Lifting -Surface Theory 



Timman, as a reply on a question on Tsakonas' staircase approximation, re- 

 plies that in his experience the detailed structure of the wake in oscillating flow 

 is not very crucial. The vortex strength oscillates and there is, at some dis- 

 tance, a cancelling effect of neighbouring vortices of opposite strength. This 

 does not hold in the near slipstream, which is, however, always poorly repre- 

 sented by theory. 



Probably there will be a reasonably close agreement between Tsakonas' 

 theory and a more exact theory (5%). The problem of comparison with experi- 

 ments is raised. 



Laitone (Berkeley) reports on experiments on airfoils at low Reynolds num- 

 bers. From NACA data it was known that at Re < 200,000 in this case the lift 

 curve slope is higher than at high Reynolds number. Experiments on rectangu- 

 lar wings to check these effects. The effects are either due to a separated 

 wake or the formation of vortices at the leading edge. At Re > 200,000 and an 

 aspect ratio of 6 results in de^ / dx = 0.075 Re > 200,000, and a lift-drag ratio 

 of 20 at Re < 50,000 aspect ratio 6 result gives ^^\ /dx= 0.085 even greater than 

 2 77. For a ring airfail a vortex is actually formed. For diameter/chord =12 

 the data went along quite well, at high Re, but below 50,000 de^ /dx is about 15% 

 higher than the theoretical value. 



To check profiles, 5, 10, 20% thick wings gives a strong vortex at the lead- 

 ing edge. 



Thieme (Hamburg) reports on experiments with similar results NACA pro- 

 files 12% thick 1958 and flat plates with different leading edges, and elementary 

 ship forms with aspect ratio 0, 1 at Re 10^. Not only lift coefficients, but also 

 moments showed a remarkable increase at the low Reynolds numbers. The only 

 explanation is the bubble at the leading edge. 



Laitone tested several profiles for gliders and found that for flat plates at 

 Re < 50,000 at 6 degrees is very linear and drops off at 45 degree. Max C^ of 

 1.2 were found; the paper gliders optimize design at that Reynolds number. 



Timman remarks that from a mathematical point of view classical theory 

 uses the Kurta condition to fix the vorticity at the trailing edge, but at the lead- 

 ing edge there must be additional empirical conditions to fix the location and 

 strength of the vortex. For ship propellors the leading edge vortex sheet is re- 

 placed by a cavity. 



Weissinger remarks that for delta wings a theory is developed which as- 

 sumed free vortices everywhere on the lifting surface. 



Milgratn (M.I.T.) reports on work on sails as an application of lifting- 

 surface theory. The chief advantage of the kernel-function method is on the 

 unsteady case. In the steady case Falkner's vortex lattice theory (1943) is very 

 successful. It gives a prescription for the numerical computation, which avoids 

 the trouble. 



Referring to Cunningham's papers, which were carried out for rectangular 

 and delta wings and no camber. A sail has a different shape and camber and a 



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