Norrbin 



loading before application to full-scale predictions. 

 Non-linear contributions to hull forces are included 

 in second order derivatives, relevant to the cross- 

 flow concept. 



The extension of the mathematical model to the con- 

 fined-water case is based upon the theoretical results 

 by Newman and others , and upon relations found from 

 special experiments. In the model the hydrodynamic 

 interferences appearing in forces and moments due to 

 the presence of port and starboard side wall re- 

 strictions and bottom depth limitations are represented 

 by additional terms containing higher order derivatives 

 with respect to three suitable confinement parameters, 

 ■n = "Hs "*" 1p» ^ = "Hs - "Hp* ^J^d t,. In a canal the asym- 

 metrical forces are considered as due to the aaded 

 effects from port (p) and starboard (s) walls rather 

 than as the effect of an off-centreline position; 

 primarily "n is a measure of this position, r\ a 

 measure of the bank spacing. 



The mathematical model is here applied for evaluation 

 of model test data obtained for a Swedish 98 000 tdw 

 tanker in the VBD laboratories. Oblique towing and 

 rotating arm tests were performed in "deep" and 

 shallow water. Oblique towing tests were also run 

 at various distances from a vertical wall in the deep 

 tank, and in two Suez-type canal sections. The effect 

 of shallow water was especially large in force non- 

 linearities. Missing data for bottom and wall effects 

 on added mass and inertia are taken from theory and 

 from test results due to Fujino, respectively. 



The deep-water predictions for zig zag test and spiral 

 loop prove to be in good agreement with full-scale trial 

 results. Analogue computer diagrams are given to 

 show the effects of shallow water upon definite 

 manoeuvres and upon course -change transients follow- 

 ing auto -pilot trim knob settings. Finally a few results 

 are Included to illustrate auto-pilot position control 

 of the tanker in free water, in shallow water, between 

 parallel walls and in a canal. 



808 



