Hydrofoil Motions in a Random Seaway 



overall phase to approximate 90° over the frequency range by all- pass networks. 

 Typical head and following sea transformed integrator frequency response char- 

 acteristics are shown in Fig. 12. 



A block diagram of the head sea simulation is shown in Fig. 13. Notice that 

 the transformed integration involved two all-pass filters, the difference in phase 

 between them being such that the phase angle between w' and z' is 90", 



Figure 14 shows the filter arrangement for following seas. Following seas 

 present special problems since the transformed wave elevation spectrum can 

 contain both following and head components for certain craft velocities; and in- 

 deed also a steady value for that component whose crest velocity is equal to the 

 craft velocity. Simulation for such a condition is clearly impossible, since the 

 transformed integrator and foil separation filters would have to be approximated 

 over an infinite number of decades in frequency. When the craft velocity is high 

 enough, however, all significant frequencies become head components and a 

 simulation is feasible. The simulation is similar to that of the head sea except 

 for the all-pass filters which are required to supply the constant component of 

 foil separation phase shift required. 



It should be noted that simulation of the effect of the separation between the 

 foils cannot be accomplished by a Pade approximation to a pure delay. The de- 

 lay is distributed, and has a phase characteristic proportional to the square of 

 the frequency. The foil separation filter required two second order all-pass 

 filters to approximate the transformed phase shift over the significant frequency 

 range of the vertical velocity spectrum. 



A second method of simulation, using a number of superimposed sinusoids 

 of appropriate amplitude and frequency, was used for simulating following seas 

 at the lower ship speed. The method was unsuitable for the other cases, how- 

 ever, because of excessive demands on computing equipment to give a sufficient 

 number of components to approximate a normal distribution. 



ANALOG COMPUTER SIMULATION TECHNIQUES 



Analog Simulation of the Equations of Motion 



As mentioned previously the lift- curve slope is the basis for computation of 

 all lift forces active on the foils. This is simulated on a function generator in 

 the analog computer. The diode function generator creates a sequence of 

 straight lines that are connected together to form the desired function. Obvi- 

 ously if a large number of segments are used then the function will be generated 

 more accurately than if just a few points are selected. In practice about 8 or 9 

 'Toreak points" will simulate most lift curves with sufficient accuracy. For ex- 

 ample consider the following lift curve [Fig. (vi)]: 



637 



