VII 



ON THE DEVELOPMENT OF THE THEORY OF 

 MARINE PROPULSION 



H. W. Lerbs 

 Hamburgische SchifTbau Versuchsanstalt 



An attempt is made in this report to survey the essential results which have 

 been obtained in the problem of hydrodynamics of marine propulsion. In this problem 

 the predominant interest is directed towards the flow and the interaction which arise when 

 a body is propelled in the usual way by means of a stern propeller. The Naval Archi- 

 tect is interested in these phenomena since rules for the most advantageous propulsion 

 of the system may be expected if we are sufficiently able to analyse the flow. A great 

 deal of work has been done to find such rules by means of model testing. It is not 

 intended in this paper to enter into this experimental work but to describe the analytical 

 attempts which have become known in this field. 



It should be mentioned from the beginning that it has not yet been possible to 

 deal with the problem in its full generality since the assumption of a given hull is made. 

 That is, variations of the ship form are not taken into account when establishing the 

 minimum condition for the propulsive power. We then arrive at a partial solution of 

 the problem which essentially means a discussion of questions related to the theory of 

 a wake adapted propeller. The complete problem, that is considering effects from 

 variations of both the hull and the propeller on the power input, is still far from an 

 analytical solution. Only a very first step in this direction is known in literature [17]. 

 Additional restrictions as well as imperfections of the theory will be mentioned later on. 



The paper is divided into 3 parts. In the first one the results of the general 

 propeller theory are reviewed, in the second one the theory of interaction between hull 

 and propeller is briefly discussed. As a synthesis of these two parts the basis of the 

 theory of a wake adapted propeller is developed in the final chapter. New results are 

 not given in the paper. However, it appeared useful to collect the scattered results 

 in order to recognize the stand of the theory which has been achieved. 



I. General Propeller Theory 



The central problem lies in the determination of the potential flow which is 

 related to semi-infinite and symmetrically spaced helical vortex sheets. The sheets 

 may be assumed of being built up by spiral vortex filaments of which both the diameter 

 and the pitch remain constant when going aft. As follows from considerations of 

 energy, this restriction on the shape of the vortex sheets is permissible with so-called 

 "moderately loaded" propellers, that is, with conditions for which second and higher 

 powers of the induced velocity may be neglected. Relative to the radial coordinate no 

 restrictions on the shape of the sheets are imposed, which is an essential point for the 

 following considerations. 



The velocity field of the spiral filaments is determined first and that of the 

 sheets is then obtained by an integration. Two ways are feasible to deduce the field 

 of the filaments, viz., an integration of Laplace's equation or an application of the 



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