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Abstract

The organized flight of birds is one of the most easily observed, yet challenging to study, phenomena in biology. Birds that fly in organized groups generally do so in one of two fashions: Line formations and Cluster formations. The former groups are typical of large birds such as waterfowl, where birds fly arranged in single lines, often joined together. The scientific questions about these groups usually involve potential adaptive functions, such as why geese fly in a V. Cluster formations are typically made up of large numbers of smaller birds such as pigeons or starlings flying in more irregular arrangements that have a strong three-dimensional character. The groups are defined by synchronized and apparently simultaneous rapid changes in direction. Scientific questions about these groups are usually concerned with mechanism such as how synchrony is achieved. Although field observations about the phenomenon date to the origins of natural history, experimental studies did not begin until the 1970s. Early experimenters and theoreticians were primarily biologists, but more recently aeronautical engineers, mathematicians, computer scientists and, currently, physicists have been attracted to the study of organized flight. Computer modelling has recently generated striking visual representations of organized flight and a number of hypotheses about its functions and mechanisms, but the ability to test these hypotheses lags behind the capacity to generate them. We suggest that a multi disciplinary approach to the phenomenon will be necessary to resolve apparently conflicting current hypotheses.
Accepted Author Manuscript submitted to Elsevier Science 16 June 2009
OR G A N I Z E D FL IGHT IN BI R D S
Iztok Lebar Bajec
Faculty of Computer and Information Science, University of Ljubljana, Slovenia
Frank H. Heppner
Department of Biological Sciences, University of Rhode Island
Correspondence to:
Iztok Lebar Bajec (ilb@fri.uni-lj.si)
Faculty of Computer and Information Science, University of Ljubljana, Tržaška cesta 25,
1000 Ljubljana, Slovenia
Frank H. Heppner (birdman@uri.edu)
Department of Biological Sciences, University of Rhode Island, 102 Morrill Hall,
Kingston, RI 02881-0816, USA
Document Properties:
50 pages
11,641 words (14,927 including References and Figures)
NOTICE: this is the author's version of a work that was accepted for publication in
Animal Behaviour. Changes resulting from the publishing process, such as peer
review, editing, corrections, structural formatting, and other quality control
mechanisms may not be reflected in this document. Changes may have been made
to this work since it was submitted for publication. A definitive version was
subsequently published in Animal Behaviour, doi: 10.1016/j.anbehav.2009.07.007
Lebar Bajec, I. & Heppner, F. H. 2009. Organized flight in birds. Animal Behaviour, 78(4), 777789.
doi: 10.1016/j.anbehav.2009.07.007. © 2009 Published by Elsevier Ltd.
Organized Flight in Birds Abstract 2
ABSTRACT
The organized flight of birds is one of the most easily observed, yet challenging to study, 1
phenomena in biology. Birds that fly in organized groups generally do so in one of two fashions: 2
Line formations and Cluster formations. The former groups are typically demonstrated by large 3
birds like waterfowl, where birds fly arranged in single lines, often joined together. The 4
scientific questions about these groups usually involve potential adaptive functions, such as why 5
do geese fly in a V? The latter, Cluster formations, are typically made up of large numbers of 6
smaller birds like pigeons or blackbirds flying in more irregular arrangements that have a 7
strong three dimensional character. The groups are defined by synchronized and apparently 8
simultaneous rapid changes in direction. Scientific questions about these groups are usually 9
concerned with mechanism; how is synchrony achieved? Although field observations about the 10
phenomenon date to the origins of natural history, experimental studies did not begin until the 11
1970s. Early experimenters and theoreticians were primarily biologists, but more recently 12
aeronautical engineers, mathematicians, computer scientists, and currently, physicists have 13
been attracted to the study of organized flight. Computer modelling of organized flight has 14
recently generated striking visual representations of organized flight and a number of 15
hypotheses about the functions and mechanisms of organized flight, but the ability to test these 16
hypotheses lags behind the capacity to generate them. It is suggested that a multiple-17
disciplinary approach to the phenomenon will be necessary to resolve apparently conflicting 18
current hypotheses. 19
Keywords 20
animat; bird aerodynamics; bird flight; bird flocking; boid; cluster formations; Canada Goose; 21
Branta Canadensis; European Starling; Sternus vulgaris; flight formations; flock simulations; 22
flocking simulations; line formations; V formation 23
Organized Flight in Birds Introduction 3
The orderly aerial manoeuvres of birds have fascinated and mystified observers since the 24
beginnings of written natural history 2,000 years ago, when Pliny suggested that geese ...travel 25
in a pointed formation like fast galleys, so cleaving the air more easily than if they drove at it 26
with a straight front (Rackham 1933). Why do geese fly in a V, and how do pigeons all seem to 27
be able to take off and turn at once? The study of these phenomena offers an encapsulated 28
model of the development of knowledge of other behaviours, starting with anecdotal 29
descriptions and speculation, measured observations of increasing precision, formation of 30
testable hypotheses, and then tests of these hypotheses. In the case of the study of organized 31
flight in birds, the first phase began at about the beginning of the twentieth century, the second 32
and third in the 1970s and the fourth in the mid 1980s. The study of bird organized flight also 33
offers a good demonstration of Kuhns (1962) suggestion that science advances in saltatory 34
fashion, each revolution being prompted by a new technique or apparatus that allows old data 35
to be looked at in a new way. 36
The early investigators of organized flight were, with a few notable exceptions, biologists. In 37
the 1970s, aeronautical engineers started to be attracted to the phenomenon, followed by 38
computer scientists in the 1980s, and physicists and mathematicians in the 1990s. These later 39
investigators have been primarily interested in modelling the behaviour. The fraction of active 40
investigators with a biological background has steadily decreased over the years. We will try to 41
demonstrate that as the elegance of models has increased, so has their distance from behaviour 42
in the field, and that future progress in the area will depend on collaborations between 43
physicists, mathematicians, computer scientists and biologists rather than specialists working 44
alone. 45
THE ERA OF ANECDOTE AND SPECULATION 46
Several ornithologists of the 1930s made visual field observations that would later be very 47
provocative to experimentalists and theoreticians. Nichols (1931) noted that in turning and 48
wheeling pigeon, Columba livia, flocks, the position of the birds at the head of a turning flock 49
Organized Flight in Birds The Era of Anecdote and Speculation 4
would be exchanged with birds at the side after the completion of a turn; there did not appear to 50
be consistent leadership in such flocks. He speculated that this behaviour might be the result of 51
faster birds in the front of the formation moving ahead of the flock, then turning back to rejoin. 52
The visual stimulus provided by the turnaround might provide a signal for the rest of the birds 53
to turn, apparently simultaneously. He suggested that a change in direction was related to a 54
change of positional leadership. 55
Selous (1931) made a 30-year series of meticulous visual observations on various species of 56
birds flying in organized flocks, and was convinced that within the limits of unassisted human 57
vision, there were occasions when birds rose from the ground, or made turns simultaneously. 58
He concluded that there could be only two possible explanations for such a phenomenon; 59
disturbance from outside the flock, say the sight of a predator, which would be instantaneously 60
received by all birds in the flock, and would be reacted to in identical manner, or an undefined 61
quality he called thought transference, or what we might call today telepathy. 62
Selous appeared convinced that there were at least some occasions when groups of birds 63
would rise from the ground, apparently spontaneously, with no discernible source of outside 64
disturbance. He also noted in contrast that there were times when a flock on the ground would 65
be indifferent to the rapid approach of an aerial predator, as when members of a flotilla of 66
Eurasian Coots, Fulica atra, leisurely swam away as a Great Black-backed Gull, Larus marinus, 67
made a low pass over their group. Penrose (1949) made a similar observation when he dove 68
from above toward a large European Starling, Sternus vulgaris, flock in a sailplane. 69
Selous also noted that flocks on the ground would sometimes take to the air in a stepwise 70
fashion. Individuals or small groups of Black-headed Gulls, Larus ridibundus, would take flight 71
without any discernible effect on neighbours, and then with no obvious temporal relationship to 72
previous small group departures, the entire remainder of the flock, hundreds of birds, would 73
take flight simultaneously. 74
Thought transference had a different standing in the scientific community in Selous time 75
than it does today, and it is not surprising that, for want of a better explanation, a careful 76
Organized Flight in Birds The Era of Anecdote and Speculation 5
observer like Selous might be led to something as heterodox as telepathy to explain an 77
otherwise inexplicable phenomenon. Rhine (1983) had started reporting the results of 78
parapsychology experiments using conventional experimental design in 1927, and England, 79
where Selous made his observations was a centre of interest in paranormal phenomena. Selous 80
never explored what the nature of thought transference might be. 81
Gerard (1943) was one of the first individuals to try to quantify turning behaviour in a flock. 82
Whilst pacing a group of approximately 100 unidentified birds in a car being driven at 35 mph 83
(60 km/h), he observed that the entire flock turned left in a flanking movement, rather than a 84
column movement, in military parlance. In a flanking movement all individuals turn at once 85
upon the signal to do so, rather than advancing to a defined point and then turning. He 86
speculated that no bird advanced more than a bodys length beyond any other bird before 87
turning, by his calculation within 5 ms of any other bird. Assuming a minimum reaction time of 88
100 ms, he proposed that any coordinating signal must have been acted on with great constancy 89
by receiving individuals. Gerards own vision must have been remarkable to be able to make 90
this observation while driving a car, but his estimate of probable reaction time was very close to 91
Pomeroy & Heppners (1977) laboratory study results of startle reaction times in the European 92
Starling of 70 ms. 93
Much of the early work on flight flocking was devoted to considerations of the biological 94
utility of flocking, from an ecological or behavioural standpoint, rather than the perspective of 95
organizing principles or mechanisms. Beer (1958) questioned whether large groupings of birds 96
had any distinctive utility, and were merely haphazard organizations. Vine (1971), on the 97
other hand, suggested that a circular grouping provided the best predator avoidance strategy 98
against visual predators. Emlen (1952) looked at flocks from the ethological perspective of the 99
times, and suggested that both flocking itself, and the structure of the flock resulted from the 100
interplay of attractive and repulsive behavioural forces. 101
One of the annoyances that has persisted over the years for those studying flocks is an 102
etymological one; there has been no consistency in the literature in terms of the definition of 103
Organized Flight in Birds The Era of Anecdote and Speculation 6
flock and categories of same. The difficulty is not a trivial one. One author might be describing 104
the properties of a class of behaviours that is quite different than those studied by a different 105
investigator, but both will use the same term. 106
For example, Emlen (1952, p. 160) described a flock as any aggregation of homogeneous 107
individuals, regardless of size or density. This definition immediately presents difficulties, 108
because there are very common aerial groupings, such as mixed blackbird groups, composed of 109
different species. Beers (1958, p. 78) definition of a flock was ...two or more birds which 110
associate with each other due to innate gregarious tendencies. This definition breaks down in 111
the face of more recent flocking studies, like Reynolds (1987), which suggest that coordinated 112
flocking may be the product not simply of gregariousness, but extremely simple behavioural 113
rules followed by each bird in the group. 114
Heppner (1974) developed a taxonomy of airborne bird flocks. The primary dichotomy in this 115
scheme was between Flight Aggregations, which are unorganized groups of flying birds 116
gathered in an area for a common purpose, such as gulls circling about a fishing trawler, and 117
Flight Flocks, which were organized groups of flying birds coordinated in one or more aspects 118
of flight, such as taking off, turning, landing, etc. However, these distinctions seem not to have 119
been universally adopted in the literature; one regularly sees the term aggregation used to 120
describe what Heppner would have called a flight flock. 121
Heppners second order division of Flight Flocks has demonstrated some persistence and 122
consistency in the literature. He differentiated flight flocks into Line Formations and Cluster 123
Formations (Fig. 1). Line formations are demonstrated by relatively large birds that fly in 124
regular lines or queues, such as geese, cormorants, or ducks. Cluster formations have a three 125
dimensional structure like a sphere, and are typically seen in smaller birds like pigeons, 126
starlings, and smaller shorebirds. Interestingly, line flying birds like geese may sometimes be 127
seen in a cluster, but cluster flying birds like starlings are rarely, if ever, seen flying in single 128
lines. 129
Organized Flight in Birds The Era of Anecdote and Speculation 7
The categories of biological questions that are raised by each of these formations are quite 130
different. Typically, how questions are raised about cluster flocks. Do the birds really turn all at 131
once? How can they achieve synchrony in taking off and landing? How do they decide when to 132
turn, and in what direction? Why questions are more characteristic of line flying birds. What 133
might be the biological advantage of flying in this configuration? Are there energy savings to be 134
had? Does the formation shape facilitate communication? A broad question that might apply to 135
both groups is whether there is a general advantage to flying in groups, as opposed to solitary 136
flight? 137
A literature search suggests that investigators recognize that the two formation categories 138
may represent quite different biological issues. Early key papers on line formations tend to be 139
cited through generations of papers on line formations, but not cluster formation studies, and 140
vice versa. For this review, we recognize the difference between these lines of investigation, and 141
will treat them separately.142
LINE FORMATIONS 143
Line flying birds typically fly in staggered, or echelon, formations rather than in straight lines 144
nose-to-tail. If two such formations are joined at an apex at the front of the formation, we have a 145
V or a J, its asymmetric variant. Franzisket (1951), von Holst (1952) and Hochbaum (1955) 146
suggested that close formation flight might provide the advantage of a turbulence free zone 147
behind a bird ahead, but that would seem to apply only if the birds flew immediately behind the 148
bird in front, like race cars, which they rarely do. 149
Two competing, but not necessarily mutually exclusive, hypotheses have been advanced to 150
explain the functionality of staggered line formations (most of the papers to be subsequently 151
cited here refer to V formations and their properties, but Gould & Heppner [1974] found in a 152
study of 104 Canada Goose, Branta canadensis, formations that Vs and Js together were less 153
common than single staggered lines, or echelons. Additionally, OMalley & Evans [1982a, b] 154
found that White Pelicans, Pelecanus erythrorhynchos, flying in line formations only flew in Vs 155
Organized Flight in Birds Line Formations 8
10% of the time). Wieselsberger (1914), an aerodynamacist, was the first to suggest an 156
aerodynamic advantage for line formation flight. He proposed that a V partitioned drag equally 157
between the two legs of the flight, and that birds flying to the left or right of a bird in front could 158
recapture energy lost to an upwash generated off the wingtips of the preceding bird. The 159
alternate, behavioural view suggests that social and perceptual factors have guided adoption of 160
staggered formations. Hamilton (1967) suggested that flying in staggered lines permitted the 161
optimum combination of visibility of neighbours, and a clear visual field to the front. Heppner 162
(1974) suggested that the fixed position of the eyes in the heads of line-flying birds might make 163
a staggered formation advantageous for keeping the image of an adjacent bird on the visual axis 164
of a given birds eyes. However, Heppner et al. (1985) found that the angle between the legs of a 165
V formation of Canada Geese that would place the image of a leading bird on the visual axis of 166
the eyes of a following bird (128°) was considerably more obtuse than the measured V-angles of 167
V-formation flying birds in previous studies (Gould & Heppner 1974; Williams et al. 1976; 168
O’Malley & Evans 1982a). They also noted that although Canada Geese have a limited amount of 169
binocular vision to the front, despite having eyes located on the sides of their heads, they also 170
have a blind cone in back of them of 29° on either side of the midline. Thus, a V angle of 58° or 171
greater would enable every bird in the formation to see every other bird, even those following 172
behind. 173
Warnke (1984) offered a third hypothesis that, judging by the number of subsequent 174
citations, seems not to have generated much enthusiasm in the V formation community. He 175
suggested that the V formation could be explained by the interaction of electrostatic fields 176
generated by flapping flight. He did not discuss how birds would be able to detect such fields, 177
nor did he explore the advantage that might accrue to a bird by basing its proximity to a 178
neighbour on the basis of these fields. There was much interest in the biological effects of 179
electromagnetic fields in the 1970s and 1980s; Heppner & Haffner (1974) suggested that 180
coordinated cluster flocks might be explained by signals sent by a leader to all birds in a flock by 181
means of a hypothetical radiated electromagnetic field. Interestingly, Hill (1972) described a 182
Organized Flight in Birds Line Formations 9
device he patented that was a wing-levelling autopilot for model aircraft that operated by the 183
differential in electrostatic fields between wingtips of a moving model airplane, so Warnkes 184
idea was not totally implausible. 185
There have been more papers addressing the aerodynamic hypothesis of staggered flight than 186
other hypotheses, and a bit of aerodynamic theory here will make the subsequent references 187
more intelligible. For a bird to fly by use of a wing requires a relative wind; a passage of air 188
over the wing. If the front of the wing is tilted up slightly relative to the wind, the relative wind 189
is deflected downward. The result is a positive force on the underside of the wing, Newtonian 190
lift (Fig. 2). Additionally, airplane wings are typically constructed so that the top of the wing is 191
curved and air moves faster over the top of the wing, creating a negative pressure on the top of 192
the wing; Bernoulli lift. In still air, we must generate the relative wind by moving the aircraft 193
forward. To do so, we must have a force called thrust, generated, for example, by a propellor. In 194
general, the faster the aircraft goes, the more lift is generated by the wing. Unfortunately, as the 195
aircraft accelerates, drag is produced, at least in part by friction between the air and the 196
surface. One type of drag, induced drag, is especially germane to bird flight. Lift is, partly, 197
created by the angle with which the wing meets the air (referred to also as the angle of attack). 198
Up to a limit, the steeper the angle, the greater the liftbut also, the greater is the induced drag, 199
which is produced as a by-product of lift. Compared to airplanes, birds are typically low-speed 200
aircraft whose wings produce a lot of induced drag. 201
The inner part of a birds wing provides most of the lift, the outer part, by a kind of rowing 202
action, provides the thrust. As air streams over a wing generating lift, it tends to form vortices, 203
which typically stream off the wing as tip vortices, essentially horizontal tornadoes. These tip 204
vortices have a rising and falling component, and in an airplane, may carry sufficient energy to 205
upset a smaller aircraft following a larger one in for a landing. It is this energy, which essentially 206
represents a cost of flight using wings, that the aerodynamic hypothesis of V formation suggests 207
might be partially recaptured by a following bird whose own wingtip was located in the upward 208
rising part of the tip vortex, or upwash, streaming off the wing of the preceding bird (Fig. 3). The 209
Organized Flight in Birds Line Formations 10
diameter of the vortex increases with distance from the producing birds wingtip, and tends to 210
dissipate with increasing distance. The placement of a following birds wingtip in relationship to 211
the vortex from a preceding birds wingtip should, in theory, affect how much energy is 212
recaptured by the following bird. To recapture tip vortex energy from a preceding bird, a 213
following bird would have to be positioned to the left or right of a preceding bird, suggesting 214
that a V (or at least a staggered, or echelon) formation would be advantageous for birds flying in 215
a group. 216
Lissaman & Schollenberger (1970) produced the first quantitative suggestion, based on 217
aerodynamic theory, of exactly how much energy might be saved by a group of birds flying in a 218
V formation. They proposed that a group of 25 (unspecified species) birds flying in a V would 219
have 71 percent more range than a single bird. Their optimum V angle appeared to be about 220
120° between the legs of the V. For later investigators, this paper was both stimulating and 221
frustrating because they did not present the calculations and formulae used to arrive at their 222
conclusions, ignored the quantitative effects of flapping rather than fixed wing flight, and did not 223
apparently consider the difference between air flowing over a smooth metal surface and a 224
feathered wing nor the aerodynamic scaling effects of small birds flying at low speeds compared 225
to aircraft. Nonetheless, this paper provided a target for experimental and quantitative 226
observational work. 227
Haffner (1977) flew Budgerigars, Melopsittacus undulatus, in a wind tunnel and used a smoke 228
stream to visualize the airflow over the birds wing. He concluded that flapping wing flight is 229
aerodynamically complex, and that calculations of energy saving for the V formation using fixed 230
wing models were oversimplified, and probably overgenerous. Using Cones (1968) theoretical 231
studies on flapping wing flight and his own experimental work, he concluded that potential 232
energy saving of V formation flight compared to solitary flight was a much smaller maximum of 233
22%. 234
Willis et al. (2007) examined the theoretical energy savings in formation flight with respect to 235
basic positioning and wing beat phase relationships between a preceding bird and a following 236
Organized Flight in Birds Line Formations 11
bird. Nachtigall (1970) found a phase synchrony in a field study of wing beats in Canada Goose 237
formations, but Gould (1972), in a similar study, failed to do so. Willis et al.s (2007) study is 238
preliminary as they do not consider the optimal formation shape or detailed flapping kinematics 239
or wing shapes. Nonetheless, their results suggest that optimal flapping phase synchrony 240
accounts for up to 20% of induced flight power savings, but that precision phase locking is not 241
required for energy savings to occur. They also observed that ideally, the following bird would 242
not be vertically elevated above or below the lead birds wake if flapping started in phase. If 243
flapping is not in phase, however, it may be advantageous to take on a vertical displacement 244
relative to the preceding bird to most effectively capture its strongest upwash regions. They 245
suggest that vertical displacements in nature probably do not happen for aerodynamic benefit, 246
as for that to occur precision flight dynamics and sensing would be required. 247
Determination of the distance between birds, and the angle of the legs of the V would be 248
necessary to test V formation hypotheses. Gould & Heppner (1974) performed the first field 249
measurement of both parameters in Canada Geese using projective geometry and still 250
photography. They reported a mean angle between the legs of the V ±SD of 34±6°, N=5, with a 251
mean distance between bird bodies ±SD of 4.1±0.8 m, N=3 and a mean flock size ±SD of 18±12 252
birds, N=5. Two years later, Williams et al. (1976) examined V angles in Canada Goose 253
formations using a radar technique. They found a range of 38−124° in the feeding flights they 254
recorded. Further, they noted that the angle in a single formation varied from 5−40° between 255
successive sweeps of the radar beam (duration of sweep not reported). Both groups of authors 256
used their respective photographic and radar techniques on the same flocks of birds in 1975, 257
and found no significant difference between the two. 258
Higdon & Corrsin (1978) refined Lissaman & Schollenbergers (1970) hypothesis by 259
considering the effects of flying in three-dimensional fashion, i.e. in a cluster, like starlings. As 260
one might suspect, the physics is considerably more complex, but they suggested that it was 261
aerodynamically disadvantageous to fly directly behind another bird, and that a tall, narrow 262
cluster flock (such as is often seen in mixed blackbird flocks) is aerodynamically 263
Organized Flight in Birds Line Formations 12
disadvantageous compared to solitary flight. May (1979) also re-examined Lissaman & 264
Schollenbergers (1970) suggestions, and concluded that the aerodynamic advantage of line 265
flight in large birds was slight, perhaps as little as 10% compared to solitary flight. 266
Badgerow & Hainsworth (1981) re-examined Gould & Heppners (1974) data on distances 267
between Canada Geese to obtain wingtip spacing, a variable they felt was more appropriate 268
than distance between body centres in testing the aerodynamic hypothesis of V formation 269
flight. When they did this, they found a number of birds had wingtips that overlapped the 270
position of the wingtips of a bird ahead, a problematic situation for producing an energy 271
advantage in Lissaman & Schollenbergers (1970) hypothesis. In contrast to Lissaman & 272
Schollenbergers (1970) predicted maximum range increase of 71% for V formation flight, 273
Badgerow & Hainsworths (1981) revision predicted a maximum increase of 51%, with a range 274
increase of 223% for the birds in a selected Gould & Heppner (1974) flock. Hainsworth (1987) 275
later provided an excellent description of the modified projective geometry technique he and 276
Badgerow used in the study above for examination of goose flocks, and applied it to his own 277
photographs of Canada Goose flocks. He noted that birds frequently shifted positions laterally 278
relative to the bird ahead, although the basic energy saving model of Lissaman & Schollenberger 279
(1970) predicted that there was an optimum position for energy saving. Using their model, he 280
concluded that the goose flocks he filmed were only enjoying a 36% energy advantage over 281
solitary flight, about half of the Lissaman & Schollenberger (1970) model. He cautioned against 282
a simplistic engineering model for explaining in toto a behaviour that might be highly variable, 283
depending on circumstance. 284
OMalley & Evans (1982a, b) broadened the examination of line formation flight by studying 285
line flight in White Pelicans, Pelecanus erythrorhynchos. They used a variant of Gould & 286
Heppners (1974) projective geometry technique to measure angles of Vs and Js, and distance 287
between birds, with much larger sample sizes (45 flocks) than in the Gould & Heppner (1974) 288
study. The angles ranged from 24−122°, with a mean ±SD of 67±8°, N=12, for V formations, and 289
70±5°, N=33, for J formations. As in the earlier goose formation measurements, there was wide 290
Organized Flight in Birds Line Formations 13
variation in the measured angles, and the means were well below Lissaman & Schollenbergers 291
(1970) predicted optimum angle of 120° for maximum aerodynamic advantage. Again, as in the 292
goose studies, V formations were less common than single line formations. 293
Hummel (1983), an aerodynamacist, further refined the theoretical aspects of formation flight 294
by considering wing shape, homogeneous vs. non-homogeneous spacing, size of bird, flight 295
speed, and straight vs. curved lines. He concluded that, under optimum conditions of the above, 296
energy savings for formation flight were possible due to aerodynamic considerations, but the 297
wide variance seen in the arrangements of flocks in the field suggested that aerodynamics might 298
not be the only factor in formation flight. 299
Badgerow (1988) took a fresh look at the aerodynamic and visual hypotheses, and tried to 300
organize the scant real field data in such a way that they could be subject to test. He suggested 301
that if aerodynamic advantage was the primary driver of line flight, there should be a certain 302
geometric relationship between birds in a formation, but if visual considerations were 303
paramount, there should be a different configuration. Unfortunately, the variation in data 304
between flocks was sufficiently large to prohibit a clear distinction between the hypotheses, 305
although Badgerow felt that there was a non-trivial (about 10%) energetic advantage of 306
formation flight over solo flight. 307
Cutts & Speakman (1994) also found wide variation in placement of individuals in their study 308
of formation flight of Pink-footed Geese, Anser brachyrhynchus. They photographed 54 skeins 309
from directly beneath, simplifying the extraction of distances and angles. They found that large 310
numbers of birds flew outboard of the position predicted by theory to maximize aerodynamic 311
savings, resulting in a postulated mean energy saving of 14%. Further, after a discussion of 312
optimum flight speed for optimum range, they suggested that if the birds in their sample flew at 313
a speed that would maximize their range, the savings would drop to 2% of that predicted by 314
Lissaman & Schollenberger (1970). Speakman & Banks (1998) later used the same technique to 315
photograph 25 formations of Greylag Geese, Anser anser. They found a great deal of variation in 316
positioning and that only 17% of birds flew in the predicted optimum position for aerodynamic 317
Organized Flight in Birds Line Formations 14
savings. They suggested, using the same assumptions as the Cutts & Speakman (1994) paper, 318
that the mean saving in induced power was 27%, and the reduction in total flight costs was 319
59% of the whole. Hainsworth (1988) also found in film studies of Brown Pelicans, Pelicanus 320
occidentális, that there was wide variation in wingtip spacing, and that there was no evidence 321
that the birds spaced to optimize possible aerodynamic effects. 322
Shortly after the turn of the new century, several papers appeared with a decidedly more 323
mathematical bent than had been seen previously, from investigators with backgrounds in the 324
control of multiple autonomous unmanned aerial vehicles, like the Predator, and Global Hawk. 325
Seiler et al. (2002) noted the wide variation in distances and angles reported in bird formations 326
in previous field studies, and in a rather puzzling table suggested that the average number of 327
birds in a V formation appeared to be small, typically under 10 birds. Other studies (Gould & 328
Heppner 1974; Hainsworth 1987) had reported mean V formation sizes closer to 20 birds. 329
Seiler et al. (2002, p. 122) noted that, on theoretical grounds, maintenance of a specific spacing 330
and angular relationship between a leader, and following autonomous robotic vehicles is a 331
daunting task, and that errors in spacing rapidly multiply with each subsequent vehicle, so 332
much so that ‘—flying in close formation is not possible (italics added) with information only 333
about the predecessors. In other words, if a vehicle attempts to maintain position in the 334
formation only by maintaining position with its immediate predecessor in line, the formation 335
itself will quickly break down. However, they proposed two potential resolutions: 336
1. the formations should be very small, and/or 337
2. leader positional information should be simultaneously communicated to all 338
members of the formation; in other words, a trailing bird should maintain its position 339
with respect to the leader, rather than its immediate predecessors. 340
The same team expanded this idea, and explored the concept of string instability, the 341
phenomenon where the trailing vehicle in a line has such difficulty tracking predecessors that it 342
oscillates in position to such a degree that it eventually cannot stay with the formation (Seiler 343
et al. 2003). In particular, they explored the difficulties of maintaining lateral positioning in a 344
Organized Flight in Birds Line Formations 15
line formation. They proposed that the difficulty in maintenance of position increases markedly 345
with position back from the leader; the positional error (assuming the birds were trying to 346
maintain an optimum position for either aerodynamic or visual reasons) of the number four 347
bird in relation to the lead bird would be twice as much as that of the number two bird. Seiler 348
et al. (2003, p. 279) concluded by suggesting ‘—that (avian) formation flight is inherently (italics 349
added) difficult. A glance overhead at a winter waterfowl assembly area displaying a panorama 350
of dozens of birds flying in each of hundreds of separate line flocks suggests a variant of the 351
catch phrase of the late Spanish ventriloquist, Señor Wences, Difficult for me; easy for you. 352
Seiler et al. (2003) suggested that their hypothesis could be tested by examining whether birds 353
further back in the formation have a greater variation in wingtip spacing than those closer to 354
the leader. This hypothesis, of course, rests on the prior hypothesis that there is an optimum 355
spacing that the birds are attempting to maintain. 356
Weimerskirch et al. (2001) have provided the best (and to date) most realistic attempt to 357
resolve in the field whether there is an energy advantage to line formation flight. They trained a 358
flock of eight Great White Pelicans, Pelecanus onocrotalus, to fly in formation behind a 359
motorboat. Energy consumption during flight was not recorded directly, but inferred from heart 360
rate data. They measured heart rate from selected individuals in the flock, and from a solitary 361
bird flying under the same conditions. Heart rates of the birds in formation were 1115% lower 362
than that of the solitary bird. From this, they concluded that they had provided empirical 363
evidence of an aerodynamic advantage to formation flight, in about the same fractional 364
proportion as the heart rate difference. 365
An alternate interpretation of the data is possible, especially given the relatively scant 366
proposed saving compared to most aerodynamic theory-based predictions. Pelicans are highly 367
social animals and the experience of flying solo might have been stressful compared to normal 368
social flight. Späni et al. (2003) found that laboratory mice housed individually had a heart rate 369
4% higher than that of mice housed in pairs. So the effect seen may have been due, at least in 370
part, to social stress rather than aerodynamic advantage. 371
Organized Flight in Birds Line Formations 16
Modelling, Simulations and Application 372
The development of very powerful, relatively inexpensive computers in the late 1990s 373
permitted a more sophisticated mathematical analysis of V formations. The first to report a 374
model producing V formations was Flake (2000, pp. 270−275), who extended Reynolds (1987) 375
model (to be discussed later) with an additional rule; each artificial bird, or animat (Wilson 376
1985; Watts 1998), attempted to move laterally away from any animat that blocked its view to 377
the front, and with that achieved V-formation flocks. 378
Assuming that there is, in fact, a reduction in collective aerodynamic drag experienced by 379
members of a flock in a V, Dimock & Selig (2003) went a step further and developed a computer 380
simulation that actually modelled the induced drag. They extended Reynolds (1987) model to 381
detect potential drag reductions by adding a rule by which each animat acted to reduce the 382
drag, and observed how the animats self-organized themselves. There was an evolutionary 383
component to this studythey used genetic algorithms to evolve the models parameters and as 384
each animat acted so as to reduce its own drag, the collective result was that the drag reduction 385
of the flock as a whole was maximized. Limiting the utility of the model, their induced drag 386
calculations were based on a rigid wing just as Lissaman & Schollenbergers (1970). In relatively 387
short simulations, their model correctly penalized collisions, and ultimately produced 388
rigid/stable flocks of perfect Vs. Using the same evolutionary theme, Andersson & Wallander 389
(2004) suggested that kin selection might explain why there appeared to be so much variation 390
in V formation structure. Most aerodynamic advantage studies propose that the lead position is 391
to some degree less advantageous than following positions, but Andersson & Wallander (2004) 392
suggested that if the flock is composed of kin, the leader might enjoy a gain in inclusive fitness, 393
even if at a personal energetic disadvantage. A casual glance at feeding or migrating flocks 394
suggests considerable shifting of position, and leadership changes within the flock, but it would 395
be useful if there were a quantitative study indicating whether all or most birds assume the 396
leader position during a flight. 397
Organized Flight in Birds Line Formations 17
Nathan & Barbosa (2008) developed a comprehensive computer model that produced V 398
formations. Their model evolved from a series of simulations that yielded cluster flocks 399
(discussed below). The animats in their model followed simple rules; each bird attempted to 400
seek the proximity of the nearest bird (while avoiding collision), each bird attempted to find a 401
position that offered an unobstructed longitudinal view (if the first rule was not applicable), and 402
each bird attempted to position itself in the upwash of a leading bird. Using these rules, they 403
were able to produce Vs, Js and echelons; as well as inverted Vs which are rarely seen in nature. 404
The model was limited in its ability to handle flock turning movements as it assumed a constant 405
heading and the rules produced only lateral displacements. An attractive feature of the model 406
was, nonetheless, that it offered the opportunity to test the relative importance of aerodynamic, 407
or communication hypotheses, by changing the values of parameters. 408
So, Why do Birds Fly in a V Formation? 409
After over 30 years of active interest in the field, we may be reasonably certain of the following 410
things; 411
1. Many large birds (but not all) fly in line formations; small birds almost never. 412
2. The V and J formations are the most striking and eye catching line formations for 413
humans to observe, but they are not the most common for birds to fly in; the echelon 414
has that distinction. 415
3. There is wide variation, from flock to flock and species to species, in positioning and 416
distances of individual birds in a line. Aerodynamic theory predicts, however, that 417
there is an optimum position and distance between birds if aerodynamic advantage is 418
to be maximized, both for individuals and flocks. 419
4. The lines are wavy as often as they are straight. 420
One of us (FH) once asked a WWII B-17 pilot why bombers flew in a V. His reply was, To keep 421
a clear field of fire for the guns to the front, and to keep an eye on the leader, who does the 422
navigation. Birds clearly need not worry about the former, but if in fact the leader is 423
Organized Flight in Birds Line Formations 18
determining the direction the flock is to take, it would be an advantage to keep it in sight, an 424
advantage in a large flock accruing to a curved or irregular line. 425
Why not fly directly to the side of the leader, or directly in back? If a bird flew to the 426
immediate left or right of another bird, a gust of wind or a startled response from the neighbour 427
might precipitate a collision. Similarly, if the bird ahead were to suddenly slow down for any 428
reason, a rear-end collision might be possible. On an uncrowded motorway, drivers rarely 429
prefer to drive for long distances alongside a car in an adjacent lane, or tuck in close behind a 430
leading car if there is an opportunity to pass, possibly for similar anti-collision reasons. If the 431
object of the staggered line formation is primarily to avoid collision while keeping a leader in 432
sight, one would expect to see wide variation in spacing and alignment, simply because there is 433
no particular advantage to one spatial relationship rather than another. Similarly, one would 434
expect to see undulations in the line. As the body of a neighbour momentarily blocked the view 435
of the leader, perhaps due to a wind gust, an individual bird could simply speed up a bit or drop 436
back to regain sight of the leader, thus precipitating a wave. 437
But what of the potential aerodynamic advantage of V flight? Aerodynamic theory suggests 438
that one exists, under certain conditions. One must ask about its relative importance and need, 439
however, as it is noted that most of the field studies of line formations have not been made on 440
migration flights, where energy savings, even small ones, might well be of importance, but on 441
short feeding flights of 10−20 km, where the energy expended in flight represents a small 442
fraction of the birds daily energy budget, and that whereas staggered lines are common, Vs and 443
Js are much less so. We simply do not know what kinds of formations large birds use on their 444
long migratory flights, which are often over water. Additionally, there may be an energetic cost 445
to flying in close formation. The stress level in flying in very close proximity to other birds, with 446
consequent collision risk, might (on migration flights) raise metabolic levels enough to partially 447
negate any aerodynamic energy advantage of close formation flight. 448
The crucial experiment, to determine if, in formation flight, there is a worthwhile energy 449
advantage to be gained for aerodynamic reasons, might be to train a group of imprinted line-450
Organized Flight in Birds Line Formations 19
formation birds like geese to fly in a wind tunnel, and then use modern airflow visualization 451
techniques to empirically determine what the upwash properties of birds flying in formation 452
really are (Pennycuick et al. 1997; Rayner 1995).453
CLUSTER FLOCKS 454
There is an extensive literature discussing the biological value of flocking in general (Krebs & 455
Barnard 1980), but very few papers have appeared with specific reference to the highly 456
organized turning and wheeling (cluster) flocks of some small birds. The most commonly 457
offered hypothesis is that the closely spaced cluster flocks offer protection against aerial 458
predators like hawks, presumably by increasing the risk of collision to the predator (Tinbergen 459
1953). Examples have been reported where flocks of starlings and shorebirds bunch up tightly 460
when attacked by a hawk (Major & Dill 1978). This hypothesis appears reasonable, but leaves a 461
commonly seen behaviour in some cluster flying species to be explained. At sunset, or just 462
before, large flocks of European Starlings will form over a roost from smaller foraging flocks 463
that have dispersed during the day from that roost. These flocks will engage in some of the most 464
spectacular group movements seen in flocking birds for periods of 30−45 min before settling 465
into the roost for the night. Two questions immediately present themselves: 1) Do not these 466
movements waste energy in species for which energy is important (Hamilton et al. 1967)? and 467
2) by occurring every night in the same location, and being highly visible from up to a km away, 468
do they not almost invite predator attack? A loitering predator would have an excellent 469
opportunity to pick off a straggler (we have seen many pre-roosting turning and wheeling flocks 470
that generate stragglers as the flock splits and rejoins). Why do these flocks not land 471
immediately in the roost after returning from foraging, and why are there often 10−15 min of 472
coordinated turning and wheeling before a flock descends to a feeding area, both expending 473
energy, and facilitating predation? 474
Wynne-Edwards (1962) proposed instead that these movements represented epideictic 475
displays that might enable individual flock members to assess the population numbers and 476
Organized Flight in Birds Cluster Flocks 20
density of the flock as a whole; information that might be used in regulating breeding behaviour. 477
This suggestion was part of a larger concept that is called today naïve group selection. This 478
hypothesis received little support at the time (Crook 1965), but has enjoyed a recent re-479
examination (Wilson & Wilson 2007) that may be useful in considering how organized flight 480
evolved. Another hypothesis was provided by Major & Dill (1978) who suggested that these 481
turning and wheeling movements were protean (Driver & Humphries 1970); irregular 482
movements designed to confuse potential predators. A number of recent studies (Biro et al. 483
2006; Codling et al. 2007; Dell’Ariccia et al. 2008) have suggested that flying in a group 484
improves homing performance in pigeons, but it is not clear that the structure of the flock has 485
anything to do with this improvement. 486
There are several questions that are usually asked when considering the mechanism, rather 487
than the function of cluster flocks: 488
1. Do the flock members truly turn simultaneously during a turning movement, or is 489
there a wave of movement starting at a centre somewhere and passing through the 490
flock? 491
2. Is there a leader in the flock who communicates an action intention in some fashion to 492
other members of the flock, or is there some emergent property of flocking itself that 493
produces coordinated movement? 494
3. What mechanism governs the departure of flocks from the roost, ground, or perch, in 495
which sometimes the whole flock departs, and at other times, subgroups will depart 496
before the main group? 497
Simultaneity (or not) of individuals making a turn has relevance to the related question of 498
leadership. A wave of turning in the flock would suggest (but does not necessarily provide 499
evidence for) a relatively simple model where a leader turns, followed by a turn by neighbours 500
after a suitable reaction time (which was established by Pomeroy & Heppner [1977] to be under 501
100 ms in laboratory studies of starlings), then a wave passing through the flock as birds 502
respond to a turn by birds distant from the leader, but who ultimately have responded to a turn 503
Organized Flight in Birds Cluster Flocks 21
initiated by the leader. Vision would be the most parsimonious medium for information 504
transmittal in such a model. If birds turn simultaneously instead (within the limits of the 505
recording instrumentation), the question becomes more interesting; either a putative leader has 506
to communicate a message instantaneously to all members of the flock, seemingly ruling out 507
sound and vision in large flocks (because the bodies of nearby neighbours would block the view 508
of more distant birds), or it would be necessary to propose an organizing principle that could 509
produce synchronized turns without leadership. Such a model only became available in the 510
1980s. 511
Davis (1980) filmed turning flocks of Dunlin, Calidris alpine, with a slow-motion cine camera 512
(72 frames/s). Dunlin are differentially coloured on their dorsal and ventral surfaces, and Davis 513
observed that some individuals in flocks of approximately 40 birds all appeared to turn within 514
120 ms, giving the appearance of a flash. Potts (1984) using a similar technique with Dunlin, 515
noted some examples of waves of turning that propagated from neighbour to neighbour within 516
14 ms, considerably faster than the measured reaction times in birds. He proposed a chorus-517
line hypothesis to account for rapid turns, in which one bird or a small group could initiate the 518
movement, which would then be followed by neighbours who responded to their immediate 519
neighbours and whose speed of response would depend on their own reaction times, but more 520
distant birds would be able to estimate and anticipate the passage of the wave, as in the 521
Mexican wave in stadiums (Farkas et al. 2002). However, Heppner (1997) suggested the 522
possibility that a perceived wave of turning in differentially turning birds might be an artefact of 523
observer position relative to the near and far borders of the flock, and that individuals in a flock 524
apparently turning in wave fashion might in fact be turning nearly simultaneously. 525
Early on it was realized that to approach these questions, some idea of the geometric 526
relationship between birds in a cluster flock would be needed, and that meant the development 527
of three-dimensional (3D) analysis techniques. These techniques are well developed for 528
laboratory studies of fish schools (Partridge et al. 1980), but are much more challenging for 529
birds in the field. 530
Organized Flight in Birds Cluster Flocks 22
Major & Dill (1978) obtained the first 3D measurements of distances between birds in free-531
flying flocks of Dunlin, Caladris alpina, and European Starlings by using a stereoscopic 532
photographic technique that utilized two 35 mm film cameras whose optic axes were parallel, 533
and which were firmly fixed on an aluminium bar 5.5 m long. They were particularly interested 534
in nearest-neighbour distances, and the angles between neighbours, as these would provide an 535
index of condensation of the flocks. They reported that the nearest neighbour to a reference 536
bird was typically behind and below a reference bird, a pattern often seen in fish shoals. 537
Pomeroy (1983) and Pomeroy & Heppner (1992) used an orthogonal 3D photographic 538
technique to obtain sequence pictures of semi-domestic Rock Pigeons, Columba livia, turning in 539
flocks of 8−11 birds. Using this technique, they were able to plot the flight paths of individual 540
birds, as well as nearest neighbour distances. They reported that the flight paths of individual 541
birds crossed over each other, such that in a 90° turn, a bird that had been in the lead would be 542
to the right or left of the flock, and after a 180° turn, would be in the rear of the flock. They 543
suggested that an individual bird would find it difficult to ‘lead’ a flock by positioning itself at 544
the head of the flock. 545
Ballerini et al. (2008a, b) and Cavagna et al. (2008a, b) have developed a powerful tool for the 546
analysis of cluster flocks by essentially solving the correspondence problem that has bedevilled 547
photographic 3D analysis techniques. Most such methods involve taking a pair of pictures from 548
slightly different viewpoints, and noting the displacement of the image of a single bird in one 549
view from the other member of the pair. With large numbers of birds of identical appearance, 550
how do you match the image of the same bird in the two views? By using a novel statistical 551
method, they were able to determine the positional relationships of over 1,000 birds in a 552
European Starling flock flying over Rome. Using data obtained by this technique, Ballerini et al. 553
(2008a) suggest that the significant factor in determining interaction between birds in cluster 554
flocks is not the distance between birds (metric distance), but the number of birds between 555
any two birds (topological distance, in their terminology). 556
Organized Flight in Birds Cluster Flocks 23
Modelling, Simulations and Application 557
Davis (1980), after reviewing the deficiencies of a leadership model for cluster flock turning and 558
wheeling movements, suggested the possibility that a self-generated synchronous activity 559
might provide a model for coordinated movements. Within a decade, the development of 560
accessible and powerful computers and programming languages produced such models. 561
Working independently, Okubo (1986), Reynolds (1987) and Heppner & Grenander (1990) each 562
developed flock flight models based on the concept that each bird in a flock followed simple 563
behavioural rules in relation to its neighbours, and that the interaction of these rules produced 564
the emergent property of a coordinated flock. Moreover, Okubo (1986) and Reynolds (1987) 565
suggested that the same concept could be employed to model schools and herds, which lead to 566
numerous studies in all three fields based on similar models, as if to find a universal theory. To 567
some extent the conceptual ancestor of all models was John Conways Game of Life, (Gardner 568
1970), one of the first cellular automata that demonstrated how complex global behaviours can 569
arise as a product of self-organization by simple components following simple local rules. 570
To be specific, Reynolds (1987) proposed that for the purpose of computer animation a flock 571
could be modelled as a group of animats (or boids, using his terminology) that followed three 572
simple rules, which might behaviourally be rephrased as drives. These drives caused the 573
animats to attempt to avoid collisions with nearby neighbours (separation or repulsion), 574
match velocity with nearby neighbours (velocity matching), and stay close to nearby 575
neighbours (cohesion or attraction). The term nearby was used to describe the animats 576
localized perception of the universe. In all incarnations of the model, Reynolds (1987, 1999, 577
2004) used drive dependent perception volumes (nearby neighbours were all animats within a 578
sphere of a predefined diameter centred at the currently observed animats origin) with a 579
biologically realistic perception model (limitations of visual perception were accounted for; a 580
blind cone [the three-dimensional equivalent of a blind spot] was subtracted from the 581
perceptual sphere at the back of the observed animat). At the time of proposal the approach 582
represented a giant step forward compared to the traditional techniques used in computer 583
Organized Flight in Birds Cluster Flocks 24
animation for motion pictures. The first animation created with the model was 1987s (Stanley 584
and Stella in) Breaking the Ice, followed by a feature film debut in Tim Burtons 1992 film 585
Batman Returns with computer generated bat swarms and armies of penguins marching 586
through the streets of Gotham City. The current state of the art in computer animation for 587
motion pictures has evolved even further (Massive 2008); these advanced models, however, due 588
to the obvious financial consequences, remain proprietary. 589
Heppner & Grenanders (1990) distinguishing features were the approach used to model 590
perception and the animats drives. In their case the same perception volume (a sphere of a 591
predefined diameter centred at the currently observed animats origin) was used for all drives 592
and limitations of visual perception were not accounted for. The animats attempted to stay in 593
the roosting area (homing), attempted to fly with a predefined flight speed (velocity 594
regulation), and attempted to move apart if too close, or closer if not too distant (interaction). 595
An additional feature was random impact, which was intended to simulate the random 596
distractions that are present in a natural environment (wind gusts, distractions from moving 597
objects on the ground, etc.). Heppner & Grenander (1990) implemented the latter by using a 598
Poisson stochastic process and admitted that without its inclusion they were unable to produce 599
a flock-like behaviour. 600
In the mid 1980s and early 1990s, computer processing power was limited and real time 601
simulations of large flocks consisting of more than a few dozen birds were infeasible. The first 602
step to simulations that would allow observing an animated output while running the 603
simulation and interactively changing the models parameters was performed by Lorek & White 604
(1993), who, just a few years after Reynolds (1987) paper was published, used a Meiko 605
Transputer System with up to 50 processors to run flight flock simulations, consisting of merely 606
100 birds at slow, but interactive rates (6 frames/s). The recent advances in multicore 607
technology (Gschwind et al. 2006) and computer graphics dedicated hardware (NVIDIA 2007), 608
and their use for scientific research (Khanna 2007; Sijbers & Batenburg 2008) give the 609
impression that barriers to real time simulations and interactivity will soon be breached. 610
Organized Flight in Birds Cluster Flocks 25
Reynolds (2006), for example, reported a multicore solution, which takes advantage of the Sony 611
PlayStation 3 Cell processor for running simulations of 10,000 fish with animated output of 612
cinematic quality at 60 frames/s. More recently, at the SIGGRAPH 2008 conference, the Game 613
Computing Applications Group of AMD, Inc. was showing a cinematic quality technology demo 614
titled March of the Froblins (AMD 2008; Shopf et al. 2008), a graphics processing unit (GPU) 615
based crowd simulation of 65,000 agents at 30 frames/s. 616
The techniques used for achieving high frame rates might at times be at the expense of 617
biological realism. It is also true that for a scientific study centred on behaviour, the ability to 618
interactively change the models parameters and observing the effects in real time is a welcome 619
plus. In computer animation for games and virtual reality (Brogan et al. 1998) high frame rates 620
are important and the modelling of flocking behaviour has a niche of its ownit falls under the 621
subject of controlling groups of objects. Disregarding the cost of achieving the desired degree 622
of visual realism, the simplicity of achieving high frame rates depends on the class of the 623
controlled group of objects. Using Parents (2002) terminology, there are three principal classes 624
of controlled groups: 1) particles, characterized as large collections of individual objects, each 625
of which obeys simple physical laws, such as momentum and conservation of energy, but has no 626
intelligence, or decision making capacity; usually, such particles interact mostly with their 627
environment, and there is little, if any, inter-individual exchange (typical examples are models 628
of fluids, gaseous phenomena, hair, fur, etc.); 2) flocks, characterized as medium (fewer in 629
number than particles) size collections of individual objects, with some incorporated physics 630
and intelligenceinteraction with the environment and inter-individual exchange (typical 631
examples are models of schools, swarms, herds, crowds, traffic, etc.); 3) autonomous agents, 632
characterized as small collections, with little, if any, incorporated physics and much intelligence 633
(typical examples are intelligent agents, autonomous robots, software agents, computer viruses, 634
etc.). All three classes are examples of independently behaving members of groups with varying 635
levels of autonomy, physical characteristics and simulated motions. 636
Organized Flight in Birds Cluster Flocks 26
Kennedy & Eberhart (1995) were the first to incorporate elements from artificial life and 637
artificial intelligence (AI) studies to allow bird flocking behaviour models to serve as exemplars 638
for more general kinds of behaviour, including human social behaviour (Helbing & Molnár 639
1995). A group of interacting animats is a ‘swarm’ in AI terms, and Kennedy & Eberhart (1995) 640
presented algorithms by which a swarm might optimize its behaviour, or adapt to serve some 641
end, such as increasing energy input. The animats in a swarm make decisions about their own 642
behaviour based on the behaviour and knowledge gained from their neighbours, as well as the 643
perceived elements of their surroundings, such as locations of feeding areas’. From the swarm's 644
collective behaviour emerges the animats' indirect approach to relatively-good solutions. These 645
algorithms are also known as particle swarm optimization, or PSO for short (Kennedy et al. 646
2001; Engelbrecht 2006). Macgill & Openshaw (1998) and Macgill (2000), for example, later on 647
used flocking behaviour to assist the analysis of geographical data. Subsequent AI studies 648
started introducing more and more intelligence in individual animats while reducing their 649
number; Odell (1998) provided a summary of the terminology and properties attributed to 650
agents in computer studies. 651
In the mid-1990s, physicists began to show interest in the mathematics and physics of 652
organized flocks, using a perspective very different from those found in earlier biological and 653
aerodynamic studies. Vicsek et al. (1995) and Toner & Tu (1995, 1998) viewed the birds in a 654
flock as particles, behaving much as molecules in a fluid or atoms in a crystal might, and that 655
they were responsive to the same mathematical rules. The models were all based around the 656
same perception model as in Heppner & Grenander (1990); inter-individual influences occurred 657
between animats that were not further apart than a predefined distance. Additionally, an overall 658
constant flight speed was assumed and the number of drives was reduced to merely one, 659
attempting to match flight direction with nearby neighbours. A stochastic component had been 660
added in these models, perhaps on similar presumptions as the random impact used by 661
Heppner & Grenander (1990). As theoretical physicists, Toner & Tu (1998, p. 4830) may have 662
been somewhat removed from realities in the field when they suggested, This correlation 663
Organized Flight in Birds Cluster Flocks 27
function should be extremely easy (italics added) to measure in simulations, and in experiments 664
on real herds or flocks, in which, say, video tape allows one to measure the positions ... of all the 665
birds ... in the flock at a variety of times t. Vicsek et al. (1995) suggested that the physics 666
concepts associated with phase transitions, as in the transition from solid to liquid forms of 667
materials, might serve to explain the puzzling shifts between orderly and disorderly flock 668
formations often seen in birds like European Starlings. All in all, their models represent a 669
substantial simplification in biological assumptions over the initial ones proposed by Okubo 670
(1986), Reynolds (1987) and Heppner & Grenander (1990). Using Parents (2002) terminology, 671
these models fall perfectly under the particles category. The model devised by Vicsek et al. 672
(1995) is also known as the self-propelled particles model, or SPP. Physicists embraced these 673
minimalist models and a number of subsequent studies have been published (see Czirók et al. 674
1997; Czirók & Vicsek 1999, 2000; Tu 2000; Li et al. 2007; Li & Xi 2008; Chaté et al. 2008; Gönci 675
et al. 2008; Huepe & Aldan 2008, for example). Recent field observations by Ballerini et al. 676
(2008a, b) and Cavagna et al. (2008a, b) seem to be making an impact in the physics community 677
and even physicists are starting to acknowledge the importance of inclusion of attractive-678
repulsive drives (Grégoire et al. 2003; Grégoire & Chaté 2004; Feder 2007). An additional result 679
of these field observations, is one that somewhat contradicts the approach commonly assumed 680
by flock flight models. These typically assume a fixed radius of interaction. Data obtained by 681
Ballerini et al. (2008a, b) and Cavagna et al. (2008a, b) seems, on the other hand, to suggest that 682
it is not the radius, but the number of influencing individuals, which remains constant. 683
Just as Kennedy & Eberhart (1995) incorporated AI elements into flight flock models to 684
devise PSO, other computer science studies applied AI algorithms to evolve the models 685
themselves. Reynolds (1993a, b), Zaera et al. (1996), and Spector et al. (2005), used genetic 686
programming, a technique for automatically creating computer programs that satisfy a specified 687
fitness criterion, to evolve the individual animats rules, or in this case programs, which, when 688
the animats interacted, produced flocking behaviour. All previous models employed constants 689
like perception radius (diameter of the sphere centred at the currently observed animats 690
Organized Flight in Birds Cluster Flocks 28
origin, by the use of which nearby neighbours are selected), weights (typically the direction of 691
flight [and flight speed] of the currently observed animat is computed as a weighted sum of the 692
individual desired flight directions that would meet the individual drives, respectively), etc. 693
Heppner & Grenanders (1990) approach was to modify these by hand and analyse the results. 694
The AI approach was to use evolutionary computing. Genetic algorithms were used to vary the 695
parameters to optimize the behaviour to a specified fitness criterion. Dimock & Selig (2003), for 696
example, used genetic algorithms on a modified Reynolds (1987) model to find parameters for 697
minimum power consumption in a flock of simulated birds. Wood & Ackland (2007), on the 698
other hand, using a Couzin et al. (2002) model, studied the evolution of group formation when 699
subjected to simulated predation and foraging. Their results replicate conventional evolutionary 700
behaviourforaging animats prefer a narrower perception volume, while the hunted prefer a 701
wider one. 702
Couzin et al. (2002) and Couzin & Krause (2003) added the next level of sophistication in 703
flocking models. The substantial difference was not in the animats drives, but in the perception 704
model, or when these drives were actually in effect. Whereas Heppner & Grenander (1990) used 705
one perception volume for all three drives, Reynolds (1987, 1999, 2004) three non-exclusive 706
perception volumes with biologically inspired limitations, Couzin et al. (2002) and Couzin & 707
Krause (2003) introduced a different approach; in their model there were three exclusive 708
perception volumes, or zones, using their terminology: 1) zone of repulsion, 2) zone of 709
orientation and 3) zone of attraction. If there were neighbours in the zone of repulsion, then 710
only the separation drive was active and the other two ignored. If, however, there were no 711
neighbours in it, the other two drives were averaged, but the animat attempted to match 712
velocity only with the neighbours in the zone of orientation and attempted to stay close only to 713
the neighbours in the zone of attraction. Additionally, the zone of repulsion was modelled as a 714
sphere, whereas the other two were modelled as a sphere with a blind cone subtracted at the 715
animats back. Couzin et al. (2002) considered what would happen to group movements if 716
individuals in the group modified their behavioural rules in response to experience with the 717
Organized Flight in Birds Cluster Flocks 29
flock as a whole. More specifically, what would happen if the diameter of the zone of orientation 718
was variable, while keeping the zones of repulsion and attraction constant. They found that, as 719
the diameter of the zone of orientation increased, the group went from a loosely packed 720
stationary swarm, to a torus where individuals circle round their centre of mass and, finally, to a 721
parallel group moving in a common direction (see also Sumpter 2006). Further on they 722
discovered that the transitions were rapid, and as the diameter decreased, the collective 723
behaviour was different. They established that two completely different behavioural states can 724
exist for identical parameters, and that transition between behavioural states depends on the 725
previous history (structure) of the group, even though the individuals have no explicit 726
knowledge of what that history is. Consequently, they suggested that the system exhibits a form 727
of collective memory. In a later study, Couzin et al. (2005) examined leadership and decision 728
making in animal groups on the move by giving knowledge of a preferred flight direction only to 729
a proportion of the simulated animals. The study revealed that the larger the group, the smaller 730
the proportion of informed individuals needed to guide the group, and that only a small 731
proportion is required to achieve great accuracy. Several recent experimental studies (Biro et al. 732
2006; Codling et al. 2007; Dell’Ariccia et al. 2008) investigated the ‘many-wrongs principle’ in 733
pigeon homing and suggest that pigeons flying in a group have better navigational performance 734
than birds flying alone, but it is not clear whether the spatial organization of the flock is 735
significant in this observation. 736
Lebar Bajec et al. (2003a, b, 2005) and Lebar Bajec (2005) introduced the concept of fuzzy 737
logic to flocking models. The basic concept of the model remained the same; three drives and 738
perception modelled as a sphere with a blind cone removed from the back. But in previous 739
models, the animats would react to their surroundings in a crisp way. For example, if we are 740
interested in two moving animats that are on a closing course with one another, there might be 741
some specific threshold distance at which they would deviate to avoid collision (e.g. when they 742
enter each others zone of repulsion [Couzin et al. 2002]). Or, in a slightly more complex 743
example, there might be a gradient for different closing angles such that the animats would 744
Organized Flight in Birds Cluster Flocks 30
deviate proportionately, but still in deterministic fashion depending on the closing angle. 745
However, with fuzzy logic, vague qualities like close or far rather than a specific distance or 746
angle can be used to describe the behavioural repertoire of the animat. In this fashion, a more 747
naturalistic type of behaviour can be produced. Indeed, Heppner & Grenander (1990) used a 748
single perception volume, Reynolds (1987, 1999, 2004) three overlapping perception volumes, 749
and Couzin et al. (2002) and Couzin & Krause (2003) advanced the model by introducing three 750
non-overlapping perception zones, the use of vague qualities enabled Lebar Bajec et al. (2005) 751
to produce a mixture of these approaches with partially overlapping perception zones. The issue 752
this model has, with respect to the others, is that it is two dimensional; animats can move left or 753
right, but not up or down. As real birds exist in three dimensions, a genuinely realistic 754
simulation needs to feature the third dimension. Moškon et al. (2007) expanded the fuzzy model 755
to account for foraging behaviour by including hunger as a drive. While doing so, they also 756
modelled foraging fields and landing and taking off from them; while this has not been achieved 757
by promoting the drives to work in three dimensions, they upgraded the model to pseudo 3D 758
nonetheless. 759
So, How do Birds Seem to Turn and Wheel Together? 760
In the 1970s, there was no conceptual alternative to a leadership model for producing 761
simultaneous or near-simultaneous turning movements in cluster flocks. With the advent of the 762
many models that treat flocks as collections of independently acting agents that produce turning 763
movements as the product of individual movement decisions, a viable alternative to leadership 764
models now exists, but such models 1) do not rule out the possibility that under certain 765
circumstances, particularly with small, or family flocks, leadership might still play a role in 766
cluster flock movements, and 2) do not provide evidence that birds use the same algorithms as 767
the models. Just as there may be several biological functions for line formations, it may be that 768
there are multiple mechanisms for producing cluster flock movements. 769
Organized Flight in Birds Introduction 31
CONCLUSION 770
Advances in the understanding of the function and mechanisms of organized flight have been 771
strongly linked to the introduction of new techniques or technologies. Heppner (1997) 772
identified several areas that might be expected to produce such advances, but a decade later, 773
although it has been possible to refine and more closely define these needs, much still needs to 774
be done. 775
1. Three dimensional simulations. Some of the existing simulations (Vicsek et al. 1995; 776
Lebar Bajec et al. 2005; Moškon et al. 2007; Nathan & Barbosa 2008), although 777
capable of producing realistic-appearing flocks on a computer screen, feature animats 778
that travel in a two dimensional universe. They may travel left or right, but not up or 779
down. As real birds exist in a 3D world, a genuinely realistic simulation would have to 780
feature the third dimension. Adding the additional dimension is not a trivial 781
programming task, but its accomplishment could be expected to pay large dividends. 782
2. Non-homogeneous models. To date, flight flock models have assumed that flocks are 783
composed of identical subjects. In reality, there will be individual differences in age, 784
gender, sensitivity to hunger, health, and other factors that may well influence the 785
collective behaviour of the flock. 786
3. Fast, cheap, field data acquisition. Cavagna et al.s (2008a) technique for obtaining the 787
3D positions of thousands of birds in a flock has yielded remarkable results, but the 788
method requires custom-made synchronizing equipment for the cameras, skilled 789
operators, lengthy processing, and a fixed location. As a result, it is difficult to 790
compare species, conditions, or fine structure over time. The current generation of 791
digital still and video cameras offers the potential for both high resolution and a high 792
frame rate at a reasonable cost. Commercial wireless technology, such as that used to 793
simultaneously fire multiple remote flash units, offers the potential of synchronizing 794
Organized Flight in Birds Conclusion 32
two (or more) cameras in the field without the necessity for custom made 795
synchronizing devices. 796
4. User-friendly simulations. The current generation of flocking simulations is primarily 797
designed to be used and manipulated by their designers, who may or may not be 798
familiar with the behaviour of animals in the field. The programs are not easily used 799
or modified by other users unfamiliar with programming. It would be very helpful if 800
future simulations came with a console, or control panel that would allow non-801
programmers to change the parameters or their values in the simulation, such as 802
preferred velocity, or attractiveness of feeding site, thus allowing field biologists to 803
examine the results of changing inputs to the program based on their field experience. 804
It might also be possible to set up detectors in the program, as is done in 805
experimental particle physics, to allow many different combinations of parameters 806
and values to be run in sequence, and the program would flag interesting behaviours, 807
such as the appearance of a V, when they appear. For example, the Boston Museum of 808
Science in Massachusetts has a large public display called the Virtual Fishtank 809
(Nearlife, Inc. 2001) that enables visitors to interactively change the behaviour of 810
individual fish in a school, and immediately see the change in the behaviour of the 811
school. 812
5. Metrics for truth testing. Current simulations offer naturalistic appearing virtual 813
flocks, but it cannot be certain that real birds use the same algorithms employed in 814
the simulation. Ideally, one would produce a simulation of a particular species’ 815
flocking behaviour, and use it to make predictions about the behaviour of the real 816
flock, and then test those predictions in the field. To do this, one would have to have a 817
metric that could be derived from the simulation, and then measured in the field. For 818
example, some simulations produce flocks that apparently turn and wheel much like 819
real flocks. Perhaps turning and wheeling could be quantified, such that one could 820
say that, for example, a flock of X number of birds of species Y will make a turn, 821
Organized Flight in Birds Conclusion 33
defined as a departure of more than 20° from the mean direction exhibited in the 822
previous 5 s, every 8.2 s. If this variable were measurable in the field, it could then be 823
possible to refine the model to produce more accurate predictions. Successful 824
prediction would, of course, not be prima facie evidence that the algorithms in the real 825
and virtual worlds were the same, but would certainly provide stronger evidence than 826
a superficial, qualitative similarity. Dill et al. (1997) discussed this issue more 827
extensively. 828
The last 40 years have seen remarkable progress in the understanding of this intriguing and 829
aesthetically spectacular phenomenon. In addition to being a phenomenon worthy of 830
examination in its own right, the study of organized flight in birds has provided a model system 831
that has demonstrated utility in the study of crowd behaviour, bird strikes on aircraft, traffic 832
theory, complex systems, particle swarms, computer animation, and control of (remotely 833
piloted) autonomous aircraft. At this time, it is possible to foresee that with the assistance of 834
biologists, physicists, mathematicians and computer scientists working together, we will, before 835
long, truly be able to say how and why birds fly in organized groups.836
ACKNOWLEDGEMENTS 837
We sincerely thank Maja Lebar Bajec, Michael Byrne, Andrea Cavagna, Marjorie Heppner, Jim 838
Kennedy, Craig Reynolds, and Timothy Williams for reading early drafts of the manuscript. This 839
work was funded in part by the Slovenian Research Agency (ARRS) through the Pervasive 840
Computing research programme (P2-0395). 841
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... Collective motion (CM) is a phenomenon occurring in homogeneous populations of 2 interacting individuals [1,2,3,4]. It is manifested in multiple forms in nature such as 3 locusts aggregate into groups [5,6], birds flocking in an organized manner [7,8], and 4 fish schools responding to predators and showing migratory movements [9,10]. During 5 the last few decades, researchers seek to elucidate the mechanisms allowing animals to 6 achieve such a remarkably synchronized motion, while lacking centralized control. ...
... During 5 the last few decades, researchers seek to elucidate the mechanisms allowing animals to 6 achieve such a remarkably synchronized motion, while lacking centralized control. 7 Empirical data from experimental observations [11,12] is analysed with the aim to 8 uncover individual's behaviour using mathematical and computational models [13, 14, 9 15]. 10 A large body of work can be categorized as agent-based models, where the collective 11 dynamics is explained by the action on the individual-level [16]. ...
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Collective motion takes many forms in nature; schools of fish, flocks of birds, and swarms of locusts to name a few. Commonly, during collective motion the individuals of the group avoid collisions. These collective motion and collision avoidance behaviors are based on input from the environment such as smell, air pressure, and vision, all of which are processed by the individual and defined action. In this work, a novel vision-based collective motion with collision avoidance model (i.e., VCMCA) that is simulating the collective evolution learning process is proposed. In this setting, a learning agent obtains a visual signal about its environment, and throughout trial-and-error over multiple attempts, the individual learns to perform a local collective motion with collision avoidance which emerges into a global collective motion with collision avoidance dynamics. The proposed algorithm was evaluated on the case of locusts’ swarms, showing the evolution of these behaviors in a swarm from the learning process of the individual in the swarm. Thus, this work proposes a biologically-inspired learning process to obtain multi-agents multi-objective dynamics.
... In aerial systems, the main energy savings comes from upwash, i.e., trailing regions of upward momentum in the slipstream, which followers exploit to reduce induced drag. Flocking to minimize energy consumption is known as line flocking in the engineering literature [8], and its name comes from the linear formation-like flocking behavior of geese, pelicans, etc [9]. ...
Preprint
The study of robotic flocking has received significant attention in the past twenty years. In this article, we present a constraint-driven control algorithm that minimizes the energy consumption of individual agents and yields an emergent V formation. As the formation emerges from the decentralized interaction between agents, our approach is robust to the spontaneous addition or removal of agents to the system. First, we present an analytical model for the trailing upwash behind a fixed-wing UAV, and we derive the optimal air speed for trailing UAVs to maximize their travel endurance. Next, we prove that simply flying at the optimal airspeed will never lead to emergent flocking behavior, and we propose a new decentralized "anseroid" behavior that yields emergent V formations. We encode these behaviors in a constraint-driven control algorithm that minimizes the locomotive power of each UAV. Finally, we prove that UAVs initialized in an approximate V or echelon formation will converge under our proposed control law, and we demonstrate this emergence occurs in real-time in simulation and in physical experiments with a fleet of Crazyflie quadrotors.
... Animal swarming behaviors are universal in nature, such as the flocking of birds [1] and schooling of fish [2]. As revealed by scientists, movement in formation may help the animal swarm to save energy and increase efficiency for long distance migration [3]. ...
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This paper studies the robust formation flying problem for a swarm of drones, which are modeled as uncertain second order systems. By making use of minimal virtual leader information, a fully distributed robust control scheme is proposed, which includes three parts. First, the output based adaptive distributed observer is adopted to recover the global flying path vector as well as the coefficients of the minimal polynomial of the system matrix of the virtual leader system for each drone based on neighboring information from the communication network. Second, based on the estimated minimal polynomial of the system matrix of the virtual leader system, an asymptotic internal model is conceived to deal with uncertain system parameters. Third, by combining the asymptotic internal model and a certainty equivalent dynamic state feedback control law, a local trajectory tracking controller is synthesized to solve the robust formation flying problem. Numerical simulations are provided to validate the proposed control scheme.
... Such "V" and "J" formations by flying flocks are suggested to be an example of coordinated group movements which various animal species display (Herbert-Read 2016). The written descriptions detailing on the organized flight in birds can be broadly divided in four phases (Bajec and Heppner 2009): (1) the first phase at about the beginning of the twentieth century, led by biologists; (2) the second phase in the 1970s where the mainstream biologists were joined by aeronautical engineers; (3) the third phase in the 1980s when computer scientists also started showing interest in this phenomenon; and (4) the fourth phase in the 1990s when physicists and mathematicians joined investigations on modelling such behaviours. Though much research focus has been on identifying local interaction rules (e.g., Ballerini et al. 2008) and group dynamics (Attanasi et al. 2014) in the flying flocks, we could not find any such published observational or experimental study which describes the echeloning in a roosting flock of migratory birds under high wind conditions. ...
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The organized aerial manoeuvres of birds in "V" and "J" flock echelons have always captivated onlookers and several of these aspects are still a matter of ongoing research. However, we could not find any published evidence or report on echeloning in a roosting flock of birds in high wind conditions. Here, we provide first evidence of an echelon in a roosting flock of the Eurasian oystercatcher (Haematopus ostralegus ostralegus) at the onset of Storm Malik in Scotland on the morning of the 29 th of January 2022, under ~ 11 ms −1 winds. This observation opens-up several new research questions on if, how, and why birds position themselves in a flock while roosting in high winds.
... Over the last few years, researchers have examined the aerodynamic aspect of the flight formations as well by analyzing its functions, mechanisms of coordination between the birds, and its aerodynamic effects in terms of power generation and savings. 1 As reported by Heppner,2 birds are observed to have different types of formations that are classified in several categories. Each provides the bird flocks with possible biological or aerodynamic advantages. 2 Avian formation flights are mainly classified as line formations, compound line formations, and cluster formations. 2 As illustrated in Figure 1, the line formation is a group of birds flying in one line as a column, row, or echelon. ...
Article
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... The highly non-linear marginal potential implies that small speed fluctuations elicit nearly zero restoring force, while larger speed fluctuations are pushed back extremely sharply, in contrast with the constant slope of a linear confining force, Fig. 1. In bird flocks, small speed fluctuations are not prevented by biomechanical constraints, but they could be depressed by energetic expenditure concerns, as changing the speed requires extra energy consumption; however, starlings prove to be very liberal about their energy expenditure habits while flocking [43][44][45] : although their metabolic rate is dramatically higher in flight than on the roost 43 , these birds will spectacularly wheel every day for half an hour before landing, expending energy at a ferocious rate; this suggests that small extra energy expenditures due to small speed fluctuations may indeed be weaker-than-linearly suppressed. On the other hand, large speed fluctuations clash against biomechanical and aerodynamic constraints, which are set very stringently by anatomy, physiology and physics [46][47][48] ; therefore, a stronger-than-linear suppression of large speed fluctuations also seems quite reasonable. ...
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Full-text available
Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations are scale-free, namely they have a range as wide as the entire group, a property linked to the capacity of the system to collectively respond to external perturbations. Scale-free correlations and moderate fluctuations set conflicting constraints on the mechanism controlling the speed of each agent, as the factors boosting correlation amplify fluctuations, and vice versa. Here, using a statistical field theory approach, we suggest that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations, is able to reconcile scale-free correlations with biologically acceptable group’s speed. We validate our theoretical predictions by comparing them with field experimental data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude.
Chapter
The aim of this work is to study the aerodynamic characteristics of solar unmanned aerial vehicle (UAV) wake surfing. First, the application of the following methods to this kind of aircraft was compared: rapid method (i.e., horseshoe vortex model, lifting line theory and nonlinear lifting line theory) and computational fluid dynamics (CFD). The results showed that nonlinear lifting line theory (NLLT) is more accurate in the calculation of the aerodynamic force. The flow field of wake surfing was evaluated with CFD and the local angle of attack was calculated with a local lift coefficient from the CFD results. It was found that the linear method that added induced angle of attack directly to the rear wing overestimated the influence of wing-tip vortices on the rear aircraft. The classical vortex model was introduced to explain this error in a way of vortex decay, which means the rear wing can influence trailing vortices of the lead wing. The error is quantitatively studied by introducing vortex core radius into the calculation, and it was found that the closer trailing vortices act on the rear plane, the stronger the decay shows. After analysis of the characteristics, the vortex core radius was finally introduced into the fast method to modify errors caused by vortex decay. The modified method can reduce the amount of computation in engineering evaluation and give more accurate predictions.KeywordsAerodynamic characteristicsFormation flightWake surfingVortex model
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The results for swarm system are mostly concerned with the collectiveness of the swarm systems themselves. Here, we further consider the synthesis of a volume compression algorithm for social force based fish swarm by four predators, which focuses on the manipulation of a swarm system subject to a mature understanding of the underlying mechanism governing the behaviors of the swarm system. The interactions among the fish swarm follow the social force model. Besides this, the fish will also evade the predators based on their relative positions. The motion of predators takes into consideration the ingredients of the positions of the fish swarm and the positions of the other predators.
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In this book Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is the computational properties of interactions that account for much of what we think of as "beautiful" and "interesting." From this basic thesis, Flake explores what he considers to be today's four most interesting computational topics: fractals, chaos, complex systems, and adaptation. Each of the book's parts can be read independently, enabling even the casual reader to understand and work with the basic equations and programs. Yet the parts are bound together by the theme of the computer as a laboratory and a metaphor for understanding the universe. The inspired reader will experiment further with the ideas presented to create fractal landscapes, chaotic systems, artificial life forms, genetic algorithms, and artificial neural networks.
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I analyzed formations of Canada Geese (Branta canadensis) with a single, direct method of testing predictions from multiple hypotheses. The results support both energetic (aerodynamic) advantage and orientation communication through visual contact as functions of this complex behavior. Comparison of observed positioning patterns with criteria for optimal function suggests priority may be given to the maximization of energy savings within limits imposed by environmental and other constraints.