Pien 



has not been developed to any useful extent, I have included only those definitions 

 which can be related to experiments in some way. 



In Fig. 1 various breakdowns of ship resistance into components are shown 

 in historical order from left to right. First we have (1-a) Froude's hypothesis 

 and (1-b) the modernization thereof by Hughes. Here the goal is mainly that of 

 model scaling, and the breakdown into frictional and residual components is 

 done on the basis of dimensional analysis, that is, Buckingham's Pi Theorem. 

 Froude's original hypothesis was that the total resistance could be separated 

 into a "residual" part, c^, depending on the Froude number and a frictional 

 part depending on the Reynolds number. In practice, the latter was estimated as 

 being the skin friction, C^, of a plank of the same length and wetted area. This 

 results in the residual resistance including some viscous effects due to separa- 

 tion. These are sometimes termed "form" and "eddy" resistance. Hughes added 

 the concept of a form effect (l+ r) on c^ derived from tests of geometrically 

 similar models (Geosim tests), this being a practical improvement only if such 

 factors do not depend strongly on the Froude number and can be estimated with- 

 out recourse to such tests. By assuming no Froude number dependence, the 

 form resistance can also be estimated on the basis of the resistance at low 

 Froude numbers where the wave resistance is expected to be negligible. The 

 corrected residual resistance, C'^ , includes the wave resistance but also an un- 

 defined portion of the eddy and form resistance, probably that part which is 

 Froude number dependent. 



The second listed breakdown is with respect to the vectorial nature of the 

 local fluid stresses at the hull boundary, i.e., tangential shear and normal pres- 

 sure. The latter are determined from a pressure survey over the entire hull 

 and then are integrated in conjunction with the known hull surface slopes to give 

 a resultant pressure drag component, Cp^.. This can then be subtracted from 

 the measured total drag to deduce the integration of tai^ential viscous shear 

 stresses. It should be pointed out that the major effects of viscous separation 

 are not included in this force component but in the normal pressure drag com- 

 ponent. The required experiments and analysis, originally done by Eggert and 

 more recently by Townsin and Hogben are quire extensive. While historically 

 interesting, this has not yet proved to be a practical means of meeting any im- 

 portant goal. 



The third breakdown is with respect to the physical phenomena involved, 

 i.e., the formation of waves and the development of a viscous shear wake. Here 

 the question of breakdown reduces to that of separating the total momentum 

 survey around a closed control volume away from the hull into (a) that portion 

 involving the viscous wake and (b) that due to wave orbital velocities, and then 

 integrating these to obtain c^ and C^ , respectively. The experimental tech- 

 niques available to measure the wave resistance, C^, are therefore either (a) 

 a direct momentum survey of the waves making a proper correction in the wake 

 region or (b) a valid viscous wake survey adjusted for the presence of waves 

 which is then subtracted from the measured total resistance. The latter method, 

 which has been employed for example by Landweber, is less direct and might 

 suffer from inaccuracies due to the process of taking differences of large num- 

 bers. In addition, one must assume that there is no third mechanism of energy 

 dissipation present, which has not been proven yet. It is the third breakdown of 



1142 



