STABILITY^ PROPULSION, AND SEA-GOING QUALITIES OF SHIPS. 11 



EESISTANCE. 



Total Resistance. 



The question of resistance may be treated in two ways, — either in gross, 

 as regarding the power required to drive a vessel of certain form and dimen- 

 sions at a specified rate ; or in detail, as regarding the exact way in which 

 the vessel and the propeller act and react upon the water which they disturb. 

 Hitherto there has been but little connexion established between the pheno- 

 mena of detail and the general result, the former not being understood with 

 any reasonable degree of certainty, and the latter also being far from settled 

 with precision. 



The variable elements which go to make resistance what it is are chiefly 

 velocity, form, condition of surface, and absolute dimension. The effect of 

 form is as varied as the number of forms which can be given to a floating 

 body. As regards dimension, assuming the forms te be geometrically the 

 same, it has been found that vessels of different absolute size do not corre- 

 spond in the degree of resistance which they encounter, whether in smooth 

 water or in waves. It will also be seen that the absolute length of a ship, 

 considered irrespectively of breadth or depth, has a direct influence on the 

 resistance. 



As regards velocity, it is usual to assume, in books on hydrodynamics, that 

 the resistance of water varies as the square of the speed. For the purposes 

 of naval architecture, this can only be taken to be roughly true under certain 

 limiting conditions, beyond which the law of the squares deviates widely 

 from the observed facts. It appears to be probable that this increase, as the 

 square of the speed, is rather a minimum than a general rule of increase, 

 and that such a minimum is only attained by ships of good form, and of a 

 length which is a certain function of the speed. The vague words good form 

 are used designedly, it being still i;ncertain what the best form may be, and 

 what extent of deviation from it takes the vessel out of its operation-. When 

 the vessel is shorter than a certain limit of length depending on the velocity, 

 the resistance seems to increase more rapidly than the square, and the power 

 needed to drive the ship Consequently increases faster than the cube of the 

 velocity. 



It may save confusion to remark that the measure of resistance is referred 

 to a unit of distance, yvhilc j^oiver is referred to a unit of time. For any law 

 of resistance, therefore, the power varies as the product of the resistance and 

 speed, and where the velocity varies we have simplj- to use the corresponding 

 integral formula. 



As already remarked, the leading formuhe of the resistance of water are 



RaV^HPaEVaV', 



the latter being the strictly necessary consequence of the former. There is 

 but little disagreement among- writers up to this point. But the moment we 

 attempt either to assign values to the constants of the equations which they 

 imply, or to introduce the corrections depending on the complex phenomena, 

 which always, more or less, mask the mere question of fluid resistance, we 

 find vei-y little agreement. 



The chief elements of the resistance of water to a body moving through it 

 are: — 



(1 ) The direct head-resistance due to the work of thrusting the water to 

 the right and left, with or without vertical motion, in order to make way 

 for the body to pass. 



