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What is the reason for the drag due to wingtip vortices?

This question is about (general) performance, but doesn't answer the drag aspect.

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    $\begingroup$ Drag and lift don't exist per se. They are components of the aerodynamic force, the sum of all forces acting on the wing. It has a direction (vector) and as any vector, it can be broken down in arbitrary components which sum up as the initial force. We conventionally split the aerodynamic force in two components: One perpendicular to the airflow (lift), one parallel to the airflow (drag). So anything which tip the aerodynamic force away from the vertical creates drag. A vortex deviates the force, so it creates drag. $\endgroup$ – mins Dec 24 '17 at 11:23
  • $\begingroup$ @mins That's not a good answer about what causes the additional drag. You can't assume the resultant aerodynamic force is vertical, after all it is made up of lift and drag. $\endgroup$ – user7241 Dec 24 '17 at 11:36
  • $\begingroup$ The question as it stands now (after Peter Kämpf's answer) seems to be more if the vortex is the cause of the flow around the wingtip, or simply the presence of the wingtip. $\endgroup$ – user7241 Dec 26 '17 at 19:18
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Wingtip vortices don't create drag, just as wet streets don't cause rain.

Lift creation and viscosity create drag. Drag is composed of pressure drag and viscous drag, and induced drag is one part of pressure drag. Unfortunately, the Internet is full of memes which attribute induced drag to those wingtip vortices, but some swirling air behind a wing can hardly cause any drag, can it?

See it another way: If the wing were not creating any lift, the air would not flow around the tip and curl up. So why don't we read that the tip vortex is the source of lift? This uses the exact same logic as saying that the tip vortex creates drag, and is equally wrong.

Wingtip vortices are just the tip of a full vortex sheet which leaves the wing. This vortex sheet is the consequence of the wing accelerating air downwards. Now instead of repeating myself all over again, please allow me to point you to the many other answers which explain what is going on:

  • This answer explains in detail how lift is created and how the downward acceleration of air is accomplished.
  • This answer goes into the formation of the wake and the wingtip vortices.
  • This answer shows why more wingspan reduces induced drag. It matters little whether the wingtips are turned up, down or continue straight: A larger wingspan reduces induced drag.

Winglets increase the amount of air involved in lift creation and reduce induced drag for the same lift. In most cases they are used to create more lift with the same geometric wingspan without incurring a disproportionate drag penalty.

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  • $\begingroup$ I'm still thinking about it and reading the links. $\endgroup$ – user7241 Dec 25 '17 at 11:47
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    $\begingroup$ ..some swirling air behind a wing can hardly cause any drag.. Why would that be such an alien assumption? Creation of a vortex does require energy. The propeller slipstream is completely downstream of the propeller, yet creating the whirl in it did cost energy. $\endgroup$ – Koyovis Dec 26 '17 at 2:44
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    $\begingroup$ @Koyovis: The swirling is just the sign that air has been accelerated before, just like water on the streets makes evident that it has rained before. $\endgroup$ – Peter Kämpf Dec 26 '17 at 12:52
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    $\begingroup$ @PeterKämpf I realise that the air streaming off of the trailing edge is accelerated downwards, that induced drag is not solely caused by wing tip effects, that downstream of the wing the discontinuity at the tip is being filled in without any energy impact for the aeroplane, and that there is a large amount of confusion about the subject. However, if there is lift created at the tip and air does flip over, how does that not have an energy impact? Related: why do elliptical and triangular lift distributions provide the least drag, if not to prevent the additional flipover swirl? $\endgroup$ – Koyovis Dec 26 '17 at 20:01
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    $\begingroup$ @mins: That is a captious comment - I want to illustrate how people confuse cause and effect. The vortex is the effect but not the cause of drag-creating flow. And lift-creating flow, by the way. But nobody claims that the tip vortex is the source of lift (which is equally false and uses the exact same logic). Go figure. $\endgroup$ – Peter Kämpf Dec 26 '17 at 23:42
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The short answer is this: Drag is not "created from" from wingtip vortices. Says McLean,

The trailing vortex sheet and the rolled-up vortex cores are often seen as the direct cause of the velocities everywhere else in the flowfield and thus also the cause of induced drag, but this view is mistaken. It is true that when a 3D wing produces its characteristic large-scale flow pattern...there must be a vortex sheet shed from the trailing edge, but the vortex sheet is not a direct physical cause of the large-scale flow; it is more of a manifestation.

More fundamentally,

In the absence of significant gravitational or electromagnetic body forces, there is no action at a distance in ordinary fluid flows. Significant forces are transmitted only by direct contact between adjacent fluid parcels. So there is no way a vortex at point A can directly “cause” a velocity at some remote point B, and terms such as “caused by” and “induced” and even “due to” misrepresent the physics.

A couple things should be noted here. First, McLean is discussing the entire trailing wake of the wing, not just the tip vortices. But the tip vortices are simply one component of the trailing wake, so the discussion can apply solely to them if you'd like. Second, "it is more of a manifestation" does not conversely mean that drag creates wingtip vortices. The flow pattern behind a wing is the result of simultaneously satisfying conservation of energy, mass, and momentum. All the cause-and-effect relations of classical aerodynamics are actually all inextricably intertwined in the physics.

So why is it often said that wingtip vortices create drag?

There are several ways to think about it, but here's the one I've found most instructive and one whose benefit is that we don't need to concern ourselves with the details of the flowfield. Says Anderson,

The wing-tip vortices contain a large amount of translational and rotational kinetic energy. This energy has to come from somewhere; indeed, it is ultimately provided by the aircraft engine, which is the only source of power associated with the airplane. Since the energy of the vortices serves no useful purpose, this power is essentially lost. In effect, the extra power provided by the engine that goes into the vortices is the extra power required from the engine to overcome the induced drag.

A couple more things should be noted here. First, Anderson is discussing just the tip vortices, not the entire trailing wake of the wing. But the tip vortices are simply one component of the trailing wake, so the discussion can apply (and really should apply) to the whole thing. Second, you bring up the issue of aircraft without engines. I'd prefer if Anderson had said "propulsion system" rather than "engine" to generalize for this case, but the physics is the same: "extra power" for a glider can be thought of as the extra potential energy needed to impart kinetic energy into the wake or even the extra kinetic energy that a towplane or thermal needs to provide to build that potential energy.

A final note on induced drag: The reason we have lift is again the simultaneous satisfaction of conservation of mass, energy, and momentum. More specifically, lift occurs as the wing imparts energy into the air in just such a way to maintain the correct pressure distribution. Somewhat unfortunately, the energy put into the air that creates lift is exactly the same energy that Anderson describes as necessary to overcome the induced drag. This coupling is fundamentally why we can't have lift in the real world without drag.

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  • $\begingroup$ A glider or sailplane has the vortices too. $\endgroup$ – user7241 Dec 25 '17 at 22:10
  • $\begingroup$ Sure does! "Propulsion system" encompasses more than just an engine. $\endgroup$ – Peter Schilling Dec 25 '17 at 22:11
  • $\begingroup$ I know, but I'm having trouble fitting gravity or thermals into the picture. $\endgroup$ – user7241 Dec 25 '17 at 22:12
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    $\begingroup$ Okay, but we don't need to concern ourselves with the detailed mechanics of the vortex to analyze the energy of the entire system. $\endgroup$ – Peter Schilling Dec 26 '17 at 5:18
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    $\begingroup$ Let us continue this discussion in chat. $\endgroup$ – Peter Schilling Dec 26 '17 at 17:54
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Wing-tip vortices increase drag in two ways:
- the pressure at the entire trailing (rear) edge of of the wing reduces, which increases the pressure difference between the leading (front) and training edge.
- It reduces lift, so you need a bigger wing to carry the same load. Bigger wings obviously have more drag.

According to, among many others, NASA Technical Memorandum 81230, 'Effect of Winglets on the Induced Drag of Ideal Wing Shapes' by R. T. Jones and T. A. Lasinski, wing lets do reduce drag. The memorandum starts with the following sentence: "It has been known for many years that vertical fins or end plates at the tips of a wing can significantly reduce vortex drag."
http://www.engbrasil.eng.br/artigos/art60.pdf

More information can also be found in this link: https://www.mh-aerotools.de/airfoils/winglets.htm#Induced%20Drag

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