SECOND-ORDER CONTRIBUTIONS 



TO SHIP WAVES AND 



WAVE RESISTANCE 



K. W. H. Eggers 



Institut fur Schiffbau der Universitdt Hamburg 



Hamburg, Germany 



The ONR-NSF Symposium on Wave Resistance Theory held in Ann Arbor in 

 1963 made clear that current research is focused around (a) determination of 

 quantities from the wave pattern representative for wave resistance, (b) formal 

 and semiempirical corrections to the classical linearized theory, and (c) more 

 refined techniques for optimizing ship forms within linear theory. In the pres- 

 ent paper I shall report on work done since then which might provide material 

 to reinforce progress in any of these directions. The "piece de resistance" of 

 this contribution is the gradual evolution of a computer program which in a 

 rationalized way gives the basic information of flow and wave components due to 

 typical singularities (as discrete doublets, doublet struts, continuous parabolic 

 distributions on submerged lines, infinite and truncated vertical planes) all 

 within linearized approach. This information lends itself readily for application 

 to item (a). Any method proposed for determination of energy flow from char- 

 acteristics of the flow, in particular from the geometry of wave pattern, can be 

 tested for accuracy and for consistency on such a theoretical wave field avail- 

 able numerically before entering into expensive experimental work which pro- 

 vides in general too little reliable information on optimal choice of region where 

 to perform measurements. The overwhelming part of the methods proposed for 

 (a) is implicitly based on validity of certain asymptotic representations for the 

 wave pattern. Only numerical calculations can tell what distances are already 

 large enough, especially regarding decay of the so-called "local flow compo- 

 nents" in order that such representations may be applied. 



For (b), the theories of wave resistance used nowadays are of second order, 

 based on linearized flow models. For calculation of wave resistance, only a 

 far-field component of this flow has to be known explicitly; for any consistent 

 approach to third-order resistance contributions, however, the knowledge of the 

 entire first-order flow is essential. Aside from some semiempirical approaches 

 to alternate formulations of linear theory, which we shall submit to some criti- 

 cal examination, and aside from an indirect approach as successfully carried 

 out by Kajitani recently, the tool for a systematic perturbation attack to the 

 higher order flow components has been provided by Wehausen (1-3) in a series 

 of papers starting with that read before this audience in 1956 up to his contri- 

 bution to the Ann Arbor conference. As, however, the step to formulate 



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