Nonplanar Wakes: The Split Tip

From among this list of possible designs, we choose two ideas to look at in a bit more detail. The first concept is based on the notion that it is the shape of the wake, not the shape of the wing that is important to the total vortex drag. By sweeping the trailing edge of the wing sharply backward or forward and placing the wing at an angle of attack, one may generate a wake shape that looks very much like the wake of a wing / winglet combination. The difficulty here is that we must twist the wing or create a planform shape that achieves the optimal load distribution that corresponds to this geometry. Moreover, for reasonable wing planforms, the amount of out-of-plane wake deformation is very limited. For this reason the potential gains associated with crescent-shaped wings or wings with highly forward-swept trailing edges are very small (about 1% or less) unless the wing has a very low aspect ratio.

To exaggerate this effect, a wing with the geometry shown below was created. The idea here was to generate a shape whose potential span efficiency gain for a given amount of out-of-plane deformation was large. Based on the previous figure, a split tip geometry for the wake was selected as a shape that could be generated by wake deflection and the wing planform shown below was investigated. The figure shows the planform shape and the shape of the wake trace when the wing is at 9 degrees incidence. Based on this wake shape, an induced drag savings of about 5% is possible when the wing is optimally loaded, and more as the angle of attack is increased.

Of course, the wake does not trail from the wing in the streamwise direction and careful computation of rolled-up wake geometry and inviscid drag shows that the effect of wake-rollup is to roughly double the gain expected for a streamwise wake. The 11% increment in span efficiency was significant and the concept was studied in more detail both theoretically and experimentally. The figure below shows the computed wake geometry and wing paneling used to compute vortex drag with the high-order panel code A502.

Two wings were constructed and tested at NASAÕs Ames Research Center. The first was an untwisted planform with an elliptical chord distribution, unswept quarter chord line, and an NACA 0012 airfoil section. The second wing of the same area and span, also untwisted with a 0012 airfoil section, incorporated the split tip geometry. Both models were designed to incorporate a sensitive internal balance so as to minimize support interference. The figure below shows the ratio of lift to drag for each of these wings confirming the predicted lower drag of the split tip geometry.

To further confirm the theoretical predictions, estimates of vortex drag and wake shape were compared from calculations, balance data, and a detailed wake survey. From the wake survey, an explicit estimate for the vortex drag can be obtained. This value agrees well with the computed result and the balance data.

The results are intriguing, and although the configuration was selected to exaggerate a particular effect rather than to serve as a good airplane wing, its application to aircraft, propellers, and rotors is currently under investigation.

Ilan Kroo (kroo@leland.stanford.edu)