Why airplanes really fly

• michelcolman

michelcolman

Hi,

I am an airline pilot, with more than 10 years of flying experience, and I would like to know how airplanes fly ;-) This may seem like a strange question for me to ask, so I will elaborate a bit:

The theory that was taught to me, and that is still taught to the vast majority of pilots all over the world (be it in airline pilot, private pilot, or paragliding training) is the following:

"An air parcel going over the curved top of the wing has to travel a longer distance, but it has to arrive at the trailing edge at the same time, hence it has to travel faster, and Bernoulli's law says that pressure decreases as speed increases."

This sounds like a good explanation at first sight, until you consider that there is no reason why this parcel would need to arrive at the trailing edge at the same time. Has it exchanged phone numbers with the parcel that went underneath the wing? Also, if you would calculate the lift based only on this theory and using the geometry of the wing, you would find a value that's about 2% of the actual lift produced by the wing. Finally, wind tunnel tests have shown that the air parcels indeed do not arrive at the same time. The air going over the top is not just going a little bit faster to arrive at the same time, it's usually going a lot faster and getting there well before the air that went underneath.

While trying to find an answer, I found a couple of other theories on the internet:

1. The simplest one, and rather obviously correct: the air leaves the trailing edge at an angle downward, and lift is simply the reaction force. Multiply the vertical speed component with the mass of air per second, and you get m/s times kg/s equals kg m/s^2, the force of lift.
2. The Coanda effect (Air "wants to" follow the curve around the top of the wing, which has to be caused by a pressure differential)
3. Circulation theory (lots of math)

The problem with the first theory (action/reaction) is that it's a bit too simple. It does a great job of explaining the very basic reason why the plane flies, but as soon as you want any more details, you get stuck. It does not say anything about pressure distributions, and it's not really clear how much air you should consider to be deflected by the wing. I suppose you should use an integral, but it's not clear how one would set it up.

The second theory, Coanda by itself, is just as flawed as the basic Bernoulli one. It, too, only accounts for 2% of the actual lift (disclaimer: that's just something I read somewhere, I never actually verified it).

The third, circulation theory, is way too complicated. Even if I could probably come to understand it with a few months of studying if I took the effort, I could never explain it to anyone without a good math background.

I finally settled on my own combined theory, which may be just as wrong as some of the others, but here it goes anyway:

Air going over the top has to indeed curve over the top of the wing. The Coanda effect makes it "stick" to the top surface, and this can really only be caused by a pressure differential. This means the pressure above the wing has to be lower than that of the surrounding air, to make the higher air curve downward. (In fact, air initially wants to go straight, which causes the low pressure that sucks it in). But this vertical pressure differential also results in a horizontal differential (air going through the low pressure area), which makes it speed up (Bernoulli's law). But as it speeds up, it will need more centripetal force to follow the curvature. Hence, the pressure becomes even lower, which again speeds up the air more, etc..., until an equilibrium is reached where the pressure is just right for both Bernoulli's law and the Coanda effect.

Meanwhile, at the bottom, air is deflected down which can only be caused by a higher pressure underneath the wing. This effect is small (even negligible) at small angles of attack, but becomes much more important at higher AOA.

Is this a bit closer to the truth already? Or is there any other way of explaining how a wing works without either oversimpiflying or resorting to complicated and unintuitive math?

Thanks,

Michel

1. The simplest one, and rather obviously correct: the air leaves the trailing edge at an angle downward, and lift is simply the reaction force. Multiply the vertical speed component with the mass of air per second, and you get m/s times kg/s equals kg m/s^2, the force of lift.
2. The Coanda effect (Air "wants to" follow the curve around the top of the wing, which has to be caused by a pressure differential)
3. Circulation theory (lots of math)
1 - better stated as the air is accelerated downwards (corresponding to lift) and slightly forwards (corresponding to drag). A couple of Newtons laws at work here. Force equal mass times acceleration, and forces coexist in equal and opposing pairs (wing exerts force on air, air exerts force on wing).

2. Coanda like effect - more generalized, just explains why air is accelerated mostly downwards and a bit forwards above a wing. Camber isn't needed, just an angle of attack. Aft of the peak of a cambered surface or leading top edge of a flat wing with an angle of attack, a "void" is introduced into the air by the upper surface of the wing, which the air must fill somehow (else a true vacuum would result). I call it "void effect", or "void abhorence effect", but I've been called the inventor of this term, although the wiki article on wing also mentions void, and it's commonly used to explain drag on a land based vehicle. If the angle of attack and camber is gradual enough the air fills in the void by mostly accelerating downwards (the "shortest" path) and a bit forwards. If the AOA is too steep, then a big vortice develops and the bottom of the vortice fills in the "void" with mostly forwards moving air.

In order for a wing to produce lift it has to be at a positive angle to the airflow. In that case a low pressure region is generated on the upper surface of the wing which draws the air above the wing downwards towards what would otherwise be a void after the wing had passed. :

http://en.wikipedia.org/wiki/Wing

3. Circulation theory is mostly theory, idealized gasses, potential flow theory, well below mach air speeds. In the case of a 747 at mach .85, there isn't going to be much "forward" flow of air anywhere, yet the wing generates lift just fine. Hypersonic (mach 5+) airfoils are more efficient if almost all of the lift is generated below the wing.

Personally I don't like the Bernoulli based descriptions for lift. One issue a signficant amount of lift is produce by a centripetal component of acceleration of air near the leading edge of a wing as it transitions from upwash to downwash over the top of the wing, and this centripetal component doesn't involve any change in speed, violating the pressure corresponding inversely with air flow speed^2 aspect of Bernoulli princple. Bernoulli applies outside the region where mechanical work is being peformed by the wing onto the air, and I have no issue with it's usage there.

equal transit theory
These pictures of lifting bodies pretty much disprove this, plus I just think these are interesting because of the unusual design.

http://www.dfrc.nasa.gov/Gallery/Photo/M2-F2/Medium/EC66-1567.jpg

http://www.dfrc.nasa.gov/Gallery/Photo/M2-F3/Medium/EC71-2774.jpg

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1 - better stated as the air is accelerated downwards (corresponding to lift) and slightly forwards (corresponding to drag). A couple of Newtons laws at work here. Force equal mass times acceleration, and forces coexist in equal and opposing pairs (wing exerts force on air, air exerts force on wing).
Indeed, I was looking at it more from a conservation of momentum point of view, but obviously the air's speed can only change if it is accellerated, which requires a force, which is somehow caused by the wing and therefore causes a reactionary force on the wing. And I was only looking at lift, but the change in horizontal speed of the air will of course result in drag on the wing. Anyway, while this is all quite obviously correct, I think it's a bit shallow as an explanation which is why I was looking for something more detailed.
2. Coanda like effect - more generalized, just explains why air is accelerated mostly downwards and a bit forwards above a wing. Camber isn't needed, just an angle of attack. Aft of the peak of a cambered surface or leading top edge of a flat wing with an angle of attack, a "void" is introduced into the air by the upper surface of the wing, which the air must fill somehow (else a true vacuum would result). I call it "void effect", or "void abhorence effect", but I've been called the inventor of this term, although the wiki article on wing also mentions void, and it's commonly used to explain drag on a land based vehicle. If the angle of attack and camber is gradual enough the air fills in the void by mostly accelerating downwards (the "shortest" path) and a bit forwards. If the AOA is too steep, then a big vortice develops and the bottom of the vortice fills in the "void" with mostly forwards moving air.
But is this sufficient to explain lift completely? I read somewhere that the Coanda effect can only explain about 2% of the lift, so there has to be more going on.
3. Circulation theory is mostly theory, idealized gasses, potential flow theory, well below mach air speeds. In the case of a 747 at mach .85, there isn't going to be much "forward" flow of air anywhere, yet the wing generates lift just fine.
It depends on the frame of reference. If you consider the airplane moving through the stationary mass of air at mach .85, quite a lot of air underneath the wing will be pushed forward. Basically, circulation theory superimposes a circulation onto the airflow, so if you look at it in the airplane's reference frame, air at the bottom is slowed down while air at the top is sped up. The air doesn't actually move forward relative to the wing, obviously. But it will move forward relative to the surrounding air.

If there would be no "forward" flow (relative to the surrounding air), the airplane would have negative drag and could simply switch off its engines. If you find a wing design that does that, please let me know ;-)
Personally I don't like the Bernoulli based descriptions for lift. One issue a signficant amount of lift is produce by a centripetal component of acceleration of air near the leading edge of a wing as it transitions from upwash to downwash over the top of the wing, and this centripetal component doesn't involve any change in speed, violating the pressure corresponding inversely with air flow speed^2 aspect of Bernoulli princple. Bernoulli applies outside the region where mechanical work is being peformed by the wing onto the air, and I have no issue with it's usage there.
I think you're not giving Bernoulli's law enough credit here. Bernoulli's law, change in pressure equals 1/2 rho v^2, will apply perfectly to the airflow: all it really says if that, if air speeds up along a flow line, this can only be caused by a pressure gradient, and the relationship between the two is quite simple to prove. The problem is that people are usually using Bernoulli's law the wrong way around, saying that speed creates low pressure.

Of course you can calculate speed from pressure and pressure from speed, but speed cannot be used to explain a pressure drop. The pressure drops for some reason (Coanda, boundary layer effects, "void abhorrance"(?),...) and this causes air to accellerate.

But anyway, you will always find Bernoulli's law to be correct along the line of flow (and therefore also between lines of flow if they come from the same source, the air mass around the plane). Because the only reason for accellerating air parcels is a lower pressure in front of them.
These pictures of lifting bodies(...)
That thing flies? Amazing! But wait till you see this...

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But is this sufficient to explain lift completely? I read somewhere that the Coanda effect can only explain about 2% of the lift, so there has to be more going on.
Usually those statements are about the equal transit theory, or the longer path over the top explanations for difference in speed, which would be small. The air is deflected downwards above a wing, and this is a more general version of Conada "like" effect, part of which is due to "void abhorrence" as mentioned in the wiki article on wings.

circulation, no forwards flow under wing at mach .85

It depends on the frame of reference. If you consider the airplane moving through the stationary mass of air at mach .85
OK, makes sense now, using the air as a frame of reference, but isn't the direction of flow mostly downwards and a relastively small (compared to downwards flow) amount forwards?

I think you're not giving Bernoulli's law enough credit here. Bernoulli's law, change in pressure equals 1/2 rho v^2, will apply perfectly to the airflow: all it really says if that, if air speeds up along a flow line, this can only be caused by a pressure gradient.
The air is also sped up via mechanical interaction (including void introduction, such as drag at the back of a bus on a highway). The overall pressure is changed by mechanical interaction, although the goal of most wings is to minimize work done on the air. In the case of propellers, the goal is thrust, and in this case:

We can apply Bernoulli'sequation to the air in front of the propeller and to the air behind the propeller. But we cannot apply Bernoulli's equation across the propeller disk because the work performed by the engine violates an assumption used to derive the equation. :

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

I have a paper here: http://arxiv.org/abs/nlin/0507032 that addresses lift. It seems pretty clear to me that lift on a subsonic wing at angles of attack below stall angle is primarily caused by the same thing that causes the Coanda effect, a lowering of pressure on the *top* of the wing. As Michel says, the air deflected off the bottom of the wing has an effect too. The whole result is a downwash off the trailing edge which is Newton's third law in action. I'd welcome comments.

I have a paper here: http://arxiv.org/abs/nlin/0507032 that addresses lift. It seems pretty clear to me that lift on a subsonic wing at angles of attack below stall angle is primarily caused by the same thing that causes the Coanda effect, a lowering of pressure on the *top* of the wing.
True for most airfoils, but not all:

from
http://www.dfrc.nasa.gov/Gallery/Photo/index.html:

Jeff,

Great photos. It's a reentry vehicle and it looks like it is not designed to gain altitude though. Is that true? Can it climb? Is it powered? The space shuttle doesn't have much lift either. Can you explain how it generates lift?

Charlie

It's a reentry vehicle and it looks like it is not designed to gain altitude though. Is it powered?
M2-F2 was a glider so it wouldn't gain altitude. The M2-F3 was rocket powered and reached a maximum speed of mach 1.6, and could easily gain altitude.
The space shuttle doesn't have much lift either. Can you explain how it generates lift?
Downwards acceleration of air via diversion of relative air flow: an effective angle of attack, combined with forward speed. The amount of total lift is related to the diversion of the relative air flow both above and below an aircraft.

The drag is usually less if most of the diversion takes place above the aircraft via a reduction in pressure, since the reduction in pressure somewhat offsets the increase in kinetic energy, in a Bernoulli like exchange of pressure for kinetic energy. The other way to reduce drag is to reduce the kinetic energy added to the air, by accelerating more air at a lower rate (twice the air and half the acceleration results in half the kinetic energy) so long wingspans are generally more efficient than short wingspans.

Since the M2-F2 and M2-F3 were re-entry prototypes, a high lift to drag ratio wasn't a goal. In this case, a high drag factor reduces the time it takes between re-entry and landing.

That's what I thought about the reentry vehicle. With rocket power, of course, you can lift anything. (LoL) Seriously though, under rocket power the lift must be pure reaction to the air impinging on the bottom. I presume the shape of the bottom was primarily to produce stability and not lift. Am I right? If you get a chance to read the paper, http://arxiv.org/abs/nlin/0507032 , I would be interested in your ideas.

That's what I thought about the reentry vehicle. With rocket power, of course, you can lift anything. (LoL) Seriously though, under rocket power the lift must be pure reaction to the air impinging on the bottom. I presume the shape of the bottom was primarily to produce stability and not lift.
The shape of the bottom is to divert air downwards. Not visible in those pictures is the tail end of the upper surface, which also tapers downwards similar to the lower surface tapering upwards to reduce drag and encourage air flow.

I would be interested in your ideas.
As I mentioned before, it's more efficient to accelerate air via reduction in pressure, since that air will then decelerate as it's pressure returns to ambient, reducing the total energy added to the air for the same amount of momentum change and lift. At high angles of attack, most of the lift occurs below a wing, regardless of the air foil. An F-16 fighter pulling 9 g's in a turn with over 20 degrees AOA is producing most of the lift from "below" the wing. For a conventional wing, I don't know at what effective AOA that the magnitude of surface pressure minus ambient pressure becomes equal above and below a wing which would imply lift generated equally above and below a wing.

Even in the case of a flat board at a small angle of attack at forward speed, most (just more than 50%, not almost all of it) of the diversion occurs above the board, for a variety of complicated reasons, but mostly because more air is affected above the board than below it.

I'm not thinking about supersonic lift. It seems to me that a lot of very interesting phenomena occur in the subsonic regime. I suspect that the Coanda effect and bow wave behavior are utilized by slots and slats and Fowler flaps. A barn door, of course, will fly but for some reason, people don't make wings flat like that except perhaps for supersonic aircraft.

I suspect that the Coanda effect
Part of Coanda effect is what I call void abhorence theory:

a low pressure region is generated on the upper surface of the wing which draws the air above the wing downwards towards what would otherwise be a void after the wing had passed.

http://en.wikipedia.org/wiki/Wing

people don't make wings flat like that except perhaps for supersonic aircraft.
Flat wings work fine for small models at low speeds, such as those dime store balsa models (gliders and rubber powered) and only need a bit of sanding in the next step up:

http://www.4p8.com/eric.brasseur/glider2.html [Broken]

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"An air parcel going over the curved top of the wing has to travel a longer distance, but it has to arrive at the trailing edge at the same time, hence it has to travel faster, and Bernoulli's law says that pressure decreases as speed increases."
While trying to find an answer, I found a couple of other theories on the internet:

1. The simplest one, and rather obviously correct: the air leaves the trailing edge at an angle downward, and lift is simply the reaction force. Multiply the vertical speed component with the mass of air per second, and you get m/s times kg/s equals kg m/s^2, the force of lift.
2. The Coanda effect (Air "wants to" follow the curve around the top of the wing, which has to be caused by a pressure differential)
3. Circulation theory (lots of math)

The theory based on Bernoulli's law fails to explain why jet fighter can fly upside down and all these other theories fail to explain why flat kites fly.

The theory based on Bernoulli's law fails to explain why jet fighter can fly upside down and all these other theories fail to explain why flat kites fly.
Bernoulli applies when no work is being done on the air. This applies to the air not in the immediate vicinity of a wing where mechanical interaction takes place (direct deflection below and/or void introduction (which results in a low pressure zone) above a wing. Away from the wing, the inverse relationship between the static pressure component of air (the other component is dynamic pressure) and speed^2 of the air holds. At the wing air interface, the total energy of the affected air is changed, so Bernoulli's equation is violated.

Another factor not commonly taken into account pressure differntials related to accelerations perpendicular (therefore no change in speed) to the direction of travel, based on the frame of reference. Using the wing as a frame of reference, at the upper leading edge, the air flow curves from upwards to downwards, with a significant "centripetal" component of acceleration, and this corresponds to a reduction in pressure without a change in speed. It's another case where the mechanical interaction between wing and air violate Bernoulli's equation.