50 



equation of the actual water line of the plate or at least its area coeffic- 

 ient (prismatic) is considered. Within the region of the second hump the wave 

 resistance of a "plate body" with a prismatic ^ 0. 9 (which is nearer to actual 

 practice than 2/3) can be 10 times higher than that of a parabolic form 4> = 2/3. 

 A special investigation was made into "hollow versus straight lines". ■'■"^ Prom 

 this work it follows that theory tends to overestimate the optimum t values. 

 Finally, two asymptotic laws have been derived :•'■•'■ ■"■ 



a. For vanishing Proude numbers, the wave resistance becomes propor- 

 tional to t^ 



R-t^ [23] 



b . For very high Froude numbers 



R~0^ [24] 



The latter law can be easily derived, also, from an asymptotic formula due to 

 Lamb.^« 



Although the practical significance of these relations is not very 

 great, two important remarks should be made: 



a. The S(>') curves here reproduced give only a rough picture. For 

 actual computations the functions must be extended to higher values of the 

 variable y; some tabulated values are published and more comprehensive 

 tables are available at the Taylor Model Basin. 



b. Theory deals only with that part of the hull which is submerged at 

 zero speed. Obviously the hull above the load water line at rest must have 

 some influence on the resistance. This point is strongly supported by Eggers' 

 experiments.^* However, resistance measurements made on models with different 

 section forms above the load water line (see Figure 29) did not disclose ap- 

 preciable differences in resistance results. Of course two experiments can- 

 not disprove the consistency of the preceding reasoning, and much remains to 

 be done on the subject following an outline given by Guilloton. 



5.U. THE INFLUENCE OF THE VERTICAL DISTRIBUTION OP DISPLACEMENT ON THE 

 WAVE RESISTANCE 



3.4.1. The Influence of the Midship Section Coefficient 



The problem may be stated as follows: In the equation ?? = X(^) Z(f), 

 the function X(0 Is kept the same; variations in resistance have to be inves- 

 tigated for various midship sections defined by the function Z(f). 



