Friam Digest, Vol 43, Issue 6 Formation Flight

[Peter Lissaman]

In connections with the comments about FORMATION FLIGHT


FORMATION FLIGHT  by PETER LISSAMAN

The formation flight of birds has long been of interest to natural
scientists.  Leonardo da Vinci discussed this in 1504, as did Lord Rayleigh
in 1889.  The Vee formation produces significant energy saving.  There is
no debate about this.  It has been established unequivocally theoretically,
measured in flight tests with aircraft, and also, indirectly, in the
remotely monitored pulse rate of formations of our feathered friends,
actually Brown Pelicans. The mathematics is complicated.  It relates to the
flows induced by the vortex wake behind a lifting wing.  Outboard of the
wing a large upwash is induced, proportional to the circulation on the
wing, and the wing man (?bird??), if he tucks up tight on the tip, is
flying in a strong upwash, with big drag savings.  That?s all there is to
it!  But, Ah, the Details!  As Leonardo said "God is in the Details"!   It
would be boring to go into those mathematics, except to say that the
procedure is considered well-understood and correct, but a helluva mess!
The birdies jus' do it, and could care less!

 The first paper I know of that treated the topic mathematically (and
brilliantly) was Wieselsberger in ZFM, 1914; and there has been a fairly
lively activity since then, as computers have removed the formidable and
intelligent math required, and made it possible for anyone to get results
without understanding them.  In 1969 Carl Shollenberger, my valued friend
and colleague, and I worked on this, and published the results in Science.
The paper (Lissaman & Shollenberger, Formation Flight of Birds, Science,
Vol. 168, 1970) shows the very large size of these savings.  We used the
impressive new IBM 360 computer at Caltech.  It occupied a three storey
building about the size of a four unit apartment block, and had men?s and
women?s toilets inside, as well as 12 real people who punched cards, fed
data and generally dealt with the I/O.   One picked up outputs at about
3:00 am each night.  My wife never really believed that was what kept me
up, although I did my thesis on mathematics of wing theory some years
before using that old 360!  And used the same story!   Computation is
clumsy, but more than Doktor Wieselsberger ever had!  Carl was killed a few
years later, flying in night mountain turbulence over the Sierra Madres.
It was a great loss to aviation ? he was a fine pilot and aerodynamicist.
I acknowledge his contribution fondly.  He would be glad that his work was
still used.   Recently I revisited this subject in a paper Simplified
Analytical methods for Formation Flight (Lissaman, AIAA. Jan. 2005) and
next week will give a paper  Neutral Energy Cycles for a Vehicle in
Sinusoidal and Turbulent Vertical Gusts (Lissaman & Patel, AIAA. Jan 2007)

The Science paper shows that in theVee, for tight formations, one can
almost double the range for a given energy input.  Also that there is a
stability mechanism, by which a member finds that moving ahead of the line
of the Vee requires power increases. So there?s a comfortable ?groove? to
fall into, which animals love!  One should always be skeptical of
attributing effects derived from theoretical calculations to animal
behavior, but the general consensus of ornithologists and aerodynamicists
is that this Vee formation saving is so significant, and its application so
ubiquitous, that migrating birds DO use it to extend their range.  The
paper addressed the savings for different positions in the Vee.  In line
abreast, the center birds experience twice the saving of the tip members,
but if the tip members find this hard work and fall back to take advantage
of the increased favorable downstream upwash of the vortex wakes of the
inner members, then a balancing of savings occurs. We calculated the angle
of the Vee for equipartition.   It is about the same as is observed with
migrating birds.  We also showed that it was not necessary have equal legs
of the Vee.  Provided there are at least about 6 birds on one side of the
Vee, the other leg can be almost as long as the birds choose to make it.  
Interestingly, for a linear Vee, the wing at the apex of the Vee has the
maximum saving.  In 1971 I was in communication with ornithologists in
Florida, who noted that their observations validated our Vee estimates and
indicated that the apex position was usually taken by the older and more
powerful birds.  They wondered why the more powerful members of the flight
should take the easiest jobs!  My answer was that most intelligent species
are pretty anthropomorphic!

It may be noted that the savings are not related to drafting, that is
following behind a draggy object to take advantage of its lower dynamic
pressure wake.  I am very familiar with this, and, as an automobile
aerodynamicist, have utilized this theory in race car design, and as is
obvious, the slingshot maneuver is very significant. But not in flight!  It
is, in fact, horrible to fly directly astern of another flight vehicle, as
every pilot knows.  Folks can, and do, get killed tangling with wake
vortices, as I know to my sadness, when an old friend and experienced Navy
pilot died as a consequence of following too close on final.

Peter Lissaman,  Da Vinci Ventures

Expertise is not knowing everything, but knowing what to look for.

1454 Miracerros Loop South, Santa Fe, New Mexico 87505
TEL: [phone]                        FAX: [phone]

[Hugh Trenchard]

Thank you for the interesting article - this listserv is proving to be a
wonderful resource!  Thanks also for clarifying that energy savings in bird
flight formations involve different aerodynamics than drafting, which is an
important difference from my perspective.  The key for me is still the
energy savings due to some positional zone where output is reduced, although
I may have call any universal phenomena in this respect something other than
a "drafting principle", which is what I was suggesting in my original note
on the subject.

Have you made, or do you know of any studies that involve the dynamics of
frigatebirds?  As I was noting, it appears to me that they align in vee
formations while gliding in relatively stationery positions.  I was
suggesting this constitutes another type of "drafting", where the agents do
not create the air flow by moving through it, but attempt to remain as
motionless as possible in the face of air that is already moving (ie.
sufficiently high winds).  If they are not flapping their wings, then does
this vee formation involve different aerodynamics from that of moving
pelicans or geese or others?

Also, would you agree that fundamentally a similar phenomenon is occurring
as that which happens in penguin huddles - where penguins reduce heat loss
by close formations?

In terms of the reason why stronger birds may take up easier positions in a
flight formation, I can actually offer a possible explanation on that.  It's
based on my own observations of energy savings in bicycle pelotons (group of
cyclists riding together), and a equation I've developed with Gottfried
Mayer-Kress (formula not yet published though):

PDR = (Pa - Pb / Pa) / D

PDR is peloton disintegration ratio

Pa is maximum power output of lead rider
Pb is max power output of drafting rider
D is energy savings due to drafting expressed as a percentage
Pa - Pb / Pa gives a percentage output difference

So for example, rider A can put out a max of 450w at 40km/h when riding
solo, while rider B may be capable of a max of 330w for a max speed of
30km/h when riding solo. But by drafting behind A, rider B can go 40km/h,
the same speed as A, while both are proceeding at their maximum outputs (B
saves 27 percent (Hagberg & McCole)).  However, if rider C is capable of say
470w for 41km/h, rider B would not be able to keep up.

Applying this to birds, depending on how much stronger a lead bird is than a
following bird and how much energy is actually saved by following, it's
possible that stronger birds are actually so strong that even the energy
savings by flying in the zone of greatest savings is not enough to keep up
(PDR would be > 1, using my equation).

So, what ends of happening is the strong birds ruin the flight formation -
so they end up with the luxury of sitting in, because they haven't learned
how to adjust their speed properly when they are the front to prevent
following birds from also hitting maximum and fatiguing too quickly.

Just as a note, my primary interest is with the dynamics of bicycle
pelotons - I do not hold any special expertise, but am an amateur scientist,
as it were.  I've made a number of observations of peloton dynamics, and am
still working on getting material published in the area.

Hugh Trenchard

----- Original Message -----
From: "Peter Lissaman" <[hidden email]>
To: <friam at redfish.com>
Sent: Saturday, January 06, 2007 9:47 PM
Subject: Re: [FRIAM] Friam Digest, Vol 43, Issue 6 Formation Flight

> In connections with the comments about FORMATION FLIGHT
>
>
> FORMATION FLIGHT  by PETER LISSAMAN
>
> The formation flight of birds has long been of interest to natural
> scientists.  Leonardo da Vinci discussed this in 1504, as did Lord
> Rayleigh
> in 1889.  The Vee formation produces significant energy saving.  There is
> no debate about this.  It has been established unequivocally
> theoretically,
> measured in flight tests with aircraft, and also, indirectly, in the
> remotely monitored pulse rate of formations of our feathered friends,
> actually Brown Pelicans. The mathematics is complicated.  It relates to
> the
> flows induced by the vortex wake behind a lifting wing.  Outboard of the
> wing a large upwash is induced, proportional to the circulation on the
> wing, and the wing man ("bird"?), if he tucks up tight on the tip, is
> flying in a strong upwash, with big drag savings.  That's all there is to
> it!  But, Ah, the Details!  As Leonardo said "God is in the Details"!   It
> would be boring to go into those mathematics, except to say that the
> procedure is considered well-understood and correct, but a helluva mess!
> The birdies jus' do it, and could care less!
>
> The first paper I know of that treated the topic mathematically (and
> brilliantly) was Wieselsberger in ZFM, 1914; and there has been a fairly
> lively activity since then, as computers have removed the formidable and
> intelligent math required, and made it possible for anyone to get results
> without understanding them.  In 1969 Carl Shollenberger, my valued friend
> and colleague, and I worked on this, and published the results in Science.
> The paper (Lissaman & Shollenberger, Formation Flight of Birds, Science,
> Vol. 168, 1970) shows the very large size of these savings.  We used the
> impressive new IBM 360 computer at Caltech.  It occupied a three storey
> building about the size of a four unit apartment block, and had men's and
> women's toilets inside, as well as 12 real people who punched cards, fed
> data and generally dealt with the I/O.   One picked up outputs at about
> 3:00 am each night.  My wife never really believed that was what kept me
> up, although I did my thesis on mathematics of wing theory some years
> before using that old 360!  And used the same story!   Computation is
> clumsy, but more than Doktor Wieselsberger ever had!  Carl was killed a
> few
> years later, flying in night mountain turbulence over the Sierra Madres.
> It was a great loss to aviation - he was a fine pilot and aerodynamicist.
> I acknowledge his contribution fondly.  He would be glad that his work was
> still used.   Recently I revisited this subject in a paper Simplified
> Analytical methods for Formation Flight (Lissaman, AIAA. Jan. 2005) and
> next week will give a paper  Neutral Energy Cycles for a Vehicle in
> Sinusoidal and Turbulent Vertical Gusts (Lissaman & Patel, AIAA. Jan 2007)
>
> The Science paper shows that in theVee, for tight formations, one can
> almost double the range for a given energy input.  Also that there is a
> stability mechanism, by which a member finds that moving ahead of the line
> of the Vee requires power increases. So there's a comfortable "groove" to
> fall into, which animals love!  One should always be skeptical of
> attributing effects derived from theoretical calculations to animal
> behavior, but the general consensus of ornithologists and aerodynamicists
> is that this Vee formation saving is so significant, and its application
> so
> ubiquitous, that migrating birds DO use it to extend their range.  The
> paper addressed the savings for different positions in the Vee.  In line
> abreast, the center birds experience twice the saving of the tip members,
> but if the tip members find this hard work and fall back to take advantage
> of the increased favorable downstream upwash of the vortex wakes of the
> inner members, then a balancing of savings occurs. We calculated the angle
> of the Vee for equipartition.   It is about the same as is observed with
> migrating birds.  We also showed that it was not necessary have equal legs
> of the Vee.  Provided there are at least about 6 birds on one side of the
> Vee, the other leg can be almost as long as the birds choose to make it.
> Interestingly, for a linear Vee, the wing at the apex of the Vee has the
> maximum saving.  In 1971 I was in communication with ornithologists in
> Florida, who noted that their observations validated our Vee estimates and
> indicated that the apex position was usually taken by the older and more
> powerful birds.  They wondered why the more powerful members of the flight
> should take the easiest jobs!  My answer was that most intelligent species
> are pretty anthropomorphic!
>
> It may be noted that the savings are not related to drafting, that is
> following behind a draggy object to take advantage of its lower dynamic
> pressure wake.  I am very familiar with this, and, as an automobile
> aerodynamicist, have utilized this theory in race car design, and as is
> obvious, the slingshot maneuver is very significant. But not in flight!
> It
> is, in fact, horrible to fly directly astern of another flight vehicle, as
> every pilot knows.  Folks can, and do, get killed tangling with wake
> vortices, as I know to my sadness, when an old friend and experienced Navy
> pilot died as a consequence of following too close on final.
>
> Peter Lissaman,  Da Vinci Ventures
>
> Expertise is not knowing everything, but knowing what to look for.
>
> 1454 Miracerros Loop South, Santa Fe, New Mexico 87505
> TEL: [phone]                        FAX: [phone]
>
>
>
>
>

--------------------------------------------------------------------------------


> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>