IBIS 140 280-287
The function of flight formations in Greylag Geese Anser anser;
energy saving or orientation?
J. R. SPEAKMAN & D. BANKS
Department oj Zoology. University of Aberdeen. Aberdeen AB24 2TZ. Scotland. UK
Twenty five formations of Greylag Geese Anser wzser were photographed from immediately
below to eliminate perspective distortion, and the lateral and longitudinal displacements
of the birds relative to each other were measured. We scaled the photographs and used
measurements of bill to tail and wing span made on 1 5 freshly shot birds to convert the
lateral displacements to wing-tip spacings. The birds flew on average with an overlap of
their wing tips (median = 17 em) which corresponded very closely with the overlap ex­
pected (16 em) from an aerodynamic model which predicted the position which maximized
energy savings. However, the variation in positions was large, and only 17'X, of birds
actually flew in the optimum range. The mean saving in induced power averaged across
the distribution of positions was 26.5'X" and the contribution to total flight costs was a
reduction of 4.5-9%. This saving was greater than we found previously in the Pink-footed
Goose Ansa hmclzyrlzynclws. There was no correlation between position in the skein and
longitudinal displacement. as would be anticipated if the birds were equalizing the savings
across the skein. This does not mean costs were not equalized because other mechanisms
are possible, There was no correlation between depth and wing tip spacing which does
not support the orientation/communication hypothesis. Body size and thus flight costs may
be a factor influencing the function of formation flights.
When geese (order Anscriformcs! fly together in flocks, they
frequently align themselves in formations. These arc often
referred to as "V" formations (e.g. Gould & Heppner 1974).
but the actual shape of the formations can vary from a true
V, where the two arms are of equal length. via 'T' forma­
tions. where the length of one arm exceeds that of the other.
to echelons where one arm of the V is missing completely
i Heppner 1(74). A characteristic feature of all these for­
mations is that the positions of the birds are sequentially
staggered such that only a single bird leads the formation
and all the others follow the bird immediately in front of
them. Similar flight patterns are found in other large gre­
garious birds such as pelicans (order Pclecaniformcs: Hains­
worth 19881.
The function of these striking flight patterns has been a
matter of considerable debate since at least the early part
of this century (Forbush 1912. Weiselsberger 19] 4, Fran­
ziskcit L9'51. Schweppenberg 1952, Hamilton 1967. Lissa­
man & Schellenberger 1970, Could S Heppner 1974. Hum­
mel 1973,1978,1983, Hummel & Bock 1981. Badgerow
"" Hainsworth 19R1. Hainsworth 1987. Hummel & Beukcn­
berg 1(89). Two main hypotheses have been advanced to
explain the adoption of V flight formations. The first hy­
pothesis suggests, on the basis of aerodynamic theory. that
birds may gain an energetic advantage by flying in forma­
tinn
J91
19S:,~, rj~;s,Tcnan
& Schollenberger 19 '70. Hainsworth 1987. Hummel & Beu-
kenberg 19891. This advantage occurs because a vortex is
shed from each wing tip as a bird flies (Hummel J 9 73.
1978,1983. Rayner 19'791. If a bird positions itself behind
and to one side of another bird in a certain location, it can
benefit by obtaining lift from the updraught of the vortex.
This lift then reduces the requirement for induced power
input (Pennycuik l 969) by the following bird, which there­
fore experiences an energy saving. The exact position of
each trailing bird is critically important because the paten..
tial savings are quite strongly dependent on lateral position
but less so on elcvational and longitudinal positions (Lissa­
man & Schellenberger 1970. Hummel & Beukenberg 1989).
This hypothesis makes a clear prediction concerning the op­
timal wing-tip spacing of the birds: The lateral position
should be maintained independent of how far behind each
other the birds are flying. and there should be no correlation
between lateral and longitudinal displacement of each bird
relative to its immediate leader.
The exact locations of the trailing vortices and hence the
optimal lateral displacement at which the trailing bird
should By have proved to be a matter of dispute. Lissarnan
and Schoilcnberger (1970) suggested maximum savings or­
currcd at a point coincident with touching wing tips. i.c.
with no overlap, but they did not consider the savings that
might accrue by flying overlapped, Later workers suggested
that the distance l.ctwccn (he centre:; of tbt-'
\'UfLiCt':J
(d,) is less than the wing span:
f U C H T FOR \L\ rr
1998
d.
= (Pil4lb
=
a.78b.
where b is the wing span (Glauert 1943. Badgerow & Hains­
worth 1981. Hainsworth 1987). In a previous paper (Cutts
& Speakman 1994). we suggested that Hummel (1973! and
Hummel and Beukenberg (1989) had derived a model in
which the distance between the vortex centres was further
apart and equal to a.89b. However. this was a misinterpre­
tation of the original articles written in German. and in fact.
Hummel's model generates the same distance between the
vortices as derived in Eq. 1 above. Since the value d, is less
than the wing span of the bird. a trailing bird. in theory.
gains the greatest benefit from the bird in front if its wing
tips overlap slightly with the bird it is following. Generally.
the optimal extent of overlap. called the optimal wing tip
spacing (VlTS",J should equal:
v\iTS",; = 0 ..5 (0.7Sb -- b) = -0.1Ib.
(2)
Note that the negative value indicates the tips of the wings
are predicted to overlap. Positive values of the wing tip spac­
ing indicate no overlap.
The effect of longitudinal position on energy savings has
been less adequately modelled. Immediately behind the wing
there is a vortex sheet which rolls up to form two tubular
vortices. Exactly where this happens has been a matter of
some debate. Some authors have suggested the roll-up point
is one or two spans behind the wing (Higdon & Corrsin
1978. Badgerow & Hainsworth 1981. Hainsworth 1987).
but other authors have suggested it rolls up at about two
wing chords behind the bird (Rayner 1979). Vortex flow
visualizations in neutral helium clouds support this latter
interpretation more than the former (Spedding 1987). In
theory. the vortices are less concentrated in front of the
roll-up point. Increasing longitudinal distance after the roll­
up point has only a minor effect on the savings (the so called
"Munks displacement law": Hummel 198 3). In practice. the
position of the vortex is likely to become less predictable as
distance increases (Cutts & Speakman 1994). We predict
then that birds should position themselves longitudinally at
the roll-up point.
Hummel (1973) and Hummel and Bock (1981) demon­
strated theoretically that. by flying in a true V formation.
the savings are not distributed equally among the birds in
the formation. In particular. the leading bird makes only
minor savings relative to other birds. each of which has
another bird to follow. However. if the birds adopt a swept
\~ with the longitudinal distance between birds getting pro­
gressively greater along the V arms. the saving is more
equable (Hummel 1978. Hummel & Bock 1981). This is
achieved because there is also a slight upwash preceding the
birds in Ilight. from the vortex bound to the wing. and at
very low longitudinal distances. the lead bird can obtain a
benefit from those !lying behind it.
The second hypothesis suggests that the formation does
not serve any energetic purpose but rather allows the birds
to communicate vvifh one another or 10 orlcntate themselves
more readily as they move between roosting and feeding
oN
INC R F Y L t\ C C; E ESE
181
grounds or between summer and winter quarters (Forbush
1912. Franziskeit 1951. Hamilton 1967. Gould & Heppner
1974. Williams et tIl. 1976. Badgerow 1988). This might be
advantageous to long-lived animals such as geese. which
exploit traditional roosting and feeding areas. often many
kilometres apart. and fly annually between summer and
wintering grounds many thousands of kilometres apart. In
particular. less experienced birds would benefit from the ex­
perience of older birds about the best places to feed and
roost. This hypothesis suggests that birds maintain orien­
tation by keeping a constant angle between themselves and
the bird in front of them. Maintaining a constant angle, in
turn. predicts a positive correlation between longitudinal
and lateral displacements of each bird relative to its imme­
diate leader. In addition. this model does not predict any
pattern where depth gets progressively greater along the
arms of the V.
These hypotheses are not mutually exclusive. By flying
behind and to one side of each other. at a constant angle
to optimize communication. birds are bound to gain some
energetic advantage relative to flying alone. In addition.
while birds are flying in the optimal location to make an
energy saving. they can also gain some benefits in terms of
communication. However. the optimum positions to perform
these functions do not coincide and. by favouring one func­
tion. the birds inevitably lose out on the other. The question,
therefore. is what is the primary function of the flight be­
haviour. rather than its sale function?
Evidence relating to each of these hypotheses has been
equivocal. For example. migrating Canada Geese Branta can­
adensis had a median position close to the optimal location
for energy saving. although there was considerable variation
between birds and between skeins (Hainsworth 1987).
Gould and Heppner (1974) interpreted the large distances
(mean 4.1 m) between the Canada Geese that they observed
as supporting the orientation hypothesis because they con­
sidered energy saving at this distance unlikely. However.
Badgerow and Hainsworth (1981) re-examined the data col­
lected by Gould and Heppner (1974) and calculated the
more relevant lateral displacement. rather than bird-to-bird
distances. and came to the conclusion that the geese were
actually flying close to the optimum position for saving en­
ergy.
In a recent paper. we evaluated the primacy of the two
hypotheses by photographing formation flights of Pink-foot­
ed Geese Anser bmchyrluzyclzus wintering in northeastern
Scotland when flying between their nocturnal roost and
daytime feeding grounds (Cutts & Speakman 1994). These
data indicated that. on average. Pink-footed Geese flew sub­
stantially outboard of the optimal location which would
maximize their induced power savings. Consequently. the
saving they would experience might be as low 14% of the
induced power and as little as 2.5% of the total flight cost.
On the other hand. there was a weak. but statistically sig­
nificant. correlation between bird-to-bird wing-tip spacing
and c1epth, 8.'; prt.'dicit;d b3' the communication hypothesis,
However, the high variability in this relationship clearly ill­
19913
F LI GH T FOR \L\ Tl 0 N IN GR E Y L,\G GEES E
283
these two measurements was taken as the bill-to-tall length.
We used this latter measurement to scale each of the pho­
tographs.
All the measurements were made with vernier callipers
and were accurate to 0.1 mrn. The implications of the ac­
curacy of the measurements varied with the actual heights
at which the skeins flew and. hence. so did the size of the
resulting image and the clarity of the image. which de­
pended on the extent of enlargement. On average. we esti­
mated that the accuracy of 0.1 rnrn was equivalent to 2.3
ern. Wing tip spacing (WTSJ was calculated by subtracting
the wing span (b: averaged for the IS dead birds) from the
observed lateral displacement.
I
I
,LATERAL OiSPLAC!=MENT :
. {",1ntor b~rd distance)
Flgure 1. Schernar«: diagram of two geese flying in formation to il­
lustrate the measurements made for Greylag Geese. The hill-to-tail
length of each goose was defined by a line joining the bill tip to the
centre or the tail tip. The body centre was defined as halfway along this
line. Depth was the longitudinal distance between the body centres of
the two geese parallel to the direction of llight. The lateral displacement
was measured as the intcrbody distance lateral to the direction of flight.
In this example. there was considerable wing-lip overlap.
consistently definable point in all the birds. We numbered
the birds in each skein. counting the leading bird as 1 and
the birds down each arm of the V as either left 2 to n, or
right 2 to H (after NachtigaIl1970). Having located the body
centre of each bird and defined its position in the skein. we
defined and measured two parameters representing the lon­
gitudinal and lateral displacement of each bird relative to
the bird immediately in front of it. The longitudinal displace­
ment (henceforth called depth) was the distance from body
centre to body centre along a line parallel to the direction
of flight. The lateral displacement was the distance from
body centre to body centre along a line perpendicular to the
direction of flight (Fig 1).
The absolute image size on each projected photograph de­
pended on how high the geese were flying and exactly how
much the negative was enlarged. To scale the photographs.
we used measurements made on 15 Greylag Geese which
had been shot recently as game at the Montrose Basin. ap­
proximately 70 krn from the study site. On each dead bird.
we measured the wing span b (the tip-to-tip length of the
outstretched wingsl, wing chord (maximum width of the
outstretched wing] and bill-to-tail length. Close-up video
film (lntJight Movie, BBC Natural History Unit films) of fly­
ing geese showed that bill-to-tail length may vary because
of stretching and retraction of the neck during flight, There­
fore. we made two measurements. one with the goose's neck
extended (neck placed forward of the bird in a relaxed po­
sition) and one with the neck outstretched (neck pulled for··
Ivan! so [hat rne neck was under tension). The mean of
RESULTS
Measurements of dead birds
The mean 'Acing span of the 15 dead Greylag Geese was
143.9 em (s.d. ::'::4.2 em. coeff. var. = 2.9%). The mean bill­
to-tail length was 78.6 ern (s.d. ::'::2.2 ern, coeff. var, =
2.8%). The mean wing chord was 26.2 em (s.d. ::'::4.1 ern).
Derivation of the optimal wing-tip spacing and
depth to maximize energy saving
We used the observed mean and variation in the wing spans
of the dead birds to derive the predicted distance apart that
the centres of the vortex filaments would be with the use
of the available theoretical models. With the model of Hum­
mel (1973) and Badgerow and Hainsworth (1981: Eq. 1).
the centres of the vortices would, on average. be O.78b apart
= 110.5 cm. Thus the optimum wing-tip spacing from Eq.
2 would be -15.6 ern. This is the distance that the vortex
centres were predicted to be inboard of the wing tips. With
a standard deviation to the wing-span estimate of 4.2 em.
the error (s.d.) on the estimated vortex centre positions
would be 3.3 ern (4.2 x 0.78), and, thus. 9S% of vortex
centres would lie in the range 110.S ::':: 6.4 cm apart. That
is. 95'Yo] of the vortex centres would lie from 104 em to 117
cm apart. and thus between 22 cm and 9 em inboard of
the wing tips. This latter range defines the predicted range
over which birds would be predicted to overlap their wings
if they were exactly following the aerodynamic model.
The range of wing-tip spacings over which birds might be
expected to be found with the use of this mode! appeared
quite wide 1.1 3 em). We therefore explored the potential of
using the morphometry data to generate a more precise pre­
diction. We reasoned that if there was a highly significant
relationship between the bill-to-tail length and the wing
span of individual birds. we might be able to use variations
in the observed bill-to-tail lengths in the photographs to lo­
cate more accurately the distance apart of the vortex fila
ments for that individual bird and thus more closely define
the optimal flight location to minimize energy costs for the
trailing bird. There was a significant positive relationship
between wing span and bill-to-tail length in the i -j dead
282
J.
R
S P L\ K M /\:\ & D. B.\:\ K S
dicated that there was no precise regulation of position oc­
curring. Saving 2.5% of the energy cost of flying between
the roosting and feeding grounds mayor may not be im­
portant for these birds in winter. The key point. however. is
that the birds could have saved significantly more energy
than this by flying in different positions if the overall irn­
petus for the behaviour was to save energy. Overall. our data
for Pink-footed Geese indicated no clear support for either
of the two hypotheses but favoured orientation as a func­
tional explanation. Badgerow (1988) examined 50 skeins of
Canada Geese and found the positioning of eight supported
the orientation hypothesis whilst 27 supported the energetic
hypothesis. Ten skeins supported both theories and seven
were indeterminate. These data also provide no unequivocal
support for one hypothesis but favour the energetic expla­
nation.
It seems possible that both hypotheses are correct but are
more or less appropriate in different species and perhaps at
different times. A critical factor in this possibility is the role
of body size, which will influence flight energy demands and
therefore the imperative for the animals to make flight sav­
ings wherever possible. Thus. larger geese, for example Can­
ada Geese, may fly much closer to the optimum position
favouring energy economy, whilst smaller geese (e.g. Pink­
footed Geese) may have lower flight costs and, thus, have
less impetus to fly in the optimum location and may use
formation flight more for orientation.
The Greylag Goose Ansa miser is the largest native goose
in Europe, measuring 1.:; m in wing span and weighing up
to 4 kg (Cramp et (/1. 1977). It is slightly larger than the
Canada Goose. formations of which have been studied ex­
tensively in the U.S.A. (Gould & Heppner 1974, Williams et
(/1. 1976, Badgerow & Hainsworth 1981, Hainsworth 1987,
Badgerow 1988). For these large birds. the costs of active
flapping flight are probably substantial (Pennycuik 1989,
Rayner et Ill. 1997). In the current paper, we evaluate the
positions adopted by Greylag Geese in formation flights be­
tween their roosting and feeding grounds in northeastern
Scotland in relation to the energy conservation and orien­
tation hypotheses. vVe predicted that, because of their larger
size, they would fly closer to the optimum position for max­
imizing energy saving than we had found previously for
Pink-footed Geese.
MATERV1LS AND M:ETHODS
The study was carried out at Loch Davan, on the Muir of
Dinner National Nature Reserve, 50 km west of Aberdeen.
northeastern Scotland ('i 7"N, 1"'V). Approximately 18,000
Greylag Geese spend the winter nights (late October-March:
at the roost site on the loch. flying out daily to feed on
agricultural land to the northeast. The exact flight routes
of the geese to and from the roost site varied from day to
day. A twin lens reflex (Mamiya C330) camera with an
80-mm lens was mounted on a tripod and 'Nus positioned
about 400 III from the loch. Preliminary observations at the
IBIS 14()
site suggested the geese often flew over this site. Despite
knowing the approximate route taken by the geese and po­
sitioning the camera in the most accessible location to in­
tercept this route, we were unsuccessful at photographing
the birds on more days than we were successful!
Photographs were taken between 11 and 25 November
1992 during the hours directly after dawn (07.00-09.30 h)
and before dusk (15.00-16.00 h), since the geese in flight
were at maximum numbers at these times. A spirit level was
used to ensure the camera lens was pointing vertically up­
wards. This avoided any angular distortion of the images of
the geese and allowed measurements of the longitudinal
and lateral displacements of the geese directly from the neg­
atives. without the need for corrections for perspective dis­
tortion. Such corrections are mathematically possible
(Gould & Heppner 1974, Hainsworth 1987): however, they
may involve substantial inaccuracies (Hainsworth 1987)
and generally also involve rejection of considerable amounts
of film acquired in the field. Gould and Heppner (1974), for
example. filmed 34 skeins of Canada Geese but obtained
useful data from only five. The method we used did not allow
an estimate to be made of the relative heights at which the
birds were flying. Although height of the geese relative to
each other does have an impact on the energy savings, it
does not have an effect on the expected wing-tip spacing
(Hurnmel & Beukenberg 1989).
The method we used assumed that the birds were Hying
in an exact horizontal plane. as is also necessary to make
the corrections for perspective distortion. However. the er­
rors which are introduced into the estimates of lateral and
longitudinal distance when the birds are directly overhead
are relatively trivial because the deviations from an exact
horizontal plane are small compared with the distance from
the birds to the camera. Thus. if a skein was flying at an
altitude of 200 m. a height difference of 2 rn between ad­
jacent birds would introduce an error of only 1 'X, in the
estimated lateral and longitudinal distances. In fact. film
taken from a camera in a model aircraft flown adjacent to
formations indicated that the deviations from a horizontal
plane were probably less than 1 m: thus, errors resulting
from this assumption can probably be ignored. This proce­
dure is the same as that we used successfully previously to
photograph skeins of Pink-footed Geese (Cutts & Speakman
1994), We used a fast film (400 ASA Tri-X Kodak) and a
fast shutter speed (1/250 s or 1/125 s) to ensure image
clarity.
Estimates of the relative positioning of the birds in each
photograph were made from measurements taken directly
from the negatives. The negatives were placed in a photo­
graphic enlarger (Durst) which enhanced the images ten
fold. Drawings were made from the images projected onto
paper. IA'e located the body centre line of each bird by draw­
ing a line between the bill tip and the centre of the trailing
edge of the tail. The length of this line represented the bill­
to-tail length of that bird. The centre of the body was lo­
cated at the middle of this bill-to-tail length line, This body
centre does not retied the centre of gravity but rather a
184
j./\ SPE:\KM:\N &
u.
IBIS 14 ()
B:\NKS
155
Aerodynamic
prediction
H
1
150~
I
E
s:
~
0­
'"c
Cl
~
145~
I
@
I
14°1
135~
I '"
I
130
72.5
o
-100-80 -60 -40 -20 0
75
Body length (em)
20 40 60 80 1001 20 140 160
Wing tip spacing (em)
Figure 2. Wing span plotted against body length for 1 S freshly dead
Greylag Geese. There was a significant positive relationship. and the
linear regression explained 42% of the variation in wing span.
birds (F'iJ = 13.4. P < 0.01; Fig. 2). We used least squares
fit regression to define this relationship because our aim was
to derive a prediction for wing span. The regression equa­
tion. wing span (em) =, 48.1 + 1. 19bill-to-tail length (em),
explained 41 % of the variation in wing span. Although this
relationship was significant. it was clearly heavily influenced
by two points derived from one large and one small bird.
The 95% predictive interval for any wing span. when the
bill-to-tail length was known.. varied between 15 em and 20
ern over the range of bill-to-tail lengths. 76-84 ern. In ad­
dition. because we could not define at what stage each neck
was in the expansion and contraction cycle and because
there were accuracy errors in the measurement of the bill­
to-tail distances with the callipers. it was evident that it
would not be possible to refine the predictions beyond the
broad inclusion ranges defined above.
Figure 3. Frequency distribution of wing-tip spacings of Greylag
Geese in formation flight. The range of values anticipated from the aero­
dynamic model is also shown.
the birds were flying in the downwash region of the bird in
front. which was defined as an overlap exceeding 0.5b (Hig­
don & Corrsin 1978). The range of observed wing tip spac­
ings was much greater than anticipated from the exact con­
formation to the aerodynamic predictions. Nevertheless.
17.4% of measurements were in the range expected from
the aerodynamic prediction.
Measurements of depth
A total of 247 individual depth values were measured (Fig
4). The mean was 18~.8 em (s.d. ± 126.1 em). The distri­
bution was heavily skewed. and the median depth was 123
em. The depth at which the pair of vortex filaments roll up
behind the bird was predicted to be 56.3 em (s.d. ±8.2 em).
Only 4.8% of birds flew with depths less than 56.3 em.
Measurements of wing-tip spacing
Only in 25 skeins were the images sufficiently defined to
analyse. These yielded measurements on 272 geese and 247
wing-tip spacings. The distribution of the pooled data across
all the skeins photographed was compared with the pre­
dicted ranges from the theoretical model (Fig. 3). The dis­
tribution had a slight positive skew. The mean wing-tip spac­
ing was -8.3 em (II = 247. s.e, :::2.56 cm). Note that the
negative value indicates wing-tip overlap. This overlap was
less than the -15.6 cm predicted by the model. Because of
the slight skew, the mean may represent a slightly biased
estimator of the central tendency of this distribution, and
the median wing-tip spacing was - 17.5 ern. which was
much closer to the prediction,
A total of 64.8% of the measurements indicated wing-tip
overlap. but only 2(% of the total were
50 (rver1apr~~d
that
20
o
o
100
200
300
400
500
600
700
800
(;CL'SC
in tor­
Depth (em)
t'ligll;r~:~.
.nt.unn
Frequency distribution of depths of Crcylag
1998
zoo
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; 50
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100
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6
8
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Position
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- 1 5 0 4 1 - - - - - , - - - - - - , . . . . . - - - - - - , - - - - 1I
o
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200~
"
c.
f=
OJ
,I
600~
e
E
..:::.
285
FLIGHT FORM,\TlON IN CREYL;\G GEESE
ZOO
400
600
800
Depth (em)
Figure 5. The relationship between wing-tip spacing and depth [or
Greylag (~eese flying in formation. There was no significant relationship,
contradicting the prediction of the orientation/cornrnurucatton hypoth­
esis.
where the vortices were predicted to have not yet rolled up.
However. only 14% of the geese flew in the 95% confidence
region for location of the roll-up point ('10.2-72.4 em), The
modal class 10G--150 ern included 27% of the depth mea­
surements (Fig 4).
Relationship between wing-tip spacing and depth
There was no significant relationship between the paired
values of depth and wing-tip spacing (1.2 == 0.008: Fig. 5).
This absence of a relationship indicated that the birds did
not adjust their lateral displacement to compensate for lon­
gitudinal displacements (and vice versa) in order to main­
tain a constant angle between birds.
Relationship between depth and position
We selected the data pertaining to depth for the first ten
birds of each skein along both left and right arms. We made
this sel~ction because only a few skeins had more than ten
birds in each ann. and these sparse data had a potentially
large impact on any relationship between depth and posi­
tion. vVithin the first ten birds. there was no evidence that
depth increased as position from the lead bird increased (Fig
6): therefore. these birds did not adopt the swept V forma­
tion.
mSCUSSWN
He\\'
close to the
On
wing-tip spacing that was predicted to bestow maximum
Figure 6. The relationship between depth and position of the bird in
the V formation. where 1 represents the leading bird. There was no
relationship between depth and position over the leading 20 birds in the
formation (ten in each arm). There was also no significant relationship
between depth and position if birds beyond the tenth bird in each ann
were included (but there were fewer data at these extremes).
energetic benefit. Despite this, the majority (c. 83°;;,) of birds
still flew outside the zone where benefits were maximized.
However, very few birds flew in the downwash region. So
while most birds did not achieve the maximum benefit, the
vast majority (>97%) did save some energy from adopting
the flight formation. The relatively high variation in the
wing-tip spacing compared with the range predicted by the
model probably stems from several sources. First. the model
was derived for fixed wings and did not account for flapping.
Second, the vortex locations were predicted for still air and
did not account for wind strength and direction. Alterna­
tively, the birds may have been attempting to track the trail­
ing vortices to save energy but were imperfect at doing so.
Our photographs were thus a snap-shot of the distribution
of savings that an individual might experience during a typ­
ical flight. Hainsworth (1987) showed dynamic changes in
positioning of Canada Geese flying in formation and sug­
gested that most of the positional variation reflected unex­
pected movements of the bird in front. It is unlikely that
measurement errors. or deviations from the assumption that
the birds were flying in an exact horizontal plane, contrib­
uted significantly to the observed variation.
When we compared our data with those of Canada Geese
(Hainsworth 1987) and Pink-footed Geese (Cutts & Speak­
man 1994). the !light patterns were similar. with very few
of these two species flying in the downwash zone, However.
Greylag Geese flew much closer to the optimum overlap po­
sition predicted by the energy saving model than did the
Pink-footed Geese and had a similar median location and
distribution to that reported in the Canada Geese. These ob­
servations accord with our a priori prediction that larger
geese might have a greater imperative to save energy during
their flights.
Vile previously evaluated. with the use of the aerodynamic
model (Hummel 1973. Badgerow & Hainsworth 1981.
1989},the
the Pink-footed Goose when flying in formation. The saving
286
1.
R. S P L\ K M II
at the average observed position amounted to 14% of the
induced energy. which amounted to only 2A°ft) of the total
flight cost. When we performed the same calculations for
the Greylag Geese observed here, the saving in induced pow­
er at the average location was about 33 'X,. The predicted
total flight costs for a 3.5-kg Greylag Goose (Cramp et al.
1977) of wing span un mare 75.2 W at the minimum
power speed of 14.4 m per sand 93.2 W at the maximum
range speed of 23.3 rn per s. Of these total costs. the in­
duced power comprised 25.4 W and 15.8 W. respectively.
With a saving on the induced power at the mean position
of 33%. the total costs at the minimum power speed were
reduced by 11 % and at the maximum range speed by 5.6%.
However, this procedure defines the saving Lr1 flight costs
only at the average position. If each individual oscillated in
its position around the observed average. then the mean
saving achieved would differ from the saving at the average
location. We revised our estimates of the energy savings by
combining the probability distribution of the observed wing­
tip spacings with the distribution of savings predicted by the
Badgerow and Hainsworth (1981) model. This revision gen­
erated a probability times savings distribution for each spe­
cies. This calculation suggests that Pink-footed Geese would,
on average. save 16.3% of the induced power. equivalent to
2.7% of the total flight costs at the maximum range speed
(S.S'X, at minimum power speed), whilst the Greylag Geese
would save. on average, 26 . .5°,{) of the induced power. equiv­
alent to 4.5% of the total flight costs at the maximum range
speed (8.9% at minimum power speed). By maintaining, on
average, a more optimal positioning. the larger Greylag
Geese effected greater economies in their flight costs.
Depth
The distribution of depths in the Greylag Geese parallelled
closely the distribution of depths in the Pink-footed Geese
(Cutts & Speakman 1994). The mean position at approxi­
mately three times the anticipated roll-up point in the cur­
rent study matched almost exactly the mean position in the
smaller goose. Moreover. only 4.8% of birds flew very close
to their leading bird, in the region where the vortices were
predicted to have not yet rolled up. The positioning of the
birds was consistent with our previous interpretation that
the greater 'distance reduces the probability of collision or
straying erroneously into the zone where the vortices have
not yet rolled up.
Another reason tor flying farther back than the roll-up
point may be connected with the variability in the vortex
locations caused by wing Happing. Immediately behind the
wing, at the roll-up point, the shed vortex must vary its
position over an arc with it radius of about 'i0 em several
times each second. These oscillatory movements in the vor­
tex location could be effectively exploited only if the trailing
bird not only regulated its position relative to the bird im­
mediately in front but also synchronized its flapping with
the bird in front. Whether this synchronization of flapping
occurs has been the focus of some debate, with some au­
x & n.
B ,\
x KS
IBiS
I-J.()
thors claiming the flapping of adjacent birds was synchro­
nized (Nachtigall 1970) and others claiming it was not (Ber­
ger 1972, Gould & Heppner 1974). In Brown Pelicans Pe­
lecalws occidentalis. flapping sometimes "vas synchronized
and at other times was not l Hainsworth 1988 I.
Oscillatory movements in the vortex location may become
damped and the predictability of vortex location improved.
the further back one moves from the wing. thus removing
the need to exactly synchronize flapping. In theory. the
damping will be greater. and thus the benefit will improve.
as distance behind the bird continues to increase; however,
in practice. the locations will at some stage become less pre­
dictable because of wind displacement of the vortices. The
observed modal depths in both species may reflect this trade­
off.
Relationship between depth and wing-tip spacing
The absence of any relationship between depth and wi.ng­
tip spacing does not support the orientation and commu­
nication hypothesis.
Relationship between depth and position
The absence of any relationship between depth and position
indicated that, in these skeins, the Greylag Geese did not
distribute the savings from formation flying equally. This was
also the case in Canada Geese studied by Hainsworth
(1987), but some of the formations described by Williams
et al. (1976) for the same species appear to conform to the
swept V model, and Hummel (1983) states that these for­
mations are "observed in nature". The main effect of flying
in an unswept V as the birds here did, is that the leading
bird makes only minor savings relative to the savings made
by all the trailing birds (Hummel 1978).
However. a swept V is not the only method by which
equability of savings can be achieved. For example, equa­
bility could be achieved by alternating which member of the
formation adopts the position of leader. There is considerable
anecdotal evidence that leadership of V formations is alter
nated between members of the formation (Gould & Heppner
1974, Williams et al. 1976. HUl1ll1lel1983). but such ob­
servations are hard to separate from the occasional breaks
in formation which might occur for other reasons. such as
gusts of wind. Moreover. equability of savings need not oc­
cur over a single flight but could be achieved if the lead bird
in a coherent long-term group of birds was alternated on
different days.
Role of body size in formation furaction and
predictions
The overall pattern we observed in the formation flights of
these Greylag Geese supported the energy savings hypoth­
esis more than the orientation and communication hypoth­
esis. This 1S corlsistcn.t with obscrvarions made on the sim­
ilar sized Canada Goose (Hainsworth 1987, Badgerow
287
1lJ lJ S
1988). In contrast. our previous data for the smaller Pink­
footed Goose (Cnits & Speakman 1994, I were more equivo­
cal. The savings were smaller at around 2. S'X,. and the birds
apparently could have made greater savings by flying in a
different location. Moreover, the patterning tended to favour
the communication and orientation hypothesis. These dif­
ferences might reflect a scaling effect in the functionality of
the behaviour. Thus, both the functional hypotheses could
be correct but more or less appropriate in different sized
species, with the communication and orientation function
being more important in smaller birds, whilst the energy
saving function might be more significant in larger birds.
There are several mechanisms by which body size could
influence the function of formation Hying. First. larger birds
generally have greater absolute !light costs (Pennyculk
1989, Rayner et £11. 1997). These greater costs may lead to
a greater imperative to save energy during !light (Badgerow
& Hainsworth 1981). Second. larger birds with slower wing­
beat frequencies may find it easier to fly with precision close
to the vortex filaments (Badgerow & Hainsworth 1981). and
locating the optimum position for making energy savings
may become increasingly difficult in smaller birds. If body
size does lead to a shift in the functionality of the behaviour.
this leads to two testable predictions. First. those smaller
geese. such as Brent Geese Bnmta bemida and Barnacle
Geese Bmnla leucopsis. which adopt V formations should not
necessarily fly close to the optimal location for energy sav­
ings but should show correlations between wing-tip spacing
and depth. Second. very large birds which fly in 'Ii forma­
tions, such as swans and pelicans. should fly close to the
optimal location and have no correlation between wing-tip
spacing and depth,
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