THE
EFFECT
OF MOLTING
ON
THE
GLIDING
PERFORMANCE
OF A
HARRIS' HAWK (PARABUTEO UNICINCTUS)
VANCE A. TUCKER
Departmentof Zoology,Duke University,Durham,North Carolina27706USA
ABSrRACT.--Themaximum lift-to-drag ratio of a Harris' Hawk (Parabuteo
unicinctus)
gliding
in a wind tunnel at 10.5 m/s dropped from 10.5 before the onset of molting to a low of 7.2
when missingprimary wing feathersleft gapsin the wing tips (36 daysafter onset).It then
rose to 10.5 again when the new featherswere complete (172 days after onset). The decrease
in wing span and area due to the missingprimaries can theoreticallyaccountfor only 39%
of this drop. The changedshapeof the wing-tip slotscould accountfor the remainder by
increasinginduced drag and profile drag. Lossof feathersother than the primariesdid not
have a major effect on the hawk's wing and body shape.Received19 February1990,accepted
24 July 1990.
THE WINGfeathers generate almost all of the
aerodynamic force that keeps a bird aloft in
flight, yet these feathers fall out during molting. However, the effect of molt on flight performanceis unexplored. ! was able to determine
with a "performance diagram" (nomenclature
from Tucker 1987),which plotsair speedagainst
sinking speed (often plotted downward) (Fig.
1). Air speedand glide angle determine sinking
speed:
this effect for a Harris' Hawk (Parabuteouni-
cinctus)trained to glide freely in a wind tunnel
during its molting period. Several studiesdescribethe molting processin raptors (Snyder et
al. 1987, Henny et al. 1985, Prevost 1983, Newton and Marquiss 1982,Houston 1975,and Stresemann and Stresemann 1966), but there appearsto be no informationon its effecton gliding
performance.
THEORY
The term glidingperformance
refersto the ma-
V• = V sin 0.
Speedsand sinking speedsof birds fall in a
performance
area.The upper boundary of this
area is the maximumperformance
curve,sometimes called a glide polar or a superpolar (Pennycuick 1989),along which Vshasits minimum
value for each V. A bird flying at a combination
of air speed(V0) and sinking speedthat occurs
on the maximum performance curve achieves
maximum performancein the sensethat when
gliding through still air at speed V0, it loses
altitude
at the minimum
rate and travels
the
maximum distancebefore coming to earth. Only
paper describesequilibrium
glidingperformance, the upper left part of the maximum perforwhich restricts the bird to movement
at conmance curve describesnormal gliding, during
stant speed along a straight path through air which sinking speedsare less than 5 m/s.
Each point on the performance diagram repthat doesnot accelerate.At equilibrium, the bird
is capable of two maneuvers: it can glide at resentsa particularvalue of the ratio of lift to
different air speeds(V), and it can glide along drag. This can be seen from the relation bepathsinclined at different angles(the glide an- tween lift, drag,and the glide angle. A bird that
glides at equilibrium must generate an aerogle, 0) to the horizontal.
The air speed, glide angle, and the bird's dynamic force directed upwards that equalsits
weight define three other useful quantities: weight. (Weight, not to be confusedwith mass,
aerodynamic
lift (L),drag(D), andsinkingspeed is body mass[m] multiplied by gravitationalac(Vs), the rate at which the bird sinks vertically celeration [g].) Lift is the component of this
through the air. ! use the ratio of lift to drag aerodynamicforce in a direction perpendicular
(L/D) to specifygliding performance.Further, to the glide path, and drag is the componentin
! show the relations between L/D and the other
a direction parallel to the glide path. It follows
neuvers a bird is capableof while gliding. This
quantitiesmentioned,and ! explain the ration-
that
ale for choosing L/D.
Many authorsillustrate gliding performance
108
L =mg cos O,
The Auk 108: 108-113. January1991
January
1991]
MoltandGliding
Performance
o
I
i
i
109
i
I
i
MAXIMUM
l0
PERFORMANCE
CURVE
•
2o
•
30
z
z
o• 40
50
I
o
I
I
I
I
I
lo
20
30
40
50
AIR
SPEED
(m/s)
Fig. 1. Theoreticalperformancediagramfor a hypotheticalgliding bird (seeTucker 1988for theory).The
bird normally glidesat sinking speedsof <5 m/s, so only a small region at the upper left of the performance
diagram representsnormal flight.
and
D = tng sin 0.
Because0 is normally lessthan 10øfor birds that
are gliding at maximum performance, cos 0 is
approximately 1. With this approximation,
agram for a Harris' Hawk (Tucker and Heine
1990) describes maximum performance with
reasonableaccuracyat airspeedsbetween 8 and
15 m/s (Fig. 2). Other gliding birds have similarly shaped maximum performance curves
(Tucker and Heine 1990).
L = tng,
The air speed and glide angle of a bird can
be measuredwhen the bird glides at equilib-
L/D = 1/sin 0,
rium in a wind tunnel. If the bird has air speed
and
L/D = V/Vs.
The last equation showsthat points on the performancediagram with the sameL/D value lie
on a straightline that passesthrough the origin.
The ratio of lift to drag is a useful measure
of gliding performance becausea single L/D
value can describemaximum performanceover
a wide range of speeds.For example, a straight
line through the origin of the performancedi-
V0and glide angle 00,it remainsmotionlessrelative to the earth when the air through which
it glides flows upward at speedV0and angle 00.
This situation can occur naturally in updrafts,
in which casethe aerodynamicand gravitational forces on the bird are identical
to those when
the bird glides at the same speed and angle
through still air.
When
a wind
tunnel
is tilted
around
a hor-
izontal axis perpendicular to the direction of air
flow, the tunnel can move a column of air up-
ward at the desired speed and angle. Birds
110
VANCE
A. TUCKER
[Auk,Vol. 108
faster than 1 cm/s. Then I tilted the tunnel toward
horizontal in •Aø stepsuntil the hawk no longer remained motionless. Instead, it drifted downwards and
0.5
backwardswhile gliding, then it moved forward by
flapping and began to glide again. I repeated this
processseveraltimes to confirm that the hawk's behavior was repeatable,and then I noted the shallowest tunnel angle (0) at which the hawk remained motionless. The hawk's body mass did not change
significantlyfrom 0.702kg during theseobservations.
I correctedmeasureddrag for boundary effectsby
adding the following term to drag:
L/D
D-t.5
03
Z
Z
(mg)21
(4CpV2),
2.5
3.0
i
I
i
i
5
iO
i5
AIR
SPEED
(derived from Tucker and Heine 1990) where C is the
cross-sectionalarea of the wind tunnel (1.5 m2) and
20
(m/s}
Fig. 2. Performancediagram for a Harris' Hawk
gliding in a wind tunnel. Each straight line connects
points that correspond to a constant ratio of lift to
drag. Points marked with + are on the maximum
performance curve.
p is the air density. Correcteddrag is given by
D = mg(sin0 + mg/(4CpV•)).
Since the correctionterm is constant,L/D depends
only on the tunnel angle:
L/D = 1/(sin 0 + 0.00846).
The hawk lostprimaries5-8 on eachwing between
15 June and 21 July. The matching featherson each
trained to glide freely in the columnare at equi- wing molted within a day or two of one another.
librium when they are motionless relative to Exceptfor primary 6, the new primaries on July 21
earth. However, the column is not identical to
were nearly as long as the original feathers.The new
primary 6, however, was short and left an obvious
a natural air mass because it is has a smaller
gap (Fig. 3). Seenfrom the side in flight, the anterior
cross-sectional
area. This difference
causes
boundary effects that influence drag, but the edgeof the gapwasabouthalf a feather-width ventral
to the posterioredge(i.e. the trailing edgeof primary
boundary effectscan be corrected.
7, which formed the anterior edge of the gap, was
ventralto the leadingedgeof primary5, whichformed
the posterior edge of the gap).
METHODS
This arrangementof primaries7 and 5 was markThe Harris' Hawk, a male whose gliding perforedly different from that of the fully featheredwings
mance was studied by Tucker and Heine (1990), in flight. When the feathersare complete,the trailing
hatched in captivity on 15 May 1988 and molted to edge of each primary overlapsbeneath and touches
adult plumagebetween15 Juneand 4 December,1989. the leading edge of the next posteriorfeather, except
During the molting period, it lived in an outdoorcage at the distal ends of primaries 6 through 10 in the
(6.1 m long, 2.8 m wide, and 3.4 m high) and wasfed Harris' Hawk. Theseendsform the separatedtip slots
mice and rats ad libitum.I collectedthe large primary typical of soaringhawks and vultures,and the anfeathersas they were shed and identified them as 5terior feather tips are above the posterior tips. Thus,
9 from photographstakenof the bird beforeit molted. the trailing edge of the feather that forms the anterior
The 10 primary feathers on a hawk's wing are con- edge of a slot is dorsal to the leading edge of the
ventionally numberedfrom 1 (nearestthe secondary feather that forms the posterioredge of the slot--just
feathers)to 10 (on the leading edge of the wing).
the oppositeof the gap that appearedduring molting.
At intervals during the molting period, the hawk
The lossof other wing and body feathersdid not
flew in a wind tunnel (describedby Tuckerand Heine causelarge gapsin the wings or make the body sur1990) at a speedequivalent to 10.5 m/s in air at sea facelook rough. The lossof primary 9 left a narrower
level in the U.S.standardatmosphere(von Mises1959). gap than the lossof primary 6, and without a raised
Standardsea level air has a density of 1.23 kg/m 3, posterior margin. Occasionally, a secondaryfeather
and the air density during the observationsdid not fell out while the new feather was 1 or 2 feather
changesignificantlyfrom 1.18 kg/mL
widths shorter than its final length. The covert feathI startedthe bird flying at an angle where it could ers on the undersides of the wings were noticeably
remain motionless relative to the tunnel for at least
thin. The hawk had a patchy appearancebecausethe
1 s. Motionlessmeans that it did not change position
new featherswere colored differently from the old.
January
1991]
MoltandGliding
Performance
io
Fig. 3. A fully spreadwing of a Harris' Hawk,
showing the gap left by the missingprimary 6. The
dotted line shows the outline
of the normal
feather.
The straight line at the baseof the wing represents
a distanceof 18.4cm. The wing outline is tracedfrom
a photographof a fully featheredgliding bird.
0
50
iO0
i50
200
DAYS
Both old and new feathers appeared smooth and unbroken throughout the molt.
The tail maintained its normal length asnew feath-
Fig. 4. Lift-to-dragratiosof a gliding Harris' Hawk
during molting. Molting began on day 0 and was
completebefore day 172.
ersgraduallyreplacedold ones.No gapswerevisible
in the tail becausethe hawk kept its tail folded during
flight. The feather conditionsand maximum L/D valuesduring the periodfrom pre- to postmoltare summarized in Table 1 and Figure 4.
somewhat for the reduced wing area and span
by extending its wings.
Another factor that could decrease L/D dur-
ing molting is a change in the normal configuration of slotsin the wing tips. Theseslotsare
DISCUSSION
thought by someto reduce induced drag (Pennycuick1983,Wi thers1981).The "induceddrag
Molting degradesgliding performanceover
factor" (also called the "span efficiencyfactor"
a period that correlateswith (1) the appearance
in the aerodynamicliterature) in the gliding
of gapsin the wing tips causedby missingpritheory adjuststhe amount of induced drag promaryfeathers,and(2) the temporaryshortening
duced by the wings at a given span. Figure 5
of the primary feathersuntil the new primary
showsthe effectof increasingthe induced drag
feathersreachtheir final length. Thesechanges
factor, and hence the induced drag, in a theoreducethe wing areaand span,and they change
retical hawk with the reduced wing span and
the shapeof the wing tips. Their effecton max- area mentioned above.
imum gliding performancecanbe evaluatedby
comparingthe observedL/D values with predictions from a gliding theory for the Harris'
An increasein the induceddrag factorof 45%,
from 1.1 to 1.6, together with the reduction of
Hawk (Tucker and Heine 1990).
The changesin wing area and span alone
cannot account for all of the decline in L/D.
The fully featheredhawk in this study had a
wing spanof 0.86m when gliding at maximum
performanceat a speedof 10.5m/s in the wind
tunnel (Tucker and Heine 1990).The theoretical
maximum L/D for these conditions is 11.0. The
lossof the primary feathers causedreductions
in wing area and span that I estimatewere less
than 0.01 m2and 0.1 m, respectively.Thesere-
ductionswould in theory reduceL/D to 88%of
TABLE1. Feathercondition and lift-to-drag ratios(L/
D) for a gliding Harris' Hawk during molting.
Day
0
36
46
7.7
7.7
New primary 6 growing into gap
56
72
94
123
172
L/D
All feathers complete
10.5
Primaries 5-8 lost, gaps in wing tips 7.2
38
42
the theoretical maximum. The lowest L/D dur-
ing molting was 69% of the premolt value. In
addition, the hawk probably can compensate
Description
8.2
8.2
New primary 6 fills gap
Primary 9 missing
Primary 10 replaced,completing
primaries. Underwing coverts,
new tail feathers growing in
New feathers complete
9.2
9.6
9.6
10.5
112
VANCE
A. TUCKER
[Auk,Vol.108
also might have forgotten how to glide at its
maximum L/D between 15 June and 21 July,
and then improvedwith practice.This explanation seemsunlikely. Once trained, the nonmolting hawk never failed to glide at its max-
<•0.9
rr
ru
imum L/D of 10.5, even when it had not flown
in the wind
LL
'0.8
tunnel
for several months.
Although the declinein gliding performance
with molting was marked in the wind tunnel,
it might not have much effecton a free-living
bird. Harris'Hawkshunt in cooperativegroups
and usually capturetheir prey by flying from
I-
•0.?
perchesrather than soaring(Bednarz1988).The
feather
O.E• I
I
.0
I
I
i.2
INDUCED
I
I
•.4
I
I
I
I
•.6
DRAG
FACTOR
loss that I have described
has an un-
knowninfluenceon flappingflight.It probably
has only a small effect on high-speedgliding
during a dive, when Harris' Hawks flex their
Fig. 5. The theoreticaleffect of the induced drag
factor on the relative lift-to-drag ratio of a gliding
Harris' Hawk. A relative value of 1 correspondsto
the theoreticalmaximum lift-to-drag ratio of 11.0 for
a fully feathered hawk gliding at 10.5 m/s with a
normal induced drag factor of 1.1. The curve shows
the relative lift-to-drag ratiosfor a molting hawk with
a wing area reduced by 0.01 m2, and a wing span by
wings,therebycoveringup gapsleft by missing
feathers.
This studywaspartiallysupportedby cooperative agreement No. 14-16-0009-87-991 between Mark Fuller, U.S. Fish and Wildlife
Ser-
vice, and Duke University.I am grateful to F.
Presley for loaning the Harris' Hawk.
0.1m.
LITERATURE CITED
wing spanand area,would accountfor the drop
in L/D seen with molting. This change in the
induced drag factorseemstoo high to be caused
by the loss of the normal tip slots alone. According to theoreticalcalculations(Cone 1962),
the lossof tip slotswould increasethe induced
drag factor by only about 25%.
However, the gaps in the wing tips during
molting also could increasethe induced drag
factor.The raisedposterioredge of the gap suggeststhat primary 5 and the feathersbehind it
were producing higher than normal lift forces
at the wing tips. Increasedlift at the wing tips
increasesthe induced drag factor (Pennycuick
1971,Tucker 1987).The gapsalsocouldincrease
the profile drag of the wing (see Pennycuick
1989,Tucker 1987 for an explanationof profile
drag).Thesechanges,togetherwith the changes
in wing area,span,and tip slots,couldplausibly
accountfor the decline in gliding performance
reported in this study.
There
could
be behavioral
as well
as aero-
dynamic componentsto the degraded gliding
performanceduring molting. The molting hawk
might have chosento flap and glide rather than
glide at equilibrium at shallow angles.My observationsdonot testthishypothesis.The hawk
BEDIqARZ,
J.C. 1988. Cooperativehunting in Harris'
Hawks (Parabuteounicinctus).Science 239: 15251527.
CONE,C. D. 1962. The theory of induced lift and
minimum induceddrag of nonplanarlifting systems. Natl. Aeronaut. SpaceAdmin. Tech. Rep.
R-139.
HElmq¾,C. J., R. A. OLSON, & T. L. FLEMING. 1985.
Breeding chronology, molt, and measurements
of Accipiter
hawksin northeastern
Oregon.J.Field
Ornithol.
HOUSTON, D.C.
56: 97-112.
1975. The moult of the White-backed
and Rtippell'sgriffon vulturesGypsafricanus
and
G. rueppellii.Ibis 117: 474-488.
NEWTON,I., & M. MARQUISS.1982. Moult in the sparrowhawk.
Ardea
70: 163-172.
PEImq¾CUICK,
C.J. 1971. Control of gliding angle in
Rtippell'sGriffon Vulture Gypsriippellii.J. Exp.
Biol. 55: 39-46.
1983. Thermal soaring comparedin three
dissimilartropic bird species,Fregatamagnificus,
Pelecanus
occidentalis
and Coragyps
atratus.J. Exp.
Biol.
102: 307-325.
1989. Bird flight performance.Oxford, Oxford Univ.
Press.
PREVOST,
Y. 1983. The moult of the Osprey Pandion
haliaetus. Ardea 71: 199-209.
SNYDER,N. F. R., E. V. JOHNSON,& D. A. CLENDHN•.
1987. Primary molt of California Condors.Condor 89: 468-485.
January
1991]
MoltandGliding
Performance
$TRESEMANN,E., & V. $TRESEMANN. 1966. Die Mauser
der Vogel. J. Ornithol. (Sonderheft) 107: 1-447.
TI•C•,R, V.A. 1987. Gliding birds:the effectof variable wing span.J. Exp. Biol. 133:33-58.
--.
1988. Gliding birds:descendingflight of the
White-backedVulture, Gypsafricanus.
J.Exp.Biol.
140: 325-344.
ß& C. HEINE. 1990. Aerodynamicsof gliding
113
flight in a Harris' Hawk Parabuteounicinctus.J.
Exp. Biol. 149: 469-489.
vON MISES,R. 1959. Theory of flight. New York,
Dover
Publ.
WITHERSß
]•. C. 1981. The aerodynamicperformance
of the wing of the Red-shouldered Hawk Buteo
linearisand a possibleaeroelasticrole of wing-tip
slots. Ibis 123: 239-247.
The Frank M. ChapmanMemorial Fund givesgrantsin aid of ornithologicalresearchand alsopostdoctoral
fellowships.While there is no restrictionon who may apply, the Committeeparticularlywelcomesand favors
applicationsfrom graduatestudents;projectsin game managementand the medical sciencesare seldom
funded.Applicationsare reviewedoncea year and mustbe submittedno later than 15 January,with all
supporting material. Application forms may be obtained from the Frank M. Chapman Memorial Fund
Committee,Departmentof Ornithology, American Museum of Natural History, Central Park West at 79th
Street, New York, NY 10024-5192 USA.
No new postdoctoralfellowshipswere awarded.Fellowshipsto RichardPrum and JefferyWoodburywere
extended through the 1990 year.
Two collectionstudygrantsfor the 1990year were awardedto StevenM. Goodman,for work on birds of
southeasternMadagascar,and to C. J. Hazevoet, for work on the avifauna of the Cape Verde Islands.
Forty-threeChapmangrantsfor 1990,totaling $23,655,with a mean of $550,were awardedto the following:
Timothy Armstrong,Graded vocalizationsof female Red-winged Blackbirds;SharonBirks, Paternity assessment in a promiscuousmegapode;Donald Burr, Behavioral ecology of the Texas Scrub Jay, Aphelocoma
coerulescens
texana;
Alice Cassidy,Songvariationand learningin SongSparrows(Melospiza
melodia);
Ken Chan,
A comparativestudy of migrant and resident Silvereyes(Zosterops
lateralis);ThomasDavisßEgg cooling and
wetting: necessaryevils in MuscovyDuck egg incubation;Linda S. DeLay, Paternalinvestmentof the cooperativepolyandrousButeogalapagoensis;
Maureen deZeeuw,Home rangesizeand habitatutilization patterns
of the Sanderling in Oregon, and comparisonwith home range in California and Peru; Curt Dimmick, The
ontogenyof the cache-recoveryforaging strategyin Clark's Nutcracker;David DuffyßInventory of the Denver
Public Library'sWilliam Vogt Archives;Daniel Dunaief, Acousticalpreferencesof fledgling and adult Brownheaded Cowbirds; Bruce Eichhorst,Genetic variation in the Western and Clark's grebes:color morphs or
species?;Richard Gerhardt, Breeding behaviorßhome range, and food habits of the Black-and-whiteOwl;
Anne Goldizen, Mate-sharingby male TasmanianNative Hens; Lynn Gordon, Rolesof endogenousand
exogenousfactorsin settlementpattern of juvenile WesternSandpipers(Calidrismauri);ShannonHackett,
Biogeographicanalysisof CentralAmericanbirds:a molecularperspective;JiirgenHaffer, The correspondence
of Erwin Stresemannwith Ernst Harterr and Otto Kleinschmidt;Paul HendricksßPhenotypic variation of
clutchand egg sizeover a latitudinal gradientfor an alpine passefinebird; HusseinAdan Isack,The biology
of the GreaterHoneyguide (Indicatorindicator);
FabianJaksic,Dynamicsof raptor guild structure:competition
or opportunism?;John Keane, Foraging ecologyof Black-throatedGray Warblers;Frank Lambert, Effectsof
selectivelogging on Bornean birds; Su Liying, Comparative feeding ecology of Red-crownedand Whitenapedcranesin NortheastChina;JohnMcCarty,Foragingecologyof Tree Swallows:influenceof competition
on diet and foragingsitechoice;Karen Metz, Why do male MarshWrensbuild somany nests?;
David Moyer,
Communitystructureof forestbirds in the Uzungwa MountainsßTanzania;Andrew Neill, Biologicalcontrol
of a nest parasitein the House Wren; Christopher Norment, Comparativebreeding biology of the Harris'
SparrowandWhite-crownedSparrow;AdrianO'Loghlen,Vocalontogenyandthemaintenance
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in the Brown-headedCowbird;JayPitocchelli,Geographicvariationin CommonMurresbreedingin Alaska;
BonniePloger,Slicingthe parentalinvestmentpie:rolesof parentsandoffspringin dividing thefooddelivered
to broods of Brown Pelicans;David Prescott,Body size, cold tolerance and differential migration in the
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choice,male competitionßand the function of songin a lekking flycatcher;Linda Whittingham, The allocation
of reproductiveeffort in male Red-winged Blackbirds;and Cottie WilliamsßFaunal compositionand changes
on Manus Island, Papua New Guinea.