Prediction of Steering and Manoeuvring of Ships 



forces and moments in the equations of motion. The mathematical model has 

 been reduced to a manageable form by retaining only those hydrodynamic coef- 

 ficients which experimental experience has shown not to be negligible. Roll and 

 heel have also been neglected in the mathematical model, since they are felt to 

 have little influence on prediction of manoeuvres, with the possible exception of 

 fast warships. 



The planar -motion mechanism system designed and built at HyA is used in 

 a conventional towing tank and designed to oscillate the same large 6-to-7- 

 metre wax models also used for resistance and propulsion tests. The mechanism 

 is designed as a low-frequency, high -amplitude oscillator in order to reduce 

 possible frequency problems and to cover adequately the various velocity and 

 acceleration parameters encountered in ship manoeuvres. 



The various tests which can be executed by the mechanism in its static and 

 dynamic modes of operation (outlined in Figs. 2 to 4) make the planar-motion 

 mechanism a versatile instrument for measurement of all of the hydrodynamic 

 coefficients, both linear and nonlinear, which appear in the mathematical model. 



The periodic acceleration-dependent and velocity -dependent forces meas- 

 ured by the force gauges in the dynamic mode of operation of the planar -motion 

 mechanism are separated and recorded by integration using a synchronous -switch 

 technique. The integration is controlled by programming circuits in a processing 

 unit, and the principles of the measuring technique have been described in detail. 



Considerations in the design of the different planar-motion mechanism tests 

 and the analysis of force measurements to determine the hydrodynamic coeffi- 

 cients have been discussed. Results from resistance, self-propulsion, and open- 

 water tests are used to compute coefficients in the X equation and to obtain the 

 important relationship between propeller rpm and speed reduction encountered 

 in manoeuvres, for different types of engines and engine settings. An experi- 

 mental program used as standard at HyA for testing cargo ships is shown in 

 Table 6. 



The influence of speed on the nondimensional coefficients has been dis- 

 cussed, and the results which supplement those previously reported by HyA for 

 the Mariner form (Ref. 5) have been presented as examples. It is found that the 

 nondimensional coefficients y;, y;, n;, and n; are almost independent of speed 

 over the speed range covered by normal merchant ships, and measurement of 

 the coefficients Y^^, y;^,, n^^, and N^^, has not been recommended as standard 

 in the experimental program. The coefficients Yj, Y';,., N', andN',, are 

 shown to vary considerably with speed, forces on the rudder being strongly 

 influenced by the propeller slip stream. The crosscoupling terms Y'^, Y,:,,^, 

 Nj^, and N^sg^ are consequently of importance in prediction of radical manoeu- 

 vres where speed loss is appreciable, and they should be measured as standard. 



It has been found that resonance with a system of standing waves built up in 

 the towing tank precludes the possibility of oscillating models above a certain 

 critical frequency. The resonance is easily avoided, however, at the low fre- 

 quency of oscillation recommended for experiments, but the range of yaw veloc- 

 ities which can be generated by the present HyA planar-motion mechanism is 



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