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Just like many curious people, the question: " How airplanes actually work?" occupied my mind for a long time.

Different sources gave different answers where most claimed the Bernoulli Principle to be the main reason while many disagreeing with that and so on.

Then I came across this: https://physics.stackexchange.com/q/51503/266050

This has many answers and all in great detail. This gave me a lot of knoweldge and pretty much outlined the many factors that are responsible.

Unfortunately, there is no unanimous consensus even on those answers. The accepted answer (like many others) is detailed and beautiful but there are comments disagreeing with that and people holding different views on which factors actually contribute primarily for the working of airplanes.

Now, usually the answers and discussion given on stackexchange would be more than sufficient but in this case what bugs me is that airplanes are actual things used daily and there are people who design and create them. These people (aircraft engineers, scientists etc) surely must be really certain about how these things work (or so I hope ?) and not be confused with things like whether the upper part of the wing pushes air down or actually pulls it up (not that they would have different outcomes or effects but one ought to know!) or whether the angle of attack really does play a role or not. The reason for my assumption of flight engineers having surity of knowledge to the core is that they need to know with high accuracy and precision the conditions and limits under which airplanes will work and when a certain principle would fail.

Why is it then that not a clear concise unanimous theory is available (or is it?) open-source etc that covers every factor and the extent to which they matter and which is accepted (or rather reffered to) unanimously without confusion?

If, on the other hand, there is a source (or sources) available after reading which I can confidently say that I know with very high certainty and with all technicalities how airplanes work, I hope to know where and how I can find it.

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    $\begingroup$ I'm voting to close this as opinion based. As you say there isn't a unanimous view, and asking why there isn't one isn't going to get fact based answers. Also, asking for a reading list of 'best' sources is also asking for opinion. $\endgroup$
    – GdD
    Jul 3, 2021 at 8:10
  • $\begingroup$ I think you're confusing the existence of multiple descriptions for disagreement (and disagreement among random people on the internet for lack of academic consensus). Each description has different applicability and level of detail, and all descriptions are ultimately a statistical simplification of the underlying quantum soup. Just find a description that is useful for you. $\endgroup$
    – Sanchises
    Jul 3, 2021 at 10:08
  • $\begingroup$ @Sanchises Finding a description useful for me is 'only useful" if its correct. As I have emphasized, the problem is not that people are giving different descriptions of the same thing. They are telling different things altogether. $\endgroup$
    – Lost
    Jul 3, 2021 at 13:10
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    $\begingroup$ "Finding a description useful for me is 'only useful" if its correct." well then unfortunately you are going to be disappointed because ALL theories are incorrect. i.e. all theories necessarily make simplifying assumptions and approximations, and thus are not correct. But many theories are useful. This is not just aerodynamics. E.g. Newton's law of gravity is "incorrect" but it is very useful in many situations. $\endgroup$
    – Daniel K
    Jul 3, 2021 at 17:13
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    $\begingroup$ The title states Flight Dynamics, the link to the Physics site is one about aerodynamics. That seems more relevant to the question and I've added the tag. $\endgroup$
    – Koyovis
    Jul 4, 2021 at 3:46

3 Answers 3

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There is unanimous agreement (at least among people who actually understand physics) that

By the second point I don't mean it's simple. Not only they are not simple, but they exhibit such complex behavior that it wasn't fully explored even from the pure mathematical standpoint.

What I mean is that all the properties described by the equations (conservation of mass, momentum and energy, viscosity and pressure) are important in creation of lift and you can't skip any of them and still arrive at something at least somewhat approximating reality.

There are some theories with which would can get fairly accurate estimates of lift like the lifting-line theory and the thin airfoil theory with much less calculation, but they all have serious limitations and depend on experimentally-determined factors. They don't really explain lift itself, only some relations around it like what is effect of increasing span or chord.

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  • $\begingroup$ "you can't skip any of them and still arrive at something at least somewhat approximating reality" Okay this somewhat clears some things up. Though tell me, is there a factor or phenomenon without which lift will be not possible or sufficient? $\endgroup$
    – Lost
    Jul 4, 2021 at 12:20
  • $\begingroup$ And by a factor or phenomenon, I mean something that is engineered into the architect of the aircraft which is so crucial without which the aircraft wouldn't lift even while other factors were present. For example, from my limited knowledge, I understand that there is a critical angle of attack which produces max lift and that the wings have a larger surface area for Bernoulli upthrust. Now, of course, both are utilized but lets suppose one of these factors were removed could the aircraft could still lift? $\endgroup$
    – Lost
    Jul 4, 2021 at 12:25
  • $\begingroup$ @Lost You can produce lift with other devices than airfoils, for example spinning cylinders (Magnus effect), but you can only do so in a fluid that has both mass and viscosity. For airfoils without viscosity the rear stagnation point wouldn't stick to the trailing edge and wouldn't be turning the air downward (the Kutta condition wouldn't satisfied). And without mass there would of course be nothing to give the momentum to. $\endgroup$
    – Jan Hudec
    Jul 4, 2021 at 12:52
  • $\begingroup$ @Lost For an airfoil, the most important feature is its sharp trailing edge. A flat plate at an angle to the stream will produce lift, and a slightly bent plate is as good at it as more complex shapes at its optimal angle of attack. But without sharp trailing edge, the air from below will bend around it, cancelling the downward slope of the wing and that will prevent generating lift. On the other hand the leading edge needs to be blunt to better split the air at different angles to keep drag low. $\endgroup$
    – Jan Hudec
    Jul 4, 2021 at 13:07
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A complete theory is taught in universities and takes at least 5 years to master. You would know quite a lot of the science of aerodynamics after obtaining your doctorate, which takes even longer.

Or you could obtain a degree in aeronautical engineering. That is where you learn about the multiple fields of technology that keeps an aircraft in the air and enables passengers to trust them with their lives when flying to Bali. But now there's an issue: there are way more subjects to be taught in 5 years than only fluid dynamics, like thin walled structures, systems technology, safety engineering, human-machine-interaction etc, plus the mathematics and physics that lies at the foundation of all of this. So now we need to start making judgements on where to stop.

What to teach and what not is a function of the end goal and the audience.

  • The design engineers of a passenger aeroplane needs to be able to integrate all relevant knowledge to an extent that enables people flying to Bali to trust the machine with their lives.
  • Focusing on pilot training: quick decision making and rapid and consistent control is the key element. The airplane is already there, it is tested in the wind tunnel, constructed in the factory, flight tested and calibrated by the test pilots etc. So it is important to provide quick understanding of the principles of flight, only relevant to keeping the plane in the air.

So why do wings provide lift? For a pilot, all knowledge of cruise, max. altitude, static and dynamic stall, anything to do with adverse aircraft state and navigation is the main objective here - we leave out what is not of direct importance, and move on to the science of wind shear at approach. The comments on the physics site comment on what is left out of a relatively simple explanation that is sufficient for 80% of cases.

There is full agreement on what is correct aerodynamics theory. Now with computers, we can finally use the Navier Stokes equations to compute aerodynamics acting on wings. But a very important decision remains: who is the audience, and what would best be left out.

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  • $\begingroup$ From the answers, it seems that in order to exactly understand what actually plays the most significant role one would have to wait till Navier-Stokes gets solved. And all the engineering and Physics that goes into building an aircraft is a continuous process of experimental refinement. Making a statement like "Bernoulli's or X is what makes the airplane fly" is highly incomplete because we don't know how much role, if any, it plays. We just know after many trials and errors that "shaping the wing and nose etc in a particular way" gives max lift. Am I thinking about this correctly? $\endgroup$
    – Lost
    Jul 4, 2021 at 12:42
  • $\begingroup$ There are many “computer fluid dynamics” software packages that solve Navier-Stokes equations, and they are being used when designing aircraft, because it's faster and cheaper than making lots of different models and testing them all in awind tunnel. The trouble is that it's a long way from a set of differential equations to a some kind of insight. But you can get a bit of that on the quantitative level. The linked Q/A already does explain that. $\endgroup$
    – Jan Hudec
    Jul 4, 2021 at 13:17
  • $\begingroup$ @Lost Note that there is no or here. Bernoulli's equation is part of the Navier-Stokes set. After all it's just the law of conservation of energy for fluids (usually given for incompressible flow, but for higher speeds the compressible form is needed, which additionally requires pulling in a bunch of themrodynamic equations to make up for the additional free variables). It is, however, just one equation with multiple free variables, so you need additional equations to get a solution. And no, it does not take the air the same time to get around the wing—the air above makes it much faster. $\endgroup$
    – Jan Hudec
    Jul 4, 2021 at 13:23
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Your question may not have a certain and definitive answer. Nevertheless, there are two particular areas (and two particular books) that can be discussed in guiding your attempt to find a definitive answer. Indeed, what is an authoritative source for understanding flight-dynamics theory?

The two areas are -

  1. The principles of flight
  2. The elements of aircraft design

These two areas are an inseparable and expansive body of knowledge. For the engineering practitioner, the common core areas linking these two areas are many, requiring an understanding of a) mathematics at least through differential equations (matrix theory and linear algebra are especially helpful), b) the principles of physics and atmospheric science, and c) engineering and applied science. Within this last area should be knowledge particularly in disciplines of d) fluid mechanics, e) strength of materials and structures, and f) applied mechanical engineering, particularly in g) materials science, h) power and propulsion systems, and i) aircraft systems design. All of these areas are inextricably linked through experimentation and assessment. Properly defining a problem requires a complete understanding of the problem. Things we think of as authoritative and complete are rarely, if ever, totally comprehensive and inclusive or exhaustive. Flight dynamics theory is as much an attempt to understand why things work, as to understand why things don't work.

For a start, the following is suggested -

Gudmundsson, Snorri, 2014, General Aviation Aircraft Design: Applied Methods and Procedures. Butterworth-Heinemann (Elsevier), Oxford. 1034 pp, several appendices.

Upon examination of this book and others, you may be given pause; "but wait... this is just what I did not want to do!" So lets look at another book that is a superbly easy read, absolutely indispensable, and requires only algebra and a little calculus to understand. That book is -

Dommasch, Daniel O., Sherby, Sydney S., and Connolly, Thomas E., 1967, Airplane Aerodynamics, 4th ed. Pitman Publishing Corp., New York. 621 pp.

This book has a clear and authoritative discussion of the principles of flight, and an overview of factors involved in aircraft aerodynamics and flight performance. When you read through this book, you will get a pretty good idea regarding the scope of flight dynamics without frying your brain. This text is particularly helpful regarding propeller driven aircraft. At the heart of the book, which is easily understood, are two central sections, 11:7 and 11:8, regarding the V-g diagram. All of the factors regarding why airplanes break are discussed therein. Gudmundsson's book has an in-depth engineering discussion of the same topic starting in section 16.4; only algebra is needed to work through his examples.

But you may say, I just want to know why airplanes fly. Most books you will read will discuss the part regarding how airplanes fly, leaving the why as seeming conceptually difficult or lacking. When you find references to theory, you should pay close attention (even if your brain gets fried) because that is where the conceptual developments and basic understanding are found; sometimes difficult, as they may be.

A suggestion would be to read, read, read. Take lots of notes, write your own personal text, capture your own ideas, maybe experiment with the math. And look at the cited references in what you read; these may be real gems. See what you think. This can be fun...

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