Davis and Oates 



(a) 



(b) 



Figure (vi) 



An arbitrary voltage scaling of 80 volts/per unit h and 10 volts per unit Cl^ 

 is assumed. The input to the function generator will be 80 h volts which gives 

 an output of 10 CLa volts. This voltage is then fed into one channel of an elec- 

 tronic multiplier and multiplied by (a^+ a^) to give Cl as a voltage. Cl is then 

 subsequently summed with other voltage variables in the dynamic equations. If 

 CjL is equal to the weight of the craft (Clo) then the heave equation for example 

 will be in balance and the output of the vertical acceleration integrator will be 

 zero. This is of course an oversimplified example, but it does illustrate the 

 basic procedure on the computer. A simplified circuit for the heave equation is 

 shown in Fig. 15. 



Cavitation 



Cavitation and its effect on the craft dynamics is very important and must 

 be simulated if a realistic representation of the hydrofoil motions is to be ob- 

 tained from the computer. Cavitation gives rise to nonlinearities in the lift- 

 curve for a given foil element. A typical example is shown in Fig. (vii). The 

 angles of attack at which partial cavitation and eventually full cavitation occurs 

 are a function of cavitation number and thus speed. The step in the curve and 

 the Cl at which the slope changes are a function of the lift- curve slope (Cl„) 

 which in turn is a function of immersion depth. The lift on a cavitating hydro- 

 foil is obviously a complicated function to simulate. However, a reasonable ap- 

 proximation can be made by simulating the lift as shown in Fig. 16 to produce 

 the curve of Fig. (vii) b. 



638 



