Canadian Hydrofoil Program. Hydrodynamics and Simulation 



and coupled subsidence modes, respectively. For canard configura- 

 tions, the coupled subsidence mode is always stable, but in airplane 

 configurations instability may result from adverse heave -pitch coupl- 

 ing. Neither the pitch nor the heave modes are significantly influenc- 

 ed by surge. 



Root locus plots showing the effect on BRAS D'OR's longi- 

 tudinal modes of varying speed are presented in Figure 12. Longitu- 

 dinal dynamics are dominated by the lightly-damped pitch mode in 

 which the damping ratio decreases and natural frequency increases 

 with increasing speed ; this mode's characteristics are a direct result 

 of the bow foil's design, which combined high ¥ j= , with low | L . 

 Similarly, the characteristics of the heave mode follow from the com- 

 bination of low d L w ith high d L in the main foil. 

 d h da 



Generally speaking, three modes of lateral motion may be 

 distinguished for passively- stabilized surface -piercing hydrofoil ships 

 (Figure 13) : a rapid convergence of little importance, an oscillation 

 governed by ship rolling characteristics, and a slow convergence 

 arising from sideslip-roll-yaw coupling. 



Simulation of Random Seas 



In Equations (l) to (6) a seaway acts as a forcing function 

 through the variation of foil immersion depth and angle -of -attack with 

 wave elevation and orbital velocity. The simulation of these seaway 

 variables is now discussed. 



The Pierson-Moskowitz spectral form is chosen as a model 

 of the sea * ' . The equation for the wave elevation power spectral 

 density is : 



»f.i = • 008 'g 2 



exp 



-.74( * ) (n; 



where V is wind speed. Significant wave height is given by : 



v 2 < 18 > 



h l/3 - 1 - 86( -IO ) 

 for V in knots. 



303 



