Prediction of Steering and Manoeuvring of Ships 



the top of the forward scotch yoke. It is seen, for example, that an IN record 

 is characterized by margin-pen marks 90 - (0/2) after the start and stop of the 

 integration period. 



The forward and aft IN @ and IN © forces are of the same order of mag- 

 nitude but of opposite sign. This is natural, as mass and submerged lateral- 

 area are distributed nearly symmetrical about the origin, and because yaw ac- 

 celeration causes the forebody to swing the port while the afterbody swings to 

 starboard, and vice versa. 



The forward and aft OUT ® (and OUT © ) forces are of the same order of 

 magnitude but of opposite sign, the aft force being positive. The centrifugal ef- 

 fect of the ship's mass acts in the same direction at both forward and aft gauges, 

 adding to the hydrodynamic force at the forward gauge and reducing the effect 

 of the hydrodynamic force at the aft gauge. The forward gauge-force is there- 

 fore usually of greater absolute magnitude than the aft. For ships with pro- 

 nounced rake of keel, however, the hydrodynamic force aft is greater than that 

 forward and the measured forces become of almost equal absolute magnitude. 



Forces dependent on acceleration are usually of greater absolute magnitude 

 than those dependent on velocity. The relative proportions of the two change 

 with frequency of oscillation and model speed, however, and, for low frequencies 

 or high speeds, the velocity -dependent forces can be the largest. 



By adding and subtracting the forward and aft IN and OUT components ac- 

 cording to Eqs. (15), side forces and turning moments are obtained as functions 

 of yaw acceleration and yaw velocity. When these values are faired, the slopes 

 of the fairing lines at the origin give the terms Yj. - mx^, N^ - i^, Y^ - mu, and 

 Nj. - itixqu. These terms contain the effects of known model mass and inertia, 

 which may be eliminated, leaving the hydrodynamic terms Y|^, N. , Y^, and N^.. 

 Ship mass and inertia values can then be reintroduced. This ability to account 

 for differences in mass and inertia between model and ship is convenient, as it 

 permits the model to be constructed without paying any regard to its inertia. 

 Model displacement is usually kept to the scaled ship value, and ballast is ad- 

 justed until the correct trim is obtained. 



Integration of Forces in Pure-Sway Tests 



The forces measured in "pure-sway" tests are treated in a manner exactly 

 analogous to the "pure yaw" tests described above. As seen in Fig. 17, the 

 forces are integrated with sign reversals related to lateral instead of angular 

 displacement. The synchronous switch is thus adjusted to give impulses to 

 Input 1 at positions of zero, maximum, and minimum sway displacement. The 

 measured forces are again designated IN and OUT to indicate in phase or out- 

 of-phase relationships with sway displacement. 



Typical records of forces measured at the forward and aft gauges, shown 

 in the bottom right of Fig. 17, are explained in similar manner to the results 

 of "pure yaw" tests. Forward and aft IN © forces are, in this case, of the 

 same sign because forebody and afterbody accelerate simultaneously to port or 



341 



