Sec. 50.3 



CALCULATION OF WAVEMAKING RESLSTANCE 



211 



This campaign was initiated by J. H. Michell in 

 1898 [Phil. Mag., London, 1898, Vol. 45, pp. 

 106-123] and carried on by T. H. Havelock, 

 W. C. S. Wigley, E. Hogner, G. P. Weinblum, 

 R. S. Guilloton, J. K. Lunde, and others, along 

 somewhat varied and independent lines. It is 

 based generally upon one or more of the following: 



(1) Utilization of the slopes of the ship surfaces 

 with respect to the direction of motion 



(2) Utilization of source-sink combinations and 

 distributions to represent the disturbance pro- 

 duced by a moving ship 



(3) Calculation of the wavemaking resistance 

 from the velocity potential derived for the flow 

 around the ship form. 



This procedure involves considerable modifica- 

 tions of Rankine's original work on point sources 

 and sinks and the later development of line sources 

 and sinks by D. W. Taylor. The stream-form ship 

 is not only brought to the surface from a region 

 of unlimited liquid all around it, but the surface 

 waves are now so large that the wavemaking 

 effects enter as a major factor in the resistance. 



A distribution of radial flow from one or more 

 sources and sinks which, in a uniform stream of 

 unlimited extent, produces a given body form, 

 requires extensive modification to produce the 

 same form at and near a free surface. Further- 

 more, the secondary surface waves set up by the 

 moving pressure disturbances incident to this 

 radial flow do not form a pattern which is sym- 

 metrical forward and aft with relation to the ship. 

 Hence, although the schematic ship moves in an 

 ideal liquid, it does possess a pressure drag due to 

 wavemaking. D'Alembert's paradox no longer 

 holds here, where the body is so close to the 

 surface that its motion produces surface waves 

 containing an appreciable amount of energy. 



The calculation of this pressure drag, along 

 theoretical and analytical lines, has been the 

 primary aim of those who have done the recent 

 work on this problem. However, it became evident 

 at a rather early stage that these methods pointed 

 the way to other achievements in calculation and 

 prediction procedures. Some of them are de- 

 scribed by F. H. Todd [SNAME, 1951, pp. 78-79], 

 among them the analytic work of W. C. S. Wigley 

 on the bulb bow, described in Sec. 67.6. Before 

 proceeding to discuss the modern lines of attack 

 in somewhat more detail, it may be well to 

 emphasize this fact, because it is often lost sight 

 of in discussions of theoretical amd mathe- 



matical methods. The fact that it is invariably 

 necessary to establish the velocity potential of 

 the flow around the ship means that there is 

 concurrently available a powerful tool for deriving 

 most of the flow characteristics and hence many 

 useful features of ship performance. 



For example, if the expression for the velocity 

 potential can be modified to take account of 

 boundary-layer, propeller-suction, and other 

 effects, if should be possible to determine from 

 it any one or all of the following: 



(a) The direction of flow over the underwater 

 hull surface at selected points [Guilloton, R. S., 

 INA, 1948, Vol. 90, pp. 48-63] 



(b) The stream function, which in turn should 

 enable a 3-diml plotting of the stream surfaces 

 in the surrounding field. This takes for granted 

 the ultimate practicability (not now achieved) 

 of expressing the stream function for the flow 

 around a 3-diml body which is not a body of 

 revolution. 



(c) The complete pressure distribution over the 

 hull form 



(d) The points in the field surrounding the hull 

 where the local velocity is equal to the ship 

 speed, such as are required for many types of 

 instrumentation 



(e) The effect of changes in the ship size, pro- 

 portions, and shape. 



An example showing the effect of changing the 

 distribution of section area in the forebody is 

 given by J. V. Wehausen [SNAME, 1951, Fig. 

 B and p. 26]. The general subject of wavemaking 

 resistance as a function of the ship form, pro- 

 portions, and dimensions is discussed by G. P. 

 Weinblum in TMB Report 710, dated September 

 1950, pages 25-61. Embodied in this is the dis- 

 cussion of a considerable number of detail features. 



In connection with (e) preceding, it may often 

 be simpler and quicker, especially with modern 

 computing machines, to introduce special con- 

 ditions into an equation and solve for the answer 

 than it is to endeavor to obtain the answer 

 experimentally. 



Regardless of the line of attack employed for 

 deriving the wavemaking resistance, it forms one 

 of the three (or more) principal components of 

 the total resistance, foUomng the W. Froude 

 subdivision of the early 1870's. The others are 

 friction resistance, eddy-making or separation 

 resistance, and the interactions listed in Sec. 12.1 

 of Volume I, if they are taken into account. 



