Str^m-Tejsen and Chislett 



The top of Fig. 21 illustrates two characteristic situations, one for positive 

 (P) and the other for negative (N) yaw velocity. It is again helpful to relate the 

 periodic forces, resulting from periodic motions generated by the planar-motion 

 mechanism, to the corresponding steady-state measurements shown at the cen- 

 ter in Fig. 21. Each of the two center diagrams in Fig. 21 illustrates one of the 

 two terms rw and vrr, assuming the other to be zero. The corresponding 

 forces acting at the Y gauges during one revolution of the mechanism are shown 

 at the bottom in Fig. 21. 



It is seen that using the Oscil. program, the in-phase measurements ob- 

 tained from a "yaw and drift-angle" test correspond to Y|.r(t), and the out-of- 

 phase measurements correspond to Y^r(t) + Y^^^r(t)v^, whereas the forces cor- 

 responding to the remaining two terms are eliminated. The component Y^^yr(t)v^ 

 is then obtained by subtracting the known value corresponding to Y^r(t). 



Similarly, use of the Const, program gives measurements corresponding 

 to Y^v + Y^^j.vr(t)^, and the component Y^j.^vr(t)^ is obtained by subtracting the 

 known value corresponding to Y^v. 



In practice, the rw term has been found to be of significant magnitude and 

 the vrr term to be small. The rw term is linear with r and thus independent 

 of the range of yaw velocity, whereas the vrr term is second order in r and 

 can only be measured if an adequate range is covered. 



DESIGN OF THE EXPERIMENTAL PROGRAM AND 

 DETERMINATION OF THE HYDRODYNAMIC 

 COEFFICIENTS 



The complete experimental program, which should be carried out in order 

 to determine the hydrodynamic coefficients, would, in addition to the various 

 planar-motion mechanism tests illustrated in Figs. 2, 3, and 4, consist of con- 

 ventional open-water, resistance, and self -propulsion tests and an experiment 

 for the determination of the model polar moment of inertia. 



Two of the coefficients are furthermore obtained from numerical calcula- 

 tions instead of experimentally. The added mass of the ship in surge accelera- 

 tion x^ is, for instance, normally assigned a value of -0.05 m based on theoret- 

 ical considerations. Similarly, the ship moment of inertia l^ is computed on 

 the basis of the longitudinal weight distribution of the full-scale ship. 



Design of the Experimental Program 



The range of motion and rudder parameters explored during testing should 

 in principle cover the range of subsequent simulation. Sway and yaw accelera- 

 tion, speed loss, drift angle, yaw velocity, and rudder angle should therefore 

 be varied systematically up to the values corresponding to maximum-rudder 

 manoeuvres for the free-sailing ship. Typical values for the range of motion 

 parameters experienced by a cargo ship during the execution of a 35-degree 

 rudder-angle turning circle and a 20-20-degree zig-zag manoeuvre are given in 

 Table 2. Corresponding maximum values obtained with naval ships are often 

 1.5 to 2 times greater. 



348 



