TRANSACTIONS OF THE SECTIONS. 257 



avoiding a collision) this mode of supplying power is fault}'. The period in which 

 a complete turn of a steam-ship is eti'ected and the diameter of the circle described 

 are important elements in the handines-s. 



On this subject I abridge from M. Bertin's ' Notice sur la Marine a Vapeur de 

 Guerre et de Commerce, 1876. In tig. 1, Plate XIII., / is the pressure on the 

 rudder O B, and F the resultant of the lateral pressure acting through the ship's 

 centre of lateral resistance and the direct resistance acting on the bows. V is 

 the velocity of the ship in direction G V. Though here the angular velocity- 

 has become uniform, G C perpendicular to G V is the diameter of the circle in 

 which the ship turns. A G V is the angle of turning described in a unit of 

 time while the ship moves through the space V. The moment of resistance of 

 the water to the ship's turning, which is nearly proportional to the square of the 

 angular velocity, is equal to the moments of the two forces/ and F. The sum of 

 the projections of these forces on the line G C is equal to the centripetal force under 



which the circle is described, and therefore to — yrp,' If, then, f and F were 



' g GO ' ' •' 



exactly proportional to ¥'■', and made with the axis O A a constant angle, the 

 length of the radius G C would be independent of the velocities, and the period of 

 a complete turn would vary inversely as V. In actual practice the velocity di- 

 minishes, the lateral resistance which is due to the small lateral velocity decreases 

 more slowly than the direct resistance which is proportional to V-, the angle made 

 by G F with G increases, and the centripetal force decreases more slowly than 

 \'-, and the radius G diminishes. The circles described thus become smaller at 

 smaller velocities. In comparing similar ships of different dimensions, / and F 

 increase as the square, while W increases as the cube of the dimensions. Hence 

 Ct C should increase nearly in the direct ratio of the dimensions. Thus the dia- 

 meter of the circle described by a ship in a complete turn should be about twice 

 that described by a similar ship of half its length. 



The smaller the diameter of the circle in which a ship turns the more handy 

 .'ihe is. Records of the performances of the most handy ships in the English and 

 French navies established five times the length as the limit below which this 

 diameter never falls. Mention has been made of the difficulty felt by naial archi- 

 tects in supplying etiective steering-apparatus in lieu of the limited power available 

 in former days at the tiller. M. Barnes, stalling from the principle that only a 

 given power couid be thus used, made an investigation of the conditions under 

 which this could be most efficiently applied. He established two propositions : — 

 (1) that for the same power to bring over rudders of different breadths to different 

 angles, the breadths should be inversely as the sines of the angles ; and (2) that 

 the efficiency of the rudder under such circumstances varies as the sine of twice 

 the angle. Hence, if a rudder of a certain length could be brought over to 15 deg., 

 a rudder of half its breadth could he brought over by the same force to oO deg., and 

 the efficiency thereby nearly doubled. He recommended subsidiary rudders to be 

 fitted so as to assist the maiu rudder when required. Such ruddeis were tried by 

 Admiral Halsted at Sheerness in 1863, but were found to diminish instead of in- 

 creasing the steering efliciency. This investigation has now little more than an 

 historical interest. It is to be observed that he finds the angle of maximum effi- 

 ciency to be 45 deg., which, however, on stream-line principles, would require to bo 

 reduced to 33 deg. or 34 deg. The law of variation of the resistance which he adopts 

 is that of the square of the sine. If that of the sine alone be introduced, it would 

 seem that the breadths of the rudders should be inversely as the square root of 

 the sines, and the angle of maximum efficiency 35 deg. 10 min., or, practically, 

 30 deg. 



It is often asserted now-a-days that the lower part of the rudder is of no use ; 

 and hence the practice of cutting it away has come into vogue. An experiment, 

 however, made by Mr. Froude, which he kindly couununicated to me, leaves no 

 doubt that this opinion is erroneous. To a model of the new ' Encounter,' 10 ft. 

 fiin. long, was fitted a rudder, consisting of two blades of equal dimensions, one 

 above the other, and tixcd at an angle of 30 deg. They were governed by the 

 same tiller, provided with a graduated arc, to which it could be clamped ; thu.«, 



