Why the airplanes flight?

Why the airplanes flight?

1. Why the airplanes fly? This is the opening question with I usually start my AERODYNAMICS OF DESIGN seminary…I shoot it, to all my audience trying to hear that simplest but precise answer, nevertheless I hear any other things… “because the engines…”, “because the physics… bla, bla, bla…”, “because the action of the forces…” and so many others, trying to impress only to be so elaborated or complex, but all is reduced to the simplest fact that an airplane flies just “because it has wings”, when I answer in that way, they believe I´m joking, but I continue saying to my audience “…so, have you seen any kind of object or animal, even an insect that flies and it not have wings?”, the answer is a big silence and many eyes wide open, that´s indicate me that they are ready to learn, “so, have you seen a glider whit an engine?, and the physics and the conjunct of forces, are applied in the wing, or not?... for that reason, without wing there is no airplane”, so you see, the answer is simple. Ok, the answer is that simple, but the detailed explanation about the lift phenomena, use the science and many scientific principia. So when I finish my simplest exposition about, why the airplanes fly? I start to explain how the wings work, in the next manner: The airplane flies because it has wings, becoming this parts or surfaces into the aerodynamics units of the aircraft, so those are who define the aerodynamics performance. And how they generates the lift?. The wing has a peculiar shape that´s allow to exploit the fluid dynamics to generate that lift. This shape can be observed when cut the wing in a traverse manner (parallel to the fuselage) “Figure 1.” to their maximum length, that is denominated wingspan, from this cut is obtained the wing cross section that is the airfoil “Figure 2.” , this shape is who make possible the lift generation.

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Eng. Roberto C. Subauste P.

IMAGINARY CUTTING PLANE

Figure 1. Cutting the wing to obtain a cross section. IMAGINARY CUTTING PLANE

WING AIRFOIL

Figure 2. The wing airfoil. Exist thousands of wings airfoils around the world, many like applications are used for each one of them. To make a general explanation of how is the lift generated, we will assume that the wing airfoil has a longest curvature upper (top camber) than the lower curvature (bottom camber), for this we are going to use the Bernoulli´s Principle and the Venturi´s Principle, from we take the statement that says: a fluid when increase its speed in a defined direction, it will increase the dynamic pressure, that is the pressure that the fluid exert in the movement direction, and at same time its static pressure decrease, this is the pressure exerted perpendicular to the movement direction, this becomes a very simple principle, but how with this can be obtained lift in a wing?, now we can develop this: Using the airfoil in the “Figure 3.” we will see what happens, to simplify, we take just two air particles, one will go to the top camber and one will go to the bottom camber, boot particles starts at the same time from the front part of the airfoil (leading edge), and by the mass conservation (because in the atmosphere no exist void parts), this two particles must arrive at the same time to the rear part of the airfoil (trailing edge), for that

this fact is met, the particle that’s goes up, will travel a longer distance and to get at the 2


same time with the particle that’s go to the bottom camber, it must be go faster, according to Bernoulli, happens then the static pressure on the top camber of the airfoil will be lower than the static pressure on the bottom camber, causing that there is over the wing a lower pressure zone that is pushed up by the relative higher pressure in the bottom of the wing, we can say that the wing is “sucked” from de top and pushed up from the bottom, so that’s the way is the lift appears. STREAM AT HIGHER SPEED LOWER RELATIVE STATIC PRESSURE The particles “Arrives” at the same time

The particles “start” at the same time

HIGHER RELATIVE STATIC PRESSURE

STREAM AT LOWER SPEED Figure 3. How the lift is generated. Well if this is the way that the lift is generates, so how generate lift a symmetrical airfoil?, this is the one that haves the top camber as same that the bottom camber, Oh! Here we need to introduce a new concept, the Angle of Attack. The airfoil has many parts “Figure 4.”, one of them is the chord (2), this line starts from the farthest point of the leading edge to the farthest point of the trailing edge joining them, from this line is measured the angle that form the airfoil with the stream lines of the air “Figure 5.”, this angle is named Angle of Attack, this become positive when is above from the stream lines and negative when is under this lines. Using this angle that is plotted the typical airfoil´s lift curve that´s shows the lift coefficient (Cl) behavior, this coefficient is a dimensionless value that express the efficiency of the airfoil shape, any airfoil and aerodynamic element posses a lift curve. In this curve we can find the 0 lift point, that shows the angle at the airfoil no produce any lift, other is the stall angle, this element shows the angle that airfoil stops to generate lift and become a “piano” “Figure 6.” “Figure 7.”, in further lines we explain better this fact.

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Figure 4. Parts of the airfoil.

ANGLE OF ATTACK

0º OF ANGLE OF ATTACK

CP: PRESSURE COEFFICIENT

Figure 5. Angle of Attack.

4


Maximum lift coefficient for different scale configurations.

Lift coefficient, Cl

Cero lift angle.

Angle of attack

 in degrees

Figure 6. Typical airfoil´s lift curve. Now with the Angle of Attack concept explained, let’s see what is happening to those two particles in a symmetric airfoil. At 0º the two particles travels at the same speed across the upper camber and the bottom camber, without make any change in the pressures, then is no generate any lift. When the Angle of Attack is increased, the impact point (at the leading edge) of the two particles lays lower than the impact point at 0º, forcing at the particle who goes through the upper camber to travel a little more distance, inducing the explained in previous paragraphs, obviously the difference in distance is very little compared at an asymmetrical airfoil, but has significance in the lift generation. That’s the reason when one reviewing the typical lift

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curve of symmetrical airfoils, you see that those are not the most efficient generating lift. And in the same manner happens in an asymmetrical airfoil flying in an inverted position.

5º of angle of attack

15º of angle of attack Figure 7. Pressure around airfoil at different angles of attack.

The symmetrical airfoil, has the same camber over and under the chord line (1), so its lift curve will show the same behavior at positive than negative angle, but compared to an asymmetrical airfoil´s typical lift curve one see that the 0 lift point is displaced to the negative part of the angle of attack, resulting that the airfoil will generate negative lift with a relative low (more negative, contradictory, right?) angle of attack. So if it is flying inverted and pretends generate enough lift to stay in flight, the angle of attack must be “higher”, becoming lesser efficient “Figure 8.”. Something that is evident in the lift curve when is compared between a symmetric and asymmetric airfoil, is that while the airfoil becomes more cambered (4), the total lift curve goes displaced to the positive region of the lift coefficient, this means that when an airfoil becomes more cambered it improves its performance concerning to a lift generation at lower angle of attack. So, there are two ways to increase the lift apart from increase the angle of attack, one will be increase the speed, what makes that the particle who goes to the upper camber increase their own speed even more, and in that way will be more lift. The other way will be increase the camber of the airfoil, this is achieved by mechanicals means in the wings and in the control surfaces of the airplane, controlling at will the lift to maneuver the airplane during the flight. Well, until here, the generation of the lift is easy to understand, but something must be cleared, everything that has been explained before, turns out to be in IDEAL conditions “Figure 9.”, such as mathematicians and physicist likes to present, just trying to avoid any 6


annoying mathematics and/or physics “variables”, and also omitting other atmospheric effects, so what´s this mean?, means that the truth is a little more complex, but without ceasing to be easy to understand, so let´s see what are the other effects has been omitted, and let´s explain in a more technical manner what´s happen in a wing:

Note: is possible to see in both plots the cero lift angle; in the symmetric airfoil is at 0º, in the other hand in the asymmetric airfoil it is at negative . If you want to reach the y value at 0º of the asymmetric airfoil in the negative side of the plot, the  will be even more negative.

Figure 8. Lift curve comparison between symmetrical and asymmetrical airfoil. First we are going to explain in the right manner the two particles issue, really this particles don´t separate only without suffering any effect or exer some to the wing surface, because if they only separate when arrives to the leading edge and rejoin at the trailing edge, then there is no any kind of lift, because it is like a cutting the water with a very sharp knife, so the particle that´s goes above no needs to go faster than that goes below, they are just “moving apart” at the wing pass. The truth is that the particles “roll” against the wing surface (by the upper camber and the lower camber), this cause that appear the fiction effects giving origin to the Boundary layer, so appears too the “surround” pressure effects (atmospheric pressure), caused by the particles that no are directly affected by the presence of the wing, and in conjunct they “smash” the particles that are directly in contact of the wing surface against it, this tiny detail, is often omitted by any explanation of lift origin, as the surrounding atmosphere does not exist and therefore neither its effects, so better we are going to explain each one of this effects to give a better comprehension about the lift generation.

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Frigure 9. IDEAL Stream around an airfoil.

1.1. Friction. Everyone has been learn that an object lays on a surface, this one exert a force over that surface, if we want move it parallel to that surface, first we must defeat the friction force, represented by the friction coefficient, analogously happens with the air particles, when those rest, they are exerting a force over the surface where are piled (pressure), being “still”, they be accommodate in some manner that many exert that pressure by contact with the surface, but if the air or the surface begins to move, the pressure that the particles exerted over the surface decrease, this is due to the nature of the fluid that is constituted by particles that no are binded one to another, there exist some “intermediate spaces”, and the particles by the movement caused, they no longer remain “still” in the same position, decreasing in this manner their “contact time” with the surface as well as the amount per surface of the same that make that contact, you must be know, that the “air block” tends to deform in the movement direction, this is what makes that decrease the amount of particles that are pressing in “normal” direction to the surface and also decreasing the fluid internal pressure that produce internal molecular movement “Figure 10.”. But how the force, the mass and the energy doesn´t creates and doesn´t destroy just transform, this decrease in the pressure over the surface, makes that other kind of pressure appears in the movement direction, this kind of pressure is the dynamic pressure that is just the particles of air “crashing” against an imaginary surface that will block it´s movement, according to Bernoulli, the sum of the static pressure plus the dynamic pressure always be a constant value, so when the static pressure decrease the dynamic pressure will increase, and vice versa. To complete the analogy with the mass that´s move over a surface, that friction force that appears, is the viscosity in the fluid, this viscosity that allow that the fluid, in our case the air, transmit the forces to the object and between the particles, it therefore depends on the intermolecular forces and the density of air, this is the denominated kinetic viscosity.

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FORCES IN A SOLID

FORCES IN A FLUID

STATIC

STATIC

WEIGTH

STATIC PRESSURE

REACTION

REACTION

IN MOVEMENT PARTICLES IN MOVEMENT, LESS STATIC PRESSURE

FORCE

PARTICLES STILL, TOTALL STATIC PRESSURE DYNAMIC PRESSURE

FRICTION

IN MOVEMENT

VISCOSITY AND INTER-PARTICLE FORCES

Figure 10. Friction forces analogy.

1.2.

Boundary Layer

What is the famous Boundary Layer?, here things will get a bit confusing but nonetheless easy to understand. Every object over the Earth is surrounding by air, but what ´s happen with the air that is exactly where the object ends and the air himself begins?, to those air particles that are in contact to the object particles, to that air “sheet” is what we call Boundary Layer, theoretically, by the friction, viscosity and intermolecular forces that layer is “unmovable” (that is no totally true, how we will see in further paragraphs), that is to say, that very thin sheet of air stays still even if the air or the object moves, to better understand and see it, let´s suppose that the airplane is on the platform in a windy day, a very thin layer of dust is deposited on the wing surface, many particles of dust will be placed at the same level of the air boundary layer. So when the airplane takes off and land in another airport, is possible to see over the wing surface, the same dust that was deposited before the airplane flew, oh!, how is this possible?, if that the airplane was flying at a considerable speed, well that the answer is that “unmovable” very thin layer, the Boundary Layer. Really Boundary Layer is called to the “layers” of air that have a speed profile from cero to the speed of moving air (non disturbed stream) or the object, so it has a defined thickness “Figure 11.”, it can be added that the more speed moves the object or the air, the 9


Boundary Layer will tend to be more thinner. This boundary layer, allows that the others air layers keeps joined between them, and to the object surface thanks to the intermolecular forces, but this layer will be in its place or be “unmovable” while the forces on it be tangential, if the forces changes their directions over the boundary layer, this will tend to become instable and tries to detach from the object, generating movement on the surrounding air, that’s to say, in the other air particles and in the pressure differences, that being adverse may will appear some suction in any point, and makes that the rest of the boundary layer will detach irretrievably, unless that the forces will be tangential again to the object surface. For that reason the dust doesn´t detach in flight, but if you use an air hose and blows perpendicular to the surface, the dust is easily cleaned getting away from the jet.

SPEED GRADIENTS OF BOUNDARY LAYER ON THE UPPER CAMBER AND THE LOWER CAMBER Figure 11. The Boundary Layer. An analog way to see the boundary layer effect at macro level, is to look a river, if you observe the current you will see that the all stream goes in one direction, now if you put a piece of wood in the middle of the current, we will see that, as it moves with the stream, will decrease it speed and tends to get close to the riverbank, this shows that´s the fluid, in this case the water, is fastest in the middle of the current, in the free stream let´s say, and slows down at it get to the riverbank, so much that the water in the shore is totally quiet, even if the river is very flowing, and this you can see every day.

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1.3.

Internal Pressure

It is known that all fluid possesses an internal pressure that is the one that keeps it integrity and makes it incompressible, this pressure is exerted equal and in all directions at a same level, this can be seen clearly in a glass of soda, have you seen how the gas bubbles rise?, and they are spherical!, this can be happen just because the gas is exerting it internal pressure to the outside, equal and in all directions, and the liquid is making the same over the gas “Figure 12.”, and even more interesting thing, you can see as the bubble approaches to the surface, it get´s bigger, and this why?, well like always, simple, because if we suppose that the liquid is a pile of layers, as we go to the surface, there are less layers, so less material of the liquid that exert pressure over the bubble that rise, until this get´s the surface. Another way to see these fluid´s internal pressure phenomena in everyday are the soap bubbles, perfect spheres. For these reason is that at more hight it´s necessary to use breathing equipment, because there is less air that is “forced” by the pressure, to get in to our lungs. This internal pressure is the one affected by the movement, because if the particles of the fluid moves their internal pressure decrease. PRESSURE

FLUID´S

FLUID´S

PRESSURE

INTERNAL PRESSURE

PRESSURE

FLUID´S

FLUID´S

PRESSURE

Figure 12. Fluid´s internal pressure.

2. How is the lift really generated? Ready, I think I have already put together most of the simplest concepts that´s are present in the lift phenomena, so now, in a more professional way, recapitulate, and joining all this tools, let´s see step by step the creation of the lift. The wing, if it is at rest, would be totally surrounded by air at atmospheric pressure “Figure 13.”, is that to say, that this air is exerting a pressure equal over the entire wing 11


surface (upper surface and lower surface). At the same way like at the begin, we suppose that the airfoil is asymmetrical, more cambered at the top surface. When it begins to move through the air, the particles that was at rest will start to move over the wing surface, separating the air in the front and rejoining at the rear, as at the speed increase the boundary layer starts to be thinner, and the particles in the upper surface start to move at more speed than those in the lower surface, trying to “fill” the space leaved by the pass of the wing.

Figure 13. Atmospheric pressure acting over the air layers. The surrounding atmospheric pressure remains constant and “crushing” the particles that´s move against the wing surface, and how in the atmosphere doesn´t exist voids, when the pressure in the upper surface descent by the movement, the non affected air will try to equal the pressures “refilling” this pressure drop, pushing the particles to where the pressure is lower, and this makes that the pressure in the lower surface rise respect to the upper surface, because the total pressure under the wing is more than the total pressure over the wing. The particles in the upper surface are “forced” to move faster than those under the wing due to the lower pressure behind the point of maximum camber in the upper surface, caused by the movement of the wing. As this movement of the wing be continuous, this push the air in the front (increase in the dynamic pressure) of it lowering the pressure behind of it, this make that the particles next to the boundary layer in the upper surface moves faster trying to fill the lower pressure zone leaved behind, the same thing happens in the lower surface, but in lesser magnitude, because the pressure drop is not that big due to that the camber of the lower surface is lesser. The air that´s moves over the upper surface tries to go to the lower pressure zone leaved by the wing, it must be confront too the air layers over it, from the not disturbed air, that too try to fill the lower pressure zone, this effect plus the viscosity, delays in some manner at the particles that will not arrive at the same time at those from the lower surface, to the trailing edge. Now, which one will be the first to arrive to the trailing edge?, well, will be those that 12


came from the upper surface, a little soon than those that started at the same time in the lower surface. But now, we not will be so ingenuous to believe that even those upper surface´s particles that´s arrives first, will not encounter with an others particles that moves on the lower surface, and those was there even before the movement begins and how the upper surface is at lower pressure, the particles that “exit” from the lower surface helped by the atmospheric pressure, will try to “climb” rapidly to the lower pressure zone, but first they must confront at the particles that leave the upper surface at “great” speed, so this effect retard a little the “climb” of the lower surface´s particles, inclinating the flow that´s leaves the wing a little toward down, in direction of the combinated speeds of the upper and lower surface´s particles, at the end, and plus the speed acquired by the curvature of the upper surface, tends to fill the lower pressure space with the atmospheric air that´s “goes up and down” from the non affected zone with its total pressure over, down and behind the wing, left by the pass of the same. This is a some interesting effect well, if that the first particles that arrive are from the upper surface, then why the vortex that forms behind of the wing, has an anticlockwise movement?, as that say, that ends “turning up”, or at lees with that tendency, “Figure 14.”.

Atmospheric pressure

Atmospheric pressure

Figure 14. Behavior of real air stream around an airfoil and atmospheric pressure action. This is the famous wing vortex or wake, that leave the same at it pass (really, any object that moves through into a fluid leaves a perceptible turbulent wake, as an example a fan). To try to minimize the develop of this wake is the challenge at the aerodynamicist designers confront, in one way or another, they has been endeavored to design airfoils that had trailing edges that try to get arrive at the same time the particles, just to try to make this wake always be lower. It is known that when this wake is generated a lower pressure zone appears behind the wing, generated by its pass, and this wake “pulls” the wing creating drag. To this effect is denominated Induced Drag, that is proportional to the lift and depends on the same, this fact has been demonstrated many times with the use of 13


wind tunnels, fluids and even in flight, with the help of tints, particles, colored smoke, etc. so this will no need further explanations. Let´s back now to the leading edge, and how we are no trying to omit the effects that really occur, then we will no suppose so incompressible to the gases, because the wing in front of it will try in some manner to compress the air (this effect can be seen in the stream lines), but how this is not confined “will slip through” by the zones that the compression action has caused that they decrease their internal pressure, generating on this manner movement in the air particles. Like an analog example, we can perceive this when with the open hand “we push” the air, ahead of it, it will try to compress the air, and it will slip through the fingers, will go around the hand behind it, leaving a turbulent wake, until the air stabilizes again. As explained in previous paragraphs, the lower pressure zone will be behind of the mayor camber, as much as in the upper surface as in the lower surface, so then the “compressed” air by the leading edge will rapidly “slips through” toward these zones, generating by its passage even a lower pressure towards the part of mayor camber, that’s will be practically the first quarter of the upper surface, besides the particles have no choice, because them can´t “back” due to the atmospheric pressure that it forces them to follow the movement line towards the zone of lower pressure. This pressure drop will also cause that the air that “crash” against the leading edge, will be unavoidable sucked to the lower pressure zone, creating some kind of stream that’s goes up, obviously this suction will only reach up a few “layers” of air over that those tends to go to the lower surface, this flow is called “upwash”, and the one on the trailing edge described before is the “downwash”, “Figure 15.” which is formed by the

Figure 15. Effects of pressure on the stream lines.

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behavior and variations in the local pressure around the airfoil, giving the impression that the air "bends", conforming it to the shape of the wing´s upper surface. If we go a little farther to see the macro effect, that all this cause in the wing, we will see that at some distance, from both upper surface and lower surface, that the flow is not affected, let's say it maintains its linearity. Between this flow and the cambers of the airfoil, a venturi´s tube is formed, some above the wing and another below, whose narrowing its formed by this fluid unaffected and the maximum curvature of the upper surface, above, and one from the below. I have clarified that they are a "some kind" of venturi, because in reality and as is obvious from what has already been explained, the lines or layers of unaffected flow are pressing those of the affected flow against the surface of the wing. The affected layers are at an internal pressure less than atmospheric, so if you look at the flow lines you can see how they approach each one to the other where the pressure is lower, thanks to the crushing of the layers at are at more pressure, this crushing generates more friction between the layers, braking those that are closest to the wing, and obviously stopping them until they are at rest (the boundary layer). If you compare the flow lines of any object and those of an airfoil, it can be seen how those of the airfoil, as it moves, backs to the "rest" state more quickly than those of any other object, this shows why an aerodynamic object displaces better, and generates a lesser turbulent wake, because it affects less air in its passage. With the effects already known and because of the venturi´s effect on the air layers farthest from the wing surfaces and those already detailed at the surface level, the air on the wing will always go faster the greater the curvature of the upper surface. With this more detailed explanation of how the lift is generated, it can be extended to what we previously saw, for the symmetrical profiles, for the inverted flight and for the control devices (curving the airfoil). Now we are going to explain why, how and when a wing that is supposed to be designed to generate lift becomes a "piano".

3. Stall Why a piano?, Have you ever seen a piano that let loose in the air, fly? well I don´t think so, it falls without remedy and even leaving a crater in the soil, well and when does this happen to a wing? so let´s see the airfoil´s typical lift curve, we will see that before reaching its maximum value of Cl, it starts to stop being a line, and becomes curved, reaches its maximum value and then decreases, in some airfoils this decrease is sudden, in others softer, but in all reaches a minimum level and ceases to exist, interpreting this means that the profile has continued to increase the angle of attack, until it stops to lift. How did this happen? If we know that in ideal conditions, when the angle of attack increases, the lift increases too, attention!, are ideal conditions, imagine the airfoil perpendicular to the flow and generating lift! or worse, inverted and flying backwards! and that there still lifting, obviously this does not happen. The stall is the moment when the airfoil loses its ability to lift, this is due to the phenomenon of the flow detaching from the upper surface. Well, airfoils because of their configuration, they do not can increase the angle of attack indefinitely. We have already seen 15


how the phenomenon of lift really happens and what causes it. How the airfoil that passes through the flow creates a zone of low pressure behind it, precisely because of the interruption of the flow (the pressure differences do the rest), and if the angle of attack begins to increase, the point of impact of the particles of air on the leading edge, it begins to descend towards the lower surface, this causes the air that will go up will travel more distance, generating a zone of even less pressure above and behind the airfoil, if we continue increasing the angle of attack, we arrive at a certain moment in that the pressure behind the airfoil is so low that the air in the boundary layer reaching the trailing edge is sucked out of the surface and when it is detached it creates a very low pressure zone at the trailing edge, the "detached" air creates a "ramp" where the air that passes from the upper surface rises and is immediately sucked towards the trailing edge in the opposite direction!, the energy with which this air returns, strikes the other particles of the boundary layer that still are still adhered trying to detach them, generating an even stronger vortex behind the wing “Figure 16.”. AT 0º OF ANGLE OF ATACK

AT 15º OF ANGLE OF ATACK

Stall´s beguins

“Reversal” flow zone, caused by the boundary layer detaching.

AT 23º OF ANGLE OF ATACK

Stall, you can note the total flow detach and big “reversal” flow zones.

Figure 16. The begin of the Stall and its evolution.

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This fact marks the beginning of the curvature on the lift graph, that as the angle of attack increases, the boundary layer continues to detaching, but the low pressure still remaining over the wing continues to generate lift, until it reaches the point where the vortex is so strong and the pressure so low that it is filled up rapidly of atmospheric air in all directions and even sucking out the flow that came out from the lower surface, at this point the air that rises from the leading edge, no longer adheres to the curvature of the wing, due to the presence of that vortex, the air practically jumps about that turbulence ceasing to exist the effect of the lift and the wing is no more than a "piano" that falls, then it is said that it has entered into stall, but if the profile decreases its angle of attack the air will again try to adhere to the surface of the upper surface and will again restore the lift generation.

4. Controversy in the lift generation This is how I learned how the lift is generated in a wing, and this is how an airplane flies, of course it lacks many things and phenomena that appear as a result of this, such as aerodynamic drag, something I mentioned very briefly; the pitching moment of the airfoil, and the consequences that happen by the velocities, why an airfoil cannot accelerate continuously?, what are the wing tip vortex?, and thousands more other questions, which can be explained in a simple way and be visualized, but that is another matter. In my inquiries of need to learn more I found with some perplexity, a book and a report that came to my hands, one in English and the other in Spanish, which in the end turned out to be the same just only translated. I could read in them how they threw to the ground what they called the "popular explanation" of the lift generation (practically everything I explained above) and wile I read them I noted that besides, if they could trample it they felt better. Throughout my experience as a professional and as a person, life has taught me to listen to everything and from that learn something, always the best to improve. I almost lost my sleep when I discovered that I had been deceived since I understood the physics of aircraft flight and all thanks to this kind of reading, with its physical theory of action and reaction, which with several obviously "well-founded" explanations ruined what which I had already learned. In addition to certain impertinent assertions, that the "popular explanation" cannot demonstrate lift in symmetrical airfoils or the inverted flight, or how an airplane adjusts in flight to constant speed while consuming fuel, or when making a turn?. I really do not understand how they "can not" explain such simple things with the "popular explanation" and being at the same time is so simple. The fact of trying to complicate things does not make them more certain, the truth is that physical phenomena are always simple and of every day, only that the tools we use to explain them are a bit complex. So that I mention our friends of "action and reaction", and showing their peculiar way of expressing themselves, I would say that if the form "so simple" of the theory they present says that: the way to generate lift is "bending the air", that is, that the airfoil is propelled upward thanks to the air that is "ejected" down by the trailing edge, like a rocket that rises by the principle of action and reaction. All this of course thanks to the fact that the trailing edge is inclined downwards, so the air "climb" by the leading edge and "go down" by 17


the trailing edge, well it's almost convincing, not totally wrong by the way, it's true that the effect of the exit of the air by the trailing edge impels something to the airfoil, but unfortunately the vortex that generates behind the wing, produces a zone of low pressure that finishes "pulling" the wing backwards, greatly diminishing the effect of propulsion, and the fact that the airfoil causes the air to "go up" when attacking it by the leading edge, ends up forcing the airfoil to try to "pitch down the nose", which is the so-called aerodynamic moment, which is accentuated more while more curved is the airfoil, since more negative pressure is generated on it, further minimizing the effect of the supposed lift, so that the contribution by action and reaction is relatively little, compared to the difference of pressures generated by the difference of speeds as I have shown before. Another and very interesting statement of these gentlemen, is to do the calculation of lift using the difference of distances, between the curvature of the upper surface and lower surface, if a problem is poorly posed obviously the answer will be poorly obtained, lift is calculated in function to the total speed, the lifting surface, the flight height and the lift coefficient, which is where the shape of the airfoil really comes in, since the lift graph is the result of the effectiveness of that characteristic form of each airfoil, in addition the proportion of sustentation equals the square of the speed, as the second law of Newton shows it:

=

= ∙

= ∙ = ∙ :

:

:

: :

:

:

:

:

=

∙

∙

∙ ∙ ∙ ∙

∙

∙

∙

(1) ∙

(2) ∙ (3)

:

:

If we do the separation of units we see that the lift force is the result of a mass (of the air, on the surfaces of the wing), by an acceleration (caused by the differences of pressure that accelerate to the air on the upper surface and lower surface) “Equation (3)”, as pre18


sented by the Newton´s second law “Equation (1)”, so let's take the Cessna 172 “Figure 17.”, a very popular high wing aircraft weighing 1045 kg (2299 lb), and let´s calculate what speed would need to lift its weight, suppose that it flies at sea level where the atmospheric density is 1.225 kg / m3 (0.076 lb/ft3), we know that its wing surface is 16.16 m2 (173.9 ft2), and that its optimal lift coefficient is approximately 0.2 (at an angle of attack, in which the lowest resistance is generated): so let´s calculate; first, the weight (W) force multiplying it by the acceleration of the gravity (approx 10 m / s2) and we will have Newtons (N), replacing and clearing we obtain (a note: the weight of the aircraft is equal to the lift in straight and level flight L = W):

Figure 17. Cessna 172 Skyhawk 10450

= ∙ 1.225

=

.

= 72.65

∙ ∙ . ∙

⇒ 261

∙

∙ 0.2 ∙ 16.16 .

(162.5

ℎ)

And it is practically the maximum real speed reached by the Cessna 172 Skyhawk at sea level and in a straight and level flight, I don´t know where they get that they would need 640 km/h (398 mph) to lift it? At stall speed 104 km/h (64.62 mph) (as in its example), where the lift coefficient would be almost 1.27 near the maximum (the 172 uses a NACA 2412 airfoil, the data comes out of its lift typical graph ), we would replace on equation (2) these data, and have a value of L = 10498 N or 1050 kg (2315 lb). Then there is nowhere to lost, a bad approach carries a bad result.

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Well now I ask, if the explanation of action and reaction is really accurate, then how do to lift a REFLEX type airfoil? “Figure 18.”, which is used by airplanes without tail plane, and which has the trailing edge that ends to up. Using the "popular explanation" you can easily see how it lift. A more complicated question, how do wing-tip vortex form?, that these are precisely caused by the difference in pressures, that is why we must learn the best of it to improve.

Figure 18. REFLEX type airfoil, can note how the trailing edge ends to up. The most interesting of these gentlemen, is that they base all their explanation on the Coanda´s effect, this effect is that which has all fluid, as a tendency, to adhere to a solid very close to its flow, now the most interesting, is that precisely this effect is caused by Bernoulli, and the pressure differences, in their text explain how a stream of water coming out of the faucet (cell, tube, etc.) when gets approaches a glass horizontally to this flow will try to "stick" to the glass, and this will exerts a force that it would try to "remove" the glass of the hand, hmm, because if it is calculated that the jet of air in Coanda effect, on the wing of a Cessna of 1045 Kg (2299 lb) is of a mass 5 times greater, that is, that the wing projects 5 tons downwards "throwing" with that same force to the Cessna upwards, then the jet of water that is almost 1000 times more dense and it is flowing to a reason, say of 0.1 Kg/s (3.53 oz/s) and we approach a plastic cup of some 0.02 kg (0.7oz) without holding it tightly, the water would end up taking the glass from the hand and throwing it to the other side of the jet, by that force. Well I tell you that I got tired trying to bring any kind of glasses of all sizes and weight to strong jets and of more flow and the result was always was the same, the closer the glass came, this ended in the floor dragged by the jet, never was such suction, not even crushing the jet to cover the entire horizontal length of the glass. Then something is not right, Our friends of action and reaction, in their exposure, they always forget the rest of the air, the atmospheric pressure, to the air that goes by the lower surface and that also suffers of such Coanda´s effect. In short, the Coanda´s effect is a consequence and not the cause of the lift. 5 tons! that Cessna would end up in the stratosphere and the pilot with enough problems to stay straight and level... And as an additional matter, the action and reaction gentlemen, suggest that if Bernoulli's theory applied to aircraft, were true, and that if all fluid that increase its speed, lower its internal pressure, then why would an aircraft that has static pressure takes, at its fuselage to measure changes in altitude, using the altimeter, that it not see a change in it when turn on their propeller, since it is pushing the air and giving to it speed around the airplane?. I must confess that this made me hesitate for several moments and it made me think a lot, it is true, how does the altimeter to measure the height so precisely, although the airplane moves in the air at high speed and also that the air around of the fuselage moves fast all 20


over its surface? , and also remembered those "sprayers" of painter that work by suction, blow air through its paint nozzle, it comes out at high speed, obviously with a very low internal pressure and passes tangent to the outlet of the paint reservoir, sucking it and this causing it to mix with the air of the jet! I already believed that all my years of learning were fall to the ground, but as always, everything has a simple explanation. First we must see how each thing works, let's start with the painter's gun or sprayer, that must be of suction for this to happen and not of gravity because there would be an obvious explanation. The paint or liquid tank is connected to the paint dispenser with a take that works as I explained before, but there is an important detail, the paint tank must be open to the atmosphere, or at least have a hole to compensate the air pressure inside the tank, otherwise, only will be two gunshots of paint and will only ends spraying air, since if the tank is hermetically closed paint will come out until the pressure of the air inside the tank equals to the low pressure of the jet of air of the sprayer and will not leave more, How does it lower the pressure inside the tank?, Simple, the paint is more dense and is at the bottom of the tank, the volume of paint contained decreases in the tank, causing the volume of air contained increases and the density decreases and therefore its internal pressure, that is, we are separating the distance between the stacked air layers and there is nothing that fills the space between them, so there is nothing that "pushes" the paint to the outlet take, and the suction of the jet of air, which has an high speed, is not enough, even in gravity paint guns is necessary pressure compensation, because equal the "vacuum"

that left by the

paint , sucks what´s remains in the tank, even winning to the gravity !. But if it is open to the atmosphere the air will quickly fill the space left by the paint and will end pushing it at the same time towards the nozzle. Well, this is not a painting manual, so let's get back to our matter, this previous explanation solves the mystery of the altimeter. But let's go step by step. First the altimeter is a very sensitive instrument to the changes in height (we have already seen that in the glass of soda, which at more high the lower the pressure is), but its sensitivity is calibrated to a minimum of 20 feet (6.7 m) and others are even less sensitive, every 100 feet (33 m), this is seen on their graduated cover “Figure 19.”, and even, in addition, it has to be calibrated every time that flies, because the atmospheric changes vary the pressure, because at higher temperature lower the density, or if there is a lot of humidity, etc., these changes always make necessary the adjustment, before the flight. Internally it has an aneroid capsule, which means that is sealed and the air inside the capsule is at a certain pressure, in this case, the pressure is the one at sea level, from where they are measured all altitudes, this capsule is enclosed in the instrument compartment, which is airtight and has no additional air inlet other than the one coming from the static take(s). It has gears and springs, which move that as the airplane ascends, the internal pressure of the altimeter compartment lowers and causes the air inside the capsule to begin to expand by inflating the capsule which in turn causes that moves the mechanisms of indicator needles, and recording the pressure changes, translating in height, and will be the reverse as the airplane descends, the pressure increases and crushes the capsule, and air enters and exits through the holes of the static takes, as the airplane as21


cends the atmospheric pressure decreases, drawing air from the inside the compartment, inflating the aneroid capsule, and if the airplane descends the pressure increases and it introduces air into the compartment crushing the aneroid capsule. Static takes to record pressure changes are spread over several locations on the airplane or one can be strategically placed (not very convenient).

Figure 19. Altimeter cutaway A friend who is avionic (who works with aeronautical, analog and digital instruments), comment me on this "simple" strategic location, "it is a nightmare to install the static take if you want to have a good and real reading on the instrument" , because the static take port must be perpendicular to the flow and with great accuracy, or there will be overpressure if it points to the flow or too much suction if it is in favor of the flow, besides it is always better and more convenient to install several and in different locations far from areas that present perturbed or turbulent flows. Ok okay, this is not an instrument installation manual, either the interesting thing about all this is that although the static take is a small calibrated orifice and is perpendicular to the flow, the suction that can make the flow of the propeller or even the air at flight speed is not sufficient to overcome the airtightness of the instrument case, it may drop by a few tenths of the pressure but will be sufficient for the internal pressure of the compartment equals the internal pressure of the flow that moves around the airplane. And a little confusion that they refer in their appendices about the "curve ball", this is 22


obtained doing turn the ball, which drags the air around it, as it moves linearly, and also creates a kind of "circulation" of air, which accelerates the air in the direction of rotation, causes the ball to tends to curve in its path, this circulation effect is called Magnus effect, “Figure 20.” which is even seen in a throwing Frisbee.

Figure 20. Magnus effect and the analogy with an airfoil As you can see with Bernoulli it is possible to explain each and every one of the problems that arise the lift and the movement of the air around an object (besides all the phenomena erroneously cited in the texts), which shows that because it is simple does not mean that is not true, it is easy to explain, but to prove it mathematically is another song, but that does not take away that is easy to understand, why an airplane flies. I recommend that you read all text that talks about lift, no matter how the lift is obtained, but now with a clear idea of how it is that Bernoulli's theory is applied to the flight, and without passions learn, that several texts bring many things and interesting concepts.

References [1]

Anderson D.F., Eberhardt S. (2001) Understanding Flight. McGraw-Hill, Inc.

[2]

Wolfgang L. (1972) Stick and Rudder, An Explanation of the Art of Flying. McGraw-Hill, Inc.

[3]

Hunecke K., (1987) Modern Combat Aircraft Design: Technology and Function. Airlife Publishing Ltd.

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