THE WAVE RESISTANCE OP BODIES OP REVOLUTION 



by 

 Georg P. Weinblum, D.Eng. 



ABSTRACT 



Following a brief review of prior work on wave resistance of bodies of revo- 

 lution carried out by Havelock and Weinblum a discussion is presented of the appro- 

 ximate relations between the shape of sectional-area curves and of hydrodynamic 

 irregularity distributions. The latter are expressed by polynomials, which lend them- 

 selves to an evaluation of the basic resistance integrals by computing intermediate 

 integrals. Values of the functions thus obtained are tabulated in an appendix. These 

 functions are then used to calculate the resistance of some simple bodies of revolu- 

 tion. Also investigated is how the resistance is influenced by asymmetry with respect 

 to midship section. Distributions leading to bodies of least wave resistance are cal- 

 culated, assuming rather severe restrictions. A rather complete set of resistance 

 curves is given for an important family of bodies. 



1 . INTRODUCTION 



When a body moves uniformly and rectilinearly in an unbounded 

 liquid the only resistance experienced by it is the viscous drag. Our 

 knowledge as to how this drag depends upon the body form is very limited, 

 but it is well-established that for streamlined, elongated hulls— with which 

 we are only concerned — the drag is roughly proportional to the wetted sur- 

 face and is rather insensitive to reasonable changes in the shape. 1 * The 

 well-known airship form with a rather blunt forebody and finer tail appears 

 to be close to the minimum resistance attainable, although it must be empha- 

 sized that earlier resistance data obtained in wind tunnels at low Reynolds 

 numbers are utterly unreliable. But that there is a slight advantage in 

 introducing some asymmetry with respect to the midship section appears to 

 be unquestioned, at least when larger end-radii are used. Matters become 

 different when a body moves close to the free surface; see Figure 1 . A 

 wave pattern is then produced and therefore a wave resistance arises. The 

 laws governing the wave resistance R are quite different from those valid 



■"■References are listed on page 58. 



"Problems of cavitation are not considered here. 



