PRINCIPLES OF NAVAL ENGINEERING 



Variation of hull resistance at moderate 

 speeds of any well-designed ship is approxi- 

 mately proportional to the square of the speed. 

 The power required to propel a ship is propor- 

 tional to the product of the hull resistance and 

 speed. Therefore, it follows that under steady 

 running conditions, the power required to drive 

 a ship is approximately proportional to the cube 

 of propeller speed. While this relationship is 

 not exact enough for actual design, it does serve 

 as a useful guide for operating the propelling 

 plant. 



Since the power required to drive a ship is 

 approximately proportional to the cube of the 

 propeller speed, 50 percent of full power will 

 drive a ship at about 79.4 percent of the maxi- 

 mum speed attainable when full power is used 

 for propulsion, and only 12.5percent of full power 

 is needed for about 50 percent of maximum speed. 



The relation of speed, torque, and horse- 

 power to ship's resistance and propeller speed 

 under steady running conditions can be expressed 

 in the following equations: 



S = k. X (rpm) 



v2 

 T = k_ x (rpm) 



shp __27rk2_ X (rpm) 

 33,000 



where 



S = ship's speed, in knots 



T = torque required to turn propeller, in 

 foot-pounds 



shp = shaft horsepower 



rpm = propeller revolutions per minute 



k. , k„ 3 proportionality factors 



The proportionality factors depend on many 

 conditions such as displacement, trim, condition 

 of hull and propeller with respect to fouling, 

 depth of water, sea and wind conditions, and the 

 position of the ship. Conditions that increase 

 the resistance of the ship to motion cause kj to 

 be smaller and k2 to be larger. 



In a smooth sea, the proportionality factors 

 k^ and k2 can be considered as being reasonably 

 constant. In rough seas, however, a ship is sub- 

 jected to varying degrees of immersion and wave 



impact which cause these factors to fluctuate 

 over a considerable range. It is to be expected, 

 therefore, that peak loads in excess of the loads 

 required in smooth seas will be imposed on the 

 propulsion plant to maintain the ship's rated 

 speed. Thus, propulsion plants are designed with 

 sufficient reserve power to handle the fluctuating 

 loads that must be expected. 



There is no simple relationship for determin- 

 ing the power required to reverse the propeller 

 when the ship is moving ahead or the power re- 

 quired to turn the propeller ahead when the ship 

 is moving astern. To meet Navy requirements, 

 a ship must be able to reverse from full speed 

 ahead to full speed astern within a prescribed 

 period of time; the propulsion plant of any ship 

 must be designed to furnish sufficient power for 

 meeting the reversing specifications. 



PROPELLERS 



The propelling device most commonly used 

 for naval ships is the screw propeller, so called 

 because it advances through the water in some- 

 what the same way that a screw advances through 

 wood or a bolt advances when it is screwed into 

 a nut. With the screw propeller, as with a screw, 

 the axial distance advanced with each complete 

 revolution is known as the pitch. The path of ad- 

 vance of each propeller blade section is approx- 

 imately helicoidal. 



There is, however, a difference between the 

 way a screw propeller advances and the way a 

 bolt advances in a nut. Since water is not a solid 

 medium, the propeller slips or skids; hence the 

 actual distance advanced in one complete revo- 

 lution is less than the theoretical advance for one 

 complete revolution. The difference between the 

 theoretical and the actual advance per revolution 

 is called the slip . Slip is usually expressed as 

 a ratio of the theoretical advance per revolution 

 (or, in other words, the pitch ) and the actual ad- 

 vance per revolution. Thus, 



Slip ratio 



where 



E = shaft rpm x pitch = engine distance per 

 minute 



A = actual distance advanced per minute 



Screw propellers may be broadly classified 

 as fixed pitch propellers or controllable pitch 

 propellers. The pitch of a fixed pitch propeller 



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