WÄJcfMtll OF THE NAVY

Following a brief reviev of prior work on wave resistance of bodies of revolution carried out by Havelock and Weinblum a discussion is presented of the approximate relations between the shape of sectional-area curves and of hydrodynamic irregularity distributions. The latter are expressed by polynomials, which lend themI 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 revolution. Also investigated is how the resistance is influenced by asymmetry with respect to midship section. Distributions leading to bodies of least wave resistance are calculated, 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 surface and is rather insensitive to reasonable changes in the shape.* 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 emphasized 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 4*&*usM(*tl»i..-<-«n»r ^-wwM.aww»!'TM«»"' ■■ ".■.»■ *«*■»■ ,■ —*»;**,,.u,.mwmmß 'i"l" i ■■ iifn ww■ ■ ■ ■ ««*»■■*»-■ **»•*• wmiimn**«mr!*rei&&?**i*'TMjitaiimamtwuBW»*«wiewWW<*iWHMHBp^B^^i --