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Why
is one arm of the 'V' formation always longer
than the other?
 n
a simple search of the Internet (geese AND
migration or "V
formation"), you will find an explanation for
why, with each dawn
of spring and dusk of autumn, we are privileged to
observe those honking
echelons in the sky.
More than one explanation, in fact. As
many as a hundred
explanations. All exactly alike. An
exclamation point might seem
appropriate for the previous sentence. Let's save it
for later.
According to Museum
of the Canada Goose, Angeles Arrien gave a speech
entitled "Lessons
from Geese" at the 1991 Organizational Development
Network based on the
work of Milton Olson. Soon after, it was transcribed and
began circulating
among Outward Bound staff throughout the United States.
The piece has been enthusiastically
scarfed up in paste
buffers and republished (usually verbatim) on websites
all over the Internet,
either attributed to "author unknown" or given a
self-asserted by-line.
With minor variations, "Lessons from
Geese" has been replicated
throughout the world and will inspire collaborative
behavior in perpetuity.
All renderings of "Lessons from Geese"
include the same
technical explanation for the V formation: "As each
bird flaps its wings,
it creates an 'up lift' for the bird following."
At first glance, one might suppose, that
such an explanation
would have seemed ironic to at least one of the
website owners, inasmuch
as most people probably presume that flapping wings
create a downward
flow of air, claiming the benefit of whatever "up
lift" there may be for
the bird doing the flapping -- decidedly not
"for the bird following."
Indeed, the aerodynamic term is 'downwash,' a
phenomenon readily observed
in wind-tunnel photographs showing smokey streaks that
droop from the trailing
edge of experimental wing foils.
Sophisticated puzzle solvers have at least
an elementary
understanding of how things fly. Many have even studied
Bernoulli's Principle
and know that the air flowing over the top surface of a
wing must necessarily
be at a lower pressure than the air flowing under the
bottom. That difference
in pressure produces 'lift.' At the extreme ends of each
wing, whether
bird or plane, the high pressure air underneath pushing
upward tends to
leak around the wingtip onto the top surface where there
exists a relative
vacuum. The resulting air flow actually spoils part of
the wing's lift.
It does something else, too.
While the air is flowing around the tip
of the wing,
the tip of the wing is moving forward, leaving behind
a circulating pattern
of air called a 'wingtip vortex.' It continues to spin
and expand, forming
a cone behind each wingtip, clockwise on the left,
counter-clockwise on
the right. In aviation, the phenomenon, wrongly
described as 'wake turbulence,'
resembles a pair of horizonal tornados.
Invisibly swirling off the wingtips of
huge aluminum birds
those vortices create dreadful hazards in the sky for
following aircraft
(see Sky Below
on this website).
In feathered flight, it is the wingtip vortex that
provides the "up lift"
exploited by migrating birds (see illustration below).
The ubiquitous essay "Lessons from
Geese" is not nearly
so remarkable for what it teaches us about geese but
for what it teaches
us about us. Consider the passage that reads
as follows:
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By
flying in a V formation, the
whole flock adds
71%
greater flying range than if
each bird flew alone.
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Critical thinking will surely be
stimulated by the precision
of that numerical assertion -- not "approximately
70%," not "more than
2/3rds," but "71
% greater flying range."
You might try turning your favorite search engine
loose on that phrase:
"71
% greater flying range" and see what you
find. Here's
a selection of -- well, 71 websites that Google found
for me in 1999...
Anti-Smoking Site, Archives Page, Australia's Fair
Dinkum, Aviary Website,
Berkeley Resort: Deep Thoughts, Best of Excel News,
Bethel Church Website,
Brotherly Love, Relief and Truth, Business Quality
Network, Candlelist
Digest, Christian Harmony- Illustrations, Church of God
in Christ Website,
CLub Loopy, Collection of AA Writings, Community Healing
Project, Discussion
Group, Mumbai Central, Elementary School, E-zine and
Magazine, Fifth Realm
Thoughts, FlyBusiness Women, Geese - on the Radio,
German Poems, Happy
News, High School Alumni Email Forum, High School
Journalism Site, Human
Resources, Human-Relations, Independence, Inspirational
Page, Inspirational
Page at a Multi-Level Marketing Site, Inspirational
Site, International
Prayer Fellowship, Islamic Network Discussion Archives,
Islamic Voice,
Jehovah's Witnesses Official Website, Junior High School
Teacher's Website,
Lessons From Geese, Lessons From Geese, Lessons From
Geese, Lessons from
the Geese, Lessons From the Geese, Lessons from the
Geese, Make a Joyful
Noise, Martial Arts Website, Mom's Cocoon, New Life
Churches of Australia,
New Zealand Site, Newsletter for Hewlett-Packard
Computing Professionals,
Newsletter-Clean and Green, Newspaper Editorial, Nursing
College, Personal
Home Page, Personal Website, Philosophy, Plum Island
Surfcasters, Poultry
Newsletter, Precision Aire, Right to Life,
S.A.F.E./Literature, Scoutmaster's
Minute, Sermon for Ordinary, Several Newspapers, Slide
Show for a Faculty
Meeting, Some Schools, Stories Sites Galore, Strategic
Studies, Superintendent
s Message, Teams Make Performance, The Goose Story, The
Motley Fool, Things
Are Look'n Up, Website for Stories, Weekly Bulletin from
a Catholic Church,
and World Association for Persons with Disabilities.
...all containing the exact same text:
-
By
flying in a V formation, the
whole flock adds
-
71%
greater flying range than if
each bird flew alone.
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So eager are people
to believe this
numerical assertion, multitudes have apparently
suspended all analytic
judgment. That indeed may be a sentence at the end of
which an exclamation
point belongs.
 erodynamics
won't generally be regarded as inspirational. That's
because aerodynamics
is mostly about drag. Drag? What the
sophisticated solver knows is
that four forces act on a body in flight: weight and
lift, thrust
and drag.
-
Weight acts upon all objects on earth.
In flight, weight
is overcome by lift. Lift is provided by wings on
aircraft and on birds.
Lift overcomes weight. In steady flight, lift
equals weight.
-
Thrust is provided by engines in
aircraft and from the flapping
of wings in birds. Drag acts upon all objects that
move through the air.
Drag tends to retard motion and must be overcome by
thrust. In steady
flight, drag equals thrust.
The ratio of lift to drag (L/D pronounced
&LOV&RDE)
is a key aerodynamic parameter. In steady flight, L/D
is equal to W/T,
the ratio of weight to thrust. For a goose flying at
migration speed, a
generous estimate of L/D = 20, which means W/T = 20. The
sophisticated
solver will regard that as a kind of 'mechanical
advantage' (like a 20-to-1
lever) and might be heard to exclaim "Hoo-hah, the goose
requires thrust
amounting to only 5% of its weight to stay
aloft."
The wing of a bird provides lift whether
it's flapping
or not. Flapping produces thrust. The shape of the
wing changes during
the downstroke to force the air underneath to flow
toward the rear. To
summarize: Thrust overcomes drag, which gets
multiplied by L/D to produce
lift, which overcomes weight. Huh?
If each goose flying in the V formation is
to add "71% greater
flying range," as alleged, 71% less drag must be
experienced "than
if each bird flew alone." We begin our
analysis with the lead
goose, the only bird in the formation not
receiving any benefit
of "up lift" from the wingtip vortex of a preceding
bird. The lead goose
necessarily faces the full force of drag as if flying
alone. The sophisticated
solver knows what the wild goose
knows --
that there are two different kinds of drag.
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'Parasite' drag is common to all
objects that move
through the air; it is the 'price' paid for motion.
Parasite drag
increases
with
speed.
-
'Induced' drag is common to all
objects that fly through
the air; it is the 'price' paid for lift.
Induced drag decreases
with speed. Counter-intuitive, that.
In order to achieve the greatest flying
range, the lead goose
is well advised to maximize L/D, which can be
accomplished only by minimizing
drag. There necessarily exists what is called 'minimum
drag speed' -- flying faster requires more thrust
to overcome parasite
drag, and flying slower requires more thrust to overcome
induced drag.
At the minimum drag speed, thrust is least, range is
most, and parasite
drag just equals induced drag.
-
Parasite drag has a common name: 'wind
resistance.' It is
easy to see that 'streamlining' reduces wind
resistance. The wild goose
is well streamlined.
-
Induced drag is determined by the
contours and dimensions
of the wing, which shapes the air flow to provide
lift. You need
a wind-tunnel and smoke trails to see that.
Nota bene,
the V formation does
nothing to reduce parasite drag. To maintain the V
formation, of
course, all the birds must fly at the same speed and
experience the same
wind resistance as if flying alone. Not so with
induced drag.
Except for the lead goose, every bird in the formation
reaps the benefit
of "up lift" from the wingtip vortex of the bird ahead.
That "up lift"
translates into a reduction only in induced drag
experienced by
the bird that receives it. The question is, how much?
 et
us make an initial -- extreme -- supposition
that each bird gets
of its lift from the wingtip vortex of the bird ahead.
In other words,
that "up lift" equals 100% of the bird's weight. The
following bird would
not
have to produce lift for itself and therefore would not
have to
overcome induced drag. It still has to flap its wings,
though. Every bird
must provide sufficient thrust to overcome parasite
drag. With an induced
drag of zero, the following bird would have to
overcome only 50% of the
drag faced by the lead goose.
Our extreme supposition was
generous to the max
and probably unrealistic. Nevertheless the widely
asserted value of
greater flying range has already been demolished,
for we must conclude
that a bird in formation will have no more than
greater
flying range than if it flew alone.
A more realistic supposition is that while
flying in the
V formation each bird gets of
its lift from the
wingtip vortex produced by the bird ahead and the
remaining 50% of its
lift provided by its own wings, which reduces its
induced drag to 50% of
that faced by the lead goose -- that plus the parasite
drag that every
bird must overcome.
Our more realistic supposition
reduces the estimated
available "up lift" such that a bird in formation will
have no more than
greater flying range than if
it flew alone.
Each bird has two wings (there's a First
Principle for you)
with which to provide sufficient lift to overcome what
we have postulated
to be half its own weight and, through flapping, to
overcome half the parasite
drag. The following bird can reap the benefit of only
one wingtip vortex
generated by the bird ahead, which cuts the available
"up lift" in half.
Taking into account the fact
that only one wingtip
vortex provides "up lift" from the bird ahead, a bird
in formation will
probably have no more than
greater flying range
than if it flew alone.
The entire motion of the wingtip vortex
must also be taken
into consideration. Since the circulating air from the
'horizontal tornado' is moving upward during only
about half of its circulation, the available uplift is
diminished accordingly.
Taking into account all these
effects, we might
reasonably conclude that a bird in formation will have
no more than
greater flying range than if it flew alone. But there
are more effects
to evaluate.
The structure of the wingtip vortex is
conical. This is a
consequence of the resistance to its inertial motion by
the surrounding
air, which slows the circulation speed with increased
distance from the
bird ahead, reducing its momentum and expanding its
radius. The "up lift"
will be adversely impacted by an unknown factor, but
probably more than
50%.
Inasmuch as the wingtip vortex
weakens behind
the bird ahead, we must adjust our estimate such that
a bird in formation
will have no more than greater
flying range
than if it flew alone.
The ability for the following bird to
capture the "up lift"
for its own benefit depends on a number of complex
variables, including
interaction if the wingtip vortex from the preceding
bird with the body
of the following bird, relative flapping phases, and
various body dimensions.
These factors -- and the need to allow for the birds to
take turns serving
as lead goose -- will further reduce the benefit of the
V formation to
each bird.
Setting aside the specious
precision in our own
numbers (four significant digits? why not five?), we
might reasonably conclude
that a bird in formation will have no more than greater
flying range than if it flew alone (not "").
To call attention to that conclusion, an
exclamation point
appears at the end of this sentence!
f
the benefit of the V formation is really only a 1-2%
greater flying range,
one might wonder why that behavior would have ever
evolved. Richard
Dawkins in Climbing Mount Improbable (W. W.
Norton 1996) provides
abundant evidence that even the smallest advantages of
a trait will assure
its perpetuation through natural selection.
Ah, but there
are other advantages
to flying in the V-formation, as described in Wikipedia.
That's what the wild goose
knows.
The wild goose knows something else,
too: not to
fly directly behind the bird ahead.
There's a double-dose of 'down-draft'
lurking back there (see diagram above) -- a real drag
for the goose and
possibly a penalty
in flying range.
Groaner Alert:
What we
see in the V formation is each individual bird avoiding
a wild goose chase.
Almost forgot... |
