ANGLE
OF CANADA
GOOSE V FLIGHT
MEASURED
BY
FORMATION
RADAR
TIMOTHYC. WILLIAMS,THOMASJ. KLONOWSKI,
AND
PHILIP
BERKELEY
A recent paper by Gould and Heppner (1974, Auk 91: 494) reports
the measurementof several parametersof formation flight by Canada
Geese(Branta canadensis)revealingconsiderablevariation in formation
flight of thesebirds and suggestingthat factorsother than aerodynamic
advantagein flight may lead to the V flight formation(see alsoHeppner
1974, Bird-Banding45: 160). Gould and Heppner used a photographic
techniqueto record the appearanceof avian flight formations,and the
angle of the V was obtainedby an ingeniousgeometricaltransformation.
The requirementsof the techniquewere suchthat of 34 formationsfilmed
only 5 yielded measurableangles. In an effort to extend thesedata we
have useda high resolutionradar to measurethe anglesof V formations
of geese.
The radar usedwas a mobile,high resolution,low power radar (termed
an Ornithar) designedfor studiesof avian behavior by T. C. Williams,
and is describedin Williams et al. (1972, Amer. Birds 26: 555). Further
detailson the useof the Ornithar will be foundin Williams et al. (1974,
Flight patterns of birds studied with an "Ornithar." Proc. Conf. Biol.
AspectsBird/Aircraft CollisionProblem,Arlington,Virginia, USAF Off.
Sci. Res.). The Ornithar is a 3-cm wavelength,3-kw peak power radar
with a 30ø vertical beamwidth (3 db points) and a 2.5ø horizontal
beamwidth(3 db points). High resolutionis obtainedby operatingat
a pulsewidthof 0.08 microseconds
and a maximum range of 1 km. The
radar antenna rotates at 32 rpm. Simultaneousvisual and radar observations on ducks and geeserevealed that the Ornithar reliably distin-
guishedtwo targets at 400-500 m range if they were separatedby at
least 50 m. Thus, the resolutionis sufficient to display the angle of a
V of geeseas shownin Fig. 1, but not to separateindividual members
of the flocks.
The Iroquois National Wildlife Refuge in westernNew York State is
a temporary stopoverfor thousandsof Canada Geese (primarily subsp.
interior) duringthe springand fall migratoryseasons.In the springof
1973 the first of thesebirds had arrived 13 Februaryand mostof the
remainingby 15 March. During March and April 1973 we positioned
the Ornitharapproximately
2 km to the southwest
of the largestpond
in the Iroquois Refuge. From this positionwe were able to watch flocks
554
The Auk 93: 554-559. July 1976
July 1976]
CanadaGooseV Formation
555
Fig. 1. A single frame of the 8-ram film used to record radar data. Arrow points
to a group of geeseflying in a V. Diameter of the area shown in radar display •--1.85 km. Other radar echoesare from objects on the ground (primarily trees and
farm fences).
of geesemovingto and from the pond on daily feedingflights, at altitudes estimated to be between 40 and 80 m above the ground. Observationswere made during 6 days and 6 nights,between 1600 and 2300
local time. The sky was clear on all days, with southwestwinds at less
than 10 kph. The temperaturewas between 5ø and 16ø C. Data reported here were obtained on 27 and 29 March; on the other 4 days,
geesechoseflight routes that did not pass near enough to the radar to
obtain goodquality data. V formationswere never seenduring the six
nightswe watched,but possiblyat night geesewere not movingor they
wereusingroutestoo far from the radar. The radar data wererecorded
on Super-8mm film from the PPI displayof the radar as describedin
Williams et al. (1972 ibid.). Each frame of film recordeddata from a
singlerevolutionof the radar and showedthe positionof one or more
V's of geeseas in Fig. 1. Single frames of the films were projectedon
large sheetsof white paper and a straight line was drawn on the paper
down the leadingedgeof each arm of the V formation. The intersection
of thesetwo lines was measuredas the angle of the V formation. If the
films showedisolatedradar echoescorrespondingto a few geesethat left
556
Wm.mxas, K•o•owsx•, .•m) Bg•xg•g¾
[Auk, Vol. 93
140 ø
120 •
100 ß
40 ø
20 ø
0
50
1O0
150
Averoge
Lengthof V (rn)
Fig. 2. Angle of V formation of Canada Geese observed with radar vs. total
length of both arms of the V. Bars indicate total range of observedangles for each
formation
observed.
the V formation,thesewere ignored. If a line could not be clearly fitted
to a flight formation,the data were not used.
We recorded 54 V formations for 2 to 10 rotations of the radar beam.
The closest V measured was 230 m from the radar and the most distant
was 920 m. V's seen for a single rotation or formations that did not
show a clear V were not measured. The V's were rarely regular and
more often shouldbe describedas a "J" (see Heppner ibid.). In many
formations,althoughthe arms of the V were relatively straight, the apex
of the V was rounded. The angle of a singleV formation did not remain
constantwith successive
sweepsof the radar beam but varied by 5ø to
43 ø. The mean values for each of the measured V's varied between 38 ø
and 124ø. The rangeand the meanof measuredanglesof V formations
are plottedin Fig. 2. The variancebetweenV's was significantlygreater
than the variancewithin V's (P < 0.001), indicatingsignificantdifferencesbetween the anglesof different V's.
Errors may be introducedin our measurementsin three ways: distortion of the angle of the V by the radar display, errors in measurements
of the recordedradar data, and departuresfrom level flight or V flight
July 1976]
Canada
Goose
V Formation
557
As seen
from
below
Me;sured•nõle
Radar
Screen
Fig. 3. Diagramillustratingdistortionof the angleof a V of geeseby the PPI
screenof a radar. V seen on screenof mobile radar is comparedwith angle of the
sameV asseenby an observerdirectlybelowthe geese.Altitudescaleand magnitude
of the distortion
is greatlyexaggerated.
Actualdistortions
wereprobablylessthan3ø.
formation
by the geese.A radarPPI displaysuchas shownin Fig. 1
shows
theposition
of objects
givingradarechoes
as a function
of slant
range(straightline distance
between
the targetand the radar) and
azimuthof the targetfromthe radar. The difference
between
the slant
rangeandthedistance
fromtheradarto a pointon theearth'ssurface
underthe targetwill resultin the measured
anglebeingsmallerthan
theangleof theV projected
on theearth'ssurface.Thisrelationship
is
illustrated
in Fig. 3. The magnitude
of this distortion
increases
with
altitudeof the targetanddecreases
greatlywithrange.(The distortion
is greatlyexaggerated
in Fig. 3.) The distortion
in a V with an angle
558
WILLIA1VfS,
KLONOWSKI,
ANDBERKELEY
[Auk, Vol. 93
of 80ø at an altitude of 60 m at a rangeof 230 m wouldbe 2.5ø; at a
range of 1000 m the distortionwould be 0.26ø. If we had incorrectly
estimatedthe altitude of the geeseby a factor of 2 and the true altitude
were 120 m, the error at 400 m range would be a maximum of 3 ø for
an 80ø V. Measurements
of the angleof a V from the radar films were
repeatableto within 5ø (2 ø in most cases). Althoughmost of the formationsof geeseappearedto be in level flight, this is difficult to ascertain from the ground. If the geesehappenedto be flying so that the
far arm of the V werehigherthan the near arm as seenfrom the radar,
then the PPI displayof the radar wouldgive a moreaccuratepicture
of the angleof the V thanwoulda photograph
takenby someone
directly
belowthe geese.For an 80ø V with armsof 100m eachat a rangeof
400 m from the radar at an altitudeof 60 m, the two geeseat the ends
of the V woulddiffer in altitudeby only 19 m to cancelthe distorting
effect of the radar'sPPI display.
As all our measurements
weremadeon the samespecies
during2 days
with almost identical weather conditions,it does not appear that the
anglesof the V formationsof geesewe measuredwereaffectedby cloud
cover, temperature,wind speedor direction. A plot of angle of the V
vs. airspeedof the birds revealedno significantcorrelation(r = 0.005,
P > 0.05) betweenthesevariables.As shownin Fig. 2 the only factor
that we foundto be correlatedwith the angleof the V was the sizeof
the flight formationas measured
by the total lengthof the armsof the
V (r =-0.482, ? < 0.01).
Our data lead us to concurwith Gould and Heppner (1974 ibid.) that
"V" formation flight by Canada Geeseis probably not the result of a
simple aerodynamicrelationshipbut may have behavioralcomponentsas
well. We would further add that one may expect the factors affecting
this type of flight to be complexas the basic formationis so variable.
Note added in proof.--On 23 March 1975 Frank Heppner and the
authors made simultaneous observations on several small V formations at
the Iroquois National Wildlife Refuge. Of these, two gave data that
were measurableboth with Heppner's optical techniqueand the radar
techniquedescribedabove. The anglesmeasuredwith the two techniques
showedno significant differences. However it was apparent that some
V formationsmeasurablewith Heppner'sopticaltechniquewere too small
to be resolvedby the radar and somelarge formationsmeasurableon
the radar were too poorly organizedat the apex of the V to be measur-
able with Heppner'sopticaltechnique.Thus, the largevariancein the
angleof V flight formationwe observed(comparedto that reportedby
Gouldand Heppner) may be due to a differentscaleof observation.
July 1976]
Canada GooseV Formation
559
This researchwas supportedby Grant 50-A107-A from the Research
Foundationof the State University of New York and the Departmentof
Biology, State University of New York at Buffalo. We gratefully ac-
knowledge
the helpof the staff of the IroquoisNationalWildlife Refuge.
Departmentof Biology, State Universityof New York at Buffalo,
Health Sciences
Building,Buffalo,New York 14214. Presentaddressof
first author: WoodsHole Oceanographic
Institute,WoodsHole, MA 02543.
Accepted 10 March 1975.