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I read,

A third physical explanation of the source of induced drag is that the wing tip vortices contain a certain amount of rotational kinetic energy. This energy has to come from somewhere; indeed, it is supplied by the aircraft propulsion system, where extra power has to be added to overcome the extra increment in drag due to induced drag.

[Source: Introduction to Flight by John D Anderson, Sec: 5.3 "Finite Wings"]

And interpreted thus,

Vortices have rotational energy which comes from propulsion. This additional requirement of "Thrust" can be balanced with Induced drag.

And this makes me question, how gliders form vortices when it does not have engines? Or even single mounted engines in prop planes that do not have engines on wings?

Could you see the vortices created by the glide of owl in the video here and here?

Also, if the phenomena of vortex is not due to engines than why there are four vortices in this famous image:

enter image description here

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    $\begingroup$ Where did you read this? Your question is full of misconceptions and this quote is misleading at best. $\endgroup$ – Sanchises May 6 at 20:18
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    $\begingroup$ Tempted to +1 just for that owl video. Consider adding a source for your opening quote, if you have one. It may not be entirely correct though. You might consider adding a sentence immediately after the quote, "Is this quote correct"? $\endgroup$ – quiet flyer May 6 at 20:29
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    $\begingroup$ Thank you for adding the context. And welcome to the site. See related: How is drag created from wingtip vortices? $\endgroup$ – ymb1 May 6 at 20:40
  • $\begingroup$ @quietflyer The video is good, but the commentary is awful and makes me want to mute it. $\endgroup$ – Peter Kämpf May 7 at 0:47
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    $\begingroup$ In the picture of the 4-engined plane, I think you are seeing exhaust contrails, which are basically moisture from the (turbulent) exhaust condensing in the cold air at altitude: en.wikipedia.org/wiki/Contrail They're not the same as wingtip vortices. $\endgroup$ – jamesqf May 7 at 1:14
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The vortices that you are referring to (I think) are wing-tip vortices, a product of the wing generating lift. Since glider wings do generate lift (due to the airflow over the wing) and are propelled (without engine created propulsion) wing-tip vortices are created. Single engine airplanes also create wing-tip vortices since lift is being generated (aided by propulsion)

The jet in your photo is showing "vapor trails" or "contrails" from condensation (from the engines' exhaust) and are not wing-tip vortices.

I'm pretty certain there are a number of engineers on ASE that could provide a more technical answer, but the bottom line is the engines of an airplane do not create vortices (in the context of wing-tip vortices that I believe you are thinking of).

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    $\begingroup$ The right trail especially seems to be folded over itself, a certain distance behind the plane. Does that folding action come from the invisible wingtip vortex next to it? $\endgroup$ – user253751 May 7 at 10:12
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    $\begingroup$ @user253751 -- yes-- from head-on they would look symmetrical-- viewed from the other side the folding would be more visible on the other side-- they are the same, each wraps up into a spiral (a vortex) with the top half moving toward the plane and the bottom half moving away $\endgroup$ – quiet flyer May 7 at 13:48
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    $\begingroup$ @quietflyer I am aware. In the picture in the question, it is most visible on the right side. $\endgroup$ – user253751 May 7 at 15:12
  • $\begingroup$ I think it's inaccurate to say "wing-tip vortices, a product of the wing generating lift". Vortices are a class of fluid dynamic behaviors caused by fluid disruption. Lift is one scenario of disruption, but there can be many others. It might be better to just say that wing-tip vortices are a product of airflow differences around the wing. $\endgroup$ – Michael Teter May 9 at 20:21
  • $\begingroup$ @MichaelTeter-I don't want to grind the definition of "wing-tip" vortices too fine. "Fluid disruption" may be a bit more complex than the OP needed. Here is the definition (FAA's Airplane Flying Handbook) of "Wake Turbulence" (the generalized pilot understanding of "wing-tip" vortices):"Wingtip vortices that are created when an airplane generates lift. When an airplane generates lift, air spills over the wingtips from the high pressure areas below the wings to the low pressure areas above them. This flow causes rapidly rotating whirlpools of air called wingtip vortices or wake turbulence." $\endgroup$ – 757toga May 9 at 21:03
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Vortices have rotational energy which comes from propulsion. This additional requirement of "Thrust" can be balanced with Induced drag.

The "vortices" in question are generated by the wings themselves, not the propulsion system. There's a whole "downwash system" in the air behind the wings, which includes the vortices coming off the wingtips themselves. The sheet of downward-deflected air behind the wings actually gets entrained in the wingtip vortices.

The meaning of the quote is not that the propulsion system directly creates a vortex, but rather that it takes energy to create the wingtip vortices, which (at least in the case of a powered aircraft in horizontal flight) creates a demand for extra power and thrust. The extra thrust required to create the vortices is exactly equal to the "induced drag", which is the drag associated with creating the vortices, or perhaps more correctly stated, the drag associated with creating the whole downwash system (which includes the wingtip vortices) behind the aircraft.

If something is not entirely technically accurate in my explanation above, I hope another answer will correct it, but that's the general idea that the quote was trying to convey.

The photo you included shows how the contrails behind the engines can help make the wingtip vortices more visible. The air behind the engines eventually gets entrained in the wingtip vortices. But you could create a similar picture just by mounting four smoke canisters under the wing of a single-engine airplane, or a glider. The airliner's engines are not actually creating the two main vortices that we see far behind the aircraft. Rather, the flow field around the entire wing is.

Hopefully this answer has made it clear that single-engine planes will have wingtip vortices, just as airliners do.

Gliders have wingtip vortices too. As for where the energy comes to create them, with no motor -- this answer may shed some light on that-- An airplane has an engine that pushes its flight. What force pushes a glider to fly?

In the case of birds, the story is different-- each wingbeat significantly affects the flow field around the entire wing, so there's a closer link between the system of propulsion, and the vortices left behind.


The question has been edited to suggest that the passage I've quoted is actually the question-asker's interpretation of a passage from a textbook. I'll just let my answer stand as is; I think it is still of some value to the asker of the question.

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    $\begingroup$ A simple way to understand where the vortex comes from is Joukowski airfoil theory. The flow pattern around a wing producing lift can be considered as the sum of steady flow (which does not produce any lift) and circulation around the wing (which creates lift and is analogous to the Magnus effect). The circulating flow is left behind as a vortex shed from the wing tip. $\endgroup$ – alephzero May 7 at 18:54
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The aerodynamics can be explained, something I cannot do for that quote. Let's address the quote story first and, once that's out of the way, let's have a look at the aerodynamics.

Wonky Quote

Vortices rotate, so they have rotational energy. That has noting to do with propulsion. Hurricanes, Tornadoes, ... are vortices, even pulling the plug in average Joe's bathtub and letting the water circle is a vortex and hence contains rotational energy. No propulsion there. (The rotational energy comes from other sources).

Thrust is not an "additional requirement". It's just that in stationary, horizontal, and level flight, thrust and drag are at equilibrium. But that's total drag, the induced drag is just a part of that.

Bottom line, I cannot support that quote.

Aerodynamics

Induced drag (slightly oversimplified) is just the tip circulation of the wing. Basically, under the wing the aircraft needs higher pressure than above, that's what is creating the lift. But as a parasitic effect, that means that during flight, there is also some air flowing around the wing tip - basically pushed from the high pressure domain below the wing to the low pressure domain above the wing. So around the wing tip, strong vortices are induced. Now, for each meter that the aircraft flies, one meter of vortex is added on either side. These vortices contain kinetic energy, and for lack of another source, it had to be provided by the aircraft. Finally, if you consider that it is "energy spent per distance", and the very definition of energy is force*distance, you can divide that energy by the distance and retrieve a force - the induced drag. That's the case for any wing, glider or jet fighter, propulsion doesn't change that. The point about gliders is only that they provide that energy by losing altitude.

Then there's a bit more theory on that, if you're interested

https://en.wikipedia.org/wiki/Helmholtz%27s_theorems

and also, the vortices aren't necessarily only two simple vortices on either side, rather they are a spacial distribution, described as a vortex field. But that's just to add more precision, not to change the picture.

The Movies They're all very great, btw

As for what you see on the 747 - it's not 4 vortices, it's four vapor trails, that roll neatly up into the vortices.

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  • $\begingroup$ Thank you for the corrections. $\endgroup$ – Carl Berger May 7 at 17:23

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