Questions about conventional theories of lift generation

1, First

     What kind of mechanism does lift generate on the wings of an airplane? Answers explaining the principle of this basic proposition have not yet converged to one.

 　I found out how it has not converged, and that many conventional explanations have been quite qualitative expressions when discussing scientific themes, etc.

     Actually, I didn't really want to say about conventional theory, but doubting conventional theory certainly helped my opinion.

     Therefore, I would like you to understand that I cannot go through it.

     In other words, where I think that it would be strange to think of the conventional theory, I would like to give my personal opinion after clearly explaining the reason.

     Of course, it is a suspicion of the "theory", and it is not a criticism to the individual who is advocating it, so I ask you not to misunderstand it.

     Then, immediately, the following two theories are currently the mainstream as the mechanism for generating lift on the wings. 　

     one    

*Circulation and Bernoulli's Theorem Theory*

     "There is a clockwise (aeroplane leftward) circulation around the wing, and the flow of air on the upper surface of the flying wing is faster than that on the lower surface. 

     Therefore, according to Bernoulli's theorem, the air pressure on the upper surface of the wing is It becomes lower than the atmospheric pressure and lift is generated." 　

     Many people in the world seem to agree with this theory.

     If you look at the web pages of university professors and high school physics teachers, most of them are explained in this theory.

     In other words, in universities and high schools, this is the way to teach. I also learned this way in the 1960s (Wow, too old!)

 The other is 

*Coanda effect and reaction theory*　 

     "The air flow on the upper surface of the wing is bent downward by the Coanda effect and is released as downwash, and the reaction force of the force that bends the air downward (Newton's third law: law of action and half action) lifts the wing.” 

     In December 2000, Dr. David Anderson and Dr. Scott Eberhardt of the United States co-authored this theory in "Understanding FLIGHT," which created a sensation in the world.

     The photograph is the second edition.

     Recently, there are many Web sites that agree with this theory and explain wing lift.

     Which theory do you agree with? I have some doubts in both theories, so I will describe their contents and my personal opinions.

2, Question and personal opinion about two theories

First, 

*Circulation and Bernoulli's Theorem Theory*

     The flow of the lift generation mechanism of this theory is as follows. 

① According to the circulation theory, a "circulation" flow is generated around the wing (clockwise in the cross section of the wing advancing to the left) 

② The flow velocity on the upper surface of the wing is faster than that on the lower surface

③ The pressure on the upper surface of the wing is lower than that on the lower surface according to Bernoulli's theorem

④ Lifting force is generated due to the pressure difference between the upper and lower wings

 Question 1: Is the circulation theory correct?

     It has been known since the dawn of airplanes that the air flow on the upper surface of the wing is faster than that on the lower surface. 

     The question is, "Why is the air flow on the upper surface of the wing faster than the air flow on the lower surface?"

     Initially widely recognized as the mechanism, the "simultaneous arrival theory" that the upper and lower airflow at the tip of the wing reaches the rear end at the same time is wrong, and the contrary, it was revealed by highly accurate experiments accompanying the development of science and technology that the flow on the upper surface of the wing reaches the rear end earlier than the flow below.　 ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 

     What is the wrong "simultaneous arrival theory"? 

     When imagining the cross section of the main wing, the flow on the upper surface of the wing, which rises and has a long distance, and the flow on the lower surface of the wing, which is relatively flat and has a short distance, come together at the rear end of the wing. 

     The gutter means that the flow on the upper surface of the wing is faster than the flow on the lower surface.

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　By the way, if the flow of the upper surface with a long distance reaches the trailing edge of the wing earlier than the flow of the lower surface with a short distance, the "simultaneous arrival theory" is denied, and "another reason" is needed. It is coming.

     On the other hand, "existence of circulation" (Kutta-Zhukovsky's theorem) was proposed by Kutta in 1902 and Zhukovsky in 1906, and has been widely adopted until today.

     It was exactly the same time that the Wright brothers flew on a power plane in 1903, it was advocated that "the existence of circulation".

     However, there are some people who are still advocating the "simultaneous arrival theory" mentioned above. It is understood by only a few people in the "simultaneous arrival theory". 

     And it seems that most people, including researchers and experts, have been understood by the “circulation theory”. This is truly a royal road.

*Circulation theory*

     I don't know if both Kutta and Zhukovsky were advocating the mechanism of the circulation in addition to the existence of the circulation, but the following explanations are currently given.

     "When the plane leaves the airfield, there is a counterclockwise (airplane left) "departure vortex" at the rear end of the wing.

     Then, a clockwise circulation occurs around the wing so as to cancel it.

     The "departure vortex" remains at the airfield, and the circulation around the wing of the flying airplane is conceptually connected to the "departure vortex" through the axis of the wing tip vortex generated from the wraparound at the wing tip.

     The departure vortex will eventually disappear, but the circulation will continue for the duration of the flight."

    Indeed, if there is a circulation flow around the wing, it is intuitively reminiscent that the flow on the upper surface of the wing will be faster than the flow on the lower surface.

     However, for example, in the case of a visible river, if the river with flow velocity A and the river with flow velocity B merge, the flow velocity will never become (A+B).

     The flow velocity after merging is determined by the river slope, that is, the height gradient of the position, regardless of the original two flow velocities.

     Similarly, once the airflow from the flight and the circulation merge, it should be determined by the pressure gradient, independent of the original two velocities.

     However, returning to "circulation theory," the following questions arise.

・What forces and how do small departure vortices develop into a large “circulation” that envelops the entire opposite wing?  What is the mechanism?  

・What is the mechanism that keeps the "circulation" around the wings for a long time during the flight after takeoff?  Where does energy come from?

     Actually, I can't find any scientific or quantitative explanation that answers these simple questions.

     The qualitative explanation is as described above, and it is a philosophical way of saying that "the counterclockwise circulation occurs so as to cancel it" or that the starting vortex that disappears is "the core of the vortex is conceptually connected". 

     Even if it is muddy by philosophical language, I cannot understand or convince.

     I have to say that this theory is not convincing at all.

 　For example, How much is the flow velocity of the upper and lower surfaces of the wings of an airplane flying at 900 km/h? How much is the circulation and how much is the pressure difference? 

     Even if I read the books I got and the explanation of lift on the Web, I feel that it is insufficient if there is no explanation there, and it makes me wonder why I have been left in such an unclear state until now.

    And if there is no "departure vortex", for example all Space Shuttles that rushed into the stratosphere from space, or hand-throwing model aircrafts will have no "departure vortex", so they can't fly ! Really?

     The "circulation theory" is all about qualitative words and does not provide a quantitative scientific basis for the circulation to occur and continue.

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     Recently, it has been explained that the "Karman vortex" is the energy source of circulation.

     But the Karman vortex is generated downstream of the object, and there is never a unidirectional vortex left. 

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Question 2: Can Bernoulli's theorem be applied?

     Apply Bernoulli's theorem to the fast air flow on the upper surface of the wing and the slower air flow on the lower surface, ”There is a circulation around the wings, creating a pressure difference enough to lift tons, tens of tons, and even hundreds of tons of planes,” so they explained.

     However, this cannot be said to be a scientific and quantitative explanation that connects the actual pressure difference and circulation.

     I will repeat the above sentence, but how many tons, tens of tons, hundreds of tons of lift force are obtained from the upper and lower velocity of the wing of an airplane flying at 900 km / h, I want to know quantitatively up to where they are producing.

     I'm sorry for the simple calculation, but for example, the maximum takeoff weight of a jumbo 747-400ER with a wing area of ​​about 541 ㎡ is 412.8 t, so

 412.8t/541㎡=412.8×1000kg/(541×10000㎠) ≒ 0.076kg/㎠ 

     In other words, in order for this jumbo machine to take off, there is a pressure difference of more than 0.076 atm between the upper and lower surfaces of the wing. It is a simple calculation that ignores high lift devices.

     The gliding speed is a number of kilometers per hour, then the circulation flow is a number of kilometers per hour. 

     As a result, the speed difference between the top and bottom of the wing becomes each number of kilometers per hour.

     Therefore, if we calculate using Bernoulli's theorem, I want to know numerically up to the point that a pressure difference of more than 0.076 atm occurs on the bottom surface.

     When I learned Bernoulli's theorem, I couldn't understand the texture of "a non-viscous, incompressible ideal gas".

     There is no music or language in human culture because no sound is transmitted in such an ideal gas, and there is no car because an engine without a compression process does not run. 

     I remember, in the end, I couldn't find any examples of applying Bernoulli's theorem to real-life phenomena around me.

*My experiment*

     In order to confirm question 2, "Can Bernoulli's theorem be applied?", the following experiment was conducted. Air is blown downward from the outlet at about 6.2 m/sec.

     I drew a square drawing paper there. The distance between the background lines is 2 cm.

     There is a velocity difference between the air flow on the upper side and the lower side of the wing. Just like that, there is a velocity difference on the left side and the right side of the drawing paper. 

     If Bernoulli's theorem applies, the drawing paper should be pulled up to the left, where the flow causes a low pressure, but that's not the case at all. 

      “Not at all”

     In other words, the pressure on the left side of the drawing paper is not lower than that on the right side, which is not flowing.

     why? The mechanism will be described later.

     By the way, in the explanation of Bernoulli's theorem, the condition "It is a theorem that holds when a steady flow of an inviscid, incompressible fluid without external force is satisfied" is always added. 

     This means, "This theorem does not apply to real-world phenomena that are viscous and compressible!", so Mr.Bernoulli refuses! 

     However, they are ignoring this.

     Why should they ignore it? The reason will be described later.

     I think that the air around us, which is extremely compressible and also has a large viscosity, is no longer a "non-viscous, non-compressible fluid" and is a "different object" that is completely different from an ideal gas. 

     Because two physical properties that define an ideal gas are very different from each other, and because it is completely different from air, Mr. Bernoulli purposely distinguishes it by the name "ideal gas". 

     Moreover, can it be said that "there is no external force" under the condition that it is strongly compressed at 1kgf per 1㎠?

     I think Bernoulli's theorem cannot be applied to an event in the air that is completely different from the ideal gas.

     So why do exist "flow velocity difference" and "air pressure difference" on the upper and lower surfaces of the wing?

     The mechanism is explained in my another document, "Mechanism of Lift Generation", so the explanation is omitted here.

     Next, I bent the bottom of the drawing paper to the right. Then the drawing paper was pulled up to the left. Let's look at the case of the flat drawing paper mentioned earlier.

     The phenomenon that this drawing paper is pulled up to the left is due to the Coanda effect. 

 　The viscous fluid flows along the surface, which is the Coanda effect. If there is a surface that does not move, the flow will be drawn to the surface, and it will wrap around even on the convex surface.

     When bending along a surface with a convex surface, pulling the object in the direction perpendicular to the surface is not mentioned in the "Coanda effect", but naturally the force relationship can be understood by considering the law of action reaction.

     In my experiment, the viscous air tries to flow along the drawing paper, and the convex portion bends the flow to exert a reaction force on the drawing paper. Speaking of atmospheric pressure, the atmospheric pressure of the convex part that bends the flow decreases.

     The drawing paper is not pulled to the left because the air pressure in the straight part is low. This video proves it.

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Mechanism of this event

     In the figure below, when the blown air flow hits the raised drawing paper, it is bent to the left once, and then it is bent downward along the drawing paper due to the Coanda effect, and flows almost straight down.

     The direction of the air flowing away is almost right underneath, so the work of bending the flow of A and B is roughly the same, but it is considered to be about the same.

     However, since the distance from the fulcrum to the point of action is very different, the drawing paper is pulled to the left by the principle of "lever". 　

     Red arrows indicate the image of force acting on the drawing paper, and the direction and position are not always accurate.

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     By the way, it has been confirmed that the flow on the upper surface of the wing is faster than that on the lower surface, and that the air pressure on the upper surface of the wing is lower than the air pressure on the lower surface. 

     In a sense, Bernoulli's theorem is actually very very useful for explaining the lift generated on the wing.

① Speed ​​difference that the flow on the upper surface of the wing is faster than the flow on the lower surface

② Applying Bernoulli's theorem, the pressure difference on the upper surface of the wing is lower than that on the lower surface 

③ Lifting force 

     It seems that there is no contradiction with this.

     That is why it is easy to make mistakes.

     The truth is, as you can see from my experimental results, 

      "There is no lower air pressure than a faster air flow than a slower air flow. This means that Bernoulli's theorem cannot be used to explain the pressure difference between the upper and lower surfaces of the wing. "

     My experimental results suggest what Dr. Anderson and Dr. Eberhardt say that

     "The air pressure on the upper surface of the wing does not decrease because the flow is fast, but the air pressure on the upper surface causes the flow velocity to increase."

     In other words, which one comes first, "difference in flow velocity" or "difference in atmospheric pressure"? 

     It's just the relationship between chickens and eggs, 

      According to "Circulation and Bernoulli's Theorem", "difference in flow velocity" comes first, and as a result, "difference in atmospheric pressure" is created. 

     According to "Coanda effect and action reaction theory", "difference in atmospheric pressure" comes first, and as a result, "difference in flow velocity" is created.

     That! ? We confirmed it at the river flow! ‥ 

     "The velocity and direction of the air depends on the pressure gradient", we confirmed !!

Next

*Coanda effect and reaction theory*

     Theory of Dr. Anderson and Dr. Eberhardt of USA.

     The lift generation mechanism of this theory is as follows.

① The air flow on the upper surface of the wing is bent downward due to the Coanda effect 

② Upward force (lift force) acts on the wing due to the reaction of the force that bends the flow downward

     I forgot how I knew about this theory, but I felt that the things I had been swayed up to that point were blown away, and at that time, I was really feeling "the scales drop from my eyes."

     However, although I generally agreed with this theory, there were still some doubts.

Question 3: Can the airplane be lifted just by the Coanda effect?

     The concept that "mass x downward acceleration" when the air is bent and downwashed becomes the lift of the airplane is a story of a world in which only wings and air exist, so Newton's third law (action reaction) , I think it should be.

     F=ma       (F: lift, m: mass, a: downward acceleration).

     In other words, it is understandable that this relationship occurs when we consider the entire air that is bent downward across the wing. (However, it does not matter if the whole lift is estimated)

     It is a fact that it is hard to understand because the opponent, which is the point of action of Newton's third law, is not the individual but the air (gas) above the wing, so it literally seems to catch a cloud. is

     And, it is natural for Dr. Anderson and Dr. Everhart to pay attention to the Coanda effect, that emphasizes only the upper surface of the wing and does not stick to the lower surface at all.

     However, I think that the work of the lower surface of the wing should be large enough like the upper surface.

     Videos showing the face coming out of the window of a car running at high speed and the soft cheeks dented by the wind, and a sandy beach rippling, throwing a round board on the water and jumping on it immediately and sliding. 

     Looking at it, I'm convinced that not only the lower surface of the wing can be ignored, but also the large force that pushes up the wing from the bottom should be working, just like the upper surface.

     And in the world of architectural engineering, the concept of "wind pressure" in which the wind hits a building and exerts a force has been established and is being utilized in the design of buildings.

*About Problems common to both theories*

Question 4: Can air be treated as incompressible? 

     Even if it is not stated explicitly in the commentary, when we quote Bernoulli's theorem, we consider air to be incompressible.

     Dr. Anderson and Dr. Eberhardt, as well as anyone else's commentary on "The Circulation and Bernoulli's Theorem", to be clear perhaps everyone but me treats air as "incompressible" when describing lift. 

     Why do they do that?

・In “Bernoulli's theorem theory”, the pressure is lower where the flow is faster than for the slower flow, that is, the Bernoulli's theorem is applied to form a direct mechanism of lift generation.

     Bernoulli's theorem was premised on an ideal gas (incompressible, inviscid).

     On the other hand, 

・Dr. Anderson and Dr. Eberhardt's "Coanda effect and action reaction theory" ,says the reason why the flow velocity on the upper surface of the wing is faster is because the air pressure on the upper surface of the wing is low.  Thus, the pressure of the air is reduced and the flow is accelerated on the upper surface of the wing."

     Dr. Anderson and Dr. Eberhardt explain the boating "water and oar" relationship that most of us have experienced, for the sake of clarity. 

     It seems that the air must be incompressible like water in order for resistance to occur.

     Water flows into the back of the oar from the surroundings in a blink of an eye, but since the mass of water is large (about 770 times that of air), the movement is dull and it looks quite different from the movement of air.

     In other words, it is easy to think that there is resistance to the creation of a vacuum because water is incompressible.

     However, I believe that air has great compressibility, but resists the creation of a vacuum just like water does. The reason is that if there is a region where the atmospheric pressure is low even in the air, the air will flow in from the surroundings with a force of 1 atmospheric pressure. Even though the flow velocities are very different, this movement should be exactly the same as for water.

     In other words, even if you move the oar in the air, the air moves exactly like the movement of water in water, but the air is invisible and the mass is very small, which is 1/770 of water, I feel that it is different from. 

     This interpretation is one of the important points in my opinion.

     Water and air are the same fluid, with the only difference being their viscosity and mass. The air moves just like the movement of water when you take a bath and move your palm in the water.

     Both doctors had to make air incompressible, just like water, to explain that there is resistance to creating a vacuum even in air. 

     They also says, "In this way, the air is accelerated on the upper surface of the wing by decreasing the pressure."  However, decreasing the pressure of the gas is nothing but expansion of the gas.      

     Perhaps there must have been a contradiction in this regard.

     In other words, the proponents of both theories had to tentatively define air as incompressible in order to make each theory valid. We must have been well aware that air is a compressible gas.

     When talking about lift, air should be argued as a very compressible substance as it is, let alone bend the physical properties and discuss under conditions different from the truth (go in the wrong direction) I think.

     Certainly, if you can't feel that the compressibility of air is "very high," that's right.

     In our daily lives, about 10 tons of force is applied to 1 ㎡, but the air weighs 1 ㎥ and weighs only 1.3 kg.

     Some people may say, "Oh, is it so light?", while others might say, "Eh? Is it so heavy? I didn't think there was weight!"

     No, since it is a substance, there is always weight (mass x gravity). However, it is about 1/770 of water.

     Because of this very large atmospheric pressure and very small mass, the "wraparound" of the air that fills the space passed by the object is so quick that we do not notice this "wraparound" itself.

     If you do not fill the tires with air or inflate the bladder, you will not be able to feel the compressibility and you will not feel any dust such as the mass of air.

     "I didn't think there was any weight!" is not unreasonable. For example, when we move our limbs, there is always a very rapid “wraparound” of air with compressibility of air called compression on the front side and expansion on the back side, but that kind of thing I can not be aware of it at all. You can't see it, and it's so light that it's natural.

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Digression

     Air flows from high pressure to low pressure, just as water flows from high position to low pressure. It means that if there is no difference in atmospheric pressure, no flow will occur.

     No, it would be a little different to say this. Air also flows from a high position to a low position. In other words, as long as air is a substance with a mass, it is pulled by the attractive force of the earth and flows to a low position. In fact, human beings live at the bottom of the air, which is attracted by the attractive force and stagnates in a low position. 

     At the same time that warmed air rises because heat expands and the density becomes smaller and becomes lighter and rises. 

     At the same time, cold air with a high density of surrounding air flows to a low place due to attractive force, so warm air with a low density It can be said that is struck out upward.

     In other words, if we discuss the flow at the same positional height like a wing, we can say that "air does not flow unless there is a difference in atmospheric pressure". 

     I mean, that means!  

     ”The air flow around the wing is actually guided by the difference in atmospheric pressure first, so it moves!” 

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Let's try to see the wraparound with the eyes of your mind  

     The quick “wraparound” of the air is invisible to the naked eye and hard to be aware of, but it is possible to associate the “wraparound” situation with the events we once experienced.

     Everyone has seen the smoke drifting from a bonfire. It's the same if you've seen it in movies or on TV.

     Now, let's associate a person running in a place where smoke is drifting.

     From the front of the running person, you can imagine how the smoke instantly circulates from the front to the back (back), and then the smoke moves in a complicated manner.

     At this time, the air is compressed on the front side of the person to increase the atmospheric pressure, and on the rear side, the air expands and the atmospheric pressure decreases.

     Air flows from high pressure to low pressure. In other words, the air instantly flows from the front to the back.

     After a person runs away, the inertia of the movement of the air when it wraps around makes a complex wobble for a while. In this way, a series of movements of the air can be associated with movements of smoke, that is, can be seen with the eyes of your mind.

     I remember that this kind of association was very important for the experimenter to read the results. Because it was necessary to immediately judge the correctness of the collected data.

     What I want to say is "Don't define air as incompressible, and quick wraparound with compressibility is a very important point to consider when considering lift as a characteristic of air.

     If you define air as incompressible, you will not be able to see this important event in reality, and you will miss an important point !!!

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