I am a lurker on this listserv and find many of the discussions here
interesting and valuable. Recently I was in Mexico and noticed a couple of
interesting complex phenomena I thought I would share with this group.
The first relates to frigatebird formations and ties in with observations of
these birds I made last year. Last year, when in Mazatlan, I noticed that
frigatebirds often hover and glide for several minutes at a time without
flapping and that they tend to glide in disorderd configurations until they
spontaneously undergo a phase change (it seems to me) when they align in vee
formations - still gliding nonetheless. These are fantastic sights to see,
since the birds seem to hang in the air in these vee formations without
passing across the sky at the relatively high speeds of geese, for example.
This year, in Cancun, I noticed frigatebirds gliding in disordered
configurations and, waiting patiently for the phase change, I was
disappointed when these changes did not occur. I wondered if I was
imagining the alignments I saw last year in Mazatlan, but fairly certain I
wasn't, I speculate why the phase changes did not occur among the birds I
saw in Cancun. Firstly it's possible the frigatebird colonies on the
Caribbean side of Mexico simply don't undergo these formations, being a
slightly different sub-species or what have you. Perhaps, but I hypothesize
that the wind speeds are the primary factor in determining whether formation
phase changes occur.
In Mazatlan last year in late Sept/early October, the wind speeds were low,
I recall. In Cancun, wind speeds were significantly higher. I suggest that
gliding in vee formations can only occur between a certain range of wind
speed - if wind speed is too low, the birds cannot glide at all; if too
high, they can glide, but they cannot align in vee formations. The critical
range allows frigate birds to draft when gliding behind another while
maintaining position, but above the range the drafting effect is too high
and the birds get "sucked" through - or tend to fall, it looked to me - the
low pressure areas and cannot hold their positions.
Drafting ordinarily has the effect of saving energy (a la cyclists in a
peloton), but if birds are gliding and already saving substantial energy by
not flapping their wings, I wondered whether any significant energy savings
benefit can be derived by aligning in vee formations while gliding. At
first I thought not, but gliding inevitably requires some energy - small
muscle coordination and positional adjustments - not as costly as flapping
wings, but some energy is required. When frigatebirds form vees, I
hypothesize there is in fact significant energy savings for those birds in
drafting positions - small muscle contractions for positional adjustments
may be reduced, and birds in these formations will expend less energy. They
would not, I suggest, align in these ways if it were not for some energy
savings benefit.
Because frigatebirds do not generate the higher air pressure behind which to
draft, such as geese do, or cyclists do, or fish in water do by propelling
themselves through the medium (air or water), I suggest this form of energy
savings constitutes a third type of "drafting". The other is energy
reduction by huddling, such as penguins undergo. So I suggest three types
of drafting occurrences:
I Occurs when system components generate effective air or
liquid pressure as they propel themselves through the medium; eg. cyclist
pelotons, fish schools, geese in vees;
II Occurs when system components remain stationery and air or
liquid pressure is generated externally; eg frigatebirds in vees while
gliding and remaining more or less positionally stable, and possibly some
types of fish (here I suggest this may occur in fish swimming upstream, such
as salmon, which may hold themselves in a stationery position against the
flow of the water - I haven't specifically observed any interesting drafting
formations as a result, although I have watched salmon swim upstream and
speculate drafting formations do occur)
III Occurs when system components remain stationery and
environment temperature drops; eg. penguin huddles
Type I exhibit phase changes from disordered states to ordered states and
back again through hysteresis loops. For cyclists, when peloton speeds are
higher than a critical speed/drafting threshold, disorder in the peloton
occurs. In a peloton, density is generally higher at low speeds and density
decreases as speeds increase. At a relatively high threshold speed, a
peloton loses cohesiveness entirely. To resume cohesion, peloton speeds
must fall to a lower threshold to resume cohesive formations (I've observed
and documented this). The loop is clockwise (speed on Y axis, density/order
on X) , but is the inverse of vehicle traffic hysteresis, for example, where
density increases as speed decreases (note that drafting is not a factor in
traffic).
For frigatebirds, because order increases as windspeed increases to a
threshold range, above which disorder occurs, wind speeds must only drop to
within the critical range for order to occur again. As a result the
hysteresis loop may not exist or is not as evident. I tentatively speculate
this windspeed range is approximately equivalent to the magnitude of
drafting benefit derived when birds are in drafting formations; similarly
the height of the hysteresis loop in drafting cyclists is related to the
drafting benefit derived (but may not precisely match it).
So drafting parameter seems to represent a constant that manifests itself in
related but different ways. For example, in Type 1 situations, drafting
parameter indicates the magnitude of the hysteresis loop; in Type II where
there is no hysteresis, drafting parameter indicates the magnitude of the
critical range of speeds within which certain formations occur. Drafting
parameter is thus also a general principle underlying the self-organized
complex behaviour of a number of different systems.
For Type III (penguin huddles), density/order increases as temperature drops
(requiring greater energy output to remain warm, so a decrease in
temperature is equivalent to an increase in speed in Type I situations);
density/order decreases as temperature increases to some threshold, after
which there is no huddle cohesion. Presumably at some very cold temperature
the huddle cannot generate enough heat and disintegrates by penguins
freezing to death. In the direction of temperature increase, the hysteresis
loop occurs when disorder occurs at a critical temperature, but must fall to
some lower threshold temperature for the huddle to occur again.
In any event there is a lot more analysis to be made, and I have more to say
even now, but here are a few observations. Basically, my point is that
through my frigatebird observations, I've identified a third type of
drafting situation. I had already identified the peloton (which is obvious
and well documented) and huddle situations (which is not as obvious and not
well documented). _____________
The second, slightly less rigourous observation I made when in Cancun was a
clustering effect among cabs. In Cancun, and likely many parts of Mexico,
all cabs are required to be of the same colors, so they are all easy to
spot. There are also many, many cabs in Cancun - it appears about one in
six vehicles is a taxi.
On the roads, it appeared to me that frequently cab clusters, or several
cabs near each other, would be driving within two degrees of each other,
often within one degree. One explanation is that they often originate in
the same location, many waiting at high person-density locations like the
airport, the bus station, etc. However, I am not sure this explains the
clustering on the roads, as cabs leaving from high density locations would
not leave simultaneously when fares are widely distributed in time; they
also do not have the same destinations. So, clustering must be due to
something else, I think.
Firstly, cab drivers tend to drive faster than the rest of the traffic,
especially when they have a fare on board. I am wondering if their fast
driving and deft abilities at weaving in and out of traffic allows them to
agglomerate at stop lights. As traffic approaches stop lights, the slower
driving traffic still leaves enough space for faster traffic further away
from the light to slip through and make up a few spaces, even as traffic
closest to the stop lights slow down and increase density. After a few such
lights, faster traffic "sifts" through to the front, and ends up at the
front. This is just an idea, and no doubt there are a number of problems
with it (for example if cabs also tend to go through yellow and red lights,
reducing agglomeration). Nonetheless, if the phenomenon is real - and I
observed it to occur more often than just chance would seem to explain -
then there must be a reason for it.
In any event, I would be interested in any input others may have about both
of these subjects.
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