
The mysteries of aerodynamic lift - LinuxBender
https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/
======
munificent
This is a somewhat confusingly written article about a famously confusing
topic. It directly parallels arguments about how sailboats are able to sail.
Sails are also airfoils so similar mechanics come into play. Interestingly,
because a sail has effectively no thickness, both sides of the sail always
have the same length, which immediately calls the Bernoulli argument into
question. Sailboats are also interesting because they generate all their power
from the wind and yet can also sail _faster_ than the wind at times.

As far as I understand it, the fundamental reason airfoils in boats and places
work the way they do _requires_ viscosity. Without that, the math falls apart
and the ship doesn't move. It is not enough to treat air as a bunch of tiny
billiard balls bouncing off the bottom of the wing (the Newton's third law
argument). Likewise, you can't pretend the air above and below the wing are
each confined to their own perfectly frictionless tubes with different
velocities (the Bernoulli argument), since the air moving over the wing is
part of a continuous whole extending out arbitrarily far.

In order to explain how fabric-thin sails are able to generate lift, how
planes with curved wings can fly upside down, and how the ground effect comes
into play, you have to treat the surrounding fluid as a continuous medium with
viscosity. That's how the math works. Unfortunately, we don't seem to have a
good intuition for how that _feels_ so it's hard to treat that as a
satisfactory explanation.

~~~
simonebrunozzi
> can also sail faster than the wind at times.

Really? Can you elaborate?

~~~
WalterBright
Take a drafting triangle that has 30-60-90 degree corners. Place it between
two objects, and squeeze the triangle between them. It'll move to the side
faster than the two objects move together.

Or you can just think of it like squirting toothpaste.

The wind pressure on the sail and the water pressure on the keel form the two
"objects" being pushed together and the sailboat "squirts" out the side.

Edit: The angle between the sail and the keel is like the angle on the
triangle. The keel really was a great invention.

~~~
luckyscs
It's like our brains aren't meant to handle resolving that not only is it
pushed through, it's sucked into a thin and ever moving void. It's pushed and
pulled at the same time, in otherwords, part of the continuum.

~~~
taneq
Suction isn't a real thing, though. It's just our description of when lower
pressure on one side of a thing allows the thing to be moved by the higher
pressure on the other side.

The pressure that the air above the wing applies to the top of the wing is
lower than the pressure that the air below the wing applies to the bottom of
the wing. The net force is upwards.

~~~
luckyscs
I'm not sure it's that simple, and my physics knowledge isn't so strong but if
it's a gradient, the force of the push can't exist without being the same
thing as the force of the pull. They seem to be one in the same, the force
isn't onna particular side, it's the effect of the delta between points on the
gradient.

------
H8crilA
I'm surprised people don't start with the basics on this confusing topic.

The third law of Newton's mechanics tells us that for the plane to get an up
force to counteract the gravity, the air must receive and equal amount of down
force. Therefore what planes _must_ be doing is deflect air masses down. A
plane _must_ be applying a downward force to air masses, with total force
value of "mass * g", i.e. supply "mass * g * 1second" worth of downward
momentum per second. As simple as that.

~~~
jvanderbot
Yes, and in rotating-wing configurations (e.g., helicopters), the lift is
basically calculated using the momentum of the column of air being forced
downward + the momentum of the chassis. By accelerating air downward in a
column below the rotating wingspan, the column of air gains a net negative
momentum (downward), necessitating a net positive (upward) momentum to the
chassis to keep the system's momentum conserved. This principle seems to work
just fine for me w.r.t. fixed wings.

~~~
lutorm
Sure, that's just momentum conservation. But how do you know _how much_
downward momentum the column of air has?

~~~
H8crilA
Airplane/helicopter mass * g * time

Assuming the plane/helicopter didn't accelerate up or down and assuming
there's no wind.

~~~
lutorm
Sure, that has to be true if the helicopter can hover. But how do you know
that's possible?

You can't postulate that something flies as part of an explanation why it can
fly...

~~~
starpilot
You can solve for the lift generated by each rotating blade. Then it's roughly
the same calculating the lift for a fixed wing, except for the freestream flow
speed varying along the span. The lift is different at each spanwise location,
so you integrate to get the total lift for one blade, then multiply by the
number of blades. Numerous ways to do this, but the simplest accurate way is
via lifting-line theory. The resulting system of equations is solved
iteratively.

------
kryogen1c
this article is so confused and unscientific i have a hard time forming a
coherent response.

> although bernoulli's theorem is largely correct ... the theorem alone does
> not explain why this is so or why the higher velocity atop the wing brings
> lower pressure along with it

this blurb is accompanied by an upside down plane with the caption "doesnt
explain why planes can fly inverted". this is a "tide goes in, tide goes out,
cant explain that" statement [1]. im speechless. some planes can fly upside
down, and some cant. its not a mystery we discover through trial and error -
theyre designed that way by people who use bernoulli's equations, et al.

equations are not explanations. calling a theorem partially correct because
you dont know why it works is totally unrelated. either the theorem accurately
represents and predicts reality, or it doesnt. no equation says why itself
works, thats nonsense talk.

[1]
[https://www.youtube.com/watch?v=_fSlJaZrUhs](https://www.youtube.com/watch?v=_fSlJaZrUhs)

~~~
FabHK
I find the article perfectly reasonable. We can model flight quite well, and
predict the behaviour of wings quite well, yet it is hard to give an accurate
account of it at a layman's level.

The article goes on to discuss two accounts that have been given historically,
and outlines why they are insufficient. A plane flying upside down is a
perfectly fine refutation to the naive Bernoulli "the wing is curved on the
upside" explanation.

Which parts do you have a problem with?

> equations are not explanations.

As the article makes painstakingly clear.

~~~
Rury
Perhaps this:

>In inverted flight, the curved wing surface becomes the bottom surface, and
according to Bernoulli’s theorem, it then generates reduced pressure below the
wing. That lower pressure, added to the force of gravity, should have the
overall effect of pulling the plane downward rather than holding it up.

This is not what Bournoulli's theorem states. Bournoulli's theorem doesn't say
anything as to _why_ fluid flows the way it flows. It just says for a fluid in
a steady state flow, increases in speed are associated in decreased pressure.
Hence the principle suggests, if you find a plane is able to fly steady upside
down, then expect to find the air flowing faster over the wing on the opposite
side of gravity under those conditions - just likewise when a plane is
normally flying right side up.

Again why fluid flows the way it does around airfoils is separate question
-and really the crux of the mystery here. Answers to this is probably hidden
in the solutions to the Navier–Stokes existence and smoothness problem:
[https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...](https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness)

------
zkms
Doug McLean (Boeing Technical Fellow) has a quite decent talk about the
question of intuitive explanations for aerodynamic lift:
[https://www.youtube.com/watch?v=QKCK4lJLQHU](https://www.youtube.com/watch?v=QKCK4lJLQHU)

Also Philippe Spalart's quote is right on the money: "It's easy to explain how
a rocket works, but explaining how a wing works takes a rocket scientist".

~~~
starpilot
We have trouble explaining it at a lay level, but we can solve the entire
time-varying (for unsteady cases) 3d flow field around a wing to very high
accuracy. Lift _seems_ like it should be intuitive because we've experienced
the force of wind and see birds flying, but therein lies the rub.
Straightforward results arise from a series of complex, interacting phenomena.

Another example might be explaining why sticky tape is sticky.

------
mech1234
I suspect if you made a wing out of a flat piece of material, tilted at the
appropriate angle of attack, it would be sufficient to fly a plane. It just
wouldn't be optimized at all.

Really, you need full Navier-Stokes behavior to explain all the forces acting
on the wing. Bernoulli doesn't generalize to a full vector field, it's a
simplified version of Navier-Stokes. Calling in the big guns doesn't make for
an easy discussion.

(mechanical engineer, I figure I had like 1/3 of the fluids classes the real
aerospace guys get).

~~~
codeduck
Flat wings work perfectly fine, they just need a higher angle of attack to
generate similar lift, and therefore have higher drag.

~~~
exabrial
And have poor stall characteristics because they're more likely to introduce
flow separations near the back of the wing.

------
opwieurposiu
A wing is a device that pumps air downward, which in turn pushes the wing
upward, by newton's third law. For a large plane, the wing will be pumping
many tons of air per second.

Start with a cube of still air, with zero mean velocity. Fly a plane through
it, and that cube will have a mean downward velocity.

[http://www.aviation-history.com/theory/lift.htm](http://www.aviation-
history.com/theory/lift.htm)

~~~
eganist
Wait a second.

Are you saying if I have a cube suspended in space, and I put e.g. a drone
inside it that just flies around in a circle inside the cube, the cube will
start to move down? What then? Will the drone crash into the ceiling of the
cube because it's independent from the cube itself?

My brain disagrees with this, but I'm a hacker, not a physicist.

~~~
czinck
I think the parent poster means a "cube of air" as in a region of air, not
something bounded on all 6 sides by glass walls.

But to your question, if it was a glass cube, I'm pretty sure the drone would
hover in the middle of the cube while gravity pulls it down exactly like if
the drone was turned off, based on conservation of momentum. Sure the drone is
pushing the air down, but then the air hits the bottom, bounces up to the top,
and then gets pushed by the drone again. It's (very literally) a closed
system, so nothing happening inside is really noticeable outside, and vice-
versa (steady state, if you smack the box the drone will notice).

------
pdonis
I've found the discussion in the following article (which is a chapter in a
much larger online treatment of all aspects of flying) to be quite clear and
easy to follow:

[https://www.av8n.com/how/htm/airfoils.html](https://www.av8n.com/how/htm/airfoils.html)

------
namirez
This is a confusing take on lift. To explain lift intuitively we need two
ingredients: the Laplace equation and the Kutta condition.

Most people have an intuitive understanding of the Laplace equation. For
example lightning usually hits the peak of mountains. The reason is that in
solutions of Laplace equations, field gradient is proportional to curvature.
In fluid dynamics, this field is called the stream function. The top of
airfoil is more curved than the bottom so the stream function gradient is
higher on top which results in higher wind speeds over airfoil.

But the second ingredient is the Kutta condition which represents viscosity.
If there were no viscosity, there would be no lift. The Kutta condition is
applied to the tail (trailing edge) of airfoil. Without Kutta condition, the
speed at the trailing edge would be infinity (because of Laplace equations.
Speed around sharp corners is inevitably infinite). Viscosity prevents
infinite velocities so we apply another condition at the trailing edge to make
the air velocity smooth.

It's kind of complicated and I agree that there is no simple explanation to
lift, but if you think about it for a little while, it's not that hard to
grasp.

~~~
lutorm
A flat plate generates lift, though, so the curvature is incidental.

~~~
namirez
That's in interesting observation. Yes, the same thing happens at the leading
edge of a flat plate due to curvature resulting in flow separation and a
vortex bubble on the top surface. If the flow doesn't separate, the velocity
at the front (leading) edge of the plate will be infinity.

The result is a vortex bubble over the flat surface which effectively changes
its geometry and aerodynamic behavior. See figure 2-12 in the following link:

[http://heli-air.net/2016/02/13/inclined-flat-plate/](http://heli-
air.net/2016/02/13/inclined-flat-plate/)

------
mannykannot
"The third problem provides the most decisive argument against regarding
Bernoulli’s theorem as a complete account of lift: An airplane with a curved
upper surface is capable of flying inverted."

Unfortunately, the author has fallen into the very trap that he is trying to
explain. If you were to measure the velocity and pressure fields around the
wing of an airplane flying inverted, you would find that they conform to
Bernoulli (so long as the airplane is flying slowly enough that
compressibility is not an issue, which is another source of complication.)

What the author is doing here is to accept some bogus, hand-waving arguments
for why the airflow velocity changes around the wing, such as the equal
transit-time 'theory', which is, quite simply, false. To answer that question,
you need the Navier-Stokes equations (which are the application of Newton's
laws to a viscous fluid), or some realistic approximation.

You may find this more informative:

[https://fermatslibrary.com/s/how-airplanes-fly-a-physical-
de...](https://fermatslibrary.com/s/how-airplanes-fly-a-physical-description-
of-lift)

------
falcolas
So, since the title is a bit baity: On a mathematical level we understand and
have consensus; but the "dirtiness" of practical applications of mathematics
makes it a bit more complicated to explain fully.

~~~
pmoriarty
Well, the quibble here is whether having equations that are solvable and
useful for making predictions is equivalent to having an understanding.

If you answer "yes", then the problem with that view is most evident in
physics where equations and successfully tested predictions result in counter-
intuitive "quantum weirdness" which is hard to reconcile with claims of
understanding. As Feynman was supposed to have said, _" If you think you
understand quantum physics, you don't."_

Another problem with such a view is it results in descriptions which sound
absurd on their face, such as claims that when people look they see photons.
But people look they see objects, fields of color, or have other experiences
which are irreconcilable with the abstractions or equations created by
physicists.

This is related to what is known in analytic philosophy circles and cognitive
science as "the hard problem of consciousness", which is how one reconciles
"scientific" explanations of how the mind works with people's actual
experiences.

~~~
falcolas
It can be explained, though. I took aerodynamics courses over a decade ago,
and they had a decent explanation which covered all of the points brought up
in the article, incorporating both Bernoulli's principle and Newton's third
principle.

The big challenge seems to be making it explainable to someone with no domain
knowledge.

------
ethn
During my plane flights I passed the time rediscovering the equations of lift.

The physical intuition I’ve found, is for plane flight, the plane must move
faster in the direction parallel to the ground than the time it takes for
those air molecules under the plane to move away and deform around the wing at
some average velocity. In this manner, the plane can push off those air
molecules as they’re unable to move out of the way quick enough to escape the
force. Similar behavior to skipping a stone on water. For lift, you apply
torque on the wing by changing the angle of attack. This also leads to some
interesting ideas on wind.

------
knolan
I lecture fluid mechanics.

There are actually two Bernoulli equations. Remember that Bernoulli’s work is
derived for and is only valid along a streamline. A streamline is an imaginary
curve that is tangent to the flow field. It’s not some invisible tube, it’s a
mathematical representation of a vector field.

The first one is the well known one mentioned in the article. It relates
pressure and velocity tangent to a streamline. So if the velocity is somehow
increased the pressure drops.

The second equation deals with pressure changes due to curvature, i.e. force
normal to a curving streamline.

On an airfoil there is an effective reduction in the area through which the
air passes between the surface of the airfoil and a far field streamline
unaffected by the airfoil. This increases the velocity (via the continuity
equation) which in turn reduces the pressure. The curvature of the airfoil
also curves the streamline close to the surface resulting in an additional
pressure reduction normal to the surface. You can imagine how this affects a
highly cambered airfoil.

If anyone is interested here are my lecture notes on the derivation.

[https://nbviewer.jupyter.org/github/nolankucd/MEEN20010/blob...](https://nbviewer.jupyter.org/github/nolankucd/MEEN20010/blob/master/3.2%20Derivation%20of%20Bernoulli%27s%20Equation.ipynb)

~~~
Bendingo
Thanks.

Minor typo in your lecture notes just after equation (22).

"The assume the flow is steady, inviscid and and incompressible."

should be

"They assume..."

~~~
knolan
Thanks!

------
Isamu
So this is about intuitive explanations of flight.

The complaint about using Newton's law is that it doesn't readily explain the
low-pressure region above the wing. Let me give it a try.

Intuitively, all the forces on the wing are manifest as air pressure measured
the wing surface and expressed as a force normal to the surface at that point.
There are no other forces from the air. You sum them over the wing and the net
force upward is called lift, the net force backward is call drag.

If there is net lift, that means the net normal forces summed over the wing
are upward, implying that the pressure is low above the wing relative to below
the wing.

The Newtonian explanation is that a force must be exerted to change the
direction of the air. The net force on the air is in the direction that the
air turns, and the reaction force on the wing is in the opposite direction.

On the underside of the wing the air is diverted downward and the reaction
force on the wing is upward, and this is measured by the air pressure on
underside of the wing.

On the top of the wing the air is again diverted downward and the reaction
force on the top of the wing is again upward, and this is measured by a
lowered air pressure, giving a net upward force.

------
lutorm
The best intuitive discussion about lift that I've come across is John
Denker's "See How It Flies":
[https://www.av8n.com/how/](https://www.av8n.com/how/)

The key ingredients that I took away from the above are that circulation and
the Kutta condition are fundamental to explaining lift.

I think people's confusion with this situation is that there's no simple cause
and effect. It's just that the fluid equations have a solution that has
circulation and that gives lift, but you can't solve for it like you can with
most mechanics problems, because you need a _global_ solution that satisfies
the fluid equations.

------
lmilcin
I don't think there is anything mysterious about lift. We can model it very
well, we have precise equations that predict the exact results (though we
can't solve them) and we know where these equations come from.

The fact that I do not understand the equations doesn't mean there is anything
mysterious behind it.

There might be some artistry with regards to actually designing the
aerodynamic shapes. We have no way of finding the best possible shape yet,
this is largely a process of trial and error (though nowadays it can be
automated with simulation without actually having to go through building
physical model).

~~~
minblaster
Wouldn’t you say something that has an equation that works but no theory of
why is mysterious?

Mysterious doesn’t mean magical, it just means there’s an unexplained gap in
what we understand, which is the case.

~~~
lmilcin
But there is no unexplained gap. This might only be "mysterious" to somebody,
but not in general. When you decide to title your article telling something is
"mysterious" it suggests it is mysterious in general.

Anything could be said to be mysterious to somebody, there will always be
somebody that has no knowledge to somebody. This way you can title anything as
"mysterious" but it is not very useful (unless you count to bait clicks).

------
jb775
Recently saw this crazy video of planes being lifted into the air during a
microburst. At the time I wondered what caused the lift...food for thought for
this discussion.

[https://www.youtube.com/watch?v=b_WmjWAGkLI](https://www.youtube.com/watch?v=b_WmjWAGkLI)

A microburst is a rare weather event where a cloud basically shoots air
downwards up to 100mph:

[https://www.weather.gov/bmx/outreach_microbursts](https://www.weather.gov/bmx/outreach_microbursts)

------
p_l
The article is... bad. Very bad. Doubleplusungood bad, in fact.

I recommend checking out
[https://www.grc.nasa.gov/www/k-12/airplane/lift1.html](https://www.grc.nasa.gov/www/k-12/airplane/lift1.html)
which is much more complete explanation, and written for school age children -
without the usual "lie to children" part that is common till you hit fluid
dynamics at university level.

------
jermaustin1
I'm tired of this headline, its an oversimplification.

We absolutely DO understand how and why they stay in the air, we just don't
have the hard numbers behind it.

~~~
FabHK
> We absolutely DO understand how and why they stay in the air, we just don't
> have the hard numbers behind it.

The article claims the opposite: we do have the hard numbers behind it (we can
predict how a wing behaves), but we don't have a good conceptual explanation
for it at a layman's level (the how and why, if you so will).

~~~
nimish
We have a very good explanation for experts though. It turns out lift is
really damn hard to explain since fluids are quite complicated. There's no
reason to expect there's a layman's explanation at all, but you can make one
from Newton's laws (Navier-Stokes -- conservation of momentum) and
conservation of energy (Bernoulli) and conservation of mass (continuity
equation)

They are very complicated and the complexity is required to understand all the
weird edge cases

------
mikorym
> There is little, if any, serious disagreement as to what the appropriate
> equations or their solutions are. The objective of technical mathematical
> theory is to make accurate predictions and to project results that are
> useful to aeronautical engineers engaged in the complex business of
> designing aircraft.

> But by themselves, equations are not explanations, and neither are their
> solutions. There is a second, nontechnical level of analysis that is
> intended to provide us with a physical, commonsense explanation of lift. The
> objective of the nontechnical approach is to give us an intuitive
> understanding of the actual forces and factors that are at work in holding
> an airplane aloft. This approach exists not on the level of numbers and
> equations but rather on the level of concepts and principles that are
> familiar and intelligible to nonspecialists.

It's funny to read this after many years of teaching myself to think
"mathematically". The situation described above is in some ways the true
mathematical ideal: to be able to describe our surroundings so precisely that
intuition and perception blurs away, giving way instead to something stronger
than what we can describe in human words. When you describe something to two
different people, the objective is to adapt each explanation to their personal
framework, much in the way an artist or musician would adapt to their
audience.

However, the objective of mathematics is to take away exactly that: the
variability in perhaps equally valid social or human explanations.

I do think that intuition and perception is a very important of mathematics,
but I think it forms the first steps of the _scientific method_ behind
mathematics. Identify perceptions and intuitions and after that try to get to
precision and rigour.

Mathematics aims not to be intelligible, but it is in fact a fortunate state
of affairs that mathematics is intelligible to humans at all! It reminds me of
what Eugene Wigner wrote about mathematics, titled _The Unreasonable
Effectiveness of Mathematics in the Natural Sciences_. [1]

One thing that should be more clearly stated in the article is that it
esentially claims that the mathematical descriptions themselves seem somewhat
incomplete, the explanation of which I don't know, as the article tries to
avoid mathematics in the first place.

[1]
[http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html](http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html)

------
savrajsingh
The way I think about lift is that at a certain point, the air can’t get out
of the way fast enough, so lift is created. If you’ve ever skydived, you know
the air at high speeds feels thick —- slight deflections and imbalances
produce drastic movements.

------
Geee
I think it's quite easy to understand how planes fly. I figured out this as a
kid when I pushed my hand out of a car window and tilted it at different
angles. This way you can feel the pressure differential and the how the air
pushes the hand upwards or downwards.

~~~
copperx
So, if a plane wing is like a tilted hand pushing air down, how come a plane
can fly upside down with no change to its wings?

~~~
GuB-42
tl;dr just point the nose up.

The thing is that what really matters is the orientation of the trailing edge.
And in airplanes the trailing edge points downwards. It is not always obvious
because of the way wing profiles are designed but it is almost always the
case. We could have it level, but that would mean the plane will need to
always fly nose up in order to create lift, it would be uncomfortable, and
most likely not ideal from an aerodynamic perspective.

When you are flying upside down the natural orientation of the wing goes the
opposite way, so the leading edge points up, and indeed you can't fly level
with the nose pointing straight ahead. You need to point the nose up in order
to compensate the natural wing orientation, and then point up even more to
create actual lift.

Of course, there are some more advanced considerations. Performance will
generally be reduced when flying upside down, because the wings are not
designed to do so. However some wings have a symmetrical profile, and in
theory, they could be flown equally well in any orientation.

------
SubuSS
Probably a very dumb attempt but

Doesn't the leading edge being thick and rounded up top deflect away air from
getting to the slant-plane right behind it creating a low pressure zone above
the wing?

Same will apply in flat-wing cases because angle of attack will cause same
effect.

What am I missing?

------
learn_more
[https://en.wikipedia.org/wiki/coanda_effect](https://en.wikipedia.org/wiki/coanda_effect)

------
mhh__
If you want to see something really mysterious yet mathematically modellable
(ish) then look between your car and the road. Tyres are hard.

------
Dansvidania
I could not find sources quoted for the controversy and doubt regarding the
physics behind lift in this article?

As a sailor with an amateur-ish passion for physics, the dynamics of lift are
clear to me for years (Dunning Kruger?) and I would love to read about where
the doubts regarding each of the theories lie.

The doubts reported in the info-graphics are really confusing, because both
the increased speed and the low pressure area above the wing are easily
explainable with vector arithmetic and fluid dynamic respectively. The
statement that Bernoulli's principle does not explain planes flying upside
down seems also very naive.

------
kyuudou
Something to consider:

[http://milesmathis.com/lift.pdf](http://milesmathis.com/lift.pdf)

------
phendrenad2
Start by understanding why paper airplanes "glide", then you can introduce
downward thrust from plane wings.

------
NikolaeVarius
Needlessly click-baity article title.

TLDR: We don't have a full solution that models flight.

We also don't have a full understanding of how bicycles work.

~~~
FabHK
> TLDR: We don't have a full solution that models flight.

We do, actually. It's just hard to explain.

~~~
NikolaeVarius
There is a Millennium Challenge problem to provide a solution to the Navier
Stokes Equations which are a fundamental component of modeling flight.

The entire article about how none of the current models fully explain how a
plane stays in the air.

So what is this full solution you are talking about because my Aero professors
must have done a bad job teaching the topic to me

~~~
FabHK
I'll let the article (which we are discussing here) speak for itself (my
highlighting though):

> accounts of lift exist on two separate levels of abstraction: the technical
> and the nontechnical. [... The former] exists as a strictly mathematical
> theory, a realm in which the analysis medium consists of equations, symbols,
> computer simulations and numbers. _There is little, if any, serious
> disagreement as to what the appropriate equations or their solutions are._

~~~
NikolaeVarius
You are misunderstanding what a full solution means and what the article is
saying.

There are a systems of equations that allow us to model flight. But they are
NOT a full model of flight characteristics, as a consequence of, like
mentioned, lack of a full solution to the Navier Stokes equations

> The solutions of those equations and the output of the CFD simulations yield
> pressure-distribution predictions, airflow patterns and quantitative results
> that are the basis for today’s highly advanced aircraft designs. Still, they
> do not by themselves give a physical, qualitative explanation of lift.

------
thrustmaster
I thought it was a combination of newtons third law and Bernoulli's principle,
the wings are hitting the air and the air exerts equal force in the opposite
direction, Bernoulli's principle allows this equal opposite force to provide
easier lift.

~~~
zarmin
Wright you are.

~~~
thrustmaster
Really? I got a few down-votes... I also know the angle of attack of the wing
is important, no angle of attack, no lift?

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redis_mlc
In aviation, we consider deflection and Bernoulli's principle as both
important.

In physics, it's mostly about pressure differentials.

When you try to get more specific than that in a forum comment, it means you
probably don't really know what you're talking about.

