppofes the fhip's head-way, or which forces her a-flern in 

 the direction of the keel. It is eafy to perceive that this 

 portion N I of the whole power of the helm contributes 

 little to turn the veflel ; for, if I N were prolonged, it 

 would be ieen that its direction pafles at a very fmall dif- 

 tance G V from the centre of gravity G, and that the arm 

 of the lever B N = G V, to which the force is as it were 

 affixed, is at molt equal only to one half of the breadth of 

 the rudder. But it is not fo with refpedi to the relative 

 force N L, which adts perpendicularly to the keel. If the 

 firlt force, N 1, is almoft ufelefs, and even hurtful, by re- 

 tarding the velocity ; the fecond, N L, is capable of a verj 

 great effedt, fince it is applied at a great diftance froil 

 centre oi gravity G of the fhip, and acts on the :'rm of a 

 lever G E, which is very long. Thus it appears, t] 

 between the two effedts NL and N I, which refult from 

 the abfolute effort N P, there is o.i>- which is always op- 

 pofing the fhip's head-way, contributing but little, tl 

 fore, to the motion of her turning; wlullt the Other al 

 produces that movement of evolution, without retarding bei 

 ■-. 



As to the mod advantageous angle made by the helm, 

 with the line prolonged from the keel, geometricius h 

 fixed it at 54° 44' (;. 1 .m :», Mi.i bai 11 



Windmill.) But it has been faiJ, that, in determining 

 4 R 2 



