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When the direction of forces is popularly explained, they say "the lifting force is directed perpendicularly, and the drag force is parallel to the oncoming flow".

example of a popular explanation

But what if it's a swept wing? In that case, which variant is more correct and why? Will the chosen variant apply to all objects affected by aerodynamic forces and, if not, what are the exceptions?

enter image description here

Also, if in reality the forces are directed as in the second variant, are most of the further formulas created in such a way as to obtain a mathematical model of the first variant? For example, the lift curveslope of a swept wing will be less than that of a straight wing - is this the result of a conversion between models? I would appreciate as much information as possible, because I want to have a solid idea.

BierRitter
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4 Answers4

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Lift is defined to be perpendicular to the flow. Drag is defined to be in the direction of the flow.

What your intuition is missing is that these are not the only two aerodynamic forces. There is also a third component of force -- typically called sideforce.

In many situations, the side force is zero or minimal, so we often work in the '2D' frame of just lift and drag. Most aircraft are symmetrical -- when they fly in a symmetrical condition, the side force generated by the left half of the aircraft cancels with the side force generated by the right half of the aircraft.

Side force is only present when the something is asymmetrical.

We can resolve any force into three perpendicular components -- Lift, Drag, Sideforce or X, Y, Z, or East, North, Up. At different times we make different choices of how to resolve a force because it makes analysis easier down the road.

Because of this, Lift, Drag, Sideforce is just one possible choice. It is the choice defined with lift perpendicular to the flow and drag parallel to the flow. One benefit of this choice is that sideforce is usually zero.

Rob McDonald
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It is not a “popular explanation”, it is the actual definition. To be more precise, there is some aerodynamic force and we call the component along the direction of airflow (relative to the wing) drag, and the component perpendicular to the flow lift. This applies in three dimensions, not just two.

Now two parallels are parallel in all views, so for drag, variant 1 is the only one possible.

For lift it is a bit more complicated though, because parallel to the flow might mean up, sideways or any oblique angle in between. For a symmetric aircraft the sideways components cancel, so the total lift will be up, but for each wing in isolation it may be slanted sideways.

But sweep does not slant it, dihedral does. Pressure always acts perpendicular to the surface, so lift is approximately perpendicular to the wing. And since horizontal swept wing is still horizontal, the lift will still be vertical. But if the wing has dihedral—is canted from horizontal laterally—then the lift will be “toed in” by about that angle.

Jan Hudec
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  • "Pressure always acts perpendicular to the surface, so lift is approximately perpendicular to the wing."??? You are conflating the concept of the aerodynamic force at a specific point with the total aggregate vector sum of all aerodynamic forces from every single point on an airframe. "Pressure always acts perpendicular to the surface" is only true for the former, and is not even wrong for the latter. – Charles Bretana Feb 06 '23 at 03:11
  • @CharlesBretana, I am not conflating anything, just perhaps being a bit too fast. Because locally the pressure always acts perpendicular to the surface, any significant aerodynamic force must be perpendicular to some significant part of the surface. And since there is no surface facing sideways (except for a tiny bit at the tip), there cannot be any sideways force. – Jan Hudec Feb 06 '23 at 06:05
  • No, sorry you are. Saying that an aggregate, mathematical abstraction, that exists only as a defined component of another abstraction, (the vector sum of an infinite number of tiny forces all over the surface of an airframe, (which are normal to the surface), is normal to that surface, when the surface in question is not even flat, (so exactly which piece of the surface are yiu tslking about), is not even wrong. – Charles Bretana Feb 06 '23 at 23:09
  • Or did I misunderstand what you said? – Charles Bretana Feb 06 '23 at 23:10
  • @CharlesBretana If the pressure is constant, the integral of pressure times normal vector (= the total force) is equal to average of normal vector. Since the pressure gradients around the wing are limited (the air accelerates to equalize pressure), and since normal vector of most of the surface is close to the average, that integral (total force) will still always be close to the average normal vector. With more variation possible in the forward/aft direction then sideways, since there is more surface sloped fore/aft. – Jan Hudec Feb 08 '23 at 09:41
  • … “the wing” is just a sloppy way to talk about a flat surface approximating the wing. Since most of the actual surface is close to parallel to this, the dominant force is close to normal to it. Not exactly, but can't be too much off. Because the area that is far from parallel to it is small, so it can't create large term in the overall integral. – Jan Hudec Feb 08 '23 at 09:49
  • Totally not true. Whst if the surface is a sphere? Whst about a box? What about a regular wing at 60 degrees AOA? You can't just make blanket statenents that are only true in special cases that happen to match the conclusions you wish to conclude with and imply that they are universally true. And remember, "lift" is an abstract mathematical concept "defined", arbitrarily, as the component of the total aerodynamic force that happens to be normal to the flight path vector. – Charles Bretana Feb 09 '23 at 03:38
  • @CharlesBretana, I am not making any blanket statements, I am making statements in context of the answer, which is about wings of practical aircraft. – Jan Hudec Feb 09 '23 at 13:09
  • @CharlesBretana. I also started the answer by defining lift as orthogonal to flow direction. However that does not define its direction, only confines it to a plane. So the rest of the argument is about constraining it to a specific direction. By observing which components the total aerodynamic force may and may not have. – Jan Hudec Feb 09 '23 at 13:13
  • Jan, with all due respect, you "defining lift as orthogonal to flow direction." then you make the incredible statement that "However that does not define its direction". I, respectfully, cannot conceive of how to rationally respond to such an obvious contradiction. – Charles Bretana Feb 09 '23 at 21:42
  • @CharlesBretana because it is not a contradiction. In three dimensions, there is a whole plane that is orthogonal to any particular vector. So saying it's orthogonal to one is a constraint on the direction, but not a complete definition. – Jan Hudec Feb 14 '23 at 08:11
  • Jan. Thete is only *one* plane orthogonal to the flow direction. Secondly, a "constraint" is not a "definition*, complete or incomplete. So that statement, as Wolfgang Pauli said, is "not even wrong". Finally, what exactly are you implying by the statement that this is not a "complete definition"? And how is it relevant to your conflation of two concepts which are each applicable to completely different physical aggregate scales? – Charles Bretana Feb 17 '23 at 20:45
  • @CharlesBretana, are you still missing the fact we are talking about three-dimensional space? One plane still has two dimensions left. It we knew the total aerodynamic force, we could project it onto the plane and get the lift. But we don't know it (yet), so the definition provides us a constraint – it must be in that plane – but not complete specification – there is still infinitely many directions in the plane. The statement is not fully formal, but it is definitely right. – Jan Hudec Feb 19 '23 at 23:01
  • As I've said now multiple times, you are conflating a statement about the physics at a point (zero dimensions), to wit "Pressure always acts perpendicular to the surface", which talks about pressure, a vector, acting in 3-D space on a surface, (a 2-D space), with a statement about an aggregate property of the entire airfoil or airframe, to wit, "... so lift is approximately perpendicular to the wing." .. and this second statement is not even wrong. Lift is not perpendicular to the wing it is, by definition , (and not for any other reason), perpendicular to the flight path. – Charles Bretana Feb 21 '23 at 13:22
  • The pressure or force ar each point on a surface is indeed normal to the surface. Of course. It is the result of the exchange of momentum between a particle of fluid bouncing off the surface in an elastic collision with the surface. Newtons third law demands this. But Lift is just an arbitrary engineering construct defined to make calculations easier. It's direction is not determined by any physics at any level, much less at the level governed what goes on at each point on the surface. It is, simply the component of all the forces pushing on the surface that is normal to the flight path. – Charles Bretana Feb 21 '23 at 13:27
  • @CharlesBretana I'm saying lift is normal to the flight path from the beginning. But there are infinitely many directions that are normal to the flight path. So which one is lift? (the one that is also orthogonal, well, approximately, to the midchord line—that's the whole point of the argument) – Jan Hudec Feb 21 '23 at 18:31
  • Jan, No, there are not an infinite number of directions normal to the flight path, there is only one. The Flight path is also a vector, defined by the acceleration that the body is experiencing. The total aerodynamic force is the vector sum of all individual forces pushing on the airframe. It is a single vector, pushing on the aircraft is a single direction. It results in a single acceleration vector, in one single direction. (How can a body accelerate in more than one direction?!) – Charles Bretana Feb 22 '23 at 03:34
  • One component of this force, the component parallel to the velocity vector, (we call it Drag) changes the magnitude of the aircraft velocity vector, and the other defined component, which is normal to the velocity, (called Lift) changes the direction of the aircraft's velocity vector. – Charles Bretana Feb 22 '23 at 03:35
  • Yes, you can foolishly define a component of the total aerodynamic force that lies to one side of the plane that is defined by the aircraft velocity and its acceleration, but that would be *NOT EVEN WRONG*. No such force can possibly exist, as it would cause an acceleration in that direction, contradicting the assumption that this force you have defined is not in the same plane as the acceleration. If you did define such a force, you would also have to define an equal and opposite force on the other side that canceled out the lateral effect of the falsely defined force. – Charles Bretana Feb 22 '23 at 03:39
  • @CharlesBretana Now all three posts you made are not even wrong. E.g. flight path is a vector, but not the one defined by acceleration of the airframe. And did you notice the question shows just a wing, not a complete airframe? – Jan Hudec Feb 22 '23 at 12:40
  • Jan, where did I say that flight path is defined by the acceleration? Please. I referenced the 2-D plane that is defined by the two vectors velocity and acceleration. Any two different vectors define a 2-D plane. And a wing is part of the airframe. Physics (fluid dynamics), not not distinquish between parts of an airframe. It applies to every point on any airframe, actually to any point on any body moving in a fluid. – Charles Bretana Feb 22 '23 at 13:07
  • Excuse me, but, in reviewing what I posted, i did mis-state one thing in the first of those three posts. I said "The Flight path is also a vector, defined by the acceleration that the body is experiencing.". That is indeed wrong. What I meant to say is that the normal force (Lift vector) is defined by the flight path and the acceleration. – Charles Bretana Feb 22 '23 at 13:20
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the direction of forces is popularly explained

Luckily enough science is not democratic: definition are not chosen by show of hands every 5 years but so that they make sense and cannot be mistaken.

When an object moves in a fluid, a fluid dynamic force arises. If we consider a 3D object moving in a 3D space, then this force can be decomposed in... well, 3 components.

One component is quite easy to choose: since a part of the fluid dynamic force is always pointing in the main direction of the flow (so called freestream or $V_{\infty}$), then one of those three components is simply aligned with the flow and termed drag.

Therefore the other two components are perpendicular in respect to the drag (i.e. in respect to the flow). How are they fixed? If the object is an aerodynamic object, then it makes sense to define one of those two perpendicular components as going from the belly to the upper surface of the body; this component is termed lift.

Finally, the third and last component points laterally from the right side to left side of the object.

So, variant 1 is the correct one.

The picture in your variant 2 is normally used to schematise how locally the airflow bends as it approaches the leading edge of a swept wing and is used to explain the reduction in transonic drag given by swept wings in respect to a straight one. Here there's a good explanation of this phenomenon.

sophit
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  • By "popular explanation" I just meant that the total aerodynamic force in such explanations decomposed in 2 components, which made me think that there is no third. Big misunderstanding on my part – BierRitter Feb 08 '23 at 16:07
  • @BierRitter: just joking Yes there's a third one which normally is not taken into account except during manoeuvres or in case of helicopters – sophit Feb 08 '23 at 16:12
  • So, generally speaking, is it possible to say that the sideforce of a swept wing will be imperceptible at non-zero angles of attack? – BierRitter Feb 08 '23 at 16:31
  • @BierRitter: due to symmetry, what happens on the right wing equals and is opposite to what happens on the left one. So what happen laterally is normally zero in total. Maybe we can see to what happens on a oblique wing. – sophit Feb 08 '23 at 18:32
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With "Variant 2", the statement that "the lifting force is directed perpendicularly (to the oncoming flow), and the drag force is parallel to the oncoming flow" would be accurate from a side view, but not from a top view, and also not from a head-on view or tail-on view.

So "Variant 2" is not an accurate depiction of the definitions of the Lift and Drag vectors for a swept wing.

"Variant 2" tends to beg the question of whether or not sweeping a wing causes it to generate some aerodynamic sideforce, acting toward the wingtip. Sideforce being a third aerodynamic force, defined as acting perpendicularly to both lift and drag. That is really an entirely separate question. This would have interesting consequences during sideslip, where one wing becomes "more swept" than the other wing, in relation to the actual direction of the airflow. Generally speaking, the answer to that question appears to be "no" -- and all-wing aircraft1, including swept-wing all-wing aircraft, are well known for generating minimal aerodynamic sideforce during a sideslip2. But I have seen a reference to the idea that "leading-edge suction" would in fact tend to cause that effect to some degree.3

Footnotes:

  1. By "all-wing" aircraft, we mean flying-wing aircraft lacking tails and fuselages, whose cross-sectional area as seen in a side view is low. Such as the XB-35, XB-49, and B-2.

  2. See for example this passage from the 35th Wilbur Wright Memorial Lecture which Jack Northrop read to the Royal Aeronautical Society on May 29, 1947:

Side force effects: All-wing airplanes, particularly those without fins, have a very low crosswind derivative; thus a low side force results from sideslipping motion. Some crosswind force is probably important for precision flight, such as tight formation flying, bombing runs, gun training maneuvers, or pursuit. This importance arises because with low side force it becomes difficult to judge when sideslip is taking place, as the angle of bank necessary to sustain a steady sideslipping motion is small. This lack of side forces has been one of the first objections of pilots and others when viewing the XB-35. After flying in the N-9M or XB-35 the objection is removed, except for some of the specific cases mentioned above. For the correction of the lack of sideslip sense, a sideslip meter may be provided for the pilot or automatic pilot, and for very long-range aircraft there is a valuable compensating advantage in being able to fly under conditions of asymmetrical power without appreciable increase in drag.

  1. Email or on-line forum statement by Stephen Morris, co-designer of Bright Star Millennium and Swift rigid-wing ultralight hang gliders.
quiet flyer
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  • This answer would benefit from addressing the issue of whether we are referencing the free-stream flow or the local flow. Will hold off for a day or two so as not to appear to be trying distract from other more recent answer(s) -- !! – quiet flyer Feb 07 '23 at 13:36
  • First of all, thank you for the tips on where to learn more. In fact, I don't really understand much about how local flow affects the wing, and that may be why my question lacks specificity. – BierRitter Feb 08 '23 at 16:54