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Most wings suffer from induced drag due to a pressure difference above and below the wing causing air to sneak around the tip, forming a vortex. There are various methods to minimize these effects, such as winglets.

However, looking at the Synergy aircraft as an example, box wings have no wing tips. Disregarding any other parts of the aircraft, are the wings actually free from induced drag? Or are they still causing induced drag, just in a way I'm not able to think of with my limited fluid dynamics experience?

Synergy aircraft with box wings

Synergy aircraft with box wings (picture source)

I've read somewhere that a traditional bi-plane design is less efficient due to the wings interfering with each other (apparently something addressed by the synergy aircraft by placing the upper wing further back or something), and the upper wing is actually more of a tail-plane, pushing down, thus further increasing the airspeed in between the airfoils if I understand correctly and eliminating the pressure differential from the top of the upper wing to the bottom of the lower wing, and both wings would of course generate normal drag by cutting through the air, but I'm only interested in the induced drag at this point.

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    $\begingroup$ looks like a fancy biplane-like design. $\endgroup$ – ratchet freak Apr 17 '14 at 9:57
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    $\begingroup$ @ratchetfreak except bi-planes have four wingtips, this one has zero. $\endgroup$ – falstro Apr 17 '14 at 9:59
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    $\begingroup$ @falstro: This has two wing tips. The meaning of "upper" surface changes over the vertical struts, so they act as tips anyway (and if it didn't change, the upper surface would produce negative lift and the whole thing would produce none and be useless). $\endgroup$ – Jan Hudec Apr 18 '14 at 10:03
  • $\begingroup$ @JanHudec; actually the upper surface does produce negative lift (as I mentioned in the last sentence of the question), it sits behind the lower wing and works like the tailplane of other aircraft. $\endgroup$ – falstro Apr 18 '14 at 13:14
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    $\begingroup$ @falstro: Nevertheless since the whole thing produces net lift, it accelerates air downward and since the air beyond it's span is not accelerated, creates wingtip vortices with the vortex lines leaving the system somewhere along the vertical struts. $\endgroup$ – Jan Hudec Apr 18 '14 at 19:55
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The box wing is only better when you compare wings with identical span. The two wings of a box wing work in different Treffz planes, so the downwash is spread out vertically. The difference in induced drag to a single wing is not big, just a few percent. The friction drag is higher (see below), as is the structural mass, so the box wing needs to create more lift. This makes the induced drag of a box wing effectively higher than that of a single wing.

What is induced drag, anyway? It is the consequence of creating lift over a limited span. The wing creates lift by deflecting air downwards. This happens gradually over the wing's chord, and creates a reaction force orthogonally to the local speed of air. This means the reaction force is pointing up- and slightly backwards. This backwards component is induced drag! Wingtips are not involved and are not causing induced drag. Lift creation is.

If you fly fast, there is a lot of air mass streaming past the wing per unit of time, so you need to deflect the air only slightly. Your induced drag is small. Sames goes for a large span: There is more air which can be deflected, so the induced drag is small.

A box wing needs two slim wings per side, which will have a smaller chord than a single wing of the same surface area. So their Reynolds number is smaller, and their friction drag is higher. Also, the wing spar is less thick and will need to be heavier to carry the same lift!

If you drop the restriction of keeping span identical, the optimum single wing can afford to have more span (due to its better structural efficiency), and away goes the advantage of the box wing. And once you look at the full picture and add structural mass, the box wing never had this advantage in the first place.

Yes, but what about the Synergy?

The Synergy is a clever design with some advantages, but it cannot cheat physics. These are the advantanges:

  • The pusher prop keeps the airframe free of wake turbulence, so more area can be kept in laminar flow.
  • The pusher prop sucks the air from the rear fuselage, effectively avoiding separation.
  • The two stubby tailbooms and fins give great protection for the propeller area on the ground.
  • The compact layout keeps the stabilizing effect of the propeller small, so maneuverability does not suffer much.
  • The use of composites and glider airframe technologies reduce friction drag.
  • The diesel engine consumes cheaper jet fuel and is more fuel-efficient than a gasoline engine.

Note that I did not mention the box wing design?

Here are the disadvantages:

  • Wing sweep in a propeller aircraft looks cool, but increases drag, because the wing must be bigger to create the same lift.
  • In total, this configuration has four vertical tails, each of them with its own interference drag and a short chord which, again, increases drag over a comparable single vertical tail.
  • The stretched-out horizontal tail is also less effective than a smaller single surface with more chord and more distance from the center of gravity.
  • The compact layout provides little pitch or yaw damping. I wonder what the ride qualities in gusty weather are.

I would expect that a more conventional layout along the lines of the fs-28 would be even more efficient.

Akaflieg Stuttgart fs-28 in flight

Akaflieg Stuttgart fs-28 in flight (picture source)

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Q: Do box wings suffer from induced drag the same way as normal wings?

A: Yes and no. Box Wing aircraft will suffer from induced drag the same as any aircraft will, if they are heavier-than-air vehicles and are using their wings to fly. Induced drag is a function of finite span loading, and moderated by various ways to improve design efficiency at a given span loading. Thus the amount of drag, and the way it is created and avoided, differs for a boxwing and a monoplane of the same span. Today this topic of induced drag includes completely different definitions than what was taught in seminal references on the subject. Even if one is talking about the same thing, the topic will hear arguments from two different camps: those who adhere to representative mathematics, and those who focus on the non-Cartesian, non-textbook actual physics on a case-by-case basis. It's quite fair to say that the former are more vocally opinionated than the latter, for the latter know less until later.

The job of a wing is to efficiently push and pull air downward as it moves forward. That action causes both a Newtonian reaction and a Bernoulli pressure differential, resulting in lift.

Making lift this way causes the nearby air to also be affected, as a time-dependent secondary result. It has to 'fall into the descending trough of air' that the wings displaced downward.

This secondary movement causes (completely unavoidable) rotational movements in the "wake" zone between air directly moved by the wings and the nearby stationary air, thereby involving more air mass than the plane needed to move just to get the lift it needed. (The momentum difference is quite literally the induced drag, although we usually teach it in ways more related to how induced drag is visualized and computed in 2-D. Other answers posted here illustrate this in conventional terms.)

Induced drag and wake vortex CANNOT be eliminated for a lifting wing system of any kind. However, most aircraft wing designs allow something else to happen that greatly increases this cost of making lift with a finite wingspan: they let high pressures under the wing be 'too close' to the low pressures above the wing for the amount of pressure difference that has developed in flight. If a high differential pressure exists at a wing tip, a strong, tornado-like vortex will form there.

Allowing any strong gradient to form between low pressure and high pressure will cause air to move toward the low pressure at a high velocity, if it can. Drag increases exponentially with the velocities imparted to the air, therefore designers use a variety of approaches to keep this equalization from happening quickly. The slower it happens, the less kinetic energy is imparted to the air by the airplane.

This is where Boxwings have a totally different way of reducing the induced drag, compared to a normal wing: they put a wall up between the low pressure above the wing, and the higher pressure everywhere else. The 'wall' can be taller than a winglet, because it has a wing above to help resist the forces that push on it from the side. At that upper wing connection, the wall-like vertical surface of a boxwing likewise stands between the higher pressure under the wing, and the lower pressure everywhere else.

If a designer does a good job with this idea (many do not), both the biplane wing surfaces and the vertical surfaces of the boxwing system will moderate the velocity of gradient-induced airflows by acting against the undesirable flows in 3-D space. They become more effective in this with greater vertical spacing.

The easier and more effective way to reduce the induced drag is simply to increase the wingspan, or reduce the vehicle weight. As a wing gets longer, the portion of the lift each unit of the wing needs to make is reduced, meaning that it will have a lower pressure differential between the upper and lower surfaces. Best practice calls for this differential to be minimized at the tip, so the gradient is weakened. The result then is that a weaker pressure gradient and a longer distance between low and high pressures will keep the equalization velocities down.

However, as an aircraft gets heavier or goes faster, this approach becomes first very expensive, then impossible. Material strength limitations put definite limits on the wingspan of conventional aircraft.

Surprisingly, box wings fare no better... perhaps worse. What appears to be a structural advantage actually merely concentrates the bending forces, generated by each wing, into the corners of the box. Making them strong enough quickly becomes excessively heavy. Therefore, a box wing aircraft should, like a biplane, have a shorter span than a monoplane of equivalent induced drag. Its span efficiency bears greater fruit among short span designs, than where wingspan can be increased.

One might think that this advantage would then bear fruit indirectly, through speed. The faster an aircraft flies, for a given span loading, the less induced drag it will make. In fact, at high indicated airspeeds, induced drag becomes a small component of total drag. However, other aspects of box wing designs seem to have impeded high-speed boxwing solutions; notably stability; and "interference drag."

In a box wing design, there is a forward set of lifting wings, and an aft set of lifting wings. In high speed flight this configuration cannot respond as stably or as quickly to certain conditions as a wing with a (downward-lifting) tail.

When set up as a tandem-lifting wing arrangement without such a stabilizer, as is typical of modern versions, boxwings have to balance at their combined center of upward lift, rather than ahead of it like conventional aircraft do, thanks to the stabilizing influence of a tail pushing in the opposite direction. This limitation and tandem-wing stall behaviors place challenging, inherent demands on boxwing designs that constrain their success at higher flight speeds.

As noted above, they also create interference drag. This type of drag can be hard to predict and is also widely misunderstood. In practice, the inherent, 3-D interference drag of a boxwing aircraft design greatly reduces the 2-D theoretical advantage of the configuration toward obtaining induced drag benefits. This is why they are not at all like "normal wings."

As mentioned in the original post, there is a new aircraft configuration that is often mistaken for a box wing design. However, it is nothing like them. It's called a box-tail or double boxtail configuration. I am the designer of the Synergy double boxtail aircraft, which is the first such aircraft to be developed.

These somewhat disappointing attributes of the otherwise logical box wing configuration were at the heart of matters during the long period of Synergy's development. It was my desire to utilize high span efficiency and laminar flow in a high speed aircraft design, while avoiding high speed landings and unpredictable, unstable behaviors at low speeds. A video of a 25% scale model in flight and a basic overview can be seen at synergyaircraft.com. A post on the topic of boxwings can be found there as well.

For more information regarding span efficiency and non-planar configurations, Ilan Kroo has published very thorough overviews of the subject. The graphic below is adapted from one appearing in his papers. It shows how induced drag can be fought in 3-D space by moving away from a flat, planar wing into the vertical dimension. Synergy builds that understanding further, into the longitudinal and time dimensions, in accord with the concepts advanced first by George C. Greene while at NASA Langley.

Span efficiency for non-planar configurations

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  • $\begingroup$ You start with a great explanation of why induced drag happens, only to fall into the old trap of "vortices created by flow around the tip" as most others here do. Sad. $\endgroup$ – Peter Kämpf Jan 17 '15 at 12:11
  • $\begingroup$ @Peter I think you're being a tad pedantic here (which would be OK if you did not call it 'sad'). While it's true that vortices are not the cause of induced drag, one can show that lift generation without vortices would be equivalent to creating lift with an infinite wingspan. Like many things in physics, cause and effect are largely dependent on ones viewpoint rather than an absolute measure. $\endgroup$ – Sanchises Sep 23 '16 at 14:50
  • $\begingroup$ @sanchises: I agree. Yes, I am pedantic, but only because I am convinced that only rigorous logic will lead to a complete understanding. Muddled thinking where cause and effect become interchangeable will lead to muddled understanding, and explaining something from that starting point will do a disservice to novices who will so easily misunderstand the details. And then you hear again from these poor people which never got a chance to learn things properly that the tip vortices cause drag. Isn't it right to feel sad about this? $\endgroup$ – Peter Kämpf Sep 23 '16 at 15:46
  • $\begingroup$ @PeterKämpf But then, being too focused on rigor leads to needlessly complicating things. Reducing wingtip vortices does lead to an increased effective wingspan reducing induced drag - so perhaps as a rough approximation, saying "wingtip vortices cause induced drag" does have a core of truth to it. But I guess as with anything in aviation, the 'simple explanation' indeed holds relatively little explanatory power, and will fall short when box wings are analyzed in detail. $\endgroup$ – Sanchises Sep 23 '16 at 16:18
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They're not free from induced drag, but the induced drag is greatly diminished, as demonstrated in Prandtl's NACA paper from 1924 and reported in this book (See chapter 11)

enter image description here

The authors of that book applied the results to the design of this aircraft

enter image description here

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  • $\begingroup$ Cool! So where does the induced drag come from? $\endgroup$ – falstro Apr 17 '14 at 10:09
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    $\begingroup$ @falstro the wings will never be perfect, some circulation will still happen. Also, the aerodynamic force vector, depending on the wing shape, can be slightly tilted backwards, creating a drag component. $\endgroup$ – Federico Apr 17 '14 at 10:13
  • $\begingroup$ wikipedia has some schematic that let C wings approach box wings $\endgroup$ – ratchet freak Apr 17 '14 at 10:58
  • $\begingroup$ @Federico: The circulation around the tips is some percent. Perhaps 10 or 20 %, but not more. Most is caused simply by applying force on air and the air, being freely movable, accelerating and taking kinetic energy with it. Nothing can be done about that. Result is that the induced drag is diminished, but not greatly. $\endgroup$ – Jan Hudec Apr 17 '14 at 21:53
  • $\begingroup$ @JanHudec I have difficulties understanding what you mean, but if I read you correctly, you speak about the whole drag, not the induced part alone. $\endgroup$ – Federico Apr 18 '14 at 7:40
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The main reason for induced drag is, that the wing accelerates the air above and below it downwards increasing it's kinetic energy and due to law of conservation of energy, it has to take that energy somewhere and the only way is by doing negative work on the aircraft, i.e. inducing drag.

The amount of air accelerated per unit of time is proportional to the wing span and speed of the aircraft. Applying the same force to more air accelerates it to lower speed and because kinetic energy is proportional to square of speed it induces less drag. That's why high aspect ration (long span) wings are more efficient and why induced drag decreases with speed.

wingtip vortices

The wingtip vortices are simply borders of this area of descending air. And because you can't generate lift without accelerating air downward (by law of action and reaction), this induced drag is principal and any finite-span wing will induce it . And it will only depend on the lift generated, wingspan and speed and nothing else.

See also How It Flies, section 3.13 (the figure is from there).

Now there is some additional induced drag caused by higher-pressure air flowing around the wing-tip which does not contribute to lift (or even slightly negatively), but contributes to drag. It is maybe low tens of percent or something like that. The several percent that can be saved by various measures are significant enough to be worth the effort, but they are still several percent. Miracles are not possible.

By the way, the box wing still has tips. Air can't flow to or from between the wings, but it can flow from under the lower horizontal surface to above the upper one. Plus the wing is relatively low aspect ratio.

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Many good points about drag reduction here.

Yes, induced drag can be reduced a few percent with a box wing, by diffusing the wing tip vortex. Makes a difference of a few percent, which is significant. About the same as a biplane.

The REAL compelling advantage of boxwings is structural. With the wings connected at the tips, it's possible and practical to design for a given strength and rigidity with less material. The wings can support each other, and damp each others natural resonance, buying some margin against flutter and failure.

Rick Gendreau, designer, Halcyon boxwing.

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Closed systems (Box Wing is only a particular type of closed wing), C-wings and biwings are actually related as far as the minimization of induced drag is concerned.

If you are interested in technical answers regarding the induced drag minimization/performance of Box Wings, closed systems, bi-wing systems, and multiwings, you can find all the details in the following publications (I can also send to you the papers if you email me at the address luciano.demasiATgmail.com):

=====Article 1 =====

Demasi Luciano, Monegato Giovanni, Dipace Antonio and Cavallaro Rauno "Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Theory", Journal of Optimization Theory and Applications, 2015, pages 1-36, DOI: 10.1007/s10957-015-0849-y, ISSN:0022-3239

=====Article 2 =====

Demasi Luciano, Monegato Giovanni, Rizzo Emanuele, Cavallaro Rauno and Dipace Antonio "Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Applications" Journal of Optimization Theory and Applications, 2015, Pages 1-25,Doi: 10.1007/s10957-015-0849-y, ISSN:0022-3239

=====Article 3 =====

Demasi Luciano, Monegato Giovanni, Cavallaro Rauno "Minimum Induced Drag Theorems for Multi-Wing Systems" ,2016,4-8 January,SciTech2016, San Diego, California, AIAA 2016-0236

=====Article 4 =====

Demasi Luciano, Dipace Antonio, Monegato Giovanni, Cavallaro Rauno "Invariant Formulation for the Minimum Induced Drag Conditions of Nonplanar Wing Systems", AIAA Journal, 2014,October,10,2223-2240,52, Doi:10.2514/1.J052837 Url: http://arc.aiaa.org/doi/abs/10.2514/1.J052837

Sincerely,

Luciano Demasi

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    $\begingroup$ The references are certainly helpful, but including some information here in the answer would be even more helpful. $\endgroup$ – fooot Jan 28 '16 at 20:25
  • $\begingroup$ You can find more information on wikipedia at the following link: en.wikipedia.org/wiki/Lift-induced_drag [several pictures are also posted there] Or I can send material if you provide an email address. Best regards, Luciano Demasi $\endgroup$ – Luciano Demasi Jan 28 '16 at 21:49

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