Formation Flight in the Canada Goose (Branta. C. canadensis)

The function of formation flight in Canada Geese and other large waterfowl is unknown, although two hypotheses have be en proposed. One hypothesis suggests that formation types are a function of visual and spatial needs; the other suggests that these birds are able to reduc e induced drag by formation flight. Published data propose that if formation flight can reduce drag, energy could be saved on long migrations. In this study, autumnal migrating flocks of Canada Geese (Branta c . canadensis) were filmed at a refuge in upstate New York during early October, 1971. The Super-8mm films were analyzed to determine the types of formations util i zed, the number of birds per flock, the relationship between wind conditions .and flight direction, the angles of Vee and Jay formations, the distance between adjacent birds along the legs of Vee formations, and wing-beat frequencies and phase relationships among the birds in a formation. This study describes a technique to measure the angles of Vee formations, by the use of three-dimensional descriptive geometry, and is the first study in which formation angles have been measured empiri cally. The results show formation angles much more acute than previously hypothesized, simi lar wing-beat frequencies among all birds, variable spacing between adjacent birds, and an apparent preference of the majority of the flocks for flight with crosswinds, and at low wind speeds . Due to the variable, and generally large, spacing between adjacent birds along the legs of the formations analyzed, it seems doubtful that these formations could be using the Vee for an aerodynamic advantage. Although the flocks filmed in this study may be more representative of daily movements than of migratory flights, it is possible that the primary function of formation flight may be to maintain flock unity, thus aiding in navigation . Further work is proposed which might resolve the question of a possible aerodynamic advantage to formation flight.

In this study, autumnal migrating flocks of Canada Geese (Branta c . canadensis) were filmed at a refuge in upstate New York during early October, 1971. The Super-8mm films were analyzed to determine the types of formations util i zed, the number of birds per flock, the relationship between wind conditions . and flight direction, the angles of Vee and Jay formations, the distance between adjacent birds along the legs of Vee formations, and wing-beat frequencies and phase relationships among the birds in a formation. This study describes a technique to measure the angles of Vee formations, by the use of three-dimensional descriptive geometry, and is the first study in which formation angles have been measured empiri cally. The results show formation angles much more acute than previously hypothesized, simi lar wing-beat frequencies among all birds, variable spacing between adjacent birds, and an apparent preference of the majority of the flocks for flight with crosswinds, and at low wind speeds . Due to the variable, and generally large, spacing between adjacent birds along the legs of the formations analyzed, it seems doubtful that these formations could be using the Vee for an aero- Ta ble 2 .
Ta ble J .  (Forbush, 1912;Bent, 1925). Geese are gregarious birds, their flocks usually composed of family groups (Collias, 1952); such a behavioral mechanism would permit the members of a family to stay together during flight. A concurrent suggestion is that the spacing observed between birds is a function of the amount of room each bird needs to fly without impediment, and the point at which the eyes of a particular bird are best focused on the bird ahead (Poncy, 1941;Van Wormer, 1968;Heppner, MS.).
The second hypothesis considers the aerodynamics of flight, and a possible mechanism flocking birds could use to conserve energy. When a bird (or airplane) flies through the air, there is a force acting against its movement; this force, or backward pressure, is called drag .
Part of the total drag is termed "induced drag" and is caused by the rearward inclination of the airflows over and under the wing. At the wing-tips these airflows meet and form a vortex; this wing-tip vortex is the major component of induced drag (Parkinson, 1944;Dwinnell , 1949) .
Many writers have suggested that birds flying in formations make use of the currents produced by the wing-tip vortices of the birds on either side of them, and are thus able to conserve energy (Munk, 1933: Storer, 1948. Lissaman and Shollenberger (1970) have developed a computer model to calculate the energy savings of birds flying in a Vee formation, and furthermore have suggested that drag can be evenly distributed among the birds in a linear formation, including the lead bird. They proposed that the angle of a formation will depend on the spacing between the birds, and that uniform drag distribution is possible even with uneven spacing.
The theoretical model of Lissaman and Shollenberger has not been confirmed through actual data obtained from 2 linear formations of bird flocks. This study presents data on the types of formations used by the Canada Goose (Branta canadensis) , the angles of Vee formations, the number of birds in the flocks, the spacing between adjacent birds in a formation, wing-beat frequencies and phase relationships, and relevant meteorological data such as wind speed and directions, and correlates these data with the above hypotheses.

LITERATURE REVIEW
The Canada Goose is a social b"rd, with a close family life . These geese appear to mate for life , and to maintain the family group of one breeding season unt il the beginning of the following breeding season (Delacour and Mayr, 1945;Elder and Elder, 1949 ;Beer, 1958). A family may be from 5 to 9 birds (Phillips, 1910 ;Hanson and Smith, 1950), and migrates as a unit. It has long been believed that large flocks of geese consi s t of many families (Phillips, 1910;Beer, 1958); Elder and Elder (1949) pointed out that although this is probable , it has not been proved.
The survival value of flocking for long-d istance flights has not been determined . Darling (1952) suggested that such social behavior must have some value for the individual bird and the species, but that further analys i s was needed. Darling (19J8) observed flights previous to migration, in wh i ch ever-growing flocks seemed to " practice " flying together; he suggested that these flights were to synchronize mood and flight . Werth (1958) stated that flocking is an innate characteristic, and Lorenz (19 37) proposed an automatic releaser--the V-shaped stripe of white on the rump of the goose --wh ich could release this behavior. However, geese do not flock throughout the year, so this "releasing" mechanism might not function during certain seasons, i.e •• the breeding season. Emlen (1952) suggested that among birds there are positive forces which cause mutual attracti a::>n, and negative forces of mutual repulsion: these have= their bases in innate neural patterns, and are influenceC:l by hormones. Collias (1952) supported this idea by stat:fil ng that the decline in gonadal activity after the breeding season reduces territorial behavior, and allows toleral.lce to flocking. within a formation has been attributed to two possible causes. One is that the leat.d bird must work harder than the other birds, because it must'break the air" for the other birds (Forbush, 1912: Bent, 1925: Van Wormer, 1968). Canada Geese are very strong and rapid flyers, and have been recorded at flight speeds up to 106 kph (60 mph) (Van Wormer, 1968). During long-distance flights their speed var i es from approx i mately 70 kph to 106 kph (Queeny, 1947;Van Wormer, 1968); easy cruising flight is approximately 35 to 53 kph (Preston, 1892;Cottam et al, 1942 ;Tucker and Schmidt-Koenig, 1971) . How long these birds  1967). Migration involves protracted flight, and any bird which attemp t s t o mi grate successfully must have methods to obtain and conserve the n eeded energy. One method is to engage in premigratory hyperphagia, and use stored fat to provide energy for migration. Many of the passerines, particularly those which make long over-water migrations, utilize t his technique (Nisbet , 1963;King and Farner, 1965;George and Berger, 1966). Flight becomes easier as the load lessens , but there is always the danger that the bird will exhaust its energy stores before the trip is over. George and Berger (1966) suggested that there is a fairly wide safety margin in these reserves, but more recent studies by Tucker (1971) suggested that such birds have small safety margins in these long, over-water flight s, unless they use additional means to obtain and conserve energy.
The fat stores of heavy birds, such as ducks, gee se, and swans, have not been studied. Pennycuick (1969) and Nisbet (1967) suggested that large birds may require more energy per unit weight than do small ones, and are unable to carry as heavy fat loads . Greenewalt (1962) has suggested that the major flight muscles of any bird constitute approximately 17% of the body weight. As geese and swans have very high wing loadings, in comparison to some of the smaller birds, how are they able to power their flights for long distances, with the same relative amount of muscle but more weight per unit area? Nisbet (1963) concurred with the idea that energy consumed in flight is proportional to body weight, but he also reported a discrepancy in the literature i although this theory seems to agree for small birds, the data on large birds are not consistent. Schaefer (1968) off ered a possible explanation for this discrepancy, from his studies of the aerodynamics I of flapping birds. He suggested that the energy needed to fly a certain distance is inversely proportional to the spe ed of flight. If this i s the case, then b i rds such as ducks and geese (fast flyers) would not require so great a fat load to fly the same di stance as woul d a passerine.
In addit ion, most migrations of the large waterfowl do not involve long over-water flights; probably they are able to obtain much of the i r energy from frequent feedings (Cone, 1968).  (Parrott, 1970;Davis, 1896;Raspet, 1950). Other birds, such as cormorants (Phalacrocorax spp.) may conserve energy by alternat i ng a series of flaps with short periods of soaring (Austin, 1961). Geese in which the body is moving (Dwinnell, 1949) and of the non-lift-producing portions of the body (Pennycuick, 1969).
The importance of the parasite drag increases as the speed of the moving body increases; induced drag decreases in signif i cance as speed increases (Dwinnell, 1949, Lissaman andShollenberger, 1970). Induced drag is pr'marily a function of the shape of the wing and the aspect ratio (the ratio of length to mean chord of the wing). If operating at high speeds a low aspect-ratio wing helps reduce parasite drag; at low speeds, a high aspect-rat io will decrease induced drag (Dwinnell, 1949). The most efficient fl ight speed will be the speed at which induced and parasite drags are equal; the lower these drags, the greater will be the energy saving and poss i bl e range increases of the b i rd.
Parasite drag can be reduced by increasing the stream-lining of a body , or by changing the fluid in which the body moves (Dwinnell, 1949) . Birds have no control over the viscosity of the air , but most flying birds possess very streamlined bodies; Pennycuick (1969) suggested that geese and swans " look'' even better streaml'ned than most birds. Raspet (1950Raspet ( , 1960 studied parasite drag of the Black Vulture (CoragyRs atratus) , and calculated that this bird has very low values for parasite drag . He suggested that stre amlining is increased by a boundary layer controlled by the feathers, and that the feathers are "selectively porous", allowing up to ten times more air to pass through the feathers in the downward direction , than in the upward direction . If true, the bird would be aided by increasing the power of the downstroke , and the rapidity of the upstroke, or " recovery stroke " (Cone , 1968 Reduction of induced drag may be accomplished by several means . Static soaring birds , operating at low speeds and with a fairly low aspect -ratio wing, would appear to have a high induced drag . The presence of " slots " between the primary feathers, however , raises the effective aspect ratio; each feather acts as a separate high aspect-ratio wing, the result being that lift is greatly increased and induced drag decreased (Raspet, 1950;Savile, 1957).
The above discussion has dealt with the reduction of drag in fixed -wing aircraft (soaring birds, or man-made airplanes). Before continuing a discussion of drag reduction, it is necessary to study how flapping -w ing flight (such as goose fl i ght) differs from fixed-wing f l ight.
A flapping-wing bird is a non-rigid (elastic) f l ight system, the center of gravity constantly changing with the change in the distribut i on of mass (Cone, 1968). The shape and position of a flapping wing also is constantly changing, the outer section of the wing propelling the bird, and the inner wing providing lift. In steady flight, the flapping has a regular periodicity. Greenewalt (1960) has suggested that bird wings act as mechanical osci l lators, which could be energy-conserving devices (Tucker, 1966).
With the constant changes i n a flapping wing, the forces acting on each part of the wing also are changing.
Thus, calculation of the total lift or drag on such a wing, without knowing every force on every section of the wing, at all times, is extremely diffi cult (Cone, 1968) . Such a calculation has never been made for a flapp i ng wi ng. Brown (1953) suggested that "a flexib l e structure such as a bird's wing can have no fixed aerodynamic properties, for these clearly change as the forces on the wi ng change." For flapping birds, Cone (1968) suggested that the i nduced drag is the largest drag source. Induced drag is caused by the rearward flow of air from above and below the wing; this airflow forms a wake (the vortex wake), strongest at the wing-tips. For fixed -wing a i rcraft, induced drag can be reduced by changing the effective aspect ratio, or by increasing speed ( Dwinne ll , 1949). For a flapping wing, this vortex wake becomes very complicated.
Cone suggested that t he vortex wake and its associated induced drag are the most complicated features of the aerodynamics of the flapping wing, and will be very difficult to compute.
Both Cone (1968) and Raspet (1950) hypothesized that flapping-w i ng birds might be able to reclaim energy from the vortex sheet; Cone stated that the v ortices may be producing a negative induced drag (i.e. thrust). In addition, the primary feathers may aid in drag reduction by spreading the vortex wake. This spreading would reduce drag, and indicates that the shape and strength of the vortex wake of a flapping bird may be significantly different from that of a fixed -wing aircraft of similar planform. Munk (1933) and others (Storer, 1948;Savile , 1957;Van Wormer, 1968;Lissaman and Shollenberger, 1970) proposed that linear formation flight may reduce induced drag.
Each bird in the formation flies behind and slightly to the side of the b i rd ahead; in this position the bird could "p ick up'' the ris ing vortex from the bird ahead, and gain extra lift . Those species observed flying in linear for -ma ions are generally large, heavy water birds, such as geese, s wans, cranes, pelicans, cormorants, flam i ng os, storks, herons, and some of the larger ducks (Austin,1961) .
As prev i ously discussed, large birds may have energy demands during migrations wh i ch coul d be met only by i ncreased aerodynami c efficiency . S i nce soaring ~ ~ is not commonl y observed among the ma j ority of t hese bi rds, format i on f l igh t and/or e f f i c i ent use of prevaili ng wi nds could be energy-con serv i ng me chanisms , parti cularl y useful for long distances. Bent (192 5 ) and Howl ey (1884 )  There is a d i screpancy among these data, further confused because these workers fai l to describe the methods used to calculate obs e rved formation angl es. Ac curate me a s urements of f ormations in flight are dif ficult to make without use of geometric relationships and/or sophisticated equi pment ; possibly these worke r s fa i led to cons i der depth perception and obliquity of v i ew .
Nachti ga ll ( 1970) suggested that there should be wi ngbeat phase re l ationships among the bi rds in an exact Vee format i on. He has demons t rated, through mo ti on-p i cture analys i s, that " the far t her out along the arms of a ' V' the g eese are located, the lat er the i r wi ngs ach i eve a given stroke pos i t i on"; and that these phase re l ationships are ne c essary if the birds are to empl oy t he vortices for energy (Geyr von Schweppenburg, 1952;Nacht i gall , 1970).
Lissaman and Sholl enberger disputed th i s theory, suggesti ng that such phase relat io nships are unnecessary . The i r d i rect fi e l d observations i ndicated random phas i ng.
The Vee formation is optimal for energy conservation, according to Lissaman and Shollenberger. They suggested that a formation of 25 birds could have up to 71% more range than a lone bird. This formation does not have to be symmetrical, if the birds position themselves for equal drag distribution. They also suggested that formations are more sensitive than lone birds to wind conditions, and that a tailwind will be of greatest advantage to a formation.
As Poncy (1941)   (2) the formation persisted throughout mo s t of the take , i . e . the birds maintained their positions relative to one a nother within the flock , so that the shape or type of the formation did not change during the take .
Those flocks which met the conditions were then analyzed to obtain the angle between the legs of the formation , the wing-beat frequency of each bird, wing-beat phase relationships among the birds , and the distance between adjacent birds along the legs of a formation , where possible .
To obtain the true angle of a formation it was first necessary to determine which frame of the take represented the m"nimal apparent angle . Since the minimal angle was not immediately obvious it was necessary to determine the angle of the formation in a series of frames ; the smallest angle in this series represented the minimal angle. Each frame in a ser"es wit in a particular take was projected on a piece of graph paper, and the images of the birds in the formation traced onto the graph paper. X and Y coordinates were assigned each bird in a frame, the " center'' of each bird being used for the coordinate point . Due to limitations in the resolution of the Super 8mm film, and to perspective, this " center" point was the only point on the birds which could be used consistently for all formations .
The center was estimated as being the center of the mass of each bird, between its wings . In addition , each bird was numbered, the lead bird as No. 1, the bird immediately I converted the minimal apparent angle between the legs of the formation, obtained from the regression analysis, to the t rue angle of the formation. This step used projective geometry (three -dimensio al descriptive geometry).

Figure 4 (a-e) il ustrates how the minimal apparent angle
is pro jected upon the camera elevation, and then projected as the true angle of the formation (Slaby, 1966) . Figure 4a depicts the angle of a formation determined from regression analysis . The shape and size of this angle are represented exactly as they appeared on the film frame of the minimal apparent angle . Point A represents the apex of the Vee; a indicates the angle of the Vee , in this case 12°. In Meas urement of distance between adja cent bir ds along the legs of a Ve e formation , at the minimal apparent angle (formation t r aced directly from pro- Use of projective geometry to determine true distance between adjace nt birds along the legs of a Vee formation w V\ the publi shed data of Ruthven and Zimmerman (1965), Terres (1968), and the field work of George Bond frames per formation were analyzed, and a n average wi ng-beat f req uency f or each b ird calculated . Phase re lationships were s tudied from the same data .

RES ULTS
The number of different formation types and t he avera ge number of bi rds in each formation t ype a r e shown in Table 1 Weather conditions var i ed slightly during the week of filming . The temperature ranged f r om 3.6°c to 23 . 5°c during the week. The average tempera ture at dawn was 9.4°c ,         (1884) and Bent (1925) that Vee formations are use for long-distance flight .
As seen in Table 1 , 82% of the 104 formations filmed were linear formations. This percentage may not indicate a preference on the part of Canada Geese for this formation type, but instead may indicate non-random filming. However , most takes involved more than one flock , and some takes were huge groups of flocks which could be considered random samples. The non-linear formations (clusters) seemed less persistent than other formations , and possibly are t r ansition stages between linear formations . Cluster formations frequently were noted (although not always filmed) immediately after a flock took off, or as a flock was landing .
The data indicate that Canada Geese " prefer" linear formations , particularly the eche l on/column .  Table 2 shows that in winds of over 9 kph all but 3 formations out of 42 flew with a crosswind .
In wind speeds less than 9 kph almost one -half the formations were flying with tailwinds . These data indicate a pr eference for crosswinds in wind speeds of greater than 9 kph , perhaps due to the variability of these winds. Allen (1939) suggested that b irds might a void strong , gusty tailwinds , since such winds would distur b the feathers and make smooth flight difficult to maintain . ~s discussed earl'er, Pennycuick (1968) hypothes · zed tha t geese might use crosswinds as a secondar y soaring technique to increase range . The data presented in this study cannot prove his theory , but indicate that further study might be worthwhile . Lissaman and Shollenberger suggested that Vee formations might be able to utilize tailw ' nds to greatest advantage , but they did not explain their reasoning. Of the five formations analyzed ·n this study, four were flying in tailwinds, but as these winds were at speeds of less than 11 kph, I cannot make any conclusions based on their proposal .
The fiv e Vee formations analyzed ( see In this study , the Vee angles did not vary consistently with the number of birds in the flocks , but they appeared to vary with the distance between adjacent birds . The data suggest (although inconclusively) decreasing Vee angles with increased spacing between birds (see Table J) . From the birds ' visual standpoint this seems logical s if an angle is very acute , and the birds very close together , there is likely to be visual impairment to the front ; with a more obtuse angle spacing can be closer with no visual problems . This is also logical aerodynamically; the more obtuse the angle, the closer the birds would have to be to gain lift from the wing-tip vortices.
The distances between adjacent birds along the leg of a formation were variable, particularly within formations A and B (S . D. = 2 . 6 and 1 . 6 meters , respectively) . Wingbeat frequencies , however , varied little (S . D. = 0. 225 beats/ second) remaining at 4 beats/second . These frequencies are within published observations , which range from 2 to J beats/second (Van Wormer , 1968) to 5 beats/second (Cone , 1968). Nachtigall (1970) demonstrated wing-beat phase r elationships among birds flying in Vee f ormations ; consistent phase relationships were not found in this study . The data suggest that the birds ' wings are acting as independent oscillators of slightly -varying frequencies ; sometimes some birds wi l l appear to be in phase, but these relationships will not persist unless the f requen cies are identical .
If the birds are employing the Vee formation for aerodynamic advantag e, then several questions arise in relation to the distances between brids , and the wing -beat frequencies .
In any one formation , all the birds are flying in the same direction relati v e to the wind, and at the same speeds (otherwis e the fo rmation wou ld n o t persist); the similar wing-beat frequencies also indicate conform ity of speed . The distances between birds varied from 2.5 meters to 12 . 8 meters . How can the birds utilize wing -tip vortices, cons ide r ing some of the large distances found (e. g . 8 -12 meters)? In light of the variab ility in distance and wing-beat phase relationships, can there be equal drag distribution?
Future investigations should resolve these questi ons .
Studies of premigratory hyperphagia in geese and correlation with energy requirements during migration are needed .
In such a study the following questions should be asked : This st u dy has presented a unique method to determ i ne t he a ngle s a nd spacing between birds in a Vee fo r mation , and is the first s tudy in wh ic h these problems have been explored empirically. The Ca na da Geese studied dem ons t rate d a preference fo r linear forma tions , and i is very like l y that a partial function of such li n ear fo rmations i s to provide each bird with a clear view of the bird ahead , and th e space to the fro t , thus enabling the flock to remain a unit. Flock unity may be im or tant in m' gratory navigation .
The Vee a ngl es calculated were more acute than previous models had hypothesized, and I suspect that earlier workers failed to account for problems of perspective .
Wing-beat frequencies varied slightly, and t he values were constant with pub li shed data (Van Wormer , 1968;Cone , 1968).
However , the sligh t differences between individual birds leads to the idea that the birds ' wings are indep e ndent oscillators ; wing-beat phase relationships were not demonstrated, contrary to the study of Nachtigall (1970). The consistent speeds of the birds within the fo rmations analyzed, and the var' ability in dis ance between bir s wi hin at east two of the forma io s, suggest that it is unlikely these particular formatio n s are using the Vee (or Jay) for the aerodyna mic advantage of equalizing induced drag among flock members . Possib ly the formations filmed in this 58 study are atypical of flocks positioned for a long migratory fl ' ght . Further work is eeded to resolve the questions raised by these stud i es.