13 



exponential term relatingthe below-surface disturbing pressures to the wave length at the sur- 



_ 2nf 



face and the depth of immersion . These forces vary approximately ase where / is the 



depth of immersion and A is the wave length . Thus as A. increases with increasing speed, 



2fff 



e also increases. The effect upon the water surface elevation of the finite draft of the 



model will, therefore, be greater at higher speeds than at low, and better agreement than that 

 actually obtained cannot be expected . 



It was found that measuring the wave profile at the bow sometimes presents serious 

 difficulties because of the steep slope of the wave in a transverse plane. Photographs of 

 wave contours along the ship may therefore prove to be rather unreliable. 



CONCLUSION 



The qualitative and quantitative agreements between the calculated wave resistance 

 coefficient C and the residual resistance' coefficient C r '(as shown in Figure 2) are very 

 satisfactory. In particular, prediction of the "third" hump* was possible in the resistance 

 curve of Figure 3 at F - 0.24 which at first escaped the attention of the experimenters. 



Because of this good agreement, the following deductions from the computations can 

 be relied upon without further checks: 



It is well known that because of the linear character of MicheU's analysis the relation 

 R~B 2 holds. 



It can also be demonstrated that at very large Froude numbers (y -» 0) the integral r 

 becomes independent of H/L provided this ratio is finite. Thus the three curves on Figure 3 

 must finally coincide and R~ B 2 H 2 , i.e., the wave resistance in this range is proportional 

 also to the square of the depth H . However, it can be seen from the figures that this asymp- 

 totic relation does not hold for high-speed displacement ships. For example, at a destroyer 

 speed of F = 0.6, y = 1.5. In this case R is proportional to H 1,5 only; at F = 0.25, R~H 2 

 where r is already less than unity. 



The studies of the method of formation of wave systems described in this report ex- 

 plain to some extent the characteristic form of the wave-resistance curve. 



It can readily be seen that with increasing speed and therefore with increasing wave 

 length, the crests of the bow wave system will alternately reinforce and dampen those of the 

 stern and shoulder wave systems . Similarly, combinations of these systems will change with 

 changing speed . These reinforcing and damping effects of the wave systems account for the 



♦The hump in the resistance coefficient curve occurring at F = 0.5 is here denoted as the "first" hump, at 

 F = 0.3 as the "second" hump, etc. (see Figure 3), contrary to the custom in naval architecture by which the 

 hump at the highest speed is called the last hump. This change appeared to be necessary since from a mathemat- 

 ical viewpoint there are an infinite number of humps between 0.5 5 F > (see also Reference 2, page 23). 



