Re: critique of "disk balloons"

[William Beaty <billb@ESKIMO.COM>]

On Sun, 7 Feb 1999, John S. Denker wrote:

<snip>

> Executive summary:
>
> * The disk-balloon model gets credit for correctly portraying several
> features of the actual airflow.
> * It even correctly portrays one rather non-obvious feature of the airflow.
> * Alas it contains a significant element of arbitrariness.

First, please note that the disk-balloon analogy is part of a page about
mistakes in K-6 textbooks.  The disk-balloons are intended as a mental
model aimed at nonscientists.  If the simplified model is stretched to
include non-simple situations, IT MUST BREAK.  Obviously a "physical
balloons" model cannot explain any situation where the patterns of
circulating air superpose: the interactions between two aircraft, for
example.



The disk-balloons are my attempt to model reality.  Do they have an
"arbitrary"  origin?  No, they have a *HIDDEN* origin because my article
does not discuss the details of how I came up with the idea in the first
place. The article does mention it though:

   All of my reasoning implies that modern aircraft actually remain aloft
   by launching "smoke rings" downwards.

Where did "disk balloons" come from?  I was looking at aircraft from a
simplified Newtonian viewpoint, and I reasoned that an airplane remains
aloft BECAUSE it pushes air downwards, and in pushing air downwards it
must create a pair of wake vortices which act to constrain a large mass of
downwards-flowing air.  Therefor:

   An aircraft remains aloft BECAUSE IT CREATES A PAIR OF DOWNWARD MOVING
   WAKE-VORTICES.


I thought that this was a fairly odd and perhaps useful viewpoint, and I
had not seen it in any texts which I had so far encountered.

The large regions of air which surround the narrow wingtip vortex threads
behind an aircraft are filled with circular streamlines.  I simply replace
"air constrained by circular streamlines" with "physical disk-shaped
balloons."  Then I go and see if this act of simplification causes the
physics to shatter, rather than just bending it a bit.  :)

The true origin of "disk balloons" comes from my childhood, when I
realized that a droplet of ink which falls into water does not move as a
sphere, but moves as a ring-vortex, and the constrained fluid carries the
ink along with it.  Such a ring has mass, and therefor KE and momentum.  A
smoke-ring launcher can knock over targets and blow out candles.  If a
segment of a smoke-ring is flung downwards by an aircraft, the aircraft
would feel an upwards reaction force.  This viewpoint focuses on Newton at
the expense of Bernoulli.

If a winged aircraft is analogous to a hovering rocket, then the massive
air surrounding the downwards-moving wingtip-vortex pair is analogous to
the downwards-rushing rocket exhaust.  (Hence my mention of Jetsons
cartoon vehicles which spew little rings downwards.)  If long, tube-shaped
air masses are flung downwards by an aircraft, then the aircraft is flung
upwards against gravity.

What determines the radius of the disk balloons?  Did I pull them out of a
hat?  No.  If the pair of disks touch each other at a point on their rims
(where the aircraft fuselage would be), then that imposes a hard limit on
their diameter.  If their centers are coincident with the tips of the
wings, then the radius of each disk is half the wingspan of the aircraft.
Simple.  And physical, since that is the same spacing as the wingtip
vortices.  The question then becomes: do the assumptions going into the
"disk balloon" analogy correctly predict the equation for drag force and
the engine power needed to combat induced drag?  They seem to.

I've added a bit more to the original article, including a crude diagram
of the flow field behind a 3D aircraft (and made it HTML rather than
TXT.)  See:

   http://www.amasci.com/wing/rotbal.html


> * It does not correctly describe the interaction of the wing with the
> ground, or with other nearby wings.


Very true.  It is intended as a crude analogy for use when discussing
aerodynamics with children and nonscientists.  (Perhaps it will even work
with highschool kids?)  It cannot take the place of full-blown
aerodynamics theory.  Physical balloons obviously do not superpose, they
collide, and therefor I would assume that they cannot be used to explain
any but the simplest situation.  They are intended to explain flight, not
to explain all of aerodynamics.


> * It violates the known equations of motion.

We can discuss this in following messages.  I must point out that the
disk-balloons always exist in pairs, and always move downwards through the
ambient air as they rotate.  In such a situation, many of the problems
vanish.

Speaking of violations of laws, I also must note that the act of CREATING
a vortex always requires that the fluid be viscous.  If a wing is to
create a spinning mass of air and fling it downwards, that air cannot be
inviscid.  I would predict that the mechanism of 3D flight CANNOT EXIST in
any simulation which uses inviscid fluid.  The wing must inject KE into
the air; the wing must stir the air into motion as it flings mass
downwards.  How can this occur if one streamline does not viscously
interact with adjacent parallel streamlines? Without viscosity, all of the
KE in the wing's chordwise circulation would rapidly leak off via the
wingtip vortices, and there would be no way for the wing to re-establish
it again.  (In other words, the vortex-lines clinging spanwise to the
wings would exit from the trailing edge of the wing and be lost, as
described in Von Mises Sec.IX.3.)  Establishment of new vortex lines
requires a viscous fluid.  It also requires energy input, and hence an
induced drag.  An inviscid fluid simulation would wrongly predict that
induced drag is always zero.  An inviscid fluid simulation would wrongly
predict that the act of flying does not require that work be done.

Do the simulations at SEE HOW IT FLYS describe the origin of induced drag?
Do they predict the engine power required to fling parcels of air
downwards?  If not, then they are an incomplete model, and by your
reasoning, they should be discarded just as disk balloons should be
discarded.  What's good for the goose is good for the gander.

  SEE HOW IT FLYS: 3. Airfoils and Airflow
  http://www.monmouth.com/~jsd/fly/how/htm/airfoils.html

In my opinion ALL MODELS ARE INCOMPLETE.  Different models emphasize
different features.  Nobody should be discarding anything.  Instead we
should know the weaknesses of each model, and their ranges of
applicability.  Instead we should be visualizing several different models
simultaneously, so that the flaws and weaknesses of each one are cancelled
by the strengths of the others.


> A more detailed discussion, including comparison with competing theories,
> can be found at:
>   http://www.monmouth.com/~jsd/fly/rotbal.htm


I've added this link to my pages.  This message is the first part of my
response.


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