Davis and Oates 



This function cannot be produced on a standard diode function generator be- 

 cause of the sudden changes in slope, therefore, an "X-Y" variplotter has to be 

 used with a conducting stylus replacing the pen and a sheet of resistance mate- 

 rial (carbon) cut at the fence positions and fed with voltages at each end of each 

 section to produce voltage as a function of position. These voltages are then 

 picked off by the stylus and fed into the equations through the necessary cir- 

 cuitry. 



I 

 Simulation of ventilation has shown that ventilation has only minor effects 



on stability if the stability margins are adequate without ventilation. However, 



if stability is marginal without ventilation then the addition of these effects will 



cause instability. 



Unsteadiness Effects 



Circulation Delay 



When the angle of attack on a foil surface is suddenly changed the pressure 

 distribution on that surface does not adjust itself instantaneously to the new con- 

 ditions. It responds in a transient manner and approaches the eventual steady- 

 state value asymptotically as shown in Fig. 17. 



This delay is due mainly to the relatively slow change of lift due to circula- 

 tion, and to a lesser extent, the lift response associated with accelerating a cer- 

 tain mass of fluid due to instantaneous reaction of that fluid against the foil 

 section. 



The circulation lift change is usually given in terms of indicial functions, 

 i.e., curves of lift change versus time after a "step" change in angle of attack. 

 These indicial functions for low aspect ratio wings start at or above the eventual 

 steady- state level and drop initially for about 1 chord length of travel to meet a 

 rising exponential which yields approximately half the lift change in about 4 

 chord lengths. Ninety- eight percent of the steady- state lift is achieved after 

 approximately 6 chord lengths of travel. 



Two exponentials of the form shown in Fig. 17 were superimposed to pro- 

 duce an approximation to the curves of Ref. 16. Ideally for a surface piercing 

 hydrofoil we should consider a varying aspect ratio, but for practical purposes 



640 



