# How can one change the wingtip geometry to enhance the wingtip vortices?

I'm doing some research on enhancing wingtip vortices as part of my Honours project. After spending a fair bit of time in the literature and on this forum I have some models which should kick-start my simulations. Because this is such a under-researched field (understandably) I wanted to mine the wisdom of those here: What design elements for a wingtip geometry would be conducive to creating a strong wingtip vortex?

The context is that I am studying how to enhance the efficiency of autonomous formation flight, using one drone as the 'tug-boat' for the other trailing drone. The leading drone would be outfitted with vortex-enhancing wingtips in order to increase the upwash experienced by the trailing drone. The overall purpose is to increase the range of the secondary drone at the expense of the first, in situations like scientific aircraft stationed in Hobart anf flying round-trip to Antarctica.

So far I have identified the Aspect Ratio, Lift Coefficient and Oswald Factor as parameters I'll need to change, based simply off the induced drag equation $$C_{d_i} = \frac{C_L^2}{\pi*AR*e}$$. This has given rise to potential solutions like using vortex generators on the wing surface to enhance lift while removing the winglet to allow the flow to curl around the tip, pitching the winglet up to increase its local angle of attack (effectively the same principle), and using a wingtip fence that runs from the leading edge to half the chord length and stops there, creating a high-pressure difference and then allowing the vortex to develop rapidly.

I'm aware I may have fundamental issues with this theory but also that I don't know what I don't know. If this won't work physically, then an explanation as to what I should be focusing on to create greater upwash outboard of the trailing edge of the leading wing would be much appreciated.

• @Jpe61 Yes, his posts shaped my initial reading at the beginning of the year. And yep, those factors are ones I've seen many times now. With a lack of ability to change the wings, I'm essentially trying to find out if there's anything I can do (and if I should be doing it) with just the wingtip geometry. Commented May 5, 2021 at 4:45

You are not interested in wingtip vortices. For now you are barking up the wrong tree. For that tug idea to work, you need to focus on the trailing vortex which is a result of the whole wing, not the wingtip.

How to maximize trailing vortex intensity? Fly slow, use a small aspect ratio and create lots of lift. This means a heavy airplane with a high span loading, flying close to stall. Niceties like the spanwise lift distribution are much less important; all low aspect ratio wings will show an elliptical or nearly elliptical lift distribution anyways.

Next, position the following airplane right. Between the two vortex cores of the leading airplane you will find severe downwash. What goes up must go down. This is not only true for aircraft, but also for the air surrounding them. So any part of the following airplane needs to stay outside of the immediate wake. In order to maximize the recovery of the energy wasted in the leading airplane you need two following airplanes, one to the left and one to the right, and ideally both need to be specific to their side since both will fly in an asymmetric flow field. If you don't account for that by optimising wing twist and weight distribution, your rudder and ailerons on the following airplanes will do that, albeit less efficiently, just in order to stay inside the upwash part of the wake.

To answer what you asked: For maximum wingtip vortex intensity you need a steep gradient of lift at the tip. This means a spanwise lift distribution which peaks near the tip. Of course this is what a good airplane design will avoid at all cost, because it not only makes it less efficient, it also results in dangerous stall behavior.

• So the optimal "tug" could be a lifting body no? Commented May 5, 2021 at 15:31
• @JohnK Yes, but that one has a poor c$_{l\:max}$. Maybe a delta wing or an F-104 would also do. Commented May 5, 2021 at 18:05
• Many thanks, this is what I was beginning to suspect. To clarify: a steep lift gradient at the tip would create stronger wingtip vortices as a result of increased lift over the wing. This would do the same thing as "Fly slow, use a small aspect ratio" etc, but less well and more dangerously compared to altering the entire wing to ehance lift. Correct? Commented May 6, 2021 at 0:25
• @HughesJC Not quite. The wing sheds vorticity over its whole span and the far-field vortex is independent of details like lift distribution, apart from the distance between the vortex cores. The near-field vorticity, however, can be increased locally by a steep gradient of lift over span, at the cost of less vorticity elsewhere. In all cases total lift will be the same. It is not about enhancing lift but to enhance the free vortex in the wake. And to help a following airplane you should focus on the far-field vortex. Commented May 6, 2021 at 4:26