Norrbin 



A close approximation to a resistance curve with typical 

 humps and hollows requires a multi-term polynomial in u. Estab- 

 lished practice in naval architecture makes use of a single exponen- 

 tial term R|(u/u| )^ to characterize the curve in the vicinity of Uj, 

 For large slow-running tankers p« 2 over the entire speed range 

 of interest, which is associated with an almost constant advance ratio 

 for the screw. In confined waters it may be necessary to include a 

 higher-order term; see Section IX, 



Forward Resistance Due to Lateral Motions 



When the ship deviates from the true forward motion addi- 

 tional forces appear in axial direction. The main cause of speed 

 loss in a turning motion is due to the axial component of the centri- 

 petal mass force and the hydrodynamic contribution X^^ • rv, of 

 second importance is rudder drag and finally the axial force due to 

 oblique-hull lift and wave-making shall be considered. 



Ideal-flow hydrodynamics identifies Xpy with - Y^, i.e. the 

 mass effect is virtually almost doubled. (Cf. (5.6).) A recent 

 analysis of turning trial data indicates much lower values of X^.^. 



In a steady turn the ship proceeds with her bow pointing 

 inwards, so that (m + X^^)rv = - (m + X^JV^/R • ^ indicates a force 

 opposed to forward thrust. In running on a straight course the fre- 

 quency of the yawing motion normally is so low that yaw rate and 

 drift angle are in phase during most (but not all) of the time, and so 

 an average parasite resistance results. 



Let the response to a sinusoidal motion of the rudder be 

 4j = 4;a • sin (wt + €r) and P = Pq * sin (cot + eg). Averaging over a 

 number of complete periods gives 



7^ = i|^cos (e^ - ^) (6.7) 



As the normal merchant ship will pivot round a point closely 

 aft of the bow at low frequencies a r ough estimate of the average 

 product is given by (rv)aj^o~ ~ (0^/2)4^0 • 



A plane wing in a uniform flow will experience an induced 

 drag as given by Cpj = (i/'rrA)CL^ According to certain experiments 

 this simple relation may still be used with a correction factor for 

 the twisted flow over a rudder behind a screw. The calculation of 

 rudder lift will be shortly discussed in the next Section; using a 

 nominal aspect ratio equal to twice the geometrical one the correction 

 factor just mentioned will be of the order of 1.2 - 1.4. 



850 



