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Re: Judgement on opposing airfoil views, pt. 1

(Note: I'm currently out of town on vacation, so I might not respond to
messages for many days)


On Fri, 27 Aug 1999, Richard Tarara wrote:

I should really stay out of this discussion since I know next to nothing
about all this, BUT:

Me too! ...very big :)


However, I deeply trust our ability to reason from first principles. If
the situation becomes too complex, then this will fail. In my opinion it
is not nearly that complex. In other words, "It's that simple."


Hi Rich! Right. However, if the wing created the chordwise circulation
in the distant past, then, in a nonviscous simplified model, that
circulation continues conceivably forever. That circulation is similar to
a coasting wheel. It inherently contains this idea: equal amounts of
upwash and downwash. If we think of the region of the chordwise
circulation as being a flywheel, we would state it like this: "one bit of
the flywheel accelerates another bit of the flywheel, and the forces
between them sum to zero and do not produce a net force upon the axel of
the flywheel." If we describe the air surrounding the wing, we would say
"one air-parcel in the pattern of chordwise circulation accelerates
another parcel of the same pattern of circulation, but the forces between
them sum to zero and do not produce a net lifting force upon the airfoil
as a whole."


BUT: Since the plane can now climb (increased lift) or descend (decreased
lift) it must be able to affect this circulation almost immediately. I
therefore have troubles imagining the circulation model where the wing is
not CONTINUOUSLY applying forces to the air (for both the upwash and
downwash).

I agree. The usual standard "Bernoulli" analysis of an airfoil is
performed upon level flight in a 2D mathematical simulation. In that
situation the circulation can "coast" forever without losses. Also, in
that simulation the forces which create the circulation in the first place
are never analyzed. (The circulation was already there when the universe
was created.) However, in 3D this no longer holds, since the energy
stored in that rotating air mass is pouring off behind the wings in the
form of a rotating wake-vortex region. If we understand nothing other
than the 2D simulation, then we become totally unable to visualize exactly
how a 3D wing *creates* massive circulation continously to make up for
that huge amount lost to the wake-vortices.

An additional problem: patterns of circulation cannot be created by
inviscid flow simulations. To inject "vorticity" into the region of gas
at the surface of the wing and so create more chordwise circulation, the
inner circular streamlines must rotate and drag against the air farther
out, and pull that air into moving as well. The circular streamlines
would grow outwards, first starting at the surface of the airfoil and
gradually becoming established at a great distance from the airfoil.
Without viscous drag between adjacent parcels of air, this cannot occur.
In other words, if we think in terms of non-viscous flow in simplified
models, we may have murdered the central explanatory concept which shows
how airplanes actually work. No joke.



The Bernoulli-ists say "No, you're wrong", but do not show me why my
assertion is faulty.

In both the VERY SIMPLIFIED pressure difference model or the VERY
SIMPLIFIED 'air thrown down' model, there is a net change in momentum in
the air (time averaged from just before the wing arives at a particular
region and just after it leaves) since the air originally has ZERO
momentum (ignoring any winds).

I must strongly disagree with your choice of time-averaging. If the
region under consideration is made much larger, then we see that the "air
thrown down" model cannot exist in the 2D mathematical model of the
airfoil and its lifting force. I may be mistaken, so please try to find my
error in the following.

In the traditional 2D airfoil lifting-force model which features
closed-loop chordwise circulation, it appears to me that far ahead of the
wing, the vertical component of momentum is directed upwards for no
reason. What created this upwards momentum there? As we fly a plane
forwards, why would we expect the air to accelerate upwards without any
force causing this acceleration? Specifically, slice the entire 2D world
into vertical slices and integrate the net vertical momentum in each
slice, then plot the graph of vertical momentum versus horizontal position
at all locations surrounding the wing. I think the result is quite
interesting.

At the location of the wing the vertical momentum certainly changes sign,
and it is directed downwards after this change. Supposedly this large
change in momentum explains the lifting force. However, if we integrate
the net momentum of the air by starting AT THE WING and adding up the
positive and negative momentum at all horizontal locations extending to
infinity, we see that the NET momentum remains zero. For every hunk of
negative momentum after the wing, there is a corresponding glob of
positive momentum ahead of it, and over horizontal distance these must
cancel out. The wing does not create a net downwards momentum change. (I
still find this stunning) It only appears to do so because we
traditionally focus our attention on the part of the momentum graph which
is at the location of the wing.

To make things a bit clearer, get rid of the airfoil and instead use a
rotating cylinder as the "airfoil". In this case the solution is clear:
the streamlines before and behind the airfoil are mirror-symmetrical.
There is positive vertical momentum in the upstream side of the airfoil,
and negative vertical momentum downstream, but these distributions of air
momentum are equal and opposite, and they sum to zero over any horizontal
region surrounding the wing as long as we make certain to integrate
between locations +x and -x (we keep the contributions of the upstream and
downstream momenta equal.)

How can this be? It clearly violates conservation of momentum (because
gravity adds downwards momentum continuously to the airfoil, yet the net
momentum of the air surrounding the airfoil never changes.) Isn't this a
huge flaw in basic aerodynamics theory? It looks clear to me that this is
true. I don't see any way out of it. Once we are made aware of it, it
even seems sensible, since those circular streamlines guarantee that every
bit of air that accelerates upwards ahead of the wing must accelerate
downwards behind it, and the forces involved must obviously be equal and
opposite, and so overall they must sum to a zero net lifting force upon
the wing.


In the pressure model the higher pressure under the wing and the
individual molecular collisions under the wing produce a net downward
momentum when compared to the collisions above the wing in the low pressure
region. [In this VERY SIMPLIFIED model there is no need for any 'wholesale'
deflection of air downwards although the model omits any explanation of
_exactly_ how the pressure difference is formed other than air moving faster
over the top of the wing than the bottom.]

You've got it. That simplified model supports the "Bernoulli"
explanation of the lifting force, but it apparantly shatters Newton's
laws. The "Newton-ists" say that lifting forces cannot arise at all
unless either (A) the wing interacts with a surface, as with ground-effect
flight, or (B) the wing creates a wholesale downwards deflection of air.
(Or C, the wing is full of helium!) It does neither, but it still
generates a lifting force, therefor it breaks Newton's laws.

The source of the problem might also be because the "Bernoulli-ists" see
that these simple models work well when explaining the Bernoulli equation,
therefor any other considerations (such as ignoring Newton's laws) are not
important. On the other hand, the "Newton-ists" will (sometimes) see the
violation of Newton's laws, and they then know that the model is so simple
that it is profoundly flawed, whether or not it works OK with Bernoulli's
equation.

In that simplified 2-D model, there is no surface for the wing to "push
against" (the atmosphere is infinite), neither does the wing create any
*NET* downwards deflection of the air. Therefor the lifting force *must*
be zero according to Newton's laws, unless there is another method to
generate a force-pair besides creating one between two solid objects (the
ground and the airfoil) or creating a force-pair between the airfoil and
the air (and therefor creating net downwards deflection.)

I've been in exactly this same discussion on numerous occasions in the
past. If the other person is a "Bernoulli-ist", they will always find a
reason to suddenly change the subject. I don't understand this. Why
don't they instead just find the flaw in my reasoning that destroys my
argument? Or acknowledge the flaw and concede the point? It's this
"debating tactics" stuff in my opinion. Trying to win the fight rather
than trying to clearly see the strengths and the flaws, including their
own.



These differences in analysis are what I have assumed to be
the difference in the Bernoulli/Newton split--at least at a very simplified
and fundamental level.

I agree strongly.

I also have not seen evidence that the more complicated phenomena are
fundamentally different than these simple ones. There are other details
to be sure, but if we deeply understand the simple models and the problems
with them, then 99% of the controversy has been illuminated in my opinion.


Again, in both models there IS a net change in the
momentum of the air (downwards) to provide the upwards change in the
momentum of the plane.

I disagree. In the inviscid 2D model, if we take into account the air far
from the wing and we don't just concentrate on the wing itself, then we
will see that the oncoming air has zero net momentum change in the long
run, even though it does have a large momentum change at the location of
the wing. (As I said before, this is because the picture is symmetrical,
and every upstream momentum change has an equal and opposite downstream
momentum change, leading to zero net force.)


Now from all the postings I realize it is not this simple, but might some of
the problems be (as Jack has suggested) that in talking about the momentum
change there confusion about the nomenclature?

Probably nomenclature confusion. It's hard to see those types of troubles
without being able to read minds. I write a word, but if I am misusing
it, I don't see the wrong definition appear in everyones mind, and I go on
assuming that I was properly understood.


To be in William's camp (I
think!), I really can't see that what the air does, long after the plane has
passed, as being very relevant to the process of flying.

I agree. In a real 3D plane, the wing itself isn't affected by the air in
the distant wake-vortex region. But that region can be used as a simple
tool in order to calculate the lifting force. We can look at the air far
behind the plane, calculate its net downwards momentum, and if we know
that the air far ahead of the plane is undisturbed, then we can learn much
about the lifting force which injected that momentum into the trailing
wake. It's like calculating the weight of a hovering rocket by looking
only at the exhaust gases many feet below the engine's outlet. The actual
forces must be applied as air pressure to a surface. But this doesn't mean
that the descending gases far from the craft are useless as conceptual
tools.

{Experiment: Use a balloon to lift a powerful jet aircraft high into the
air and hold it at rest relative to the air. Release the plane and fire up
the very powerful engines. Does the plane not develop lift AS SOON as it
starts moving forward? Certainly long before any forces conveyed by the air
molecules transmitting a force to the ground and back could occur.}

Exactly: the surface is too far away to participate. If the craft creates
a net downwards momentum in the air (flings air down,) then it will be
immediately flung upwards as a result. This process obviously doesn't
depend on the surface of the earth being there (except in the special case
where the plane gains some extra lift when flying within about a wingspan
in altitude of the earth.)


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William J. Beaty SCIENCE HOBBYIST website
billb@eskimo.com http://www.amasci.com
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