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| DATE | 2023-04-24 |
| FROM | Ruben Safir
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| SUBJECT | Subject: [Hangout - NYLXS] Whyh do planes not crash?
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https://getpocket.com/explore/item/no-one-can-explain-why-planes-stay-in-the-air
o One Can Explain Why Planes Stay in the Air
Ed Regis
21–26 minutes
illustration of a plane
Photo by CSA Images/Getty Images
In December 2003, to commemorate the 100th anniversary of the first
flight of the Wright brothers, the New York Times ran a story entitled
“Staying Aloft; What Does Keep Them Up There?” The point of the piece
was a simple question: What keeps planes in the air? To answer it, the
Times turned to John D. Anderson, Jr., curator of aerodynamics at the
National Air and Space Museum and author of several textbooks in the
field.
What Anderson said, however, is that there is actually no agreement on
what generates the aerodynamic force known as lift. “There is no simple
one-liner answer to this,” he told the Times. People give different
answers to the question, some with “religious fervor.” More than 15
years after that pronouncement, there are still different accounts of
what generates lift, each with its own substantial rank of zealous
defenders. At this point in the history of flight, this situation is
slightly puzzling. After all, the natural processes of evolution,
working mindlessly, at random and without any understanding of physics,
solved the mechanical problem of aerodynamic lift for soaring birds eons
ago. Why should it be so hard for scientists to explain what keeps
birds, and airliners, up in the air?
Adding to the confusion is the fact that accounts of lift exist on two
separate levels of abstraction: the technical and the nontechnical. They
are complementary rather than contradictory, but they differ in their
aims. One 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. 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 is on this second, nontechnical level where the controversies lie.
Two different theories are commonly proposed to explain lift, and
advocates on both sides argue their viewpoints in articles, in books and
online. The problem is that each of these two nontechnical theories is
correct in itself. But neither produces a complete explanation of lift,
one that provides a full accounting of all the basic forces, factors and
physical conditions governing aerodynamic lift, with no issues left
dangling, unexplained or unknown. Does such a theory even exist?
Two Competing Theories
By far the most popular explanation of lift is Bernoulli’s theorem, a
principle identified by Swiss mathematician Daniel Bernoulli in his 1738
treatise, Hydrodynamica. Bernoulli came from a family of mathematicians.
His father, Johann, made contributions to the calculus, and his Uncle
Jakob coined the term “integral.” Many of Daniel Bernoulli’s
contributions had to do with fluid flow: Air is a fluid, and the theorem
associated with his name is commonly expressed in terms of fluid
dynamics. Stated simply, Bernoulli’s law says that the pressure of a
fluid decreases as its velocity increases, and vice versa.
Bernoulli’s theorem attempts to explain lift as a consequence of the
curved upper surface of an airfoil, the technical name for an airplane
wing. Because of this curvature, the idea goes, air traveling across the
top of the wing moves faster than the air moving along the wing’s bottom
surface, which is flat. Bernoulli’s theorem says that the increased
speed atop the wing is associated with a region of lower pressure there,
which is lift.
Mountains of empirical data from streamlines (lines of smoke particles)
in wind-tunnel tests, laboratory experiments on nozzles and Venturi
tubes, and so on provide overwhelming evidence that as stated,
Bernoulli’s principle is correct and true. Nevertheless, there are
several reasons that Bernoulli’s theorem does not by itself constitute a
complete explanation of lift. Although it is a fact of experience that
air moves faster across a curved surface, Bernoulli’s theorem alone does
not explain why this is so. In other words, the theorem does not say how
the higher velocity above the wing came about to begin with.
There are plenty of bad explanations for the higher velocity. According
to the most common one—the “equal transit time” theory—parcels of air
that separate at the wing’s leading edge must rejoin simultaneously at
the trailing edge. Because the top parcel travels farther than the lower
parcel in a given amount of time, it must go faster. The fallacy here is
that there is no physical reason that the two parcels must reach the
trailing edge simultaneously. And indeed, they do not: the empirical
fact is that the air atop moves much faster than the equal transit time
theory could account for.
There is also a notorious “demonstration” of Bernoulli’s principle, one
that is repeated in many popular accounts, YouTube videos and even some
textbooks. It involves holding a sheet of paper horizontally at your
mouth and blowing across the curved top of it. The page rises,
supposedly illustrating the Bernoulli effect. The opposite result ought
to occur when you blow across the bottom of the sheet: the velocity of
the moving air below it should pull the page downward. Instead,
paradoxically, the page rises.
The lifting of the curved paper when flow is applied to one side “is not
because air is moving at different speeds on the two sides,” says Holger
Babinsky, a professor of aerodynamics at the University of Cambridge, in
his article “How Do Wings Work?” To demonstrate this, blow across a
straight piece of paper—for example, one held so that it hangs down
vertically—and witness that the paper does not move one way or the
other, because “the pressure on both sides of the paper is the same,
despite the obvious difference in velocity.”
The second shortcoming of Bernoulli’s theorem is that it does not say
how or why the higher velocity atop the wing brings lower pressure,
rather than higher pressure, along with it. It might be natural to think
that when a wing’s curvature displaces air upward, that air is
compressed, resulting in increased pressure atop the wing. This kind of
“bottleneck” typically slows things down in ordinary life rather than
speeding them up. On a highway, when two or more lanes of traffic merge
into one, the cars involved do not go faster; there is instead a mass
slowdown and possibly even a traffic jam. Air molecules flowing atop a
wing do not behave like that, but Bernoulli’s theorem does not say why
not.
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. 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.
Moreover, aircraft with symmetrical airfoils, with equal curvature on
the top and bottom—or even with flat top and bottom surfaces—are also
capable of flying inverted, so long as the airfoil meets the oncoming
wind at an appropriate angle of attack. This means that Bernoulli’s
theorem alone is insufficient to explain these facts.
The other theory of lift is based on Newton’s third law of motion, the
principle of action and reaction. The theory states that a wing keeps an
airplane up by pushing the air down. Air has mass, and from Newton’s
third law it follows that the wing’s downward push results in an equal
and opposite push back upward, which is lift. The Newtonian account
applies to wings of any shape, curved or flat, symmetrical or not. It
holds for aircraft flying inverted or right-side up. The forces at work
are also familiar from ordinary experience—for example, when you stick
your hand out of a moving car and tilt it upward, the air is deflected
downward, and your hand rises. For these reasons, Newton’s third law is
a more universal and comprehensive explanation of lift than Bernoulli’s
theorem.
But taken by itself, the principle of action and reaction also fails to
explain the lower pressure atop the wing, which exists in that region
irrespective of whether the airfoil is cambered. It is only when an
airplane lands and comes to a halt that the region of lower pressure
atop the wing disappears, returns to ambient pressure, and becomes the
same at both top and bottom. But as long as a plane is flying, that
region of lower pressure is an inescapable element of aerodynamic lift,
and it must be explained.
Historical Understanding
Neither Bernoulli nor Newton was consciously trying to explain what
holds aircraft up, of course, because they lived long before the actual
development of mechanical flight. Their respective laws and theories
were merely repurposed once the Wright brothers flew, making it a
serious and pressing business for scientists to understand aerodynamic
lift.
Most of these theoretical accounts came from Europe. In the early years
of the 20th century, several British scientists advanced technical,
mathematical accounts of lift that treated air as a perfect fluid,
meaning that it was incompressible and had zero viscosity. These were
unrealistic assumptions but perhaps understandable ones for scientists
faced with the new phenomenon of controlled, powered mechanical flight.
These assumptions also made the underlying mathematics simpler and more
straightforward than they otherwise would have been, but that simplicity
came at a price: however successful the accounts of airfoils moving in
ideal gases might be mathematically, they remained defective
empirically.
In Germany, one of the scientists who applied themselves to the problem
of lift was none other than Albert Einstein. In 1916 Einstein published
a short piece in the journal Die Naturwissenschaften entitled
“Elementary Theory of Water Waves and of Flight,” which sought to
explain what accounted for the carrying capacity of the wings of flying
machines and soaring birds. “There is a lot of obscurity surrounding
these questions,” Einstein wrote. “Indeed, I must confess that I have
never encountered a simple answer to them even in the specialist
literature.”
Einstein then proceeded to give an explanation that assumed an
incompressible, frictionless fluid—that is, an ideal fluid. Without
mentioning Bernoulli by name, he gave an account that is consistent with
Bernoulli’s principle by saying that fluid pressure is greater where its
velocity is slower, and vice versa. To take advantage of these pressure
differences, Einstein proposed an airfoil with a bulge on top such that
the shape would increase airflow velocity above the bulge and thus
decrease pressure there as well.
Einstein probably thought that his ideal-fluid analysis would apply
equally well to real-world fluid flows. In 1917, on the basis of his
theory, Einstein designed an airfoil that later came to be known as a
cat’s-back wing because of its resemblance to the humped back of a
stretching cat. He brought the design to aircraft manufacturer LVG
(Luftverkehrsgesellschaft) in Berlin, which built a new flying machine
around it. A test pilot reported that the craft waddled around in the
air like “a pregnant duck.” Much later, in 1954, Einstein himself called
his excursion into aeronautics a “youthful folly.” The individual who
gave us radically new theories that penetrated both the smallest and the
largest components of the universe nonetheless failed to make a positive
contribution to the understanding of lift or to come up with a practical
airfoil design.
Toward a Complete Theory of Lift
Contemporary scientific approaches to aircraft design are the province
of computational fluid dynamics (CFD) simulations and the so-called
Navier-Stokes equations, which take full account of the actual viscosity
of real air. 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.
In recent years, however, leading aerodynamicist Doug McLean has
attempted to go beyond sheer mathematical formalism and come to grips
with the physical cause-and-effect relations that account for lift in
all of its real-life manifestations. McLean, who spent most of his
professional career as an engineer at Boeing Commercial Airplanes, where
he specialized in CFD code development, published his new ideas in the
2012 text Understanding Aerodynamics: Arguing from the Real Physics.
Considering that the book runs to more than 500 pages of fairly dense
technical analysis, it is surprising to see that it includes a section
(7.3.3) entitled “A Basic Explanation of Lift on an Airfoil, Accessible
to a Nontechnical Audience.” Producing these 16 pages was not easy for
McLean, a master of the subject; indeed, it was “probably the hardest
part of the book to write,” the author says. “It saw more revisions than
I can count. I was never entirely happy with it.”
McLean’s complex explanation of lift starts with the basic assumption of
all ordinary aerodynamics: the air around a wing acts as “a continuous
material that deforms to follow the contours of the airfoil.” That
deformation exists in the form of a deep swath of fluid flow both above
and below the wing. “The airfoil affects the pressure over a wide area
in what is called a pressure field,” McLean writes. “When lift is
produced, a diffuse cloud of low pressure always forms above the
airfoil, and a diffuse cloud of high pressure usually forms below. Where
these clouds touch the airfoil they constitute the pressure difference
that exerts lift on the airfoil.”
The wing pushes the air down, resulting in a downward turn of the
airflow. The air above the wing is sped up in accordance with
Bernoulli’s principle. In addition, there is an area of high pressure
below the wing and a region of low pressure above. This means that there
are four necessary components in McLean’s explanation of lift: a
downward turning of the airflow, an increase in the airflow’s speed, an
area of low pressure and an area of high pressure.
But it is the interrelation among these four elements that is the most
novel and distinctive aspect of McLean’s account. “They support each
other in a reciprocal cause-and-effect relationship, and none would
exist without the others,” he writes. “The pressure differences exert
the lift force on the airfoil, while the downward turning of the flow
and the changes in flow speed sustain the pressure differences.” It is
this interrelation that constitutes a fifth element of McLean’s
explanation: the reciprocity among the other four. It is as if those
four components collectively bring themselves into existence, and
sustain themselves, by simultaneous acts of mutual creation and
causation.
There seems to be a hint of magic in this synergy. The process that
McLean describes seems akin to four active agents pulling up on one
another’s bootstraps to keep themselves in the air collectively. Or, as
he acknowledges, it is a case of “circular cause-and-effect.” How is it
possible for each element of the interaction to sustain and reinforce
all of the others? And what causes this mutual, reciprocal, dynamic
interaction? McLean’s answer: Newton’s second law of motion.
Newton’s second law states that the acceleration of a body, or a parcel
of fluid, is proportional to the force exerted on it. “Newton’s second
law tells us that when a pressure difference imposes a net force on a
fluid parcel, it must cause a change in the speed or direction (or both)
of the parcel’s motion,” McLean explains. But reciprocally, the pressure
difference depends on and exists because of the parcel’s acceleration.
Aren’t we getting something for nothing here? McLean says no: If the
wing were at rest, no part of this cluster of mutually reinforcing
activity would exist. But the fact that the wing is moving through the
air, with each parcel affecting all of the others, brings these
co-dependent elements into existence and sustains them throughout the
flight.
Turning on the Reciprocity of Lift
Soon after the publication of Understanding Aerodynamics, McLean
realized that he had not fully accounted for all the elements of
aerodynamic lift, because he did not explain convincingly what causes
the pressures on the wing to change from ambient. So, in November 2018,
McLean published a two-part article in The Physics Teacher in which he
proposed “a comprehensive physical explanation” of aerodynamic lift.
Although the article largely restates McLean’s earlier line of argument,
it also attempts to add a better explanation of what causes the pressure
field to be nonuniform and to assume the physical shape that it does. In
particular, his new argument introduces a mutual interaction at the flow
field level so that the nonuniform pressure field is a result of an
applied force, the downward force exerted on the air by the airfoil.
Whether McLean’s section 7.3.3 and his follow-up article are successful
in providing a complete and correct account of lift is open to
interpretation and debate. There are reasons that it is difficult to
produce a clear, simple and satisfactory account of aerodynamic lift.
For one thing, fluid flows are more complex and harder to understand
than the motions of solid objects, especially fluid flows that separate
at the wing’s leading edge and are subject to different physical forces
along the top and bottom. Some of the disputes regarding lift involve
not the facts themselves but rather how those facts are to be
interpreted, which may involve issues that are impossible to decide by
experiment.
Nevertheless, there are at this point only a few outstanding matters
that require explanation. Lift, as you will recall, is the result of the
pressure differences between the top and bottom parts of an airfoil. We
already have an acceptable explanation for what happens at the bottom
part of an airfoil: the oncoming air pushes on the wing both vertically
(producing lift) and horizontally (producing drag). The upward push
exists in the form of higher pressure below the wing, and this higher
pressure is a result of simple Newtonian action and reaction.
Things are quite different at the top of the wing, however. A region of
lower pressure exists there that is also part of the aerodynamic lifting
force. But if neither Bernoulli’s principle nor Newton’s third law
explains it, what does? We know from streamlines that the air above the
wing adheres closely to the downward curvature of the airfoil. But why
must the parcels of air moving across the wing’s top surface follow its
downward curvature? Why can’t they separate from it and fly straight
back?
Mark Drela, a professor of fluid dynamics at the Massachusetts Institute
of Technology and author of Flight Vehicle Aerodynamics, offers an
answer: “If the parcels momentarily flew off tangent to the airfoil top
surface, there would literally be a vacuum created below them,” he
explains. “This vacuum would then suck down the parcels until they
mostly fill in the vacuum, i.e., until they move tangent to the airfoil
again. This is the physical mechanism which forces the parcels to move
along the airfoil shape. A slight partial vacuum remains to maintain the
parcels in a curved path.”
This drawing away or pulling down of those air parcels from their
neighboring parcels above is what creates the area of lower pressure
atop the wing. But another effect also accompanies this action: the
higher airflow speed atop the wing. “The reduced pressure over a lifting
wing also ‘pulls horizontally’ on air parcels as they approach from
upstream, so they have a higher speed by the time they arrive above the
wing,” Drela says. “So the increased speed above the lifting wing can be
viewed as a side effect of the reduced pressure there.”
But as always, when it comes to explaining lift on a nontechnical level,
another expert will have another answer. Cambridge aerodynamicist
Babinsky says, “I hate to disagree with my esteemed colleague Mark
Drela, but if the creation of a vacuum were the explanation, then it is
hard to explain why sometimes the flow does nonetheless separate from
the surface. But he is correct in everything else. The problem is that
there is no quick and easy explanation.”
Drela himself concedes that his explanation is unsatisfactory in some
ways. “One apparent problem is that there is no explanation that will be
universally accepted,” he says. So where does that leave us? In effect,
right where we started: with John D. Anderson, who stated, “There is no
simple one-liner answer to this.”
--
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