Smith 



%^ 



AMPLITUDE 



OF 

 MOTION -7 



Vy = 0.3105 COS(17t) 



-CALCULATED 

 Fig. 7 - (Continued) (b) frequency = 17.0 U/c 



two different frequencies. The close agreement between the experiment and the 

 prediction of the effect of frequency are encouraging. 



Kiissner, Wagner, and Theodorsen functions were calculated by the exact 

 step-by- step procedure for airfoils of several thicknesses, thus identifying the 

 effects of thickness on the Kiissner, Wagner, and Theodorsen functions. The ef- 

 fect of thickness is significant. Results for thin airfoils indicated good agree- 

 ment with classical results derived from flat-plate theory (4). 



Comparison of Theoretical and Experimental Forces on an Oscillating 

 Airfoil - Spurk (7) has experimentally measured forces on several airfoils os- 

 cillating symmetrically as shown in Fig. 8, which presents the results for one 

 test. Reduced lift and moment coefficients are used; the imaginary part repre- 

 sents phase lag, and the real part, amplitude ratio. At low reduced frequencies 

 rather good agreement occurs, but as frequencies increase, theory and experi- 

 ment diverge considerably. Because many more studies in addition to those 

 presented here indicate that the present method has great accuracy for a per- 

 fect fluid, the failure to agree with experiment can probably be attributed to 

 viscous effects, i.e., the boundary layer, although it should not be forgotten that 

 experimental determination of dynamic effects is difficult and not highly accurate. 



Examples of Two -Body Problems 



Two Airfoils Passing Each Other in Opposite Directions - Two airfoils 

 passing each other in opposite directions is an exciting problem, if it is thought 

 of as two airplanes passing each other close-by in opposite directions. Two 8.4- 

 percent-thick von Mises airfoils at angles of attack of 5.73° (Fig. 9) are initially 

 at rest with noses spaced one chord length apart. They are impulsively moved, 

 and the motion is traced. Figure 9a shows the wake shape after the airfoils have 

 each traveled 1.5 chord lengths. Figure 9b shows the lift history as the airfoils 



334 



