ON THE FORCE OF TttE RUDDER, &C* 363 



the sides of the vessel will impel the rudder under the same angle, 

 that is 30 degrees. The part of the rudder under water being 14 

 feet in length and two in breadth, presents a surface of 28 square 

 feet, impelled at an angle of 30 degrees, by a body of water flowing 

 with the velocity of nine feet per second. But the action of such a 

 current, if it impelled a similar surface in a perpendicular direction, 

 would be 2205 pounds, which must be reduced in the ratio of the 

 square of the sine of incidence to that of radius, or in the ratio ^ to 

 one, since the sine of 30 degrees is , radius being one. The effort 

 therefore of the water will be 551 pounds. Such is the force exer- 

 cised perpendicularly on the rudder ; and to find the quantity of 

 this force that acts in a direction perpendicular to the keel, and 

 which makes the vessel turn, nothing is necessary but to multiply 

 the preceding effort by the cosine of the angle of inclination of the 

 rudder to the keel, which in this case is \/4 <> r 0-866, which will 

 give 477 pounds. 



The above computation is made on the old supposition, that the 

 force of the water is diminished in proportion as the square of the 

 sine of the incident angle is less than the square of the radius. But, 

 by more accurate experiments it is found (Dr. Hutton's Math, and 

 Philos. Dictionary, Tab. 3, Resistance), that at an angle of 30 de- 

 grees, the absolute force is diminished only in the ratio of 840 to 

 SJ78 J hence then, the whole force 2205 pounds, reduced in this 

 ratio, comes out 730 pounds, for the effective or perpendicular 

 force on the rudder, to turn it or indeed the ship about, supposing 

 the rudder held or fixed firm in that position. 



But there is one cause which renders this effort more consider- 

 able : the water which floxvs along the sides of the vessel does not 

 move in a direction parallel to the keel, but nearly parallel to the 

 sides themselves, which terminate in a sort of angle at the stern- 

 post, or piece of timber which supports the hinges of the rudder; 

 so that this water bears more directly on the rudder by an angle of 

 about 30 degrees: hence, in the above case, the angle under which 

 the water impels the rudder will be nearly 60 degrees : we must 

 therefore muke this proportion, as the square of radius is to the 

 square of the sine of 60 degrees, or as one is to f; so is 2205 to 

 l653. The force therefore which acts in a direction perpendicular 

 to the keel, is io\53 pounds. Or, by the table in the Dictionary 



