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