Naval Architecture and Ship Building 127 



originally a civil engineer associated with Brunei and Scott Russell in 

 the days of the Great Eastern, whose ideas were taken up by the British 

 Admiralty about 1870. Upon William Froude's death in 1876, his 

 mantle fell upon his son, Mr. R. E. Froude, who continued and expanded 

 his father's work. The elder Froude's outstanding achievem.ent was the 

 demonstration of the reasonable accuracy of his "Law of Comparison," 

 commonly called by naval architects "Froude's Law," by which, from the 

 resistance of a sm.all but accurate model of a ship, towed at lov/ speed, we 

 can closely estimate the resistance of the full-sized ship at her actual 

 speed. Frolide's Law is a particular case of the general law of mechanical 

 similitude which seems to have been first enuhciated by Newton and 

 recognized in the last century by French mathematicians. Mr. Froude 

 seems to have been the first to obtain practical results from it. 



The fundamental principles of Froude's method are very simple. 

 He divides the resistance of a ship moving through the water into two 

 portions- — first, that due to the friction of the water upon the surface, 

 and second, the residuary or remaining resistance due to the formation 

 of the waves and other disturbances in the water, caused by the ship's 

 passage. To determine the frictional resistance, Froude made a number 

 of experiments with plane surfaces of various lengths towed at various 

 speeds, and his results are still standard, although they did not cover as 

 wide a field as would be desirable. It is to the residuary resistance — a 

 minor factor for low-speed vessels, but a major factor for vessels making 

 high speed — that Froude's Law of Comparison applies. 



Suppose we have a 500-ft. vessel which we wish to drive at 30 knots, 

 and make an accurate model of the hull 20 feet long, the ratio of dimen- 

 sions being as 20 to 500, or 1 to 25. We tow a model at what we call a 

 "corresponding speed" to the speed of the full-size ship, the correspond- 

 ing speed being as the square root of the ratios of the linear dimensions, 

 in this case as the square root of 25, or as 5 to 1, so we tow the 20-ft. 

 model at 6 knots, or one-fifth of the 30-knot speed for the full size ship 

 and determine its residuary resistance by deducting from the total the 

 frictional resistance calculated from Froude's coef^cients. This resi- 

 duary resistance needs simply to be multiplied by the ratio of the dis- 

 placements to determine the residuary resistance, at 30 knots, of the full- 

 sized ship. In this case the linear ratio being 25, the displacements are 

 in the ratio of the cube of 25, or 15,625, so we multiply the residuary 

 resistance of the model at 6 knots by 15,625 and obtain the residury 

 resistance of the 500-ft. ship at 30 knots. 



Froude's methods have been applied to the problem of the propeller 

 with great success. But here we find a partial failure, not of Froude's 

 Law, but of our ability to properly apply it. Strictly speaking, the 



