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Cambered airfoils generate induced drag because they have a pressure differential between the upper and lower surface. However symmetrical airfoils don't. So does this mean that symmetrical airfoils have no induced drag? enter image description here

Image source:https://en.m.wikipedia.org/wiki/File:Airfoil_camber.jpg

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    $\begingroup$ The airfoils alone don't - but the wings made with them do. Especially if they have finite span and produce lift. $\endgroup$ Commented Jun 26, 2022 at 14:05

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If an airfoil is producing lift, then it will be producing induced drag.

Both cambered and symmetrical airfoils have an angle of attack at which they produce no lift, no induced drag, and no pressure difference between top and bottom. While this angle lines up nicely with the geometrical mid line of the symmetrical airfoil, it is offset from the apparent mid line of the cambered airfoil.

The cambered airfoil can produce more lift before the stall in the 'normal' lift direction, which is why it tends to be used for surfaces loaded in only one direction, like wings. A symmetrical airfoil would be used for control surfaces which might see equal loading in either direction.

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It depends on the angle of attack. If it is non-zero there will still be a different airflow on both sides - leading to different pressures and thus induced drag.

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Mmh, here there is a MISUNDERSTANDING OF TERMINOLOGY and even the wiki.en page about induced drag is a bit misleading.

Induced drag is a strictly 3D phenomenon, so speaking about induced drag for an airfoil is physically and mathematically not correct since airfoils are, by definition, 2D geometric shapes.

An airfoil generates lift, drag and moment, even if it is a simple 2D shape. But what is defined as "induced drag" is an additional contribution to the drag that appears only introducing the third dimension (it is a bit like when the flow becomes supersonic, then yet another source of drag - the wave drag - appears as well). So, the exact geometry of the 2D airfoil is not important here, only the fact that the "wing ends" is involved in generating the induced drag.



Qualitatively the induced drag can be explained looking at what happen at the wing's tips i.e. when the wing ends. On the upper surface of the wing there is an underpressure while on the lower part of the wing there is an overpressure. At the tip, the underpressure over the wing sucks in the air which is pushed away from beneath the wing and "escapes" around the wingtips. This generates behind the wingtip a typical vortex as visible in the following picture:

B-727 in flight during vortex study with wingtip smoke generators B-727 in flight during vortex study with wingtip smoke generators. Source: https://www.dfrc.nasa.gov/Gallery/Photo/B-727/Large/ECN-3831.jpg

More correctly, a "sheet of vortex" is released from the trailing edge of the entire wing as visible in this standard representation:

Vortex sheet in the wake of a wing of finite span Vortex sheet in the wake of a wing of finite span. Source: https://cdn-images-1.medium.com/max/1600/0*2gL-QOXqx51qNdAE.jpg

But normally only the vortex at the tip is taken into account for the sake of simplicity (even if this is not really correct). This vortex sheet locally decreases the angle of incidence therefore reducing the total lift generated by the wing. To compensate for this reduction, the angle of incidence has to be increased with a related increase of drag. This latter, and only this, is the induced drag. I perfectly agree that the naming is a bit misleading, but this, and only this, is the definition of induced drag.

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  • $\begingroup$ I find en.wikipedia.org/wiki/Lift-induced_drag a way less misleading explanation than any talk about flow around the wing tips. While both are correct, just using different levels of description, talking about the flow around the wingtips leads people to think the induced drag can be significantly affected by changing the wingtips, while in fact changing the wing tip is at best equivalent to slightly increasing the wingspan. The angle of force and/or conservation of momentum and energy arguments don't have that problem, and immediately explain the inverse dependence on speed. $\endgroup$
    – Jan Hudec
    Commented Aug 14, 2022 at 17:31
  • $\begingroup$ It is only a strictly 3D phenomenon according to the lifting line theory. Conservation of energy and momentum prove that any 2D section producing lift must also produce induced drag in an off itself without need to consider the wing tips. $\endgroup$
    – Jan Hudec
    Commented Aug 14, 2022 at 19:56
  • $\begingroup$ @JanHudec: Using a 2D airfoil to describe a fundamental 3D phenomenon is physically and mathematically incorrect, even if Wikipedia says so 😉 And yes, modifying the wingtip geometry is a useful (and used) way to control induced drag, together with other expedients like adjusting aspect ratio, sweep angle, taper ratio, t/c, twist angle and, obviously, airfoil geometry. In modern jetliner even the stiffness of the structure is "tailored" according to the different aerodynamic environments due to different loading conditions. $\endgroup$
    – sophit
    Commented Aug 14, 2022 at 20:20
  • $\begingroup$ @JanHudec: Again, here there is a misunderstanding in terms. Navier–Stokes equations prove/model that an airfoil (or even a slice of a washing machine) generates lift, drag and moment, even in 2D. What is defined as "induced drag" is an additional contribution to the drag that appears only introducing the third dimension, so it is a strictly 3D phenomenon (that Prandtl smartly simplified via his lifting-line theory enough to make it solvable by hand) 🖖 $\endgroup$
    – sophit
    Commented Aug 14, 2022 at 20:38
  • $\begingroup$ Then there are two definitions that are clearly incompatible with each other. Because so far I always heard “induced drag” to mean the drag due to generation of lift (as opposed to friction and pressure drag that are there even if no lift is generated), but that is there even in 2D, even though yes, in 3D there is an additional contribution. Not a huge additional contribution though. $\endgroup$
    – Jan Hudec
    Commented Aug 14, 2022 at 21:39
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Would you believe I have a draft journal article about this. The use of the term "aerofoil" is a clear implication of 2-dimensional flow, or what Hurt [1] (and many others) call and infinite wing (AR = $\infty$). The tern wing is a clear implication for 3-dimensional flow. There is a clear logical distinction between how we teach these in aerospace (aeronautical) engineering and is best captured by Anderson [2]. That is, we teach 2D aerodynamics first, then we teach 3D aerodynamics.

Now, the aforementioned journal article I am working on is about confusions with this. In that, I have studied education literature on lift, and only one third of the time when an "aerofoil" is used and the implication is 2D flow, do they actually get this correct. For wings and 3D flow, this is much better, it is three quarters of the time when they are talking about wings and 3D flow that it is correct. So, as is reflected here in this discussion, there is a misunderstanding about the fundamentals of 2D flow.

As has been pointed out by others, there is no induced drag in 2D flow. Hence, the answer to the question is no, symmetric aerofoils, like all aerofoils, do not produce induce drag. Induce drag results from 3D effects, whereby energy is wasted by a wing imparting a downward velocity component to the air. This image from Hurt [1] is the best reference to this and is sadly never referred to once in 105 articles about lift education (or in books on the topic). As such, I recommend reading Hurt for the best description of induced drag. You will note in the image that the vertical velocity component for 2D flow returns to zero, while for 3D flow, it does not. Happy to share either some potential flow of CFD sims that support what was clearly well known in the 1960's. Upwash and downwash in 2D and 3D flow

1 Hurt, H. H. (1965). Aerodynamics for Naval Aviators. Aviation Supplies & Academics. PDF (25 MB)

2 Anderson, J. D. (2016). Fundamentals of Aerodynamics. McGraw-Hill Education. Publishers Link

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  • $\begingroup$ Nice picture. This also clearly shows that a (2D) airfoil does not generate lift "pushing down" the air beyond it and receiving a kick back from Newton's third law $\endgroup$
    – sophit
    Commented Aug 14, 2022 at 21:31
  • $\begingroup$ @sophit, just because the vertical velocity component for the flow does in fact become zero in the far field for a 2D flow around an aerofoil (again happy to share potential flow and CFD sims) does not mean there is no momentum transfer. This is why there is confusion, because people have become obsessed with statements of momentum transfer, even though every day in experiments aerodynamicists are busy measuring pressure to determine coefficients of lift. $\endgroup$ Commented Aug 15, 2022 at 1:41
  • $\begingroup$ Yes sure, lift, drag and moment are created but not because Newton's third law has pushed the airfoil upward 😉 $\endgroup$
    – sophit
    Commented Aug 15, 2022 at 7:17
  • $\begingroup$ @sophit, it is an accepted fact that the streamlines in the far field return to horizontal, that is at an infinite distance away v_y = 0. Where lift can be expressed at the outlet boundary is in the divergence of the velocity vector. Note that Navier-Stokes requires conservation of a mass, and hence div(v) = 0. If the wake behind an aerofoil is slowed, that gives a -ve div, hence to balance this, the flow converges. The downwash is hidden in the asymmetry of the convergence, where flow above has a greater -v_y, while the flow below has a smaller +v_y. $\endgroup$ Commented Aug 16, 2022 at 6:05
  • $\begingroup$ Reading many answers here, it seems to be not so accepted 🖖 $\endgroup$
    – sophit
    Commented Aug 16, 2022 at 7:36
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Induced drag is just the component of any aerodynamic force which lies in the direction the aircraft or airfoil is traveling in (aligned with the relative wind). So of course it does. If it is producing any aerodynamic force, then there must be drag. Only if we arbitrarily separate the total drag into multiple pieces and call one of the pieces induced drag can we make this distinction. How we use the words sometimes makes things unnecessarily confusing. Remember, we used to describe the forces generated by the airflow in the cavity between the F-14 engine nacelles as "Lift". Does that Lift generate Induced Drag? How about the Supersonic Shock Wave Lift generated by the XB-70 when it lowered the wingtips? Much confusion is generated by using definitions designed to be useful in one context in areas where they are not applicable.

It could, (and doubtless will), be argued, (strictly based on arbitrary semantic definition), that unless there is Lift, there cannot be induced drag, but that argument is based on semantics, (that induced drag, by it's own name, is the drag induced by, or due to Lift). That definition however, although useful at times, is at best misleading. It ignores the fact that Lift itself is a component of the same aerodynamic force - the component that lies normal to (perpendicular) to the aircraft/airfoil direction of motion or relative wind. Lift AND Induced drag are both just components of any aerodynamic force. One is not the cause of the other. Going strictly by this interpretation, If there is no "Lift", (because the total Aerodynamic force is itself aligned perfectly with the aircraft velocity vector), then it doesn't make sense to call it Induced Drag. It is, however, still there, and it is still the component of the force aligned with the velocity.

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