It is true! The popular theory of flight is just a theory. From the material I've read in the classroom, my textbooks, and my flight instructors, my writeup is considered correct. However, it may be that vuo and his new-age science is right. Then again, this is all theory, and all of these writeups could turn out to be wrong in the long run! Who knows? If there was a single definitive answer, the writeup would be titled "how things fly" not "the theory on how things fly." Keep an open mind and decide for yourself!
The Theory of Flight is something that is difficult (but not impossible) to explain in text-only format, so if you really badly want to learn and have it make sense, it is best to find a visual resource. Microsoft Encarta has some good visuals, and there are many websites out there that can show you nice pretty moving diagrams. If you decide to barrel on ahead anyway, put on your imagination caps and be prepared to visualize situations by waving your hands around in the air like miniature airplanes. It might be best to lock your door.

I'll do my best.

As I said, your hand is a very ineffecient wing; you can only get lift if you angle your hand upwards in the wind. Since your hand presents a bigger frontal profile in doing this, there is a lot of air friction and drag pulling your hand backwards and slowing you down. This would be a bad thing in an aircraft. What they found, however, is if they made a roughly-teardrop-shaped wing, you could get lift even when the wing is facing straight into the wind. This reduces that frontal profile, there is less friction, less drag, and therefore the airplane can go faster. Just like you notice in your car - the faster you go, the more lift you create! The high pressure/low pressure thoery is the basic fundamental behind lift, which is known as Bernoulli's Principle.

Now for the technical stuff. This will take a few paragraphs before it all seems to come together for you. It may benefit to read this twice.

A wing of an aircraft is roughly teardrop shaped, or, as I like to think of fit, garden-slug shaped. I'll do my best at an ASCII artwork.
```                     ___...___            (--- a
....,,,----'''''''         \           (--- b
------------------------------'           (--- c
```
Does that make sense? Sure it does. Ignore the "a b c" for now, I'll get to that later. It is a bit hard to draw out in ASCII format, but the top of the wing is supposed to bubble upwards a little bit and taper backwards; no part of it is really flat. The bottom side is, for the most part, flat. The front of the wing will be the right hand side, the rear end the left. The front edge is rounded and is called the leading edge, and the back edge is tapered to a point and is called a trailing edge. A line drawn directly from the frontmost point on the wing to the rearmost point is called the chord of the wing, sometimes referred to a as a chord line.

All aircraft with fixed wings have the wings set at a slight angle away from the aircraft's body. As I mentioned a few paragraphs back, you have to angle your hand into the wind quite a bit to get any noticable lift. The same goes for a wing, though the angle doesn't have to be quite as exagerated. The Angle of Incidence is known as the amount the wing is designed to be angled away from the axis of the aircraft... To call upon the hand-in-the-wind example again, your car would have an axis from back to front and your hand would be sitting in the wind, not producing any lift. If you added a few bags of brick into the rear seat, the back end of your car would sink but the front would remain at the same height - this would not change the angle that you have your hand at in reference to the car, but it would change the angle of your hand in reference to the wind. With your hand - or a wing's chord line - headed straight down the vehicle's body, it would be said that the angle of incidence is zero degrees. Most wings are in the vicinity of 5 degrees or less.

Bernoulli's Principle states that the pressure of a fluid decreases as the speed of the fluid increases. This also applies to gas, and therefore, to the atmosphere... That is why when the weatherman says a Low Pressure system is moving in, it's usually more windy than when he says a High Pressure system is on it's way to your house. If you look at the crudely drawn diagram above, I have labelled three imaginary "channels" of air that are about to pass over the wing, channel A, B, and C. For the purposes of this example, pretend that the wing is at a very slight angle - say, 5 degrees of an upward bank. (So small of an angle that even if I wanted to draw it, ASCII art doesn't have a high enough resolution to show it) Channel C is going at, say, 100 knots and is going to pass straight under the wing and deflect off of it a tiny bit. This will press on the underside of the wing (generating some lift) and the airflow is going to slow down - to about 95 knots. No big deal. Air channel A is going to pass straight over the wing at 100 knots, and isn't going to be touching the wing at all. The interesting channel is Channel B. It hits the wing right on the nose and travels up and over the wing, and down the backside. This wind, due to friction and being deflected all over the place, is going to initially slow to about, say 60 knots.

Now it really gets messy. If the air on top is moving slower (60 knots), and the air underneath the wing is moving faster (95 knots), what is filling that gap on top of the wing? Look at it this way: In front of the wing, you have, let's say, 10 units of air. Behind the wing you also have 10 units of air. 5 units pass on top of the wing, and 5 units pass under the wing. Yet the air on top is moving slower! This, in an extreme circumstance, would create a vacuum on top of the wing. In normal aircraft, however, this merely results in a very low pressure zone. What does low pressure do? Suck! It sucks the air back over the wing, speeding it up to match the speed of the air below the wing.

Great, so now you're thinking "so the air on top of the wing is travelling at the same speed as the air below the wing." Wrong. The top of the wing, if you remember, is bubbled upwards - the air travelling over the wing has to go a farther distance to reach the back of the wing as compared to the wind under the wing that just flies straight to the back. If you were to take a string and pull it tight over the top of the wing, and then take a string and pull it over the bottom of the wing, the top string would be longer would it not? For air to travel over the wing and meet up with the air under the wing, it would have to travel FASTER to arrive at the same time. I'll try to demonstrate this with another example.
```
b   b   b
b   b   b   b     ___...___ b
b b b  .-----------------'         \ b b b b   (--- b
c c  ------------------------------' c c c c   (--- c
c   c   c   c   c   c   c   c   c

```
(I changed the wing design to make it a bit easier to see, but imagine it is a normally shaped wing.) As you can see, Airflow B and C both have the same volume of air - 15 units each. You can also see that airflow B and C are also always in line with each other - from front to back, B never lags behind C or vice versa. Air before the wing and behind the wing is nearly undisturbed. Airflow B, however, travels a much farther distance, and the spacing between each B is quite a bit farther apart than the spacing between the Cs. So now that the air has "caught up with itself," you can visually see how the upper portion of the wing has less air per square inch; therefore a lower pressure. Lower pressure, again, equals suck - since it cannot suck the wind any faster (it's already caught up with itself!), it is the wing that gets "sucked upwards" into the low pressure zone, trying to fill the void. This is the main source of lift, and is the basis of Bernoulli's Principle.

That should just about explain it. I strongly recommend you understand this concept before you learn how to fly; it makes ground school all that much easier.
Post-Edit: Some common questions are being asked! Here I will attempt to explain them.
How do aircraft fly inverted?
Well, turn your hand upside down the next time you have it hanging out of the car window. Tilt it upwards until you feel your hand "lifting." Ta-da! Remember: The upward bubble in the wing only allows the aircraft to face relatively straight forward yet still produce some lift, thereby decreasing the frontal surface area and therefore reducing drag. This reduction in drag results in more speed, and more speed produces more lift! It simply makes the wing more effecient. You are correct in assuming that the upward-bubbled wing will "fight" the lift and drag you down a bit while inverted, but this is overcome by angling the wing upwards a little bit more. Arcing the wing into an upward bubble or slug-shape alone is not enough to make an aircraft fly - you still need that fast flowing wind "striking" the bottom of the wing to get Bernoulli's Principle working!

What about fighter jets and other fast jets? I don't see big thick wings on those aircraft!
Thinner wing designs, also known as laminar wings, work on the theory that if you fling the aircraft forward fast enough, you don't really have to have that extra lift. Imagine you are driving down the highway at 600 miles per hour. You put your hand (with some effort) straight into the wind, and it doesn't move. But at the slightest rotation upwards, the air pressure is so great that it rips your hand off. Ta da! Even better lift. The problem with these wings is that they don't produce a lot of lift at low speeds, so their minimum speeds are higher - they need longer runways for takeoffs and landings, and they also need bigger and more powerful engines. If you put one of those Bernoulli teardrop-shaped-wings on an F-16, it would actually add weight and drag to the aircraft and do more harm than good. The teardrop-shaped-wings are best placed on slower, less expensive aircraft.

How does the air on top of the wing know it has a "date" with the air under the wing?
It doesn't "know," but keep in mind that there is very fast moving wind behind it, urging it to keep moving! If the air on top of the wing moved slowly, there would be a huge buildup of air in front of the wing. If you put a rock in the bottom of a river, the river still flows at the same speed! But the water immediately above the rock has to speed up, lest it be "crushed" by the water behind it. This is why a great big wide river moves rather slowly, but as it passes through a narrow canyon it speeds up (rapids!).

First, the Coanda effect is a theory just as Bernoulli's Principle is. But, if you think long and hard about it, the Coanda effect results in a Bernoulli pressure-differential effect, and thereby produces lift. By saying that the Coanda effect is the true source of lift, it's like your saying that a bicycle doesn't run because the pedals are moving, it runs because your legs are moving the pedals. Yes, that's why the system works, but it isn't how the system works. In any case, time will eventually show that all of these crazy theories were all wrong and some grand unified theory will explain everything. (Similarly; Did you know that E does not equal MC^2? It's very close for all currently practical applications but when you start doing math with really big numbers it makes quite a difference.)

Sources: Most of this info is straight from my head, but the class that I got the knowledge from uses From the Ground Up as a reference. Very good book; has quite a few diagrams and better drawings of wings than I could ever do. ISBN 0-9680390-5-7 published by Aviation Publishers Co.

There is another book named Theory of Flight that happens to deal exclusively with this material in great, great detail; unfortunately I do not own it and cannot reference it. You can find it on amazon.com.

#### What is the popular theory?

Lift is usually explained with the equal transit times theory, which was abandoned a century ago and which is flat out wrong. You find this theory in schoolbooks, though it has been known for a long time it's a false simplification motivated with a lie. For instance, how would inverted flight be possible? What would we need an angle of attack for, shouldn't that worsen the lift? The theory assumes that the airflows below and above the wing move a different distance in the same time, causing a pressure difference by the Bernoulli effect and then lift. The simple rebuttal is: how does the air molecule below know it has a date with the air molecule above the wing?

#### Why the popular theory doesn't work?

This theory has many weak points. For instance, it does not agree with the reality: the airflows do not meet. Reality is always right in natural science. However, the airflow above does flow faster. Could Mr. Bernoulli explain it alone? Eberhardt and Anderson (2001) have calculated this:

Take the case of a Cessna 172, which is popular, high-winged, four-seat airplane. The wings must lift 2300 lb (1045 kg) at its maximum flying weight. The path length for the air over the top of the wing is only about 1.5% greater than under the wing. Using the Popular Description of lift, the wing would develop only about 2% of the needed lift at 65 mph (104 km/h), which is "slow flight" for this airplane. In fact, the calculations say that the minimum speed for this wing to develop sufficient lift is over 400 mph (640 km/h). If one works the problem the other way and asks what the difference in path length would have to be for the Popular Description to account for lift in slow flight, the answer would be 50%. The thickness of the wing would be almost the same as the chord length.

#### So, how does it work?

Cessnas don't fly 640 km/h. The equal transit times theory is theoretically impossible and experimentally insufficient, but what really proves it false is that a wing does work, force times distance. We have the gravity, which constantly accelerates the airplane downwards. Free air is not a support, no matter at which pressure it is at, so the airplane should accelerate towards the ground. A force is a rate of change of momentum. The weight of the airplane is a force, so what do we do to prevent the plane from falling? Change the momentum of air instead of the plane! We conserve momentum, it's only air that's falling down fast, not the plane.

How does the wing do this? The reason is the Coanda effect. Air, no matter how thin it is, is a fluid, a flowing substance. Fluids tend to follow curved surfaces - this is the Coanda effect. Look at the wing: the convex top surface of the wing is curved such that it points slightly downwards. In practice, this angle is 5-15 degrees. Incoming airflow flows along the top and is expelled downwards - a change of momentum. By Newton III, when the wing forces air down \/, the air forces the wing up /\. This force is called lift. In aviation terms, the flow of air downwards is called downwash.

A typical Cessna forces downwards 6 ton/s of air to counteract its weight of one ton. For incoming air, the top surface of the wing generates a "scoop" that forces air downwards. (Eberhardt and Anderson 2001).

Lift is also generated from the airflow below the wing. The surface below wing at an angle - angle of attack - deflects air downwards. The total impulse on the wing points upwards at an angle to the vertical. However, this force is small compared to the force from the air above the wing. The top is the critical surface, which explains why extra fuel tanks, bombs, etc. are placed below, not above the wing.

#### Show me an example!

You can demonstrate Coanda lift with a thin stream from a tap/faucet and a spoon, which functions as a wing. Suspend the spoon such that convex part is against the stream - call this direction "up". Let the spoon lightly touch the stream. The stream immediately sucks the spoon "upwards", leaving it hanging at an angle. You can see how the spoon forces the water "downwards" and the water forces the spoon "upwards".

#### Why there's a Coanda effect?

Why does air follow the curve of the wing? This is the point where somebody messed up with the Bernoulli effect. Now, imagine a wing at a good angle of attack. A fluid flows above the wing. The fluid just behind the top surface is sucked in to this flow. This would generate a vacuum above the wing if nothing else happened. You can think of the vorticity a vacuum just above the wing would induce in the incoming airflow. This "potentially vacuum" area is filled by fluid from the incoming flow. There! The fluid accelerates downwards and flows along the curve of the top surface. Similarly, in the area just below the wing, air would accumulate and generate infinite pressure, so it flows downwards, changing its momentum and giving lift. So, we do have a difference in pressure, which generates force.

We see the Coanda effect and understand the whole picture best with it. For the air, communication of force is possible only with pressure and this can be misunderstood as the only thing that's happening. Most popular explanations in textbooks ignore the propulsion of air downwards. That's analogous to kids' Computer Science books explaining the operation of a computer with zeros and ones and not mentioning digital logic gates. Yes, that's what happens inside the system, but that's not why the system works.

For a more exhaustive explanation and more explained phenomena, such as wing efficiency, ground effect and wing vortices, see Scott Eberhardt's and David Anderson's webpage on their book Understanding Flight.
http://www.aa.washington.edu/faculty/eberhardt/lift.htm
More myths at William J. Beaty's Science Myths in K-6 Textbooks and Popular culture.
http://amasci.com/miscon/miscon.html
Thanks to Ken Fuller. Grammar corrected by Shr00m.

Replying to weasello above: "In any case, time will eventually show that all of these crazy theories were all wrong and some grand unified theory will explain everything." You are using the "just a theory" argument. It is a problem of the precise definition of "theory" and "true" in the English language. We are trying to explain, not prove a theory.

The "true" source of any force on an object suspended in free air can only be a difference in pressure. However, this does not give a clear picture. The Coanda effect gives. This isn't proof and isn't meant to be. Proof is actually applying the equations or making a simulation.

Brontosaurus says Interesting, but how does this explain inverted flight?
Inverted flight isn't different from conventional flight. Planes designed for inverted flight have symmetric wings, so that when turned upside down, the wing has the same shape for airflows as before. It's only dependent on the angle of attack at which the airflow meets the wing. Acrobatic airplanes have symmetric wings and generate lift up is the nose is up and down if the nose is down. This makes it easy to fly inverted: just point the nose at the same angle with respect to vertical.

A more rigorous explanation of aerodynamic lift.

vuo does an excellent job of explaining why the popular theory, also called the equal transit time fallacy, is false. His explanation of lift using the Coanda effect, is partially right, but incomplete, and is not the method engineers use to calculate the distribution of forces acting on a body in a fluid flow.

First, a word on the coanda effect. The coanda effect refers to the tendedncy or a jet of fluid to follow a curved surface. This is self evident because a fluid follow streamlines, and any non-permeable surface is a streamline. And it is true that the fluid flow is derected downwards as it travels over the surface of the airfoil, and this change in momentum requires a downward force on the fluid, and an equivalent upward force acting of the airfoil, via Newton's second the third laws. The problem is that it is very difficult to use this information to get useful data on the distribution of the forces acting on the airfoil. This information is important because it describes the pitching moment created by the wing, which is important for the stability and control of the aircraft.

So how can we find that info? The answer is by using the continuity equation, and bernoulli's equation. The continuity equation relates the velocity of a fluid flow with the cross sectional area of the flow. If a fluid flow has to flow through a smaller area, it must speed up for the total mass flow to be the same, and vice-versa if the area increases. Bernoulli's equation shows that the static pressure decreases as the fluid velocity increases. When the flow hits our airfoil, it splits in two, and the top stream has to be squeezed over the top, while the lower stream has a pretty smooth and uninterrupted path. So the top stream has to speed up, and thus the pressure drops, and the pressure differential creates lift. This theory predicts that the suction will be strongest at the front of the airfoil, and gradually taper down towards the rear as the flow area increases and the flow slows down, and this is exactly what we see in wind tunnel tests of actual airfoils.

Keep in mind that the conservation of momentum isn't necesarily wrong. Do the pressure forces cause the flow direction to change, or does the changing flow direction cause the pressure forces? It doesn't matter, F=ma, the two are complimentary, so if you know one you can find the other. The change in momentum explanation is good for explaining lift to people who have a good basic physics background, but aren't well versed in fluid dynamics, but the continuity/pressure explanation is what is used by actual aerospace engineers to find the forces acting on airfoils and other bodies moving through fluids.

I have read with interest the theories of lift and the arguments to support them. The first ever lecture I gave was on Helicopter Theory of Flight, in 1974, supported by Bernouli's Theorem. At about the same time in my life it was my job to stand underneath a hovering helicopter and, as you can well imagine, it was drafty! For many years until 2009 I would have supported the idea of the application of Bernouli's Theorem to produce lift from wing shape. Between these occurences I had also learnt to fly and sail. Without thinking I accepted the proposal that the sail was effectively a wing on it's side, producing a lateral force, also called lift.

In 2009 I was asked to lecture on aerodynamics and decided to brush up on my theory, expecting to find Bernouli's theorem everywhere. I was surprised and discovered a great controversy which made me re-evaluate my beliefs. I had meanwhile made the personal discovery that the principle that produces "lift" from a wing was the same as that for a propeller (ship's or aircraft) and a rudder (likewise). Also I was reminded that there is indeed a significant downwash from a hovering helicopter and, of course a rearward wash from a propeller. The problem I therefore have with the application of Bernouli's excellent and accurate theory on fluid flow and pressure drop to aerodynamics is that a sail doesn't have much of a difference in distance round the inner and outer surfaces - indeed it can be considered negligible. But it produces significant lift! Then I thought some more and considered that if the air below the wing is at a higher pressure than the air above the wing, the direction of airflow (high to low) would always be UP. How come air was coming down in significant quantities from the hovering helicopter? So, in conclusion, based on the fact that the travel distance of air round a sail is almost exactly the same and therefore the application of Bernouli's Theorem would be wrong and the fact that a propellor does the same job as a wing, I now believe that the correct application for lift must be equal and opposite reaction (Newton 3)caused by a change in momentum of air downwards. I have several books of the theory of flight and have spent hours online researching, but it is observation of personal experience that carries weight and as a sailor and a flyer, I agree with the camp that supports downwash and Newton.

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