A most important application was made by Dickmann to the problem of 

 ship and propeller interaction. ^' ^" '^^ By replacing the latter (only when 

 considering the mutual interaction of the system) by a sink or a sink distri- 

 bution a comprehensive theory of thrust-deduction phenomena was developed. 



Further interesting results can be obtained by applying this method 

 to the calculation of forces and moments due to the motion of a wholly but not 

 too deeply submerged body moving steadily parallel to the free surface; in 

 principle this solution is given when the vertical velocity at any point of 

 the image system representing the body is known. 



U. WAVE RESISTANCE 



Many curves representing wave resistance as a function of Proud e 

 number deduced from theory and experiment have been published; they are char- 

 acterized by "humps" and "hollows" over definite ranges of speed -length ratios 

 due to interference effects of different v/ave systems. The experimental curves 

 reveal a smaller fluctuation than the theoretical because of the influence of 

 viscous forces. 



Various attempts have been made to calculate the wave resistance 

 from the wave profiles; the most valuable proposal is due to R. Guilloton.-'-'' 

 A great difficulty in using wave profiles for resistance computation is the 

 loss in accuracy due to difference errors. This difficulty is increased by 

 the fact that the vertical pressure distribution due to waves does not follow 

 closely the simple exponential law. We shall consider here the wave patterns 

 only with the purpose of obtaining some general ideas about Interference ef- 



90 92 96 



fects. The basic work on this subject is due to Wigley ' ' and 



,T 1 1 67,68,76 



Havelock. 



A distinction must be made between a "wave" and "non-wave" portion 

 of the profile; the latter does not contribute anything to the resistance in 

 an ideal fluid and is, therefore , less important from the present viewpoint. 

 Following Wigley we consider a cylinder (vessel of infinite depth) whose water- 

 line is a parabola with some parallel middle body. 



The wave part of the profile consists of: 



a. Wave systems due to the finite angle of entrance and run (the sys- 

 tems at bow and stem are identical when the angles are equal). 



b. Systems due to the curved parts of entrance and run. 



c. Systems due to the shoulders if these are pronounced. 



However, the definition of such systems is made to a great extent by consider- 

 ations of easy integration, so that different interpretations and divisions 

 are possible. 



