[Reprinted from the PROCREDINGS OF THE RoyaL Socrety, A. Vol. 82] 
The Wave-making Resistance of Ships: a Theoretical and 
Practical Analysis. 
By T. H. Havetock, M.A., D.Sc., Fellow of St. John’s College, Cambridge, 
Lecturer in Applied Mathematics, Armstrong College, Newcastle- 
on-Tyne. 
(Communicated by Prof. J. Larmor, See. R.S. Received April 1,—Read 
April 29, 1909.) 
CONTENTS: 
PAGE 
1. Introduction and SUMMALY..........:cceereeeceeseseeeeeeeeees 276 
2, Pressure system travelling over deep water ............ 279 
3. Diverging wave SySteM ........ssseseeeeee essere eeee eee eens 282 
4. Interference of bow and stern wave-trains ............... 284 
5. Comparison with experimental results ..............00000 287 
6. The effect of shallow water...........ccsscossessecnecreereenee 293 
7. Further types of pressure distribution.................+6.5 299 
§ 1. Introduction and Summary. 
The theoretical investigation of the total resistance to the forward motion 
of a ship is usually simplified by regarding it as the sum of certain 
independent terms such as the frictional, wave-making, and eddy-making 
resistances. The experimental study of frictional resistance leads to a 
formula of the type 
1h, SS SN (1) 
where § is the wetted surface, V the speed, f a frictional coefficient, and m 
an index whose value is about 1°83. 
After deducting from the total resistance the frictional part calculated from 
a suitable formula of this kind, the remainder is called the residuary resist- 
ance. Of this the wave-making resistance is the most important part; the 
present paper is limited to the study of wave-making resistance, and chiefly 
its variation with the speed of the ship. The hydrodynamical theory as it 
stands at present may be stated briefly. 
Simplify the problem first by having no diverging waves ; that is, suppose 
the motion to be “in two dimensions in space,” the crests and troughs being 
in infinite parallel lines at right angles to the direction of motion. Further, 
suppose that the motion was started at some remote period and has been 
maintained uniform. We know that, except very near to the travelling 
disturbance, the surface motion in the rear consists practically of simple 
periodic waves of length suitable to the velocity v of the disturbance. Let 
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