Measured Wind Tunnel Results:

Tested configurations:

Since the wind tunnel diameter was 10 feet, the wing  to be tested was made-up of two extended with tips as sown in the following pictures. The wing profile  was an LS 10413

- The span was 5.118 and 6.037 feet respectively.

- The surface was 11.571 and 14.563 sqf respectively.

- The aspect ratio was 2.264 and 2.501 respectively.

Configuration Without WVEs  

Configuration with WVEs

1- At iso Cl, a 2° less of angle of attack is needed (see point 1, in attached Fig 1.)
  -Actual equation to calculate the Cl slope is:
dCl/dalpha = .109662*AR/(2+(4+AR^2*beta^2*(1+(lambda/beta)^2))^.5) where
AR = aspect ratio, beta = compressibility factor, lambda = sweep tangent

2- The 75% added wetted surface compensated for 0.3° of attack  (see point 2, in attached graph)

3- The Cdi ratio of 63/38 = 1.66 - 39% are due to increased span by 6.037²/5.118² = 1.39: that make 66-39 = 27% accounted to WVEs. (see point 3, in attached graph)                         

4- The Cdi coefficient k of .727 versus 1.00 for an elliptical wing (Ludwig Prandtl Formula)

5- Increased Trailing Vortex dissipation by 3 (see Air & Cosmos July 3 1998 in Research section)

Fig 1. This graphic shows Cl/Cd and Cl slope.

Fig 2. Cl²/Cd graph

Ludwig PRANDTL equation for induced drag: Cdi  = k/P * Cl^2/ AR. Till today the best value for k =1 was achieved by an elliptical wing, like the World War British " Spitfire ". Any other shape had a larger value k>1 Except the WVE one which bring the measured value of  "k" = 0.727, that is simply exceptional.

From L. Prandtl equation we can write k = dCd/dCl^2*P*AR

For the test without we then have        k = 0.0290/0.2*3.1416*2.263 = 1.022*

For the test with WVEs we then have  k = 0.0185/0.2*¨3.1416*2.501 = .727

*This figure is pretty good, because configuration tested was fitted with Horner Wing tips.

If you have comments or suggestions, email me, Henri CHOROSZ, at

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