ship Maneuveving in Deep and Confined Waters 



they are used for comparisons with ship model values in Figs, 33 

 and 34. (A limited comparison of sway force and moment derivatives 

 derived for the SSPA tanker model was included in [ 92] . A small 

 adjustment of model force derivative appears in the present compari- 

 son, due to modified assumptions for non-linear viscous cross -flow 

 contribution; cf. Section X.) 



The lateral forces acting on a body of revolution in axial 

 motion in close presence of a vertical wall have also been studied 

 by Newman, [93]» The source distribution inside the body is 

 mirrored in the wall, and in addition the calculations require the 

 original distribution to be off- set towards the wall. This three- 

 dimensional source distribution defines the velocity potential and 

 so the forces may be found by use of the Lagally theorem. As 

 expected from experience and approximate image theories for 

 bodies not close to the wall there is an attraction towards the wall, 

 increasing monotonically up to a finite value of body-and-wall con- 

 tact. It is concluded that for geometrically related bodies with 

 same sectional-area distribution the suction force will be inversely 

 proportional to the length, whereas the yawing moment will be inde- 

 pendent of length variation. The results also indicate that there 

 will be a bow-away-from-wall moment for bodies with a stern, which 

 is blunt compared to the bow, and vice versa. 



In Fig. 23 calculations by Newman's method are compared 

 with the results of force measurements on a tanker model towed 

 along the vertical wall of a ship model basin, (Cf. Section X.) 

 Basin depth was equal to 0,29 Lpp, total basin width equal to 

 2.7 • Lpp, The diagram is plotted on ratio of wall distance to 

 maximum radius of equivalent body of revolution, defined by length 

 and displacement of model hull + image. The better agreement is 

 obtained for that equivalent body, which also has the same sectional 

 area curve, but even then the experimental results are some 25 per 

 cent in excess of the prediction. At larger separations the differ- 

 ence is still larger, Connparative Ccilculations using Silversteins 

 "not-too-near-wall" results for an equivalent ovoid [77] , are 

 included in the diagram; in this case the prediction is better for 

 larger separations , but in all much too high. 



As long as the body is not too close to wall contact the 

 Newman theory gives a linear dependence for the lateral force on 

 ratio of body radius to centre-line wall distance, i.e. it is propor- 

 tional to "Hg or T|p defined for starboard or port wall distances in 

 next Section. This linear dependence suggests that the lateral force 

 on the ship between two parallel vertical walls may be obtained by 

 adding the effects from each one, which idea may also be supported 

 by the new presentation of old DTMB data [94, 95] given in Fig. 24. 

 The diagram includes force and moment measurements on a twin- 

 screw tcinker model in several canal sections of simple rectangular 

 form. 



873 



