66 



problem of Interaction Is concerned, a suitable "model" for the propeller is 

 furnished by a sink distribution over its disc and for greater distances even 

 by a single sink only. The "input" is given by 



Q = AvG [30] 



where 9 is the ratio of the slip stream to the propeller speed, and A the pro- 

 peller disc area . Denoting the flux through the propeller disc by Q, the 

 thrust is written 



T = pQvd +|) [31] 



Prom Legally' s formula a force of attraction is obtained between the hull and 

 the working propeller, since the afterbody represents a sink system which is 

 closer to the propeller sink than the positive forebody system. The internal 

 force is the thrust deduction or resistance augmentation in an ideal fluid. 

 One can further compute the wave resistance due to the working propeller alone. 

 Dickmann found that for normal conditions of depth of immersion and loading 

 factor this resistance is a small fraction of the thrust, say of the order of! 

 percent; it depends on a Froude number v/]^h (h immersion) and can reach great- 

 er values for high loading factors and small immersions. The interference be- 

 tween ship and propeller waves causes more important effects. 



Following F. Horn-'-^^ the propulsive efficiency depends on the posi- 

 tion of the propeller relative to the wave created by the hull; in a wave 

 crest the orbital motion is directed horizontally forward, thus generating a 

 favorable positive wake, while in a trough conditions are just the opposite. 

 Dickmann^'''"*' '■'■•'■ has proved Horn's reasoning in a rigorous manner by means of 

 wave theory; he has further shown that beautiful experiments by Yamagata sup- 

 port his conclusions. In the light of these ideas wave patterns at the loca- 

 tion of the propellers should be more carefully studied. 



Thus, the theory developed by Dickmann has succeeded in revealing 

 the mystery which for a long time enveloped the intricate problem of inter- 

 action between hull and propeller; but one is far from a complete quantitative 

 solution. We may note some facts where no complete agreement between theory 

 and experiment has been reached. 



The thrust deduction (contrary to the wake) should be fairly inde- 

 pendent of wave phenomena or, otherwise expressed, the part of the thrust de- 

 duction coefficient due to waves t isvery small. Some experiments, however, 

 indicate that the thrust deduction can be influenced by variations in the en- 

 trance of a hull which to our knowledge affect measurably only the wave 



