Norrbin 



difference of about 5 per cent. In case of a bottom depth of 15 m 

 this again corresponds to a ship speed of 16 knots. 



In Ref . [ 79] Weinblum demonstrated that the wavemaking 

 in a canal is a complicated function of speed, depth and width. In 

 general it is therefore not possible to define a single effective 

 length to characterize the canal dimensions in a speed number. 

 However, effective canal speed includes the back-flow, and just as 

 a critical speed in shallow water is defined by the speed of the 

 solitary wave, ^fgh, experimental evidence advocates a critical 

 speed in a certai n canal co rresponding to a certain Boussinesque 

 number B = F^^^f(h./W) + 1. (Here W is equal to i\,alf the mean 

 width of the section.) For a rectangular section Muller proved that 

 the maximum wave resistance occurred at Fpj^ = (2(h/W) + i)'^^, 

 [80], In a canal 15 m deep and 120 m wide this corresponds to 

 ^nh ~ 0.81, Again, let it be assumed that a significant change of the 

 wave resistance due to the confinements will be found only at a speed 

 equal to or higher than 70 per cent of this critical speed: this now 

 gives a speed of about 13 knots, much to high to be experienced in 

 canal transits involving normal blockage ratios. It may be concluded 

 that the additional resistance terms to appear in the speed equation 

 normally need not to account for the oscillatory wave-making com- 

 ponents . 



Reference shall here be given to recent studies of the un- 

 steady flow conditions existing within a critical speed range for a 

 ship in a canal; this range tends to zero when the width of the canal 

 tends to infinity, [ 81 , 82] . 



At sub- critical speeds the wave-making itself may influence 

 the lateral force and moment on a ship moving along a bank, as 

 shown by Silverstein, [ 77] . In case of the low Froude numbers met 

 with in practice also these effects may probably be ignored, and the 

 water surface may thus be treated as a solid wall. At F^|_ = 0.078 

 or Fj,^ = 0,32, realized for a 98 000 tdw tanker proceeding at a 

 speed of 14 km/h through the Suez canal, the longitudinal waves will 

 have a length of some 10 m, i. e. only 4 per cent of the length of the 

 ship. 



The back-flow producing an increase of frictional resistance 

 will also produce an increase of sinkage, and in case of small bed 

 clearances this will of course indirectly affect the lateral forces 

 sensitive to the clearance. These secondary effects must be born 

 in mind when comparing predictions from theory with results from 

 force measurements on models , which are free to heave and trim. 

 In the normal evaluation and presentation of such measurements, 

 however, it will be considered more practical always to use the 

 nominal under-keel clearance. 



The viscous resistance, including frictional as well as 

 viscous pressure resistance, may be calculated accepting a plate 



868 



