Norrbin 



100 A|./LT 



Fig. 18. Results from first-order analysis of full-scale zig zag 

 tests with three 40 000 tdw tankers, similar except for 

 stern arrangements. 



realized that a minor modification to a rudder does not appreciably 

 affect this fin effect or the size of a hysterisis loop in the yaw- 

 velocity-versus-steady-helm diagram of an unstable ship. However, 

 the higher control force per degree of helm then possibly achieved 

 will help in actual directional control, where the history of yaw 

 velocities and helm angles takes place well within the height of the 

 steady-state loop, (See also Section I,) 



The general propulsion case will be represented by an arrange- 

 ment including one centre line screw and two wing screws, develop- 

 ing thrusts Tq, Tg and Tp, respectively. Hull interference 

 generates axial forces t^T^,, tgTg and tpTp, in the opposite direc- 

 tions, as well as lateral or sideward forces s, " ' "" 



I 



and 



T 

 P P 

 e factors t — 



In order to adhere to the thrust deduction concept th 

 which are not necessarily constants — will be taken as positive, 

 so that the force in postitive x direction is - t • T. The factor 

 Sg will be positive, and Sp = - Sg. Roughly Sg = tg • cot a, where 

 a is the effective waterline angle in front of the propeller. 



Normally the lateral forces due to Tg and Tp are in balance, 

 but if Tp =3t Tg there is a resultant force applied some 0,4 L behind 

 the C.G. of the ship. The turning moment thus obtained is much 

 larger than that produced by the axial forces along the shaft lines, [ 57] . 



854 



