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This answer asserts that "at high angle of attack the engine is producing aerodynamic lift". In the context of that answer, we are concerned about the increased torque that raises the nose of the aeroplane with respect to the center of gravity, so we should narrow down our interpretation of the otherwise vague word "lift" as the force component that is perpendicular to the wing or fuselage of an aeroplane. We define the angle of attack as the angle between the fuselage and the incoming airflow direction at infinity (shorthand word for "reasonably far away"). It is very different from the angle of the fuselage makes with the horizontal at high speed while very close to the latter at very low speed. It puzzles me in two ways.

  1. It claims the engine itself produces fuselage-perpendicular force in addition to the thrust parallel to the fuselage and wing, despite the thrust of the engine is directed parallel to the fuselage and thus the wing. How is that perpendicular force produced?

  2. It claims that fuselage-perpendicular force thus produced is dependent on the angle of attack. How does that work?

I would like to see a technical elucidation of this claim or some references supporting or refuting it, best if they come with mathematical derivation.


Edit:

Some answers below observe that when the plane moves, without engine turned on, against the airflow, part of the airflow curves downwards to conclude that a net force perpendicular to the fuselage is exerted. It is not that simple as looking at part of the flow stream, since part of the flow stream goes upwards above the separating point. The net force is the integration of all the pressure on the whole surface, and the pressure on the opposite side of the object presses in the opposite direction. In fact, in a potential flow, the D'Alembert's paradox shows that the net pressure is exactly zero. Of course, real airflow is not potential flow, but this refutes the overly simple rationale of using downward airflow to derive the fuselage-perpendicular force.

However, when the engine is turned on, especially at high power. The situation may be different so long as the airflow is consistently flowing in the downward direction long after exiting the engine. The momentum of the airflow through the engine may overwhelm other parts of the airflow. But the argument must be more sophisticated than just the downward direction of the airflow.

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    $\begingroup$ "Lift is defined to be the external force exerted perpendicularly on the wing or fuselage of the aeroplane." - I've never heard that definition before; where are you getting it from? As far as I know, lift is defined to be the component of the aerodynamic force which is perpendicular to the relative wind (not the fuselage). Of these two possible meanings of the word "lift", which one are you asking about? $\endgroup$ – Tanner Swett Apr 18 at 3:31
  • $\begingroup$ @TannerSwett: I realize now there is ambiguity in the word "lift". I have now edited the question. Please review. $\endgroup$ – Hans Apr 18 at 5:07
  • $\begingroup$ Hans, what exactly do you mean with "It is very different from the angle of the fuselage makes with the horizontal at high speed while very close to the latter at very low speed."? Do you perhaps mean to say that the angle of incidence is negligible at high AoA? I would say the most prominent divergence between pitch and AoA is due to climbing or descending, not speed. $\endgroup$ – Sanchises Apr 18 at 12:06
  • $\begingroup$ Also, why did you define lift as perpendicular to the wing and fuselage (which, by the way, can differ by an angle called the incidence angle) rather than the more commonly accepted force perpendicular to the freestream velocity vector? (I don't mean to be pedantic, but since you seem to want a precisely defined answer, it might help to precisely define the question as well) $\endgroup$ – Sanchises Apr 18 at 12:08
  • $\begingroup$ @Sanchises: For the sake of simplicity, I am assuming the axis of the cross section of the wing is parallel to the axis of the plane. The free-stream velocity direction is usually not horizontal. When the plane is moving at high speed and ascending or descending, the angle between the fuselage axis and the free-stream (AOA) is different from that between the fuselage and the horizon. Only when the plane is moving horizontally while its axis is not horizontal (nose up), the two angles are the same. I am trying to distinguish AOA from the angle of the fuselage axis with the horizon. That is all. $\endgroup$ – Hans Apr 18 at 23:53
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Anything, even a metal plate creates "lift" when it is under an angle with an air flow. Lift isn't a magical attribute to "wings", it is just a physical consequence of the law of conservation of momentum: when you push a stream of air down, the reactive force is upwards.

the fuselage/engines also act as minor lifting surfaces: when they are under an angle they, inefficiently, redirect the airflow downwards.

For the engine this is also a bit due to the definition of thrust: thrust equations consider an inlet in the same direction of the thrust vector. So the inlet & compressor redirect the flow "downwards" under high angles of attack. - This effect has to show up somewhere: as a lift force generated by the engine.

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  • $\begingroup$ You are confusing the concepts. Please see the Note in the last paragraph of my question. $\endgroup$ – Hans Apr 17 at 22:22
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    $\begingroup$ I'm not, as I said indeed there is a vertical component of thrust when it is under an angle. However the trust equation for an engine "expects" a trust that is parallel to the engine direction. Under high angles of attack this no longer holds. So the compressor has to do extra work to align the airflow. - This aligning is however omitted from the trust equation, yet it does provide a force perpendicular to the engine direction - thus a lift force. (both a lifting drag as well as an upwards component). $\endgroup$ – paul23 Apr 17 at 22:45
  • $\begingroup$ @Hans: This answer is correct: You have two components, one from pressures on the outside of the nacelle and one from the vertical component of thrust. Mentioning both in one answer does not mean they are confused. $\endgroup$ – Peter Kämpf Apr 18 at 5:26
  • $\begingroup$ @PeterKämpf and paul23: Right. I mistook angle of attack for the angle of the fuselage with the horizontal line. It should be the angle between the incoming airflow relative to the aeroplane and the fuselage. The two are close when the aeroplane speed is very low. However, your use of the words "up" and "down" lead me to think you are simply referring to the vertical direction relative to gravity, while I am concerned about the direction relative to the plane itself. It would be great if you could modify your first paragraph. Also, I know the force of airflow on a nonparallel plate. $\endgroup$ – Hans Apr 18 at 6:43
  • $\begingroup$ "When you push a stream of air down, the reactive force is upwards". True but it does not account for the net force on an object in a flow stream, since part of the flow stream goes upwards above the separating point. The net force is the integration of all the pressure on the whole surface, and the pressure on the opposite side of the object presses in the opposite direction. In fact, in a potential flow, the D'Alembert's paradox shows that the net pressure is exactly zero. The fluid dynamic force is more complicated than just glancing at part of the flow stream. $\endgroup$ – Hans Apr 18 at 19:15
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Thankfully, you have a very clearly worded question. Unfortunately, though, the simple mathematical derivation you desire is not within the scope of a regular answer here (and would be everything but simple).

I agree that some of the other answers confuse lift and thrust, but I think this has more to do with definitions and unclear concepts. So let me first get the definitions out of the way:

Lift is defined as the fraction of the aerodynamic force which is perpendicular to the direction of flow at infinity. This direction is equal (but opposite) to the direction of movement if no wind is present. So per definition the lift of all aircraft components points in the same direction.

Thrust is defined… — well, there is no common definition that would be as simple as the one for lift. Thrust is created by accelerating air. But the same is true for lift, so we need to define a boundary which separates the acceleration which is interpreted as lift and the one which is interpreted as thrust. This is bookkeeping — you need to meticulously add up all pressures acting on all surfaces of the aircraft and then decide which to call lift and which to call thrust.

A lot happens around the intake lips of fan engines, especially at low speed. The intake diameter is dimensioned for a compromise between take-off, when a lot of air is sucked into the engine and high-speed flight when some of the air flowing toward the engine will spill over the intake lips, to flow around the nacelle. In case of the 737 MAX, the compromise was shifted to a smaller diameter in order to keep nacelle size manageable. Therefore, on the 737 MAX you get a lot of suction on those intake lips. The intake is slightly angled in order to support even flow at high angle of attack, so the intake is already doing quite some flow bending. This flow bending is lift - or is it? The vertical component of thrust is also the result of this flow bending.

What is important is where this happens - the engines on the MAX have been shifted quite a bit forward, so this lip suction has a large, destabilizing lever arm. And the suction grows with angle of attack - disproportionally even, due to the angled intake. In the end, this is where most of the destabilizing moment comes from, and it sure is perpendicular to the fuselage.

EDIT: Now I've had some time for the more mathematical answer desired by @Hans, but I will not dig deeper than fist-order-of-magnitude calculations because solid figures are hard to come by. For example, I did not find the mass flow figures for the 737 MAX's CFM LEAP 1B engines, but this source (thanks @mins!) should be close enough. The 485 kg/s cited there for 145 kN thrust should scale to 436 kg/s for the 130 kN of the LEAP 1B. Next assumption: The airplane's angle of attack is +15° (remember, no flaps when MCAS is active!) so the change in flow direction effected by the intake is 436 kg/s by 15°. This work has to be done at the intake face because once the flow is inside the intake it flows with the angle of the nacelle already. The intake dimensions are the third piece of guesswork here and I assume 1.7 m at the intake face. The last assumption is the air density; I use 1.15 kg/m³ for what follows.

This now allows us to calculate the incoming impulse: 436 kg = 379 m³ flow through an area of π·0.85² = 2.27 m². This needs a flow speed of 167 m/s (Mach 0.5 at sea level - looks very credible).

Next, the intake lips need to add a downward acceleration to a vertical speed component of sin(15°)·167 = 43.2 m/s. The reqired force for this is 436 kg/s·43.2m/s = 18.84 kN, and it all has to act on the intake lips. To put that into perspective: A fully loaded 737 MAX 9 has a mass of maybe 80 tons, so it weighs around 785 kN. Since we have two engines, the total force required for flow bending at the intake faces is 4.8% of the aircraft weight. At the increased lever arm of the new engine location this is already causing a noticeable nose-up pitch.

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  • $\begingroup$ Without asking for a full mathematical derivation which I'm sure is outside the scope of this answer; do you have an idea of the order of magnitude of this lip suction effect compared to the aerodynamic lift from just the nacelle shape (like in Mike Swonsun's answer)? (For comparison, the latter is apparently about 1% of the total lift on a 747) $\endgroup$ – Sanchises Apr 18 at 7:24
  • $\begingroup$ Looks like an illuminating answer. Let me look into the intake lip spillage before discussing some details with you. $\endgroup$ – Hans Apr 18 at 7:55
  • $\begingroup$ This intake "suction" may create lift at high AOA inside the nacelle from the top due to flow deflection (like the bottom of a wing) and from the bottom (local vacuum/flow separation) like the top of a wing (sides cancel)? What have the created here? Where should it be mounted? Thanks for improving understanding of this, ahh, phenomena. $\endgroup$ – Robert DiGiovanni Apr 18 at 8:11
  • $\begingroup$ @RobertDiGiovanni: Please consider that the flow speed inside the duct is considerably higher, so the suction forces on the lower lip and inside the intake are much higher than on the upper lip and the outside of the nacelle when the intake flies at positive angle of attack. $\endgroup$ – Peter Kämpf Apr 18 at 13:41
  • $\begingroup$ Seeing some similarities here to the Lippisch Aerodyne, where the thrust was directed downward to control pitch. It may be best for the engine to solve its own problem. Small elevons in the exhaust could also provide pitch and roll control (differential thrust for yaw) giving aircraft 3 axis control even with complete loss of ailerons, elevator, and rudder. Hope they can turn this positive. $\endgroup$ – Robert DiGiovanni Apr 18 at 16:09
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It is not only the engine thrust producing lift at high angles of attack. The lower surfaces of the engine nacelle ALSO produce aerodynamic lift at high angles of attack.

Even at idle thrust there is additional aerodynamic lift being produced. All engine nacelles do this.

The problem with the B737 MAX is that the engine nacelles are placed farther forward and and have a greater lifting “moment” than previous engines used on the B737.

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    $\begingroup$ Correct explanation: The nacelles produce aerodynamic lift, just as the fuselage does. However, with idle engines less lift would be produced. A big portion comes from suction on the intake lips at low speed and high power settings. Lip-o-suction, if you want. $\endgroup$ – Peter Kämpf Apr 18 at 5:23
  • $\begingroup$ Thanks Peter. I have edited my answer. $\endgroup$ – Mike Sowsun Apr 18 at 11:02
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An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards. For an aircraft that flies a horizontal path at high angle of attack, the airflow approaches the engine horizontally and leaves the engine in a downward angle, close to the negative angle of attack.

In order to make the flow turn downwards, the engine must exert a downward force on the airflow. According to the third law of Newton,there is an opposite force on the engine. The component of this force that is perpendicular to the incoming undisturbed airflow is the additional lift force caused by the engine.

enter image description here


One way to analyse the thrust of an engine is to look at the rate of change of momentum of the air flowing through and around the turbine.

Momentum is the product of mass and velocity: $\vec{p} = m \vec {V}$ As you see, momentum it is a vector quantity.

The rate of change of momentum $\dot{\vec{p}}$ of a mass is equal to force on the object.

By analysing the change of momentum of the air flowing around the engine, we can determine the thrust vector of the engine.

In the image below, the engine's axle is perfectly aligned with the incoming flow of air. I choose an imaginary volume around the engine, such that the static pressure at the boundary is equal to the static pressure far ahead of the engine. Because the boundary pressure = $p_0$ at every point on the boundary, the integral of pressure over the surface of the volume, the resulting net force would be zero.

enter image description here

The top and bottom boundaries are chosen to be along the streamlines.

The left boundary is experiencing a constant influx of air; the flow is uniform across the left boundary.

The right boundary is experience a constant outflux of air; the flow in non uniform due to the difference in flow velocity in the core and the bypass section of the engine.

The influx of mass through the left boundary is equal to the outflux of mass through the right boundary; I neglect the burned fuel here.

The influx of momentum through the left boundary $\dot{\vec{p}}_{in}$ is equal to $\dot{m}\vec{V} = \iint_{l} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The outflux of momentum through the right boundary $\dot{\vec{p}}_{out}$ is equal to $\iint_{r} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The difference between the inflow of momentum (indicated by the blue vector below the drawing) and the outflow of momentum (indicated by the red vector below the drawing) is the force exerted on the volume of air. The thrust (indicated by the black vector) is the reaction force.


When we now introduce an angle of attack, the bounding volume will change shape. Also the influx and outflux momentum will be different. What is most important is that the thrust generated is no longer purely axial; the thrust vector develops a transverse component. This is the additional lift (and a bit of drag) that the engine creates a high angle of attack.

enter image description here

When the engine is mounted well in front of the centre of gravity, a high angle of attack / high thrust situation will cause an upward pitching moment. This is the case in the Boeing 737 MAX where this effect was changing the handling characteristics at high angles of attack. To make sure the handling would be similar to earlier 737 models, Boeing introduced the - now infamous - Maneuvering Characteristics Augmentation System (MCAS).

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  • $\begingroup$ is the jet engine not running into the air (what "flow" is being deflected)? There are 2 sources of thrust here, from the fan and from the jet. The air is stationary (no kinetic energy) before it is ingested. But we could mention torque effect around the CG too. $\endgroup$ – Robert DiGiovanni Apr 18 at 0:55
  • $\begingroup$ But the (large) nacelle does deflect air downwards. $\endgroup$ – Robert DiGiovanni Apr 18 at 1:02
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    $\begingroup$ Good explanation, but two things might be added: At low speed this effect is particularly big due to the high bypass ratio of the new engines, and then you get even more lift from the flow distortion around the intake lips. As shown in your drawing the air passes straight through the intake, but in reality the engine sucks in air from a wider area at low speed, creating additional lift on the intake lips. Oh, and please correct your last sentence: This additional lift is exactly the tilted thrust force vector. $\endgroup$ – Peter Kämpf Apr 18 at 5:15
  • $\begingroup$ @PeterKämpf you make an interesting point about the lift on the lips. At lower speed this force will increase, but we will see an opposite force on the upper lip. I need to do some additional drawings and calculations tonight (I will include the math in my update). For now I can't (yet) agree on that the additional lift is exactly the tilted thrust for vector. $\endgroup$ – DeltaLima Apr 18 at 13:02
  • $\begingroup$ You say "An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards." It is not that simple as looking at part of the flow stream, since part of the flow stream goes upwards above the separating point. The net force is the integration of all the pressure on the whole surface, and the pressure on the opposite side of the object presses in the opposite direction. In fact, in a potential flow, the D'Alembert's paradox en.wikipedia.org/wiki/D%27Alembert%27s_paradox shows that the net pressure is exactly zero. $\endgroup$ – Hans Apr 18 at 19:19
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It is admirable to seek the higher plane of sophistication to gain greater understanding.

First, air is compressible, so D'Alembert is out. Probably would not be true if velocity was great enough for cavitation, but I did consider sailing battleships blunt end first to see if more energy could be recovered as flow is pulled back into the trailing edge. There is also some evidence that air curling up and towards the front of a thin undercambered wing (or a jib sail) gives it almost magical lift properties through recovery of drag energy.

But as far as the engine creating lift force 90 degrees from its thrust (making definition of lift even more specific), we may be talking impossibility without deflection of the airstream by some other physical structure. Tilting the engine out of the direction of travel does create some interesting ideas, but does the pitching or lifting tendency exist without the cowling around the fan?

It will be interesting to see (beyond software) what they do to solve this. They might want to take a look at an RB-57 Canberra.

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    $\begingroup$ You do not understand the logic of my argument. The use of D'Alembert paradox is not to use it to compute (the net pressure) but to refute the argument used in many of the answers here. $\endgroup$ – Hans Apr 18 at 23:44
  • $\begingroup$ Thanks anyways. $\endgroup$ – Robert DiGiovanni Apr 18 at 23:56
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    $\begingroup$ Also, for compressible fluids, so long as it is inviscid, irrotational and subsonic, the D'Alembert paradox holds, unlike what you claim. The reason for the net pressure in the airflow is that air is viscous, not its compressibility. $\endgroup$ – Hans Apr 19 at 0:42
  • $\begingroup$ Water is inviscid, but air has viscosity. Oh, please!!! I love theory, but am more an applications type. Again, thanks. $\endgroup$ – Robert DiGiovanni Apr 19 at 11:53
  • $\begingroup$ Yes, air has viscosity. Do you agree or disagree? Also I have precisely specified the definition of lift. I do not know what your contention is. $\endgroup$ – Hans Apr 20 at 8:24

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