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  • Gabriel
    replied
    Originally posted by Evan View Post
    Is that way off?
    Yes!!! Again you are taking individual concepts that are ok and making a fruit salad of them. So some loose ideas:
    - I am repeating myself here but the circulation is a speed profile, not a force. Only pressure gradients can make the air accelerate and bed its path.
    - The air doesn't has upwash, downwash, accelerates above and slows down at the bottom BECAUSE of circulation Circulation is THE NAME THAT WE GAVE TO this distribution of speeds.
    - The circulation is NOT a vortex. The circulation is the distribution of speeds around a vortex. A vortex has rotor. Around the vortex however the rotor is zero ("rotor" is a vectorial magnitude of a vectorial function (like a speed field), it can be understood as how fast would a ball rotate around its own axis if you hold it in one position (not free to move but free to rotate). Around a 2D airfoil (or around a spinning cylinder), outside of the boundary layer, the rotor is zero.
    - The bound vortex is not induced by the starting vortex, they are created simultaneously because vorticity shall be conserved (like energy or momentum).
    - In a 2D airfoil (that can be though as a wing of infinite wingspan) there is no starting vortex. The vortex is considered to continue infinitely along the infinite span and you never see the vortex bending back near the wingtip and joining back at the starting vortex. You can think that the wingtips and the vortex ends meet in the infinity (think that they form a circle of infinite diameter) and such a closed vortex has voticity zero (like a smoke ring) so you are not creating or destroying vorticity by increasing or reducing the lift. But you don't have "one vortex". You have a system of vortexes that add up to a finite vorticity (finite in 2D, it becomes zero if you extend it to infinity) and that can be replaced by a single vortex that will work very well to model the lift force but not to model the lift around the airfoil.
    - In a 3D wing, the situation is much more complex The figure that I think you have in mind, like a long rectangle where one off the short sides is basically the wing (or the bound vortex), the other short side is the starting vortex, and the long sides get longer and linger as the wing moves forward (with the bound vortex) and the starting vortex remains still is a gross simplification, useful for some things, but not to describe in detail the flow of air around a wing.
    - Both in the 2D and 3D versions, if you use the single vortex model, you can explain and measure accurately many things including lift, induced drag, induced angle of attack in the tail, ground effect... but you will have air flowing through the walls of the airfoil. Reality is more complicated than "a vortex". If you want I can go to the more complete explanation.
    - In any event, vortexes don't occur in potential flow because the rotor in potential flow is always zero (but potential flow ha solutions for cortices introduced artificially in the model as singularities, and you don;t even need to establish the vortex itself, you can establish the circulation caused by it, like with the Kutta condition). In reality, all the vorticity (not the circulation) happens in regions where the viscosity cannot be neglected and hence the flow cannot be modeled as potential, like the boundary layers and the core of the vortex systems (like the core of the wingtip vortexes). That is complicated to do (it can be done, computers do it all the time) so it is useful to artificially out vortexes here and there as singularities in the potential flow model, with that vortexes having a similar effect to the vorticity that takes place in those regions.
    - And now you want to deal with non-stationary aerodynamics? With an airfoil that is not moving steady in a steady stream of air but that is changing airspeed an d angle of attack? And that will make the explanation more clear?

    Evan, before trying to explain the lift it terms to your satisfaction, please try to explain to me, in terms to your satisfaction, why does the tracks of the train in a curve make the exact force that they make on the train?

    And by the way, even if your explanation was right, I don't see how that would satisfy neither the pilot nor the 8 years old.

    Leave a comment:


  • Evan
    replied
    Originally posted by Gabriel
    Evan, I will address several of the points in your latest posts. I tried to be brief but I failed miserably. There was too much to cover and I tried to make longer but simpler explanations than highly condensed super-technical ones.

    But there is ONE SINGLE BIG point that I think is the key, and that is the way that you try to separate the different effects in different components or contributions, when in fact we don't have neither different effects nor different component or contributions. It is one complex, intertwined system where you have variables interacting with each other in a way that cannot be described as a one-way cause-effect and where also different variables are sometimes the expression of the same situation from different points of view which are in fact equivalent and not competing nor collaborating.
    I want you to know that I am absorbing everything you are offering here, as well as everything else I can consider reliable.

    But first, let's take a moment to review the scenario driving my inquiry:

    ----------------------------------------------------

    I'm in middle-row. As if that isn't bad enough, there's a smart, endlessly inquisitive eight-year old future Gabriel next to me in the window seat. And in the aisle seat is a deadheading 50,000 hour airline pilot.

    The kid turns to the pilot and says, "How does the wing work?"

    The pilot tells him (as he learned long ago in his pilot training), that the wing shape creates a pressure differential that causes lower pressure on the top of the wing and so the higher pressure on below the wing pushes it upward.

    "Why?" The kid asks him.

    "Because the curved distance on the top is longer than the less curved distance on the bottom and thus the air must travel faster across the top to rejoin the same air at the wingtip, and that lowers the air pressure above the wing.", the pilot confidently replies.

    After nearly choking on my Vodka and Xanax, I interject, "Uh, no disrespect to your lengthy credentials or your veteran airmanship, but that is actually incorrect".

    "Oh really?", the pilots snaps back at me, "So then, please explain to us the correct answer!"

    The kid looks at me with much suspicion.

    Ok, now I'm in a predicament. If I recite Gabrielesque posts #33 and #95, I'm going to cause the pilot to change his seat and cause the kid to give up hope and we are going to be closing our tray table and returning our seats to an upright position before I get halfway through it.

    I need an answer that can at least compete, in terms of general comprehension and brevity and satisfactory logical appeal, with Mr. 50,000 hour Pilot's answer. It has to be no longer than a short paragraph.

    That is my goal here. You seem to be saying that it can't be done. Your short answer, that the "Wing pushes air down, air reacts pushing wing up" is the equivolent of saying, "Go away kid"; it doesn't provide satisfactory logical appeal. And your more descriptive answers are, let's just say, not brief.

    So maybe it just isn't possible. If that's the case, than so be it. I'm not quite ready to accept that though.

    -------------------------------------------------------------

    A lot of what you wrote here I understand quite well now (Having learned quite a bit since post #5). A few things continue to puzzle me.
    • Circulation

    My—apparently flawed—understanding is that this 'circulation' is a closed-loop, bound vortex, which exists to satisfy the Kutta Condition by providing a force that will relocate the rear stagnation point from the upper wing surface to the tip of the trailing edge, and that this vortex is the product, via the Magnus Effect, of another initial 'starting' vortex that is created aft of the wing when the wing first begins to push through the air (or with changes in AoA or airspeed). Now, I visualize this 'bound' vortex in my mind as being a clockwise (when viewed with the leading edge to the left) flow above the boundary layer that mixes with, and thus alters the velocity of, the main oncoming airstreams. (One question this raises in my mind is how a closed loop vortex as described can turn around the trailing edge).

    Now, in terms of chicken-and-egg (where does the cycle start, hence, how can it be explained cyclically) The—apparently flawed—order of events I gleaned from Denker is:
    1. Airfoil is stationary in still air
    2. Airfoil begins to move forward / airflow is introduced to airfoil - stagnation point is on the upper aft wing surface / causing cleaved airflow to produce an inital 'starting' vortex aft of the wing.
    3. Airflow increases / 'starting' vortex induces an opposing 'bound' vortex encircling the wing / 'bound' vortex + airflow = the amount of force necessary to relocate the stagnation point to the trailing edge / lift is now possible / 'starting' vortex is left behind.
    4. Bound vortex produces forces that a) increase the airflow speed across the top and b) reduce the airflow speed across the bottom (note the diagram with the black line showing where undisturbed air would have reached vs the upper and lower 'cleaved' airstreams from the airfoil. The upper flow is has been sped up but the lower flow has been slowed down.)
    5. And from there, Bernoulli and Newton take over, and increases in AoA restart the cycle to produce a stronger 'bound' vortex circulation, thus a more pronounced pressure differential and thus more lift.


    Is that way off?

    Leave a comment:


  • Evan
    replied
    Originally posted by brianw999 View Post
    Provided that they keep on doing that then I don't care HOW it happens !!
    Noted.

    Leave a comment:


  • 3WE
    replied
    Originally posted by brianw999 View Post
    Wouldn't it be more simple to just agree that planes fly ?

    In so doing they take people to and from places.

    Provided that they keep on doing that then I don't care HOW it happens !!
    You forgot the aspect that they make awesome roaring and whistling sounds...

    Leave a comment:


  • elaw
    replied
    Simple? yes. Fun? no.

    Leave a comment:


  • brianw999
    replied
    Wouldn't it be more simple to just agree that planes fly ?

    In so doing they take people to and from places.

    Provided that they keep on doing that then I don't care HOW it happens !!

    Leave a comment:


  • 3WE
    replied
    ...the way that you try to separate the different effects in different components or contributions, when in fact we don't have neither different effects nor different component or contributions. It is one complex, intertwined system where you have variables interacting with each other in a way that cannot be described as a one-way cause-effect...
    That’s one hot stinking gray mess Gabieee. Isn’t the black and white thinking kind of always the problem?

    https://youtu.be/p1DoFP78r6k

    Leave a comment:


  • Gabriel
    replied
    Evan, I will address several of the points in your latest posts. I tried to be brief but I failed miserably. There was too much to cover and I tried to make longer but simpler explanations than highly condensed super-technical ones.

    But there is ONE SINGLE BIG point that I think is the key, and that is the way that you try to separate the different effects in different components or contributions, when in fact we don't have neither different effects nor different component or contributions. It is one complex, intertwined system where you have variables interacting with each other in a way that cannot be described as a one-way cause-effect and where also different variables are sometimes the expression of the same situation from different points of view which are in fact equivalent and not competing nor collaborating.

    This is the main mindset that, in my opinion, you need to deconstruct in your head. You mentioned the chicken and the egg situation, and it IS a chicken or egg situation except that in the chicken and the egg we know that the egg came first. Not in the generation of lift. Does the reduction in pressure cause and increase in speed or does the increase in speed cause a reduction of pressure? That's a nonsensical question, they come together, both of them are effects of the same cause that is that you have an obstacle in the middle of the flow and the flow cannot flow through that obstacle, it needs to contour it. I already mentioned this like 3 times in this thread: I drop a ball. Does the increase in momentum cause an increase in the kinetic energy or the other way around? Neither. The speed increases and both the momentum and the kinetic energy increase with the speed. Does the speed increase because potential energy turns into kinetic energy or because the weight accelerates the ball down? Both. How much of the increase of speed is due to the contribution of each? Nonsensical. F=m*g=m*a and m*g*h+1/2*m*v^2 are two ways to express (or view) the same phenomenon.

    Please please PLEASE keep that in mind.

    The way I currently understand it from reading the link you provided, the chicken-and-egg question of airspeed and pressure differentials can be explained as follows:
    The circulation (the span-wise 'bound' vortex) is responsible for acceleration of airflow adjacent to the wing by imparting an opposing force against the lower airflow and an additive force to the upper airflow, and that THIS is what results, thanks to Bernoulli, in the areas of pressure differential that give the wing its lift. Any change in AoA will have the effect of increasing or decreasing circulation, so AoA is included within the equation as 'circulation'. Other contributing factors are the air being turned by the wing volume (or impenetrability) and deflected down by the lower wing surface in a positive angle of attack. Do you agree with that?
    You mention a bunch of concepts that are in general true but combine them in a way that is not correct. For the reasons explained at the beginning.
    The circulation doesn't impose a force on the fluid. What do you think that cause the circulation? Don't you think that you need to force the air somehow to circulate around the airfoil? And don't you think that you need a "force" (note the quotes) to force it? So does the circulation cause the "force" or does the force cause the circulation? And that circulation/force causes the acceleration/retardation that due to Bernoulli, causes the pressure to drop/increase? Wait a second.... If the pressure drops or increases, doesn't that impose a force on the fluid? And doesn't that force cause the accelerations? SO it seems that the acceleration causes the acceleration? Circular reasoning? Yes, and hence wrong. The circulation is a mathematical model to describe the acceleration / retardation. It doesn't CAUSE that acceleration/retardation. The drop of pressure is not CAUSED by the increase of speed, and the increase of speed is not CAUSED by the reduction of pressure. These are all things that HAPPEN together. And what causes all this is the need of the air to go around the airfoil (not through it) and separate in the trailing edge. It is simply the only way that the air can do it. If it did it in another way it would either not comply with the contour conditions (go around the airfoil and separate at the trailing edge) or the individual parcels of air would violate F=m*a.

    It is the 3rd time that I am mentioning this example: You have a train running on a track. There is a curve. The tracks will make a side force on the train. What will cause the tracks to make exactly the force they make on the train? It is the condition that the train needs to remain on the tracks and that it must also comply with F=m*a. But how does the rail "know" EXACTLY what force to make to keep the train on the tracks? It doesn't. It will just make whatever force is needed to keep the train on the tracks and comply with F=m*a. There is just nothing else that the tracks can do. If the force was anything else, the train wither would not follow the tracks or it would violate F=m*a. There is just nothing else that the track can do other than the force that they apply on the train.

    Something similar happens with the air around the airfoil, but with a couple of caveats. One is that the "force" in a parcel of air is in fact a gradient of pressure. Another is that you are not free to apply a force on a parcel of air in one specific direction. If you have the pressure Po (the atmospheric pressure in the free stream) far enough from the airfoil in all directions and you have a pressure lower than Po immediately above the upper surface of the wing, we have a few things to consider:
    1- The pressure immediately above the upper surface is lower than Po but the pressure far above the upper surface is Po, this means that a parcel of air flowing above the upper surface will have a gradient of pressure that points down (higher above the parcel, lower below the parcel). This is what pushes the air down to contour the upper surface and also ultimately leave the airfoil with a downward component of speed.
    2- But wait a second, the pressure immediately above the surface is lower than Po but far away ahead of the airfoil it is Po. This means that as the parcels of air in this stream line approach the airfoil they face a pressure gradient pointing back (higher ahead of the airfoil, lower immediately above the upper surface). This accelerates the parcel (I am jumping over the fact that this parcel of air will first face a big gradient of pressure as it approaches the stagnation point so it will first slow down, and then accelerate).

    So here you have HOW Bernoulli: How an increase of speed is tried with a reduction of pressure. But they come together, they are part of the same phenomenon. Asking whether the increase of speed causes the reduction of pressure or if the reduction of pressure causes the increase of speed is akin to asking, in a free-falling ball, if the reduction of potential energy causes the increase of kinetic energy or if the increase the kinetic energy causes the reduction of the potentiality energy. They are not cause an effect, they are both effects of the ball falling. But wait, there is more:

    3- Let's take an incompressible flow. The parcel of air that goes faster over the upper surface will cover more space in a given amount of time than what the same particle of air covered earlier far away ahead of the airfoil where the speed was slower. That means that the parcel will be longer (to visualize this, imagine 2 rigid cubes one trailing the other, if the one that goes forward accelerates before the other one, they would start to separate. With the air, that separation will be filled with air from the same parcels, so they get longer). But because the parcel of air needs to keep its volume (incompressible flow), then in must get thinner (length times height must remain constant). And here you have the "constriction" that you mentioned many posts ago. So does a constriction cause an increase of speed or does an increase of speed cause a constriction? In a free flow, neither, they happen together. ll three, constriction, increase in speed and drop in pressure happen together, they don't cause each other. (if it is a flow in a pipe and the pipe has a constriction, then the constriction becomes a boundary condition and I will happily say that it is the cause of the increase of speed and drop in pressure, but here the cause of all 3 is the airfoil that the air needs to contour and depart in the trailing edge, which doesn't generate a constriction a-priori, but the constriction is the result). We (and I am including myself here) tend to say "because of this, the speed increases, and because of Bernoulli that increase in speed causes the drop in pressure", but that is an oversimplification that, when you are trying to understand the phenomenon at the level that you are trying to understand it, confuses rather than helps.

    That equation is lifted from Denker. It is the Kutta-Zhukovsky theorem, as I'm sure you know.
    Lift = airspeed × circulation × density × span (lift is equal to the airspeed, times the circulation, times the density of the air, times the span of the wing.)
    Yes, I know that, and it is a mathematical MODEL that takes into account potential incompressible flow. And I want to focus in the POTENTIAL part. Potential means, among other things, that there is no viscosity (or, better, no viscous phenomena at play). The circulation is what they needed to invent and force in the model to meet the Kutta condition. As you quoted from Denker (I think in the post that you deleted): "How much circulation? As much as needed to meet the Kutta condition". But the Kutta condition happens because the flow is NOT potential, because there is viscosity, and because that viscosity cannot be neglected when the air tries to accelerate to infinite speeds to go around the sharp trailing edge. Put viscosity in the model and the Kutta condition will happen naturally, no need to impose any circulation. The "circulation" will happen naturally but it is not the CAUSE of the acceleration / retardation of the flow above/below the airfoil. The flow will accelerate / slow down and the circulation is how we describe that phenomenon. The circulation IS the acceleration / retardation.

    I'm think he means the total area of the wing span there.
    Actually not. Span is span, the "length" of the wing from tip to tip. The chord adds to the circulation. An airfoil twice the chord will produce twice the circulation at the same AoA.

    I was acting "naive and layman" when I asked you all those questions. I wa acting as I thought some Evan would act when faced with the explanation of lift that you gave.

    Or as Boeing (Aero) states it:
    Lift is a function of speed, air density, wing area, and AOA.
    Yes, and that's the equation that I gave that you said cannot be a technical equation.

    This is what I gave: Lift = k * r *V^2 * AoA (k is a constant, r is the density, V is the speed)
    The constant k is Cla*S/2, where Cla is the slope of the curve of lift coefficient vs AoA, and S is the area of the wing (chord x span for a rectangular wing)

    The full equation (the function you quoted from Boeing) hence is:
    Lift = 1/2*r*V^2*Cla*AoA*S

    (note that 1/2*r*V^2 is the dynamic pressure, or how much the static pressure will increase if you slow down the speed to zero, that will be the pressure in the stagnation point; note also that this equation considers that you take the AoA of zero lift as the reference for AoA=0, if you instead take the conventional way of measuring the AoA with reference to the chord line you need to modify it putting (Clo+Cla*AoA), where Clo is the lift coefficient for AoA=0, what middle school kids know as the Y-intercept, or "b" in the linear equation of the form Y=m*X+b)

    So AoA is built into the circulation aspect. As I understand him, for a given airspeed, you cannot have increased circulation without having increased AoA, so one implies the other. And a wing with zero circulation has zero lift.
    Correct. We could also say that circulation is built into the AoA aspect though. I would say that here we do have a cause-effect. The AoA is something that you can directly control and adjust, and changes int eh AoA will cause changes in the circulation.

    The part that I absolutely disagree (but this is just a matter of opinion and taste) is:

    I didn't think we should include AoA in the general explanation of lift, because it would become, once again, too complicated, and isn't necessary to the basic understanding.
    I just think 'circulation' is more instructional and understandable to a general understanding than the more esoteric 'angle-of-attack'.
    For a couple of reasons:
    1- As I say, you control AoA, not circulation, You can explain to a pilot how pitch - path = AoA. You can explain how the elevator controls the AoA. I will not say that you can not do all that with circulation, but boy, I don't think that any pilot will agree that replacing AoA with circulation improves the explanation of lift or makes it any more easy to understand or makes more sense.
    2- In particular, it is much easier for me (and I would risk to say to most) to intuitively understand how if I increase the AoA I will be shoving air more down than how increasing the circulation will make the same. We see ceiling fans, airplane and ship propellers, screws, etc and used to the concept of pitch that can be quickly associated with AoA. We "see" how if I incline the flat plywood more, I will be deflecting the air more.

    Circulation strikes me as much more "esoteric" than an airfoil (or the blade of a ceiling fan) anted at an angle.

    I also found this gif helpful in visualizing the effects on velocity. Do you find it accurate?

    https://en.wikipedia.org/wiki/File:F...und_a_wing.gif
    Yes BUT... This seems to be a mathematical model based on potential flow forcing the Kutta condition, which is in general ok. But...
    1- As all models based on potential flow, I don't see the boundary layer being modeled (except the Kutta condition)
    2- It looks to me that, in the real world, at that angle of attack we would at least start to have separation progressing forward from the trialing edge on the upper surface (something that the potential flow model cannot predict by itself)

    But, if you care to comment on this:

    An airfoil developing lift causes the flow approaching it to bend upward. This is because the lower pressure on top of the airfoil pulls air up toward it. ~ Paul Bogataj, former Boeing engineer
    It is a common mistake to think that upwash exists because the wing is sucking upward on the air. ~ John S Denker

    Perhaps these are not opposition statements. Perhaps it's just the wording. But they seem to be oppositional.
    What can I say that I didn't say before....

    The air reacts to gradients in pressure and only to gradients in pressure (outside the boundary layer). Gradients in pressure IS the force that accelerates the parcels of air. If you have a parcel of air that was moving horizontally and later you find it moving mostly horizontally but also with an upwards component, be sure that it was subject to a gradient of pressures pointing up, and that means a lower pressure above the parcel tan below the parcel. And that profile in pressures is a continuous that ends up being the lower pressure / higher pressure areas above / below the wing. You can see that with the shades of blue in the Wikipedia animation. So Paul is right.

    Now, is that the wing sucking the air up? No. It is more air at lower pressure above the wing sucking the air up. So John is right too.
    Let me enlarge John's quote:

    Beware: It is a common mistake to think that upwash exists because the wing is sucking upward on the air. Such suction would cause a downward force on the wing, making a negative contribution to lift.
    (Pause to say that that part is brilliant. Let's continue)
    In fact the upwash flows uphill, into a region of high and increasing pressure, slowing down as it goes.
    That is correct but also misleading, in my opinion.
    First, go to the Wikipedia animation and take a seat on board an air parcel, one that eventually will pass very close to the trailing edge.
    You can see that, hes, you are traveling uphill in a zone of increasing pressure. That is what causes you to slow down But that is not what causes you turn upwards. What causes you to turn left is that you have greater pressure on the right of your track than on the left of it.
    Second, he never explains what causes the upwash. Based on the later discussion on circulation, one might deduct that circulation is what causes the upwash (but, to be fair, he doesn't say so). I don't like that idea. The upwash is part of the circulation pattern, The upwash ahead, the downwash after, the increased speed above, and the reduced speed below IS the circulation.

    Finally, let me quote another part of John:

    air is a fluid, which means it can exert pressure on itself as well as other things. The air pressure strongly affects the air.
    See? The air affects itself, changes in speed are coupled with changes in pressure which in turn imposes a force over air parcels inducing changes the speed which are coupled to changes in pressure that..... This seems like an infinite recursion, but it is not.

    For each outside condition, there is ONE solution where the pressure distribution is such that it accelerates the air parcels in such a way that they will have a speed distribution that exactly matches the aforementioned pressure distribution, thus complying with Bernoulli. As I said, there is only ONE thing that the air can do while going around not through the airfoil, separating at the trailing edge, and having its parcels of air comply with F=m*a. That ONE THING is the fields of speeds (velocity and direction) and pressures that you can see in the Wikipedia animation. No pressure causes speed, no speed causes pressure, no circulation causes speed, no of nothing of that. They are all caused at once, it is the only thing the air can do. Think of the force that the tracks make on the train.

    Let me give you an example in a different subject where something similar happens, but is more "graspable": The induced drag is a function of the weight of the plane. The amount of fuel needed is a function of the induced drag. The weight of the plane is a function of the amount of fuel. So the amount of fuel is a function of the amount of fuel, great! So you say airplane weight W, so I need to add X fuel, but now that I have X fuel the plane wights Y so I need additional Z of fuel which increases the wight and.... Infinite recurrence?

    Let's see:
    Drag = parasire drag + induced drag
    Induced drag = k1 * weight.
    Fuel needed = k2 * work done = k2* drag * d (flight distance)
    weight = zero fuel weight (ZFW) + fuel

    Let's make fuel = fuel needed

    Fuel needed = k2 * drag * d = k2 * (parasite drag + induced drag) * d = k2 * (parasite drag + k1 * weight) * d = k2 * [parasite drag + k1 * (ZFW + fuel needed)] * d

    So we have
    Fuel needed = k2 * [parasite drag + k1 * (ZFW + fuel needed)] * d

    We have fuel needed as a function of fuel needed!!!! Yes, but don't tell me that you don;t know how to find fuel needed from that equation. It is very simple:

    Fuel needed = k2 * [parasite drag + k1 * ZFW + k1 * fuel needed] * d = k2 * d * parasite drag + k2 * d * k1 * ZFW + k2 * d * k1 * fuel needed.

    Let's subtract k2 * d * k1 * ZFW + k2 * d * k1 * fuel needed from both sides:

    Fuel needed - k2 * d * k1 * fuel needed = k2 * [parasite drag + k1 * ZFW + k1 * fuel needed] * d = k2 * d * parasite drag + k2 * d * k1 * ZFW

    (1 - k2 * d * k1) * fuel needed = k2 * d * (parasite drag + k1 * ZFW)

    fuel needed = k2 * d * (parasite drag + k1 * ZFW) / (1 - k2 * d * k1)

    Done, now the fuel needed is not the function of the fuel need anymore. You can find ONE value that will meet the conditions imposed.

    Granted, aerodynamic is a different animal. You are dealing not with simple algebra but with differential equations. And you have 2 continuous 3D fields to solve. One scalar field (pressures) and one vectorial field (speeds). But the same logic applies: You have speeds and pressures that are function of the very same speeds and pressures. But once that you imposd these three conditions:
    - A constant speed profile of the incoming flow far ahead of the airfoil
    - The air flow cannot penetrate the airfoil
    - The air flow separates from the airfoil at the trailing edge
    There is only ONE distribution of pressures and speeds that comply with that (and with F=m*a for the parcels of air). That solution has the faster speed above than below, the lower pressure above than below, the constrictions, the upwash, the downwash, the circulation, all... Everything included.

    What causes all that? The three conditions and the laws of Newton.

    Leave a comment:


  • Evan
    replied
    Originally posted by Gabriel View Post
    Evan, did you delete a post of yours? I was answering to it and "poof", it's gone. One where you, among other things, cited John Denker saying that it was a myth that the upwash was caused by the lower pressure on the upper surface.
    Yes, I decided that I want to concentrate on the definitive part of lift and leave the conflicting arguments out of it. But, if you care to comment on this:
    • An airfoil developing lift causes the flow approaching it to bend upward. This is because the lower pressure on top of the airfoil pulls air up toward it. ~ Paul Bogataj, former Boeing engineer
    • It is a common mistake to think that upwash exists because the wing is sucking upward on the air. ~ John S Denker


    Perhaps these are not opposition statements. Perhaps it's just the wording. But they seem to be oppositional.

    Leave a comment:


  • Gabriel
    replied
    Evan, did you delete a post of yours? I was answering to it and "poof", it's gone. One where you, among other things, cited John Denker saying that it was a myth that the upwash was caused by the lower pressure on the upper surface.

    Leave a comment:


  • Evan
    replied
    Originally posted by Evan
    The amount of lift = airspeed × circulation × air density × wingspan.
    Originally posted by Gabriel
    Do you mean that the angle of attack and the chord or area of the wing doesn't have anything to do with the generation of lift?
    That equation is lifted from Denker. It is the Kutta-Zhukovsky theorem, as I'm sure you know.
    • Lift = airspeed × circulation × density × span (lift is equal to the airspeed, times the circulation, times the density of the air, times the span of the wing.)

    I'm think he means the total area of the wing span there.

    Or as Boeing (Aero) states it:
    • Lift is a function of speed, air density, wing area, and AOA.


    I just think 'circulation' is more instructional and understandable to a general understanding than the more esoteric 'angle-of-attack'.


    And as Denker also states:
    • As the angle of attack increases, the amount of circulation needed to meet the Kutta condition increases.


    So AoA is built into the circulation aspect. As I understand him, for a given airspeed, you cannot have increased circulation without having increased AoA, so one implies the other. And a wing with zero circulation has zero lift.

    I also found this gif helpful in visualizing the effects on velocity. Do you find it accurate?

    https://en.wikipedia.org/wiki/File:F...und_a_wing.gif

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  • elaw
    replied
    Originally posted by Evan View Post
    - Many, many people (if not most people) who know a thing or two about aviation, some of whom are pilots, have a false understanding of how lift is generated.
    Well there's your problem: you need to find people who know at least 3 things about aviation.

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  • Gabriel
    replied
    Originally posted by John S Denker
    Kutta condition- It is a bit of a mystery why the air hates turning a corner at the trailing edge, and doesn’t mind so much turning a sharp corner at the leading edge — but that’s the way it is.
    I disagree with that part. Air (or any fluid) hates turning any sharp edge anywhere, so it doesn't. The leading edge is not sharp in most cases and if it is, there will be separation there too unless the AoA is such that the stagnation point is exactly at the leading edge. Now, if the AoA is not too big, the separated air can form a bubble and re-adhere on the upper surface later on. But now the air is going around the bubble, not the sharp leading edge.

    And the reason for the Kutta condition is not a mitsery. The centripetal acceleration is V^2/R. On a sharp edge R->0 so for any non-zero speed the normal acceleration is infinite. It gets paradoxical because an infinite acceleration requires an infinite force on the parcel of air turning the sharp edge, which in turn would require infinite low pressure and hence infinite high speed. In other words, the potential flow model predicts a singularity in the trailing edge, a singularity that would put the flow out of the scope of the model (potential flow = no viscosity and there is no way that you can neglect the viscosity wen you have infinite speed). It is quite obvious that a real flow will not be able to achieve the conditions needed to turn around a sharp edge.

    It is true that, in the early ages of mechanics of fluids, when they were working with the potential flow model, it eventually became apparent (intuitive, obvious and also observed) that the flow would separate at the trailing edge but there was no model to explain that. So it was an external condition imposed to the model (together with "the flow will not penetrate the airfoil", which is something that no model "predicts", it is a condition imposed from outside of the model, in the same way that "the train will follow the tracks" in an example I gave in a previous post).

    Now, model a boundary layer (for which you need to take viscosity into account) and now the model predicts the Kutta condition.

    Now, air is difficult to see, so let's play with water. Take that spoon and hold it hanging lightly from the tip of the handle, now put the round part under this stream of water from the tap. Slowly. SO what did you see? Correct! The shape of the spoon gets the water is deviated, pushed to one side, and the spoon is pushed to the other side.
    Ok, that's a bit of out-of-context and a bunch of my bad. I thought of adding a clarification but remember it was an explanation for a 5-years-old.

    The Coanda effect (the tendency of a stream of flow to remain attached to the surface of an object) is not how a wing creates lift because, simply, there is no "one jet of flow".
    The stream of water surrounded by air or a jet of air surrounded by static air would be Coanda effect.

    My intention was related to explaining the action-reaction. The spoon pushes the water and the water pushes the spoon. It is noice because you can SEE the water being displaced in one direction and you can SEE the spoon displaced in the opposite direction and defeating gravity (it is not hanging vertically). And when you stick your hand out of the window at an angle of attack, you hand pushes the air and the air pushes your hand. I hoped it would be intuitive that a thing at an AoA would push the fluid. But the reason why the hand pushes the air is not the same than the reason why the spoon deviates the water.

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  • Evan
    replied
    Originally posted by Gabriel View Post
    Why? How?
    It has to be a summary of the hows and whys, but it's balance of how much understanding you can provide in a summary. As I said...

    If anyone wants to know about the Kutta condition and Navier–Stokes equations and viscosity and the Magnus effect and Newton and Bernoulli and all the actual mechanisms and physics involved in detail, they can dive down that rabbit-hole to their heart's content.

    Forget abotu why and how... Whaaaaat?
    Do you mean that the angle of attack and the chord or area of the wing doesn't have anything to do with the generation of lift?
    And that there are other contributor factors other than the pressure differential above vs below the wing?
    The way I currently understand it from reading the link you provided, the chicken-and-egg question of airspeed and pressure differentials can be explained as follows:
    The circulation (the span-wise 'bound' vortex) is responsible for acceleration of airflow adjacent to the wing by imparting an opposing force against the lower airflow and an additive force to the upper airflow, and that THIS is what results, thanks to Bernoulli, in the areas of pressure differential that give the wing its lift. Any change in AoA will have the effect of increasing or decreasing circulation, so AoA is included within the equation as 'circulation'. Other contributing factors are the air being turned by the wing volume (or impenetrability) and deflected down by the lower wing surface in a positive angle of attack. Do you agree with that?

    I didn't think we should include AoA in the general explanation of lift, because it would become, once again, too complicated, and isn't necessary to the basic understanding.

    I see it as very complicated.
    I know, but everybody can't be Gabriel. You are assuming certain a priori knowledge of concepts that most people lack.

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  • Gabriel
    replied
    Originally posted by Evan View Post
    It can't be a technical equation.



    The problem with this is that it is too simple. Too vague. Therefore, it is wide open to misintepretation.

    A better 'simple' version would be: "The wing, interacting with the surrounding airstream, produces a lower pressure above the wing than below it, which causes the wing to lift upward."

    But, that is still too simple and open to misinterpretation and erroneous understanding of the 'whys' involved.



    #23 was an explanation of wing shape, not lift itself (but very informative on that subject).
    #62 was a list of misconceptions.
    #33 was very helpful but too detailed and tooooo looong for most non-aeroengineers.

    So, continuing to build on:


    1) Circulation cannot be explained simply, but the reason for it can be included (as a 'convenience').
    2) We don't need to name-drop. We can omit Bernoulli and replace him with the general theorum.
    3) Same goes for Newton.

    So, let's try this:

    As the wing begins to move forward, the interaction of the wing and the surrounding air produce an initial air disturbance called a vortex
    Why? How?
    and this vortex, in turn, produces an opposite 'bound' vortex
    Why? How?

    , or 'circulation', which flows around the entire wing shape, moving from front to back across the top of the wing and back to front along the bottom of the wing.
    Forget abotu why and how... Whaaaaat?

    his force of this circulation causes the air travelling above the wing to move faster and the air travelling below the wing to slow down. Since a faster-moving parcel of air has a lower pressure than a slower-moving parcel of air,
    Why

    this creates an area of lower pressure above the wing which pulls up on the wing and pulls down on the air. This, along with some other contributing factors, causes the wing to lift upward. The amount of lift = airspeed × circulation × air density × wingspan.
    Do you mean that the angle of attack and the chord or area of the wing doesn't have anything to do with the generation of lift?
    And that there are other contributor factors other than the pressure differential above vs below the wing?

    Now, keep in mind that this is an explanation for a general audience intended to replace the equally brief erroneous explanations that currently pervade everything from the internet to actual piloting manuals. This requires it to be brief and succinct. If anyone wants to know about the Kutta condition and Navier–Stokes equations and viscosity and the Magnus effect and Newton and Bernoulli and all the actual mechanisms and physics involved in detail, they can dive down that rabbit-hole to their heart's content.

    Would you disagree with that general explanation?
    If you find it useful, I am happy for you. I see it as very complicated. The reduction of air pressure with increased speed is Bernoulli. The circulation is the Kutta condition which I find much more simple, understandable and intuitive than the circulation. And the circulation, Kutta condition and the Magnus effect exist because of viscosity.

    And in any event, why is the circulation the magnitude it is so the speeds above and below are what they are and not something else (for example not something that would make the parcels above and below arrive together at the trailing edge)? I don't think that your explanation fixes any of the objections or complaints that you had with the other explanations, rather the opposite, and it is much more complicated and difficult to understand.

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