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Mechanics and energetics of ground effect in flapping flight Cueva Salcedo, Horacio Jesus de la 1992

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MECHANICS AND ENERGETICS OFGROUND EFFECT IN FLAPPING FLIGHTByHoracio Jesus de la Cueva SalcedoB.Sc., The University of British Columbia, 1982A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(Department of Zoology)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMay 1991© Horacio de la Cueva, 1991Signature(s) removed to protect privacyIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of c’ >1The University of British ColumbiaVancouver, CanadaDate q, , ?DE-6 (2/88)Signature(s) removed to protect privacyAbstract.Ground effect (GE) is an interaction between a wing and a surface that increaseslift and reduces induced drag, stalling, minimum power, and maximum range speeds(Vataii, Vmp,Vmr, respectively). Four bird species utilising GE during flapping flight werestudied: Double-Crested Cormorants (Pholacrocoraz auritus) at Mandarte Island B.C.,Brown Pelicans (Pelecarius occideniali.s) at Ensenada Méico, Black Skimmers (Rynchopsniger) at San Diego California, and Barn Swallows (Hirundo rstica) at Ladner, WilliamsLake, and English Buff, B.C. Films were taken at 60—64 Hz in nature and digitisedfor vertical wing displacement analysis. Flight speeds of swallows and cormorants weremeasured with a Doppler radar.Best-fit sinusoids of dicular-linear regression (Batschelet 1981), periodic ANOVA(Bliss 1970), and Fourier series (Lighthill 1958, Bloomfield 1976) were used to describevertical wing movement. Linearised sinusoids were used to show vertical wing displacementand average height of wings above the surface. Methods of evaluating GE for fixed wingswere compared to determine simple, realistic calculations for flapping flight. Averageinterference coefficients were used to evaluate the influence of GE, utilising the theory ofReid (1932). Results were compared to those for oscillating (Katz 1985 ) and bankingwings (at an angle to the horizontal) (Binder 1977).The effect of GE on the daily energy balance (DEB) was evaluated in cormorants.DEBs were constructed considering GE, metabolic, reproductive, and fight costs.Powercurves were constructed using fixed-wing quasi-steady aerodynamic theory(Pennycuick1975). Thght speeds Vmp=10.9 ms out of ground effect (OGE), 6 m•s, in GE(IGE), arid Vmr16.3 ms1 OGE, 15.4 ms IGE and flight costs IGE and OGE ofcormorants were compared to speeds measured during the 1987 and 1988reproductiveseasons. Cormorants observed at Mandarte Island obtain savings of up to40% of totalpower when flying in GE. If cormorants fly with a fixed cargo per trip(0.3 kg) fromIithe feeding site to the nest the predicted number of trips per day is 3—4 as observed byRobertson (1971). Cost of Transport (cost of moving a unit weight a unit distance) wascompared for flights IGE and OGE, with and without a load. Foraging radius (Pennycuick,1979) calculates maximum distance travelled on available energy. Foraging radii ICE andOGE of double-crested cormorants limit potential food sources. Flight IGEis significantlycheaper than OGE for the double-crested cormorant.Flight energy expenditures were compared for the four species. Swallows and skimmersshow savings of up to 50% when IGE, but most savings are obtained only atspeeds <8m•s’. Cormora.nts and pelicans showed energy savings going from 5% at speeds > 15m•s’to 20% at speeds <8 ms1.111Table Of ContentsAbstractList of Tables.iiList of FiguresList of SymbolsAcknowledgementsChapter 1. Introduction.IntroductionBird FlightPassive FlightActive flightFlight BehavioursEcology and Flightixxv111349111213Study AreasMaterials, Methods, and Preliminary AnalysisFilming.DigitisimgMorp hornetricsSpeed MeasurementsObservationsiv13131315192021Perspective of the current studyChapter 2. Materials and MethodsChapter 3. Preliminary Statistical Analysis of Wing Movement. 24IntroductionDescription of analytical methodsLinea.risationResultsReliability of the statistical testsComparison of analytical methodsStatistical results and equationsConclusionsChapter 4. The Power Curve and Ground EffectIntroductionThe Power CurveMaintenance CostsAerodynamic CostsThe Power Curve of the double-crested cormorantGround Effect in Flapping FlightConclusionsChapter 5. Flapping flight in ground effectIntroductionMetabolic arid Maintenance CostsReproductive CostsV4950505559657477• . . . 77• . . . 808024• . 26•. 31• . 32• 32• 32• 33• 40• . 49Cost of gonadal growthCost of egg productionCost of incubationCost of chick rearingEnergy Input.Field ObservationsFlight records .References 140cOrmOTard .Power curves and flight records for the double-crestedPenalty curves for the double-crested corrrtorantCost of 2’ransportDaily Energy BalanceForaging radiusConclusionsChapter 6 General Discussion81818282838585• 86• 86.94• 97105107108108109114117120Introduction . . .Aerodynarriics of GEEcology of GE • .Conclusions • • .Appendix AVList of Tab’esI. Time IGE whilst flying for four bird speciesII. Flight ifim sequences, species, and codesIII. Correlation between stopwatch and radar speedsIVa. Circular-linear regression of best fit data from Po 3lVb. Periodic ANOVA for Po 3Va. Areas under Po 3 and its least-square fitted curvesVb. Equations of two different algorithms for Po 3Via. Summary of linearisation of circular-linear regression of Po 3VIb. Summary of linearisation of periodic ANOVA of Po 3VIc. Correlation between periodic AN OVA and circular-linear regression.VII. Summary of best-fit circular-linear regression equationsVIII. Summary of best-fit periodic AN OVA equationsDC Summary of first two terms of Fast fourier transformsX. Mean monthly temperatures at Victoria International Airport (1988).XI. Maintenance rates of double-crested cormorantsin JoulesXIIa. Anatomical characteristics of dissected double- crested cormorants.2162230303535363636373839525360vi’XIIb. Pectoralis and total muscle mass of dissected double-crested cormorants. . . . 60XIII. ‘ values for raw data and best-fit equations of wing movements on GE 71XIV. Characteristic speeds of double-crested cormorants 76XV. Prey species fed to nestling double-crested cormorants 84XVI. Flight speeds (m.s’), OGE for double-crested cormorant (August 1987). . . . 87XVII. Flight speeds (m.s1), ICE for double-crested cormorant (August 1987). . . . 88XVIII. Flight speeds (m.s), OCE for the double-crested cormorant (August 1988). 89XIX. Flight speeds (m.s’), ICE for double-crested cormorant (August 1988). . . . 90XX. Two-way Anova of flight speeds for summer 1987 and 1988 91XXI. Flight type, speed, time and power of double-crested cormorants. 99XXII. Mldmonth day arid night lengths of the reproductive period 100XXIII. Characteristic speeds and powers ICE and OGE for four bird species. . . . 118viiiList of FiguresFigure 1. Time span of film sequences selected for analysis 17Figure 2. Correlations and differences between radar and stopwatch speeds 23Figure 3. Best fit, residuals, linearizations, correlations, and components for Po 3. . 34Figure 4. x2 probability levels at 2 degrees of freedom. 41Figure 5. 2-tailed t significance levels of intercepts from circular linear regression. . . 42Figure 6. 2-tailed i significance levels of slopes from circular linear regression. . . . 43Figure 7. F,2 of multiple regression from circular linear regression 44Figure 8. F,2 of multiple regression from ANOVA curves 45Figure 9. Two-tailed i significance levels of intercepts from ANOVA curves 46Figure 10. Two-tailed i significance levels of slopes from ANOVA curves 47Figure 11. F,.,2 of multiple regression of from ANOVA 48Figure 12. Maintenance rates of double-crested cormorant during reproductive season. 54Figure 13. Ratio between Pennycuick’s pro=l and the P,.0 used in this study. . . . 57Figure 14. Power curve for the double-crested cormorant at Mandarte Island 61Figure 15. Characteristic speeds of the double-crested cormorant power curve. . . . 63Figure 16. Power ratios at different speeds through the reproductive season 64xFigure 17.Figure 18.Figure 19.Figure 20.Figure 21.Figure 22.Figure 23.Figure 24.Figure 25.Figure 26.Figure 27.Figure 28.Figure 29.Figure 30.Figure 31.Figure 32.Figure 33.Reid’s (1932) interference coefficient u and h/bWing shape of a double-crested cormorant during the downstroke.Raw data and best-fit regression, GE incurred, and GE range for Pa 1Summary of range and mean us for the double-crested cormorants.F0 and Find curves for the double-crested cormorantBox plots of IGE and OGE speeds of the double-crested cormorants.Fight cost and speed of double-crested cormorant ICE and OGE.Penalty curves for the double-crested cormorant IGE and OGE.Cost of Transport for the double-crested cormorantDEBs for the double-crested cormorantRequired daily fish catch of the double-crested cormorant.Proportion of daylength spent flyingDouble-crested cormorant foraging radiiPower and penalty curves for double-crested cormorants.Power and penalty curves for brown pelicansPower and penalty curves for barn swallowsPower and penalty curves for black skimmers959610110210410611011011011067•. 69• . 72• . 7375• . 9293xFigure 34. DEBs of barn swallow using GE. 110Figure 35. Raw data and best-fit regression, GE incurred, and GE range for Pa 2. 121Figure 36. Raw data and best-fit regression, GE incurred, and GE range for Pa 3 . 122Figure 37. Raw data and best-fit regression, GE incurred, and GE range for Po 1 . 123Figure 38. Raw data and best-fit regression, GE incurred, and GE range for Po 2 . 124Figure 39. Raw data and best-fit regression, GE incurred, and GE range for Po 3 . 125Figure 40. Raw data and best-fit regression, GE incurred, and GE range for Rn 1 . 126Figure 41. Raw data and best-fit regression, GE incurred, and GE range for Rn 2 . 127Figure 42. Raw data and best-fit regression, GE incurred, and GE range for Rn 3 . 128Figure 43. Raw data and best-fit regression, GE incurred, and GE range for Rn 5 . 129Figure 44. Raw data and best-fit regression, GE incurred, and GE range for Rn 6. 130Figure 45. Raw data and best-fit regression, GE incurred, and GE range for Rn 7 . 131Figure 46. Raw data and best-fit regression, GE incurred, and GE range for Rn 8 . 132Figure 47. Raw data and best-fit regression, GE incurred, and GE range for Rn 9. 133Figure 48. Raw data and best-fit regression, GE incurred, and GE range for Hr 1 . 134Figure 49. Raw data and best-fit regression, GE incurred, and GE range for Hr 2. 135Figure 50. Summary of range and mean o-s for the brown pelicans 136Figure 51. Summary of range and mean as for the black skimmer sequences 1 to 5. 137Figure 52. Summary of range and mean as for the black skimmer sequences 6 to 9. 138Figure 53. Summary of range and mean as for the barn swallows 139List of abbreviations, symbols, and their units.(dimensionless symbols are followed by a blank)Symbol Definition Unitsa2 Fourier coefficientA amplitude of wingbeat mAp frontal plate area m2aspect ratio (b/c)b wingspan mbapp apparent wing span mFourier coefficientBMR basal metabolic rate Wc wing chord mCDb body drag coefficient mCDpro proffle drag coefficientCDpara parasite drag coefficientC1 lift coefficientCLmaz maximum lift coefficientCT Cost of TransportDEB daily energy balanceD portion of day not spent flying sinduced drag NDIT total D in a two wing system NDpa,’ parasite drag Ne aerofoil efficiencyEday diurnal maintenance energy Wnocturnal maintenance energy Wtotal energy input Jenergy output Jf replicates per sampling intervalFR foraging radius kmg(t) function of trigonometric polynomialG energy content of egg WGE ground effectIGE in ground effectOGE out of ground effecth height of wing above surface mh/b height to wingspan ratioj energy availablek number of sampled pointsK1 parasite & profile powers constant kg.m’K2 induced power constant kg.m3s1induced power constant IGE kgm.scont...11L lift Nm mass kgM inesor or mean wing height mn number of points in sequencep period of egglaying cycle daysPam absolute minimum power WPchick chick growth and maintenance WFind induced power WPme metabolic power WPmp minum fight power WPmr maximum range power WPnoc night maintenance power WPpar parasite power WFpara Fpar+ Fpro WPpro proffle power WF0 total power WQ wing loading N•m2r correlation valueRe Reynold’s numberR1 W & Dpar resultant Ns varianceS wing area in2Sb0d maximum cross sectional area of body in2Sd wing disk area in2wing angle during flapping radacrophase = maximum angle of wing radT period ssum of all sampled valuescos(wi)sin(wt)V forward figh speed m.s1V induced velocity ms1Vga in maximum energy gain speedVmp minimum power speedVmr maximum range speed m.sV01, optimal flight speed ms1Vataii stalling speed m•s1w angular velocity of wingW weight NWapp apparent weight under GE NY height of wing above water incont...xli’a wing’s angle of incidence radr air circulation around wing,metabolic to mechanical efficiency8j wing angle during flapping radic energy spent per distance flown J/mp air density kg.m3o GE interference coefficientö average CE interference coefficient4’ acrophase=maximum angle of wing radw angular frequency rads’xivAcknowledgmentsI would like to thank my supervisor RW Blake for his encouragement and helpfulsuggestions and discussions that made the completion of this project possible. The inembers of the thesis committee: CL Gass, J Gosline, DJ Randall, and JNM Smith providedmany suggestions for improvement of the manuscript and refinement of ideas. M Kshatriya helped polish many of the ideas presented here. B Kolotylo helped with the fieldwork. The weenies at the Biological Data Centre: A Blachford, J Messer, C Mathieson,and S Ertis pulled me out of many holes in computer analysis. The support of A August,MA Charney, and B Strasmich is kindly appreciated. 0 Avila was a real brother. Thiswork is dedicated to Horacio de la Cueva M, Teresita, Tere, Gerardo, and la vdg, and theanarchists of the world.xvChapter 1.Introduction.IntroductionThis study describes the use of ground effect (GE) for birds in flapping flight. Itfocuses on the flight and daily energy balance (DEB) of the double-crested cormorant.The use of GE in three other species: brown pelican, barn swallow, and black skimmeris compared. I begin with a review of the relevant animal flight literature (Chapter 1).Chapter 2 describes how flapping flight of each bird was analysed, and how morphometric,and flight speeds measurements were made. Chapter 3 describes wing movements usingperiodic equations (Lighthill 1958, Batschelet 1981, Bliss 1970, Bloomfield 1976). GE inflapping flight is discussed in chapter 4, in the context of reductions in induced drag (D1)and increases in lift (L) on the total power consumption during flight. Chapter 5 discussesthe role GE plays in the energy balance and reproductive strategies of the birds studiedfocusing on the double-crested cormorant. Finally, in Chapter 6 the use of GE by the birds(Table I) is compared and contrasted.Bird FlightThe study of bird flight has involved the development of aerodynamic theories appliedto both aircraft and birds and the measuring instruments necessary to test them. Forexample, high speed photography and cinematography (e.g. Brown 1948, Pennycuick1968b, Spedding e a!. 1984) has been used to describe wing movements. The accuratemeasurement of flight speeds has been made with Doppler radar unit (Schnell 1965,1974,Schnell and Hellack 1978,1979, Blake e a.!. 1990) and an ornithodolite (Pennycuick 1982ab,1Table I. Time IGE whilst flying for the four birds species.Species Use TimeDouble-crested cormorant o and from nest 1OOBrown pelican to and from nestBlack skimmer foraging whilst foragingBarn swallow foraging occasionally21983) and has been used to test predictions of optimal flight speeds. Traditionally birdflight has been dassified into active and passive forms.Passive Flight.Passive ffight does not imply the absence of energy expenditure by birds. This typeof flight (gliding and soaring) involves an energy expenditure of approximately 2 times thebasal metabolic rate (Baudlinette and Schmidt-Nielsen 1974) to hold the wings in flightposition. Gliding and soaring flight patterns were understood in principle in the l9century (Rayleigh 1883). Walkden (1925) developed models of soaring to predict optimalflight patterns of albatrosses.Gliding. In gliding birds travel forward and loose altitude at a rate dependent onthe forward speed (V), maximum lift coefficient (CLmar 1.5), body or parasite drag(CDpara), lift to drag ratio, and wing loading (Q, unit weight per unit area of wing, N•m2) (Pennycuick 1975). The study of gliding based on fixed winged models has beenextensive (e.g. Raspet 1950, 1960; Parrot 1970; Pennycuick 1960, 1968a; l97labc;Pennycuick and Scholey 1984; Tucker and Parrot 1970; McHagan 1973; Tucker 1987).A good glider is an animal whose glide ratio, or ratio of forward to sinking speed, is high,e.g. black vulture (Coragyps a1,’rcius), osprey (Pandiom haliaeus), andean condor (Vulurgryphus), and common crane (Grus grus) (Kerlinger 1989). Tucker (1987) calculates theperformance and polar areas of a loggar falcon (Falco jugger) and a black vulture from windtunnel measurements, considering the variable geometry of the wing. Spedding (1987a)investigated the vortex wake of a bird whilst gliding and compared the performancesmeasured by an elliptically loaded airfoil of the same span as a kestrel (Falco innunculus)and discussed the dose agreement between vortex and classical aerodynamical theories.Raspet (1950) compared the aerodynamical performances of his Kirby Kite sailplane anda black vulture by following the bird with the plane. He concluded that the bird neededlittle power to stay aloft, because it had a large lift coefficient (1.57) and dosed the top3slots in its wing to reduce the effective aspect ratio (, wing span over mean wing chord),and that overall the bird was able to fly with a small expenditure of energy.Soaring. In soaring, birds extract energy from the environment to stay airborne.Soaring flight is subdivided according to the source of energy employed by the birds toremain in flight. Slope aring Bird use updrafts of air deflected by a prominent geographicfeature, such as sea cliffs, mountains, and buildings (e.g. Peruiycuick and Webbe 1959,Pennycuick 1960, Kerlinger 1989). Thermal waring The birds exploit thermals created bythe differential warming of the air in contact with the surface of the ground. Ti a thermal isto be used by a bird to gain altitude, the lift component of the forces created by the thermalmust be greater than the sinking rate of the bird (e.g. Cone 1962, Pennycuick 1975,Obrecht 1988, Kerlinger 1989). Dynamic aring in this characteristic flight of albatrosses(Diomedidae), birds take advantage of the wind shear above the water surface and gainaltitude from which to initiate a glide (e.g. Rayleigh 1883, Cone 1964, Wood 1973, Wilson1975).Soaring and gliding are not discrete activities. A bird will change from soaring togliding and vice versa, depending on the instantaneous environmental d.rcumstances, andon its purpose for flying. For this reason most of the literature on passive flight incorporateselements of soaring and gliding (e.g. Newman 1958, Pennycuick 1972).Active FlightIn contrast to passive fight the energy expenditure required by powered flight hasbeen estimated to be from 6 to 23 times the basal metabolic rate (Utter and LeFebvre1970, Tucker 1973, Torre-Bueno and Larochelle 1978, Tatner and Bryant 1986). Brown(1948) adapted an Arditron discharge tube and synchronised it to a high speed ciné camerato obtain records of the slow flight of a pigeon (Columba. livia). Brown discussed wingmovements in relation to the action of the muscles and made inferences about fast forward4fight. Brown (1953) furthered his study by analysing films of pigeons and gulls at differentfight speeds and assessed aerodynamical properties of various wing configurations. Walker(1925, 1927) employed numerical analysis to show that rooks could generate enough forceto fly horizontally or climb, provided that they generated lift during both up and downstrokes by the inner portion of the wing. He also concluded that flapping flight comparedfavourably with the efficiency of a screw propeller.To date three aerodynamicai theories have been used for the study of fight mechanics of flapping flight: steady state momentum jet theory (e.g. Pennycuick 1969, 1975;Tucker 1973; Norberg 1976b,c), blade element theory (e.g. Pennycuick, 1975; Norberg1976b,c) and quasi-steady vortex theory (e.g. Weis-Fogh 1973, Rayner 1979a Ellington1983, Pennycuick 1988b). Nachtigafl and Dreher (1987) clearly differentiated between themomentum jet and vortex models: “momentum jet is often used for rapid and useful esti.rnating calculations, as for example the performance of helicopters. This does not meanhowever, that the principles of the fluid dynamics of vertical sustaining force creation canbe explained by this method.” In other words momentum jet is a predictive theory onlywhilst vortex theory is both explanatory and predictive.In momentum jet theory a bird engaged in active flight flaps its wings, sweeping outa wing disk with area Sd. The action of the wings causes the air to accelerate downwards.Part of this acceleration occurs before the air reaches the disk because of reduced pressureon the dorsal and forward side of the disk. This results in the air attaining a downwardinduced velocity V2 as it passes through the disk. The air is accelerated further since thereis a region of increased pressure behind and below the disk which is a mirror image of thearea of reduced pressure ahead and above the bird. After leaving the disk the air continuesto accelerate downward until, far behind the bird, it reaches an eventual downward velocity2V(Pennycuick 1975). Blade element theory divides the wing into small chordwise wingsegments of area S that must generate a proportion 1L of the total lift L. This method5calculates the angular velocity of the wing w necessary to generate a lift force equal tohalf the weight of the bird by integrating the forces generated by each wing segment(Pennycuick 1975).The vortex theory of bird and bat flight was evaluated by Rayner and his colleagues(Rayner 1979a b c, Spedding 1982, Spedding ci ci. 1984, Spedding 1986, Rayner ci al.1986). Rayner ei aL employed a method for flow visualisation of vortex rings, combininghigh speed photography with neutrally buoyant helium bubbles. Rayner and co-workerstrained different animals to fly through the bubbles, allowing them to test some of theassumptions and predictions of the theoretical models of bird flight. Their flow visualisationmethod is based on the approach of Kokshaysky (1979) who employed clouds of small lightparticles to construct a qualitative model of the general configuration of the wa)e. Rayiierand colleagues (Spedding 1982, Spedding ci ci. 1984, Rayner ci ci. 1986) concluded thatthe differentiation of flight gaits between slow and fast flight is given by the iole of theupstroke in the flapping cycle and the shape of the wing. In slow flight there is a smallforward speed component while the wings are beating at a relatively fast rate (i.e. theaverage speed of the wing tips is much greater than that of the body) (Cone 1968). In thisgait the upstroke generates no thrust or lift and the wingtips are expected to come closeto the body to minimise friction drag and inertial forces. Here transverse vortices are shedat the top and bottom of the downstroke, and the upstroke is flexed and inactive (Raynerci a.?. 1986). This form of flight generates a vortex ring waice. Fast flight implies a slowerwing movement relative to the forward speed (Cone 1968). In this gait the vortex sheetsshed from the wings’ trailing edges roll into a pair of discrete vortex lines. For long wingedspecies, e.g. kestrel (Spedding 1987b) in fast flight the upstroke is considered active, as itgenerates lift and thrust.The study of the mechanics of flapping flight has also examined other aspects offight such as coordination of breathing movements and the storage of elastic energy in6the wishbone. Goslow et al. (1990) linked the use of the pectoralis muscle, wing, andbones of the shoulder and thorax. The movements of these bones seem to serve as asecondary pumping system between the air sacs and the lungs that is capable of operatingindependently of inhalation and exhalation and that might serve the increased metabolicdemands of flight. Dial el al. (1987, 1988) demonstrated the relationship between flightmuscles and wing movements. Both studies also established that the wishbone of thestarling acts as a spring (Jenkins ci iii. 1988).Studies of bird flight have also focused on wing morphology and the aflometric relationships of flying animals. Savile (1957) discussed wing shape and the evolution of birdflight classifying them into four shapes: elliptical wing adapted to operation in confinedspaces; high-speed wing for birds feeding aereafly or involved in long migration flights; highaspect ratio wing for oceanic soarers; and slotted high-lift wing for terrestrial soarers andpredators that must carry heavy loads. Further studies on the relation of wing morphologyand the relation to the biology of the bird include those of UM Norberg (1979) who studied the functional morphology of wings, legs and tail of three coniferous tits (Parus wter,P. rrnianus , and P. crisiasus), goldcrests (Regulus regulus) and tree creepers Cerihiafamiliaris). She correlated the morphology with locomotor patterns and feeding stationselections, and concluded that the differences in feeding station selection require differentstructural adaptations of the locomotor apparatus. Chari ci al. (1982) compared the flightcharacteristics, moment of inertia and flight behaviour of two aerial insectivores (Dirususa.dsimilis and Merops orientalis), concluding that the low wing-loading and low aspectratio values give these birds high manceuvrabllity. Also, the similarities in certain flightparameters appear to be convergent adaptations for catching insects during flight. Alataloei al. (1984), studying the difference in size between conspecific young and older passerines,suggest that young birds have a shorter arm designed for better manceuvrability, whereasadult wings are better for faster flight. Kerlinger (1989) makes the same suggestion for7young and adult hawks. Greenwalt (1962, 1975) compiled data on the dimensional relationships of flying animals and linked them to aerodynamical properties in relation tobird body type (duck, shorebird, or passerine), providing allometric relationships betweenmass, wing size, fight muscle mass, and power requirements for fight. Warham (1977)assessed the flight capabilities of procelariiformes based on their wing loading and wingshapes. Amongst the 48 species studied, wing loading and aspect ratio increase with bodyweight. Pennycuick (1987), studying flight in seabirds, divided the requirements of powered flight into four categories: catching food, commuting to and from the feeding ground,access to the nest sites (ease of landing and departure), and migration. He concluded thatneither migration nor feeding, except for the use of wings underwater, are major factorsin flight adaptations. Flight adaptations in seabirds seem to be determined mainly by therequirements of foraging and access to nests.Power consumption during fight is dependent on speed, giving a characteristicU-shaped curve (Pennycuick 1969, 1975; Tucker 1973, Rayner 1979ab). This curve predictsoptimal speeds at which birds ought to fly if they are to maximise the amount of time spentflying (minimum power speed Vmp), or the amount of distance covered (maximum rangespeed Vmr) on a given amount of fuel, or the maximum rate of energy brought back tothe nest (1’9(Lm) (RA Norberg 1981, Pyke 1981). Flight speed measurements have usedstopwatches and theodolites or car speedometers (Cooke 1933, Allen 1939, Cottam etal. 1942, Brown and Goodwin 1943, Meinertzhagen 1955, Tucker and Schmidt-Koening1971, Gill 1985, McLaughlin and Montgomerie 1985), Doppler radar units (Lanyon 1962;Schnell 1965, 1974; Schnell and Hellack 1978, 1979; Kolotylo 1989; Blake e aL 1990)or ornithodolites (Pennycuick 1982ab, 1983; Peunycuick and de Santo 1989). Speedmeasurements with ornithodolites or Doppler radar units provide large and precise samplesthat allow statistical tests of the fight speeds of birds.8Flight BehavioursFlight is an energetically expensive activity, and it is assumed that birds have evolvedstrategies that would minimise this expenditure. Active flight strategies that minimiseenergy expenditure when compared to constant flapping flight include:Intermittent ffight: Periods of wing flapping alternate with periods when the wingsare not used (Alexander 1968, Rayner 1985, Ward-Smith 1984ab). In this type of flight,mechanical energy does not flow steadily from the bird to its environment, but it is storedtemporarily in the bird’s body in the form of potential or kinetic energy during the passivephase and then released generating thrust and lift during the active phase (Rayner 1985).Intermittent flight is the result of an imbalance between available power output, limited bymuscular efficiency, and the optimum power output for steady flight. This flight strategyis further divided into: Undulating flight: birds glide and then regain altitude with afew strokes, typical of good gliders that are bigger than woodpeckers. Undulating flightreduces energy expenditure at most flight speeds, permitting a bird to fly slowly buteconomically (Rayner 1985). The need for musculature to operate at or dose to conditionsof optimum thermodynamic efficiency appears to be a factor controffing the proportion oftotal flight which is devoted to the powered phase in undulating flight and can be achievedonly at minimum drag speed (Vmp) (Ward-Smith 1984ab). Bounding flight: the wingsare folded during the unpowered phase. This type of intermittent flight is typical of thesmaller birds. Bounding ffight saves energy only at higher speeds and does not reduce themechanical cost of transport (Rayner 1985). This type of flight can be seen as a strategyfor increasing flight speed without incurring the penalty of increased energy expenditureassociated with increased flight speed under the conditions of steady horizontal flight(Ward-Smith 1984b). Rayner (1985) concluded that both bounding and undulating flighthave evolved as compromise adaptations between the strenuous and confficting constraintsimposed by the physiology and mechanics of flying birds. Bounding flight in birds has been9accompanied by reduction in body size and widening of adaptability to trophic conditions,while undulating ffight permits larger birds to accommodate the power economy of glidingwith efficient flapping flight.Formation flight. Formation flight is a mechanism for reducing energy expenditureduring long migration flights that is available to flocking birds. In this type of flightthe induced drag of the flock is reduced. Lissaman and Shollenberger (1970) developeda model for formation flight. Assuming birds had fixed wings, and they concluded thatthe typical vee formation, with a determined spacing between the wings, would result inenergy savings. Heppner (1974) classified the flight formations by their shape. Higdon andCorrsin (1978) examined the induced drag of the flock and Haimmel (1983) examined howdissimilarity of sizes within flight formations would benefit the smaller birds. Hainsworth(1987) looked at the positioning of birds within a flock.Ground effect. Birds that fly near smooth surfaces, such as cormorants, pelicans,skimmers, and occasionally birds like swallows and seagulls, can take advantage of theground effect (GE). GE is a reduction in induced drag (Di) accompanied by an increase inlift (L) and can be expressed as the interference coefficient o on the induced drag equation(Reid, 1932). GE reduces induced drag and increases lift as long as the wing is within 1.5wingspans of the surface. The advantages of GE to the energy budget of certain fish andbirds have been shown for the mandarin fish, and the gliding and flapping flight of the blackskimmer Rynchops niger (Blake 1979, Withers and Timko 1977, Blake 1985, respectively).Spedding (1987ab) looked briefly at the interaction between vortices generated by a kestrel(Falco tnnunculus) and the ground in both gliding and flapping flight. He concluded thatfor the case of flapping flight the qualitative wake structure described is probably notsignificantly affected by GE, although, particularly towards the end of the downstroke, theinduced velocities behind the wing trailing edge may be. Hainsworth (1988) showed thatfor brown pelicans flying in ground effect (IGE) the average height of the body above the10water was higher for flapping (0.52m) than gliding birds (0.33rn). He estimates the Dsavings for gliding flight averages 49% and for flapping birds, calculating the savings atthe average height of the body, would give a saving of 36%.Ecology and FlightThe cost of flight and other energetic demands imposed on birds whilst foraging duringand outside the reproductive season can give rise to predictions such as which form oftransportation they should use to gather food (Houston 1990), or at what speeds birdsought to fly if they are to exploit patches efficiently (RA Norberg 1977), or bring themost energy back to the nest (RA Norberg 1981) An important question being askedby ecologists is how well an organism meets its daily and seasonal energy requirements.Schoener (1971) and Stephens and Krebs (1986) have extensively reviewed the subject.Birds must meet their daily energy requirements including the cost of searching for andcarrying their food (RA Norberg 1977). Energetic cost of foraging will be higher duringthe nesting and brooding seasons (RA Norberg 1981, Blake 1983).Factors determining how a bird maximises its net energy intake will depend onmorphological characteristics such as aspect ratio (), wing loading (Q), maximum poweravailable from the flight muscles, the structure of the environment (a seashore and a denseforest require different flight behaviours), the spatial and temporal distribution of resources(patchiness) and the resource utilisation overlap with other species (e.g. UM Norberg1981). For example, the vultures in the Serengeti plains, using the morning’s narrowthermal street (a reliable source of external energy) to become airborne, have a low A.wing, enabling them to exploit this energy source (Pennycuick 1979, UM Norberg 1981).In contrast, the double-crested cormorant (Phalacrocoraz aurius) has a high Q and fliesclose to the surface of the water. This bird cannot rely on thermals, and employs GE as away or reducing its energy expenditure whilst flying (Chapter 5).11Perspective of the current studyThe present study assesses GE in flapping flight and examines how this ffight strategyis used by different birds. Four species of birds were chosen: double-crested cormorantPhalacrocorax auritus, barn swallow Hirundo rustica, black skimmer Rynchops nigra, andbrown pelican Pelecanus occidenialis. The birds chosen represent a range of morphologicaltypes and life styles.Double-crested cormorants are sea birds that nest colonially (Lewis 1929, van Tets1959, Drent ci a!. 1961, Drent ci a!. 1964, Robertson 1971), have a high Q and fly at highspeeds IGE most of the time. They are known to fly long distances between nests andforaging areas (up to 42 km round trip, P Arcese, W Hochachka, pers. comm, pers. obs.)IGE. Double-crested cormorants bring large loads ( 20% body weight) back to the nest(chapter 5). Barn swallows have low Q, fly at high speeds (Blake ci a!. 1990), bring small( 1% body weight) loads back to the nest, and may utilise GE whilst foraging. Blackskimmers, first birds for which any work in GE was done (Withers and Timko 1977; Blake1983, 1985), use GE during their foraging and prey capture episodes and carry small loadsback to the nest. Brown pelicans like the double-crested cormorants carry large loads backto the nest, whilst flying IGE to and from the foraging sites and taking advantage of otherenergy saving devices such as formation flight (Hainsworth 1988).12Chapter 2.Materials and Methods.Study Areas.Birds were filmed and observed at the following locations:Double-crested cormorants: Mandarte Island, B.C., a large bird coiony near Victoria,48° 38’ N, 125° 17’ W, and at Brunswick Point in Ladner, B.C., at the Fraser RiverDelta, 49° 04’ N, 123° 09’ W.Barn swallows: At an abandoned barn in Brunswick Point, B.C., 49° 04’ N,123° 09’ W, and at a pond in Vanier Park, Vancouver, B.C., 49° 15’ N, 123° 07’ W.Black skimmers: At a channel in the salt evaporators at the southern end of San DiegoBay in San Diego, California, USA 32° 15’ N , 117° 07’ W.Brown pelicans: At Todos los Santos Bay, Ensenada, Baja California,Mexico, 31° 50’ N, 116° 40’ W.Materials, Methods, and Preliminary Analysis.Filming.The dné films taken at San Diego, Ca. (black skimmers), Ensenada, Baja California(brown pelicans), and Mandarte Island B.C. (double-crested cormorants) were filmed witha Paiflard Bolex variable speed camera model H16 Sbm, powered by a Bolex EMS 12VDC motor, set at 50Hz. The camera was fitted with a Kern Vario-Smitr fl.9, 16-100mmBolex H16RX lens with a through the lens automatic exposure meter.13Films taken at Vanier Park (barn swallows) and Brunswick Point (double-crestedcormorants) were taken with a Paillard Bolex variable speed hand-winding camera at60Hz. The camera was fitted with either a Kilar f3.5, 150mm lens or a Century TeleAthenar f5.6, 500mm lens. Film exposure was determined with either Sekonic StudioDeluxe or Gossen Lunasix 3 exposure meters adjusted for the proper film and cameraspeeds.Both cameras were used at their maximum nominal ifiming speeds, 64Hz for the Pall-lard Bolex hand-winding camera and 50Hz for the Bolex H16 Sbm electric motor drivencamera. To determine the ciné cameras’ “real” speed a digital stopwatch (ProfessionalQuartz Timer Sports Timer) was filmed at each camera’s maximum speed. At least fivesequences of one second length each were used to find the average maximum filming speedof each camera. The manufacturer specified rate for the motor driven camera was found tobe accurate. The hand-winding camera rate set by the manufacturer as 64Hz was 60Hz.Any of four 16mm films in 30.5m rolls were used, depending on film availability andlight conditions. Eastman Ektrachrome 80 ISO/ASA (colour) and Plus-X Reversal 50ISO/ASA (black and white) films were used under bright light conditions. EastmanEktachrome 400 ISO/ASA (colour) and 4-X Reversal 400 ISO/ASA (black and white)films were used under dark or overcast conditions. All films were developed commerciallyby Alpha Cine Services, 916 Davie Street, Vancouver, B.C..The double-crested cormorants at Mandarte Island were filmed from a inflatable boat.The films of the brown pelicans in Ensenada were taken on board a rented wooden fishingboat, and the films of the black skimmers were taken from the bank of a channel in SanDiego. All these films were taken with a handheld camera. The filming was done with themotor off and the boat drifting in currents <1 knot. For the films of the double-crestedcormorants at Brunswick Point and the barn swallows at Vanier Park the cameras weremounted on a tripod.14Filming under field conditions creates parallax problemsthat must be accounted forwhilst analysing the data. The flight of the subject and the camera are not necessarily inthe same horizontal plane, distorting the perspective of theflapping wing movement, andthe perceived distance from the wing to the water. The problem of wing perspective isovercome by using best-fit algorithms that bring about symmetry to the flapping sequence(see Chapter 3, Preliminary Statistical Analysis for more details). The problem of wing towater distance was determined by either looking for a point of contact between the wingand the water in the sequence, or, by following the wing and its reflection in the water andfinding the closest point between the two in a sequence,assuming that that. distance wasthe minimum distance between the wing and the water. On a boat the camera is not fixedin the horizontal plane and the waves will alter periodically the perspective from whichthe wing movement is being filmed. This problem was solved by partitioning the sequencebeing analysed into segments in which the median height of the wingtip above the waterwas equal.Digitising.All films were previewed, then selected sequences were analysed. A selected sequence,for both in and out of ground effect flight, shows at least one complete wingbeat cycle insharp focus, with no visual obstruction by an object, the water, or the body of the birdand no undetermined wingtip locations. The film sequences of each species selected fordigitising are listed and coded (Table II). The duration of each sequenceis shown on Figure1. All sequences selected for digitising show a calmsea ranging from almost still water(barn swallow films) to small current driven waves 1 knot, (double-crested cormorantsfilmed at Mandarte Island).15Table II. Film flight sequences, species, and codes.Species Sequence Codedouble-crested cormorantPhalacrocoraz aurius Pa 1Pa2Pa3black skimmerRynchops nigra Rn 1Rn2Rn3Rn4Rn5Rn6Rn7Rn8Rn9brown pelicanPelecanws occidentalis P0 1Po2Po3barn swallowHirundo rustica Hr 1Hr 216Figure 1. Time span of film sequences selected for analysis, codes as in Table II.Pa3Pa2PalRn9Rn8Rn7Rn6 C.)________a)Rn5 DC)Cl)Rn4 —.C,Rn3 IRn2RnlPo3Po2PolHr2Hrl0.0 0.5 1.0 1.5 2.0 2.5Time, s17The selected film sequences were projected with a Photo Optical Data Analyser Elmprojector, (Model 224A MKV The Athena Co., USA) capable of variable speed, frameby frame, and forward and reverse film motions. The projector was equipped with aSuper Sankor-16 f1.3, 38mm lens. The sequences’ frame numbers were determined with aPhotographic Analysis Ltd. (Canada) electronic frame counter. The images were projectedto and digitised by a Projection Analysis Unit ZAE 76 equipped with a crosswire eyepiece(P.D.C. Ltd., England).To determine actual bird size from the projected film image, height of the wing abovethe water and wing length, and to compare the flapping flight of the bird IGE and OGE,the maximum length of the bird in the digitiser’s horizontal (X) axis scaling control was setat 100 units. The vertical (Y) axis scaling control was then calibrated so that equal lengthdisplacements of the digitiser’s eyepiece in the X and Y directions would give an equalnumber of displacement units. This procedure was carried out to standardise digitisingprocedures by making the projected image size of the whole bird equal to 100 units. Thesemeasures were then converted to real size based on my own data or literature values (vanTets 1959, Hartman 1961, Withers and Timko 1977, Dunn 1973, Blake 1983, Dunning1984) for the determination of wing motion and the aerodynamic power requirement curvesfor each bird.To determine the movement of the wing tip with respect to a fixed origin whendigitisiug flight sequences, the coordinates’ origin was placed at either the most distalpoint of the beak of the bird or at the water surface immediately below the wingtip at theend of the downstroke. If the first method was used, the distance between the water andbeak was also measured.To determine the minimum height of the wing above the water in the case of theorigin being located at the beak, the minimum wing to water distance was determinedby subtracting the maximum observed wing length during the downstroke of the sequence18being analysed from the beak to water distance. In the case of the origin being locatedon the water, the distance between maximum observed wing length at the end of thedownstroke of the sequence and the water was measured to obtain minimum distancebetween the wing and the water.Morph ometrics.For measurements of wing length, wing area, total weight, and weight of the pectoralisand supracoracoides (flight) muscles, specimens of double-crested cormorants, browii pelicans, and barn swallows were photographed, dissected, and weighed as described in detailbelow. No specimens of black skimmers were available and morphometric data are takenfrom the literature (Withers and Timko 1977, Blake 1983 , Dunning 1984). Additionaldata for brown pelicans, double-crested cormorants, and barn swallows was taken fromvan Tets (1959), Hartman (1961) and Dunning (1984).Four frozen double-crested cormorants were obtained from Dr. David Jones, University of British Columbia. One frozen brown pelican was obtained from San Diego StateUniversity (San Diego, California, USA), four brown pelicans mounted in flight positionswere photographed at the San Diego Natural History Museum (San Diego, California,USA). Five barn swallows were captured in a mist nest at Brunswick Point, B.C. (permitNo. PC BC 86/11), killed, placed in plastic bags, and frozen for later dissection in thelaboratory. One brown pelican wing, one black skimmer wing, one barn swallow wing, andtwo double-crested cormorant wings were photographed at the Washington State Museumat the University of Washington in Seattle, Wa., USA.To determine wing area, the frozen double-crested cormorants were thawed and placedwith their wings fully extended and fixed. All birds and wings were photographed and8 x 10” black and white prints were prepared. The photographs were digitised on an Applegraphics tablet with an Apple II Plus computer. The area was determined by using an19area calculation programme that requires one known distance (a 30cm or a 15cm gradedruler in the specimens’ photographs).To minimise dessication the birds were weighed and their right and left supracoracoides and pectoralis muscles dissected immediately after the photographs were taken.The respective weights of the birds and their flight muscles were measured with Pesola(Switzerland) spring balances. These weights were used for calculation of flight muslcepower output.Speed Measurements.The flight speeds of double-crested cormorants and barn swallows were measured witha K-15 M.P.H. Industries (USA) hand held Doppler radar gun equipped with an F.C.C.Data A.05.000011 transmitter, modified to give velocities in metres per second ( m.s’)with a range from 3 to 30 m•s’ and capable of receiving the reflecting signals fromobjects as small as a sparrow at distances up to 10 m The radar gun was powered by a12 V rechargeable gel cell or a 12 V car battery. It was calibrated against ahsolute timeon a Professional Quartz Timer Sports Timer (Honk Kong) digital sports watch, knowndistances, and fixed or random speeds of vehicles passing at different angles of incidencewhich varied from —50° to + 5(O to the beam of the radar gun.The reflecting signals of objects as small as a bicycle and rider with angles of incidence> ±30° were not detected up by the radar gun and that neither double-crested cormorantsnor barn swallows were detected at angles 10°. Therefore any reflected bird signal isaccurately recorded with E thcos 10° of the displayed speed, or 2% error. There wasno significant difference between the stopwatch speed and the cosine corrected radar speedat either 10° (1 = 1.714, p = 0.09, n = 25) or 20° (i = .135, p = 0.89, n 25). Recordedflight speeds were corrected by a cosine factor as indicated in the unit’s Operator’s Manual.The correlation between cosine corrected radar speeds at 10° and stopwatch speeds are20shown on Table III. Figure 2 presents the regression lines between cosine corrected radarsspeeds and stopwatch speeds.Wind speeds when filming and recording flight speeds were measured with a DeutaAnemo (W. Germany) wind meter. All wind speed measurements were l m•s1.Observations.Daily activities of cormorants in Mandarte Island were observed with binoculars ortelescope. To avoid detection by cormorants observations were made whilst lying down onan inflatable boat near Mandarte Island. For further details of the reproductive behaviourof the double-crested cormorant. colony on Mandarte Island see Drent et a!. (1964).21Table III. Correlation between stopwatch and cosine corrected radar speedsat a 100 angle of incidence between radar and subjects.Component Coefficient Standard Error t value ProbabilityIntercept 0.926 1.838 0.504 0.622Slope 0.977 0.0932 10.482 < 0.001Multiple r2= 0.827 n = 25 F1,23 109.876 df, p< 0.0122Figure 2. Best fit correlations and differences between radar cosine correctedspeeds and stopwatch speeds. Panels a, c, and e for 10, 20, and 30°, respectively.The differences between cosine corrected radar speeds and stopwatch speeds areshown in panels b, d for 10, and 20°, respectively. In panels a, c, and e, regression lines are solid, dashed lines’ slopes=1.C0E2Lc,0U)Ii’)10 1514 16 18 20 22radar rn’s24 26 28U>4”7 b16 18 20 22 24radar, rn/s26c’JCOc’J800•016 18 20 22 24 26 2radar rn/sdradar rn’sLC)c’J‘1220 25 30radar rn/s23Chapter 3.Preliminary Statistical Analysis of wing movements.Introduction.GE increases as the wing approaches a surface (Reid 1932 , Kücheman 1978 McCormick 1979, Houghton and Carruthers 1972), and miriimises loss of altitude when birdsglide near surfaces (Blake 1983). Birds in forward flapping flight are IGE as long as thewing or a part of it is 1.5 wingspans(b) in height above the ground during some portionof the downstroke phase of the flapping cycle (Reid 1932, Withers and Timko 1977, Blake1985). To study GE in birds with different lifestyles several bird species were filmed ICE.Barn swallows were filmed at Brunswick Point and Va.nier Park IGE in forward horizontal flight ther at the end of a dive or during long foraging runs (> 25m) along a dyke.Black skimmers flying over the San Diego salt evaporators were observed flying IGE whileforaging by skimming the water in horizontal forward flight. Brown pelicans ifimed atBahfa de Todos Los Santos, Ensenada, Mexico, and double-crested cormorants filmed atMandarte Island flew not only in horizontal forward flight, but also in both ascending anddescending powered flight ICE. To understand how GE affects birds during flapping flightit is important to determine not only the GE in level forward flight but also its overalleffect during ascending or descending powered flight.GE during flapping flight is analysed by considering changes in height through thewingspan during the downstroke phase of the wing-beat cycle. This is the phase of thewingbeat cycle in which most of the lift is generated, although lift can also be generatedduring the upstroke in large flying vertebrates (UM Norberg 1975, 1976; Rayner 1981). Toanalyse the wing movement during the downstroke it is essential to find accurate, reliableand mathematically manipulable descriptions of the movement of the wing on the vertical(Y) axis.24Movement of a wingtip during flapping flight can be described by a sinusoidal curve.The digitised film sequences in this study trace these curves that can then be describedby time series analysis. Bloomfleld (1976) defines a time series as a collection of numericalobservations arranged in a natural order, usually associated with a particular instant orinterval of time. He defines the Fourier analysis of a time series as a decomposition ofthe series into a sum of sinusoidal components. Fourier series can be used to describeany data-analysis procedure that describes or measures the fluctuation in a time series bycomparing the series with sinusoids (Bloomfleld 1976). So, the changes in height abovethe ground in the vertical (Y) axis of a flapping wing, can be described by their Fourierseries. It is possible to approximate nearly any time series by means of a series expansion,i.e. by a a series of simple sinusoidal expression whose sum recreates the original curve toan extent limited by the analytical technique used and the sample size (Broch 1981).Three statistical methods were chosen to describe the periodic sinusoidal vertical wingmovement. Circular-linear (periodic) regression and correlation (Batschelet 1981), periodicAnalysis of Variance (ANOVA) (Bliss 1970). and discrete Fourier analysis of time series(Bloomfield 1976).The circular-linear regression and periodic ANOVA algorithms calculate the meanheight of the wingtip (mesor, M) and the first two terms of a Fourier series that describesthe particular flight sequence analysed. The discrete Fourier transform analysis renders anumber of harmonics equal to the half the number of points sampled in the flight sequencebeing analysed.Both circular-linear regression and periodic ANOVA require random and independentsampling. Neither of these two conditions are met by the sampling technique and samplingapparatus used, i.e. a ciné camera i-tinning at a constant speed, nor by the actual event, i.e.a periodic wing movement in which the wing position at any moment can be predicted bythe previous one. Nethertheless, Batschelet (1981) recommends the use of circular-linear25regression techniques for the description of periodic phenomena, such as the vertical wingmovements. The strength of these techniques is demonstrated by the highly significantresults obtained here, by the fit of the calculated curves to the points and by independenttest of areas under the original and calculated curves.A Fourier series is a representation of a periodic function f(x) as a linear additivecombination of cosine and sine functions (Lighthill 1958). Fast Fourier transforms producewhere n is the number of points, discrete Fourier harmonics from the initial waveform(Hobbie 1988). Given that the number of calculated harmonics of the Fourier series thatdescribes the vertical wing movement is directly proportional to sample size (Bloomfield1976), it is important to establish the statistical significance of any particular harmonicand its corresponding physical reality. While carrying out the analysis I found that thestatistically most significant Fourier coefficients of any flapping sequence were the meanheight of the wingtip (M), which also represents the bird’s body height, and the first twoharmonics, which represent the movement of the wing. In all sequences the sum of theadditional terms contributed <<0.01% towards explaining the original wave.Description of Anaiyticai Methods.Circular linear regression and periodic ANOVA describe phenomena of the generalform:Y=M-fAcosw(i—t0) (I.)where t is the independent time variable. The other parameters of the equation are: Mmean level or mesor, A = amplitude (A 0), (mamum distance between M and t0).L’=the angular frequency, related to the period T by w = 27r/T, and i, = acrophase (i.e.phase angle where the sinusoid reaches its highest point).Batschelet (1981) and Bliss (1970) fit a general trigonometric polynomial of the type:g() = M + A1 cos(w—+ A2 cos(2w1—) + ... + A. cos(kwt — 4k) (2)26Batschelet’s (1981) algorithm requires a minimum of n = 6 equally spaced time instantsfor a good fit. Bliss’ (1970) algorithm requires at least one and a half wavelengths and aminimum n = 8 equally spaced points per wavelength to calculate the Sums of Squares,otherwise a negative sum will result in the Error Sum of Squares.Batschelet (1981) defined drcularlinear correlation as:r = corr z,y = coy (z,y)/s1s2wherecoy (x,y) =1 (x — Z)(yj—y)and s and 2 are the variances.He then sets the correlation coefficients as:= corr (y,cos ),rs = corr (y, sin 4),rcs = corr (cos qS, sin ),where 4’ = wt to define the correlation coefficient between y and 4’ for the first term in theFourier series as:r2 = (rc + s — rcrsrcs)/1 — TS) (3)where y and 4’ are independent and when n is large:ni’2 (4)Eq. (4) is Batschelet’s (1981) test statistic.27Since the sine and the cosine are orthogonal and additive transformations of time, thesignificance of the Fourier factors eq. (1) can be expressed as:Y = a0 + a1 cos(w) + b1 sin(wt) (5)(Bliss 1970) aflows the constants in eq. (1) to be determined from the regression coefficientsa1 and b1. If we let u1 = cos(wi) and v1 = sin(wi) then eq. (5) may be written as:Y=a0+ajuii+biv1 (6)where u1 = = E(ui vi) = 0. The regression coefficients a1 and b1 have thesame denominator, k, for all uniformly spaced series of Ic intervals, so that EuEv? k. When f(number of replicates per sampling interval)= 1 at each time , theyare computed as:- (uay)- [uiy]a1 —V’ 2 1L. 1E(viy) — [viy]Evkwhere the square brackets [] designate the sums of squares or products measured from themeans of the variates. With f replicated ys at each i, totaling T, the regression coefficientsare computed directly from 2 as:[u 2’.] [v1 T]a1=fkand b1=‘fkT is the sum total of all values, k is the sampling frequency. The same rules apply for thesecond and any subsequent harmonics (Bliss 1970).Sequence Po3 (a pelican in descending flapping flight) was chosen to test the reliabilityand statistical significance of the algorithms that describe the travel of the wingtip. The28null hypothesis states that there is no periodic relationship between time and the verticallocation of the wing tip. The sequence consists of 3.5 wingbeat cycles with an averageof 19 recorded points per cycle, thus fulfilling all the requirements of both the circular-linear regression (Batschelet 1981) and periodic ANOVA (Bliss 1970) algorithms. All othersequences chosen were analysed with either or both methods.The AN OVA test is performed by comparing the mean square of each harmonic andthe mean square of the scatter in the curve against the error mean sum of squares. Thestatistical gniflcance is determined by standard F-distribution tables or by the methoddescribed in the results section of this chapter. Table Wa presents the results of thecircular-linear regression and Table IVb the results of the periodic AN OVA for Po3. Bothmethods provide statistically gniflcant results.29Table IVa. Circular-linear regression of the best fit datafrom Po3.r2 2vulue p(ri * r2)0.703713 53.4822 <0.001Table lVb. Periodic Analysis of Variance for the digitized sequence Po 3 ofa pelican flying in ground effect.Source Sum of Squares D. F. M. S. F-ratio pa1b 7.916 2 3.958 67.232 < 0.001a2b 0.002 2 0.001 0.017 .998scatter 0.088 15 0.006 0.099 .906error 3.297 56 0.059TOTAL 11.302 7530Lin ear.isaüon.The nusoids representing wingtip movements were linearised to provide a measurement of A and M that would allow comparisons both between and across species. Bydefining:z = (cos ç5— (7)where = wi and ç = i0 and= (cos bj—(8)theng()=M+Ai(cos—0 (9)becomesY=M+A1x (10)and eq. (2) becomesY=M+AIZH-2z+...-FAkxk. (11)(Batschelet 1981).Standard linear regression and correlation techniques can then be applied.The algorithms for both circular-linear regression and circular-linear AN OVA werewritten, tested and calculated at Biosciences Data Centre (BDC) of the University ofBritish Columbia. The regression of the linearisation and the correlation between testswere done using the ‘S’ data analysis and graphics package. The Fast Fourier Transformswere done with the ‘S’ statistical package enhancements designed at the University ofWashington and installed in the BDC’s computer.31Results.Reliability of the statistical tests.The aim of the chapter is to find mathematical expressions that describe the verticalwing movement of birds IGE. The wingtip movements of Po 3 , the best fits by rcularlinear regression, periodic ANOVA and Fast Fourier transforms, ther residual plots ofcircular-linear correlation and periodic ANOVA, the correlation between these two methods, and the componets of the Fast Fourier transforms are presented in Figure 3. Both thecircular-linear regression and the ANOVA algorithms calculate least square curves that donot follow the exact descending motion of the bird’s wing.If the area under each of the best fit curves equals the area under the original data, anindependent test of the reliability of the algorithms is obtained. Also, if the area under thecurves is the same, it is then possible to assess with best-fit algorithms GE on horizontal,ascending or descending powered flight. Table Va presents the results for the areas underPo 3 and its best fit curves employing the digitiser and area determination software ofthe BDC.Given the small differences in areas between the raw data and the best fit curves, theareas can be considered identical. The best fits given by the algorithms developed in thepresent study are an accurate representation of the data, and their results can be used todescribe the GE during forward horizontal, ascending, or descending flight.Comparison of analytical methods.Although circular-linear regression and periodic ANOVA give different equations (Table Va), they differ by less than 10%. Table Vb presents the equations resulting fromthe use of the circular regression and periodic ANOVA algorithms on Po3. The results of32the linearisation of the circular-linear regression and the periodic AN OVA can be seen ofTables Via and b, respectively.The residual plots of circular-linear regression and periodic AN OVA (Fig. 3b, top andcenter, respectively) show that nce the algorithms find the least square lines, the largestdifferences occur in those points further away from the best fit curve, i.e. beginning andend of the descent. Note that the residuals between the algorithms and the original dataset are not random but periodic.11 the circular-linear regression and the periodic AN OVA algorithms produced thesame best-fit curve, the plot of the resulting points of one algorithm against the resultingpoints of the other would produce a line of b (slope)=l and r2 = 1. The scatter plot ofthe two algorithms can be seen in Figure 3d, and the resulting correlation in Table VIc.Figure 3d indicates that periodic ANOVA provides a fit identical to that of circular-linearregression.Statistical results and equations.All data sets that fulfilled the requirements described for each of the tests describedin the section of Materials, Methods and Preliminary Analysis of chapter 2 were analysedby the appropriate method (circular-linear regression, circular AN OVA, or Fourier transforms). The statistical results of the circular-linear regression analysis are reported onFigure 4, and the statistical results of the its linearisation on Figures 5 to 7. The statistical results of the periodic ANOVA analysis are reported on Figure 8 and the statisticalresults of its linearisation in Figures 9 to 11.Table VII summarises the equations for circular-linear regression, for the sequencesanalysed with this method. Table VIII summarises the equations for the sequences analysed with the periodic AN OVA. Table IX presents the first two terms of the discrete Fouriertransforms for all sequences used in the present study.33Figure 3. Best fit curves, residual plots, and linearizations; correlation between circular ANOVA and circular-linear regression; and Fast-Fourier transformcomponents for Po 3 wing-tip pattern. Panel a presents the best fit curves fordrcular-linear regression (top), periodic ANOVA (centre), and Fast-Fourier transform (bottom). Panel b presents the residuals for circular-linear regression (top),and periodic AN OVA (centre). Panel c presents the linearization of circular-linearregression (top), and periodic ANOVA (centre). Panel cs the correlation betweencircular-linear regression and periodic ANOVA. The Fast-Fourier transform components are: periodogram (e), amplitudes (i), and acrophases (g).a b d>0zC0.0 0,4 06 12 1.6 0.0 0.4 0.1 12 1.6 -0.6 -02 02 04 0.6 -0.6 -0.2 02 04 06The s XA o) c.,La-6n. ree f g0 5 10152020 0 10 20 30 40 0 10 20 30 40Feq.eoy T r.zn*r Turn34Table Va. Areas under Po 3 and its least-square fitted curves. Theareas are used to compare the fit of both circular-linear regressionand periodic ANOVA to the raw data of Po 3 a pelican flightsequence.Curve Area Difference Percentageunits2 units2Po 3 72.198Regression 69.854 2.344 3.36ANOVA 67.084 5.114 7.62Table Vb. Equations obtained with the two different algorithms employedfor describing Po 3Method EquationRegression —0.019 + 0.463 * (t1 — 0.044) + 0.024 * (2 — (_0.027))ANOVA —0.040 + 0.456 * — 0.133) + 0.007 * (t2 — (—1.220))35Table Via. Summary of the linearization of the aErcular linear regression ofPo3.Component Coefficient Standard Error i Value pIntercept -0.026 0.0244 -1.060 0.8541st sinusoid 0.992 0.0743 13.350 < 0.0012nd sinusoid 1.019 0.9595 1.062 0.292Multiple r2 0.710 n= 76 F2,73 = 89.184 p=OTable VIb. Summary of the linearization of the periodic ANOVA of Po 3Component Coefficient Standard Error Value pIntercept -0.026 0.0248 -1.064 0.2911st sinusoid 1.002 0.0769 13.018 < .0012nd sinusoid 4.708 4.9468 0.952 0.342Multiple r2 0.699 n= 76 F2,73 = 84.776, p0Table Vic. Summary of the correlation between periodic AN OVAand circular-linear regression algorithms.Component Coefficient Standard Error t Value pIntercept -0.020 0.0027 -7.285 < .001Slope 0.981 0.0083 118.020 < .001Multiple r2 = 0.998 n= 76 F1,74 = 13928.8, p=O36Table VII. Summary of best-fit circular-linear regression equationsY = M ± A1 cos—i) + A2 cos(2wi —Sequence Mesor A1 A2 kPa 1 0.334 0.100 4.641 0.0278 3.417 9Pa 2 0.430 0.089 0.176 0.0103 3.881 10Pa 3 0.387 0.0837 0.677 0.007 -1.501 10Po 1 0.913 0.681 0.361 0.082 -1.362 17Po 2 0.303 0.493 0.679 0.048 -0.483 18Po 3 -0.040 0.458 O.709 0.046 1.062 19Rn 1 0.285 0.270 0.510 0.021 -0.115 10Rn 2 0.333 0.274 1.276 0.072 1.548 8Rn 3 0.790 0.385 -0.920 0.074 2.962 13Rn 5 0.889 78.663 1.066 9.615 0.102 12Rn 6 0.857 68.640 0.248 7.555 -0.687 13Rn 7 0.113 0.301 0.096 0.029 4.337 17Rn 8 0.059 0.184 -0.366 0.020 4.688 22Rn 9 0.340 0.244 0.837 0.023 -0.337 12Hr 1 0.146 0.043 -0.785 0.039 2.284 7Hr 2 0.008 0.098 1.086 0.025 2.509 637Table VIII. Summary of best-fit periodic ANOVA equationsY=M+Aios—i)+A2cos(2wt ).Sequence Mesor A1 A2 kPa 1 0.334 0.124 2.788 0.022 1.830 10Pa 2 0.430 0.089 0.176 0.010 3.880 10Po 1 0.879 0.602 0.549 0.098 3.039 17Po 3 -0.040 0.456 0.133 0.007 -1.220 20Rn 1 0.282 0.244 0.025 0.024 2.958 11Rn 2 0.022 0.274 -0.186 0.023 1.814 9Rn 5 0.055 0.290 0.373 0.087 2.961 15Rn 6 0.022 0.274 -0.186 0.022 1.814 14Rn 7 0.102 0.283 0.127 0.043 3.547 17Rn 8 0.042 0.164 -0.297 0.010 2.568 22Rn 9 0.346 0.267 0.831 0.029 0.733 12Hr 1 0.146 0.043 -0.785 0.039 2.283 7Hr 2 0.008 0.098 1.086 0.025 2.510 638Table IX. Summary of the first two terms of Fast fouriertransforms performed on selected dataY=M+Aicosw—4i)+A2cos(2 i-).Sequence Mesor A1 A2Pa 2 0.430 0.025 -1.102 0.022 .793Pa 3 0.387 0.042 -1.284 0.035 1.481Po 1 0.879 0.110 3.770 0.211 2.380Po 3 -0.040 0.207 4.686 0.097 3.754Rn 1 0.282 0.056 -1.173 0.118 -1.174Rn 2 0.351 0.075 1.287 0.285 -0.0595Rn 3 0.777 0.396 1.187 0.061 0.326Rn 5 0.055 0.230 0.400 0.227 -1.543Rn 7 0.102 0.081 3.431 0.030 3.421Rn 8 0.0421 0.057 4.139 0.087 3.46939Figures 4 to 11 present a novel method for summarising statistical results throughsignificance level curves. By locating the appropriate calculated statistic in the figurewith the probability plane corresponding to the appropriate distribution (x2, i, or F) anddegrees of freedom it is possible to ascertain its significance level without having to consulta standard statistical table. A distribution probability plane for 2 degrees of freedomis presented in Figure 4. Figures 5, 6, 9, and 10 are two-tailed Student’s t probabilityplanes. Figures 7, 8, and 11 are one-tailed F distribution probability planes for 2 degreesof freedom in the numerator.Conclusions.The aim of this chapter was to find mathematical expressions that describe the verticalwing movement of birds IGE. Both circular-linear regression and periodic AN OVA describeto an statistically highly significant level the vertical displacement of the wing, as long asthe appropriate prerequisites of sample size for the algorithm are fulfilled. These estimatestend to obscure ascent or descent manceuvres of the bird by building the best-fit sinusoidaround the median height of the wing (M) during the sequence and modifying the overallamplitude by taking into account the highest and lowest points of the sequence whenconstructing the sinusoid. Nontheless the general trend of the flight sequence can beobtained. Fast-Fourier transforms describe precisely the recorded vertical movement ofthe wing. These transforms can be cumbersome to manipulate given that the number ofFourier terms is directly proportional to the number of data points. Also, such a precisedescription masks any trends on the data, precluding generalisations of the film sequencebeing analysed. Despite the particular limitations of any of the three methods used in thisstudy for describing the vertical wing movements of a bird in flapping flight, any of themcan be used with coafidence. To analyze the film sequences I selected the method thatprovided a statistically significant result and was easiest to manipulate.40Figure 4. x2 probability levels at 2 degrees of freedom for of the best fit curvesfor the circular-linear regression algorithm. The horizontal represent standardrejection levels (p = 0.05, p = 0.01, and p = 0.001), The Y axis representsthe calculated value and the ordinate gives the exact probability of obtainingthe calculated x2• The diagonal dotted line is an exact probability line for x2values for 2 degrees of freedom. The horizontal lines represent standard rejectionlevels indicated in the box. x2 values falling below any of the horizontal lines arestatistically significant at an a level smaller than the probability value of the line.>005 10 15 20 25 30 35Chsquared valuesCCCCCQCCCC0C041Figure 5. Two-tailed Student’s significance levels of the intercepts resultingfrom the linearisation of the circular-linear regression algorithm. The abscissarepresents degrees of freedom and the ordinate obtained i values. The lines represent rejection levels of c 0.05, 0.01, and 0.001. To find the significance levelof a calculated for the appropriate number of degrees of freedom, the obtainedvalue is plotted on the graph. i values falling above any of the lines are statistically significant at an c level smaller than the probability value of the line.*** V0)2CO>— IC) 0\ —--—VCx0I I0 20 40 60 80 100Degrees of Freedom42Figure 6. Two tailed Student’s i slgaificance levels of the slopes resulting fromthe linearisation of the circular-linear regression algorithm. See Figure 5 for explanation.0.05I-frRn———0.01 V Po———- 0.001 PaC)DCC>0CCCI10TV0 V0I’0*.‘0 20 40 60 80 100Degrees of Freedom43Figure 7. F-distribution significance levels at 2 degrees of freedom numerator of the multiple regression analysis of the linearisation of the circular linear regression algorithm. The abscissa represents degrees of freedom and theordinate obtained F values. The parabolic lines represent rejection levels ofa 0.05, 0.01, and 0.001. To find the significance level of a calculated F forthe appropriate number of degrees of freedom, the obtained value is plotted onthe graph. F values failing above any of the lines are statistically significant at ana level smaller than the probability value of the line.CL()- -- 005 X HV —— 0.010.001 * pVCCV00C)>L1 0\ \C—\ ‘•-_.I I I0 20 40 60 80 100Degrees of freedom denominator44Figure 8. F-distribution significance levels at 2 degrees of freedom numerator ofthe best fit curves for the periodic AN OVA algorithm. See Figure 7 for explanation.00IL,________________-- 0.05 X HrI Rn0.01 V Pch—— 0.001 * Pa0CVVC).2>U\\ \— ..---It, •.—-xI I0 20 40 60 80 100- Degrees of freedom denominator45Figure 9. Two-tailed Student’s i gniflcance levels of the intercepts resultingfrom the linearisation of the periodic AN OVA algorithm. See Figure 5 for explanation.a)>Degrees of Freedom1000L)0It,00 20 40 60 8046Figure 10. Two-tailed Student’s t significance levels of the slopes resulting fromthe linearisation of the periodic AN OVA algorithm. See Figure 5 for explanation.a)>0CU,CCCU,U,0.05HrRn——-—0.01 V Po———-0.001 Pa40 60Degrees of FreedomI1V0 20 80 10047Figure 11. F distribution gnificance levels at 2 degrees of freedom numeratorof the multiple regression analysis of the linearisation of the periodic ANOVAalgorithm. See Figure 7 for explanation.0CIt,0.05 X Hr0 Rn——0.01 P00.001 E Pa00V0It,C)>x\ \o-\\NIt) . -0- 20 40 60 80 100Degrees of freedom denominator48Chapter 4.The Power Curve and Ground Effect.Introduction.Flapping flight requires a large energy output when compared to the basal metabolicrate or the maintenance energy. The calculation of a bird’s flight power requirementshas been approached from two perspectives. The first approach has been to measure thephysiological power expenditure whilst flying (e.g. Tucker 1966, 1972; Torre-Bueno andLarochelle 1978; Tatner and Bryant 1986; and Rothe e al. 1987). Although this approachgives a physiological estimate of the power consumed during active flapping flight, it doesnot directly reflect the aerodynamic forces that must be overcome in flight. The secondapproach directly considers aerodynamic forces and the power requirements of active(flapping) flight for birds and other flying vertebrates. These forces have been assessedvia fixed wing aircraft quasi-steady aerodynamics theory and momentum jet theory withmodifications that take into account the drag generated by the flapping of the wings (e.g.Pennycuick 1975), or by using a vortex theory of forward powered flight (e.g. Rayner 1979ab c). Quasi-steady aerodynamic theory is employed here because of its ease of computation.Nethertheless, the estimation of the aerodynamic forces required for flapping flight throughthe momentum jet theory does not explain these forces. Vortex theory does provide anexplanation for the creation of the aerodynamic forces (Nachtigail and Dreher 1987), butit is computationafly complex. To assess aerodynamic forces generated during forwardflapping flight a power curve which takes into account the the different aerodynamic dragcomponents must be created.The mechanical energy available from flight muscles and the energy required to flyimpose an upper limit to the size of a bird engaged in flapping flight and to its payload49(Pennycuick 1975). Limitations imposed by a bird’s morphology and energy available forflight and maximum payload, and stalling speed (V8ta) can be overcome by using GE. GEreduces induced drag (D2) and stalling speed (V8a11)whilst increasing lift (L).The Power Curve.The assessment of the total power requirements for flapping flight must take into account both the aerodynamic forces that must be overcome by the bird and the physiologicalrequirements that the bird must meet in order to fly. The assessment presented here follows Pennycuick (1975) by considering the maintenance metabolism and the aerodynamicforces. It then combines these two components and adds an estimate of the energy requiredby the bird for gas exchange and circulation.Maintenance Costs.To give an idea of the minimum energy cost a bird must incur to survive, a measure of metabolic rate is employed. Metabolic rate can be measured by calculating thedifference between the energy value of all food taken in and the energy value of excreta,by determining the metabolic rate from the total heat production of the organism or bymeasuring the amount of oxygen used in the oxidation process, provided information aboutwhich substances have been oxidised (Schmidt-Nielsen 1979). The metabolic rate (W) ofa non-passerine bird can be estimated by the allometric equation:Fme = 3.79m°723 (12)(Pennycuick, 1975 based on Lasiewski and Dawson, 1967), where Pmet is the metabolicrate and m the mass (kg). Metabolic power (Pmet) gives a good indication of the minimalenergetic requirements of a bird. By taking this assessment into account and convertingthe metabolic energy into a mechanical power equivalent by multiplying with an efficiency50factor q of 0.23 (Pennycuick 1975). A 1.88kg double-crested cormorant should have ametabolic rate of 5.98 W or 1.38W in mechanical equivalents.A more realistic approach than that obtained by eq. (12) is the use of the maintenanceenergy. Henneman (1983) measured maintenance energy of double-crested cormorantsunder different environmental conditions recreated in the laboratory. He discovered thatthe birds had a higher basal rate than that predicted by the equation of Aschoff andPohl (1970) describing metabolic rates for starving birds sitting in the dark. Henneman(1983) also discovered that the double-crested cormorant’s metabolic rate is lower at night.Henneman (1983) gives the following equations for calculating the maintenance rates:Eday = (1.48 — 0.0281°C)5.58, (13)for daytime, andEnight = (1.25 — 0.0290°C)5.58, (14)for night. In these equations E is the rate of metabolism in cm302 . g’ . hr’ and ° C isthe environmental temperature. These figures were converted to W by multiplying by afactor of 5.58 to express them in SI units compatible with the calculations of aerodynamicpower.The temperatures used here to calculate metabolic rates for the double-crested cormorants are those registered at the Victoria International Airport, near Mandarte Island,for the summer of 1988. The temperatures (provided by the Canadian Atmospheric Environment Service) are shown in Table X. The calculated mechanical maintenance energies(Pme) of the double-crested cormorants for night and day during the reproductive seasonare calculated using the masses of the double-crested cormorants of Table XIIa and areplotted in Figure 12 as a ratio of the metabolic rate calculated via eqn. (12). The actual values of the mechanical equivalents of maintenance rates can be seen in Table XI.Eq. (12) underestimates energy expenditures. The seasonal (temperature) dependence ofmetabolic cost (Fig. 12) will be accounted for when calculating the energy expendituresof the double-crested cormorants.51Table X. Mean monthly temperatures of theVictoria International Airport for 1988.Month Mean max Mean mmoc ocApril 13.6 4.2May 16.3 6.4June 19.1 8.3July 22.5 10.1August 21.5 10.2September 17.8 6.852,III)C?3II II IIII3c)11C.3PC)a-I.CIcnCDCDFigure 12. Ratios of day and night maintenance rates of double-crested cormorants, eqs. (13) and (14), to Pme eq. (12), for the reproductive season atMandarte Island.+++H-+ HCDACdaynightI I ElMar Apr May Jun Jul Aug Sep Octmonth‘54Aerodynamic Costs.Three forces must be overcome by a flapping flyer in order to thrust itself through theair: parasite, profile and induced drag forces. Each force has an associated power term.Parasite OW (Ppar) is the power required by the bird to overcome the drag generatedby the shape of the body and is usually calculated as.Ppar = pVApCDpar (15)where: p is the air density in kg . m3 (1.256kg m3) at a standard atmosphere, V is theforward speed of the bird in m•s1,A is the equivalent flat plate area of the body at itswidest point (Pennycuick 1975) and is calculated as:Sbody Cij (16)where Sb0d is the cross sectional area of the widest point of the body and can be estimatedfrom the allometric relationship:Sb0d = 8.13 x 103m°66 (17)where m is the mass in kg. (Pennycuick 1975)CDb is the body drag coefficient which is determined by the Reynolds number (Re)at which the bird is flying (Pennycuick et al. 1988). CDb is calculated as:CDb 1.57 — O.IOSln(Re) (18)whereRe = 1.25 x iO/. (19)Profile power (Ppro) is the power required to overcome form and friction drag of thewings during the power stroke, and it is the most difficult power to calculate (Pennycuick551975, Rayner 1979a b). Pennycuick (1975) assumes that Pp.0 is constant (i.e. independentof speed) over median speeds and is equal to 1.1 times the absolute minimum power (Pam).Pam will be discussed later on this section.The present study assumes that Ppro is proportional to the speed, and it is calculatedPpro = pSVCDpro (20)where S is the wing area, and CDpro is the profile power coefficient, assumed to have avalue of 0.02 (Rayner 1979a).Estimating the power curve with eq. (20) results ii Vmp and Vmr speeds higher thanmaximum values of flight speed recorded for the double-crested cormorants at MandarteIsland. Figure 13 illustrates the ratio between Pennycuick’s PprO and the P,,.0 used in thisstudy.560DiFigurelated in13. Ratio between Pennycuick’s (1975) constant and the Ppro calcuthis study.It)CCIt)oCdIt)Q0cC6I I8 10 12 14 16 18 20Vm!s57Induced power (Find) is the power required to generate the force required to supportthe weight of the bird. This force is generated, under vortex theory, by the shedding ofvortices from the wing tips of the bird. Momentum jet theory assumes that aback anddownward momentum is imparted to the air. This momentum is a product of the massflow (mass per unit time) passing through an arbitrarily defined wing disk (Sd).The wingdisk is the area of a circular disk with the wingspan as diameter Sd (Pennycuick1975).Pd is inversely proportional to speed; as a directconsequence, at a forward speed ofzero the requirements for P2nd would be infinite. This isnot the case; Find is calculateddifferently under those circumstances. Such calculationscan be found in Pennycuick(1975) and Rayner 1979a,c for momentum j€t and vortex theory, respectively and arenot applicable to this study since cormorants do not hover. Find at speeds higher than 0is calculated as: R2Find= 2pVSde(21)where Sd is the wing disk area, and e is an airfoil efficiency factor of 1.0 and Rf is theresultant of the weight and body drag (Pennycuick, 1989a) and is calculated as:Rf = JW2 + Dar (22)where W is the weight in Newtons N and Dpar is the bodyor parasite drag:.Dpar = .pv2A (23)Following Blake (1983) let:K1 = PSCDpro + pApCpar(24)and R2K2= (25)2pSde58thenPpara K1 V3 (26)andPind = K2 V’ (27)The sum of the aerodynamic power requirements produces the characteristic U-shapedcurve, but leaves aside physiological considerations. The lowest point of the curve reflectsthe speed at which a bird should fly for minimum power consumption, or minimum powervelocity (Vmp). It is this “absolute minimum power” (Pam) that Pennycuick (1975) usesto generate his estimate of .Ppro. Pennycuick (1975) considers P,.o to be 1.1 times P,. Amore realistic curve (Pennycuick 1975) is generated if the metabolic or the maintenancepower (expressed in a mechanical currency) is added. Lastly, the cost of ventilationand blood circulation necessary to provide the oxygen to the flight muscles must to beconsidered. Pennycuick (1975) uses a factor of 1.1 based on Tucker’s (1973) estimates ofpower expenditure by the heart and ventilation during exercise (5% each), and the samestandard will be used here.The power curve for the double-crested cormorant.To calculate the power requirements for double-crested cormorants some of theiranatomical characteristics must be known. The necessary measurements were obtainedby dissecting 4 cormorants (for details see chapter 2, Materials and Methods). The resultsof the measurements of the dissections can be seen in Tables XIIa and XIIb.The power curve for double-crested cormorant is shown in Figure 14. The sum ofthe aerodynamic power components give a characteristic U shaped curve which includesmaintenance power. For more details see the legend to Figure 14.59‘-CDCD01OCDH-PPPPi-”CD—xy0C)I-qi-C)1C)Cl) JqCD ci)DcDJ)1H-PPPC)0bC)lL’3ci, CDci)CD0 ‘1C)CDCDDCCDIcDCDcoc’L’3C)CD ci,t:’3cici,HDOPCCD-,t3t.)C.)’C’:)ci’8H-PPPP-(Dk)C3I.Figure 14. Power curve for double-crested cormor&nts at Mandarte Island. ais Find, b Ppar, c and d is the to which the muintenance and exerciseexpenditures (e) have been added in mechanical equivalents.Cr)C)0V(m/s)20e —I I I I0 5 10 1561Figure 15 illustrates the two characteristic speeds of the power curve: the speed atwhich the least amount of energy is consumed, allowing the greatest time in air, (i.e. theminimum power speed, Vmp, and the maximum range speed (Vmr), the speed at whicha bird flies the longest distance for a given amount of fuel). Vm,. is found by drawing atangent line from the origin to the power curve or by finding the minimum ratio betweentotal power and speed.As shown in Figure 12, P, in the double-crested cormorant varies with ambienttemperature. Power consumption ratios based on minimum calculated mail)tenance powerare presented in Figure 16. It can be seen that the energy consumption during flight bya double-crested cormorant changes by about 5% for the range of temperatures recordedduring the reproductive season of 1988.62Figure 15. Characteristic speeds of the double-crested cormoraiit power curvefor the month of July.C) Vmrc’JVmp 15.10)0ci-11 .1I I0 5 10 15 20V(m/s)630•1-0Figure 16. Ratios of power consumption at different speeds throughout the reproductive season of the double-crested cormorants at Mandarte Jsland. The Xaxis represents flight speeds, the Y axis power ratios.L()qq1C1cJc1ccq .1 ii I I I I6 8 10 12 14 16 18 20Vm/s64Ground Effect in Flapping Flight.GE explanations fall into two separate categories. The first effect is due to the reducedmass flow under the wing in the presence of the ground where it tends to increase thepressure at the wing’s lower surface for a positive angle of incidence (a), resulting in anoverall gain in the lift of the two dimensional wing section. The second effect is due tothe velocity induced by an imaginary reflected wing at a height (y —Ii) that can beexplained by the lifting line model. In the case of a positive a, the wing experiences anadditional forward velocity (V = F/47rh) (where F is the circulation around the wing)that reduces the free stream velocity and thereby decreasing lift. The extension of thevortex line model on a three dimensional finite wing leads to the conclusion that the wingtip vortices will always increase the lift of the wing ICE (Katz 1985).Reid (1932) explains ground effect by saying that “a wing flying close to the groundbehaves as though it were one wing of a certain imaginary biplane in a limitless expanseof fluid; the hypothetical biplane is composed of the real wing and its mirror image in theground plane. If the height of the wing above the ground is h, the biplane has the gap 2h.’‘Since the lifts of the wing and its image are equal in magnitude and of opposite sign,the self induced and mutually induced vertical velocities at each wing also have oppositesigns. The vector sum of the self-induced and mutually induced velocity give a new verticalvelocity.”The total induced drag of the two-wing system is:DIT = D11 + D12 + D22 (28)where is the induced drag experienced by the real wing, D12 the mutual induceddrag, and D22 the induced drag experienced by the image wing. The part experiencedbythe real wing is:L2 LL’= pirV2b2+ 4pirV2bbt(29)65since b = b’ and LL2Di= 2(1 (30)p7rbReid (1932). The value of a depends on h and b, and is Illustrated in Figure 17.Chapter 3 showed how a Fourier series can describe the vertical movement of the wingtip of a bird during flapping flight. The present chapter considers the vertical displacementof the whole wing through the downstroke phase of flapping flight and how these changesplay a role in the amount of GE experienced by the bird. Previous studies of GE duringflight in birds have been based on fixed-wing aircraft aerodynamic models and have notconsidered other existing aerodynamic models of GE. For example, these studies haveassessed GE for black skimmers in gliding flight without explaining changes in altitudeloss (Withers and Timko 1977 ), gilding without loss of altitude (Blake 1983 ), or haveconsidered that the average height of the wing during the downstroke is sufficient toestimate GE during flapping flight (Blake 1985).Employing the model of Reid (1932), a quasi-steady approach is taken here, wherethe wing is fixed and parallel to the ground and requires a unique measurement of both h.and b. A flapping wing changes its height with respect to the ground in a periodic fashion.This change in height is best expressed by computing it from the wing length and changesin its angle with respect to the horizontal. The wing obtains its highest absolute angularvalues at the beginning and end of the downstroke and its minimum angle (0 radians) atthe instant the wing is parallel to the ground. These changes in height through time areexpressed by the sinusoids of chapter 3.To date no detailed study of the biomechanics of flapping wings in GE exists. Neitheris there an aerodynamic model that can describe wings with both variable geometry andlarge oscillations (Prof. J Katz pers. comm.). The biomechanicai approach to the studyof GE in flapping flight of the black skimmer used the lifting line theory model of Reid(1932) and the mean wing height during the downstroke to calculate GE (Blake 1985).66Figure 17. Reid’s (1932) interference coefficient for GE, o, plotted against the‘wingspan to wing height to wingspan ratio (h/b).E0)U)0.0 02 0.4 0.6 0.8 1.0 1.2 1.4 1.6hib0000067Blake’s (1983) model indicates that GE is important in the daily energy balance of theblack skimmer during the breeding season.Recent aerodynamic approaches to the study of GE on banking wings (Binder 1977)or oscillating wings (Katz 1985) have used two dimensional wing models. The study ofBinder (1977) on GE for fixed wings at banking angles from 0 to 20c found a reductionin D dependent on the banking angle. Katz (1985) studied GE on plunging (rapidlyascending and descending) wings subject to oscillations of 0.1 of the chord (the chord isthe distance from the leading edge to the trailing edge of the wing) concluding that thetime to reach a steady lift coefficient C1 was reduced and L increased. Neither Blake’s(1983) biological study, nor the aerodynamic approaches of Binder (1977) and Katz (1985)reproduce the actual conditions of GE in flapping flight. The flight of the birds in GE ischaracterised by large amplitude and low frequencies. Both the Binder (1977) and Katz(1985) models indicate a reduction in D1 for oscillating and banking wings, respectively.Any model that attempts to predict GE in flapping flight should agree at least qua)itativelywith the results of Binder (1977) and Katz (1985).The wing shape during downstroke was determined by filming birds flying towards oraway from the camera. It was found that the wing can be described as a rigid spar hingedat the wing root (Fig. 18). Since GE can be assessed through lifting line theory modelsemploying only the wingspan (b) and its height above the ground (h), GE is assessed byassuming that the wing behaves like a straight hinged spar and that the flapping cycleis symmetrical around the longitudinal axis of the body, allowing an averaging of theinterference coefficient cr over the whole cycle.68Figure 18. Front view of a downstroke by a double-crested cormorant ifimed at60 Hz. The lines indicate wing positions at different frame numbers.1234669u is assessed at 0.7b at each measured and calculated best fit point of the downstrokeportion of the wing flapping cycle. These series of us are then averaged and a mean u, a isreported. The ãs for all the sequences are shown in Table XIII. Table XIII also shows thatalthough in most cases the difference between the ö for the raw and best fit data is small,this is not always the case. In Po 1 , Rn 5 , and Rn 6 , the best fit curve underestimatesa for the raw data, whilst in the case of Hr 1 there is an overestimate.GE was calculated for every sequence in its raw data and best fit forms. Figures 19and 35 to 49 (appendix A) illustrate the sequences with their respective c-s and a.Figures 20 and 50 to 53 (appendix A) summarise the findings of the interference coefficient u and for each species. Figure 20 is for the double-crested cormorant sequences,Figure 50 for the brown pelican, Figure 51 and 52 for the black skimmer, and Figure 53for the barn swallow.To calculate the power curve IGE u is incorporated into the calculation of P2nd:—K2.(1 —u).V’ (31)Figure 21 shows the power carves IGE and OGE and their respective Find curves.The change in induced drag calculated by Reid 1932 can also be expressed as:= c-L2 (32)then the apparent b (bapp) IGE is:bapp=(33)Changes to bapp should be reflected in changes in wing area and consequently in V11 i.e.2W= t.F_, (34)‘—‘Lmaz70Table XIII. Mean u values for theraw data and best-fit equations ofwing movements on ground effect.Data set Raw data Best-fitPa 1 0.38 0.38Pa 2 0.29 0.29Pa 3 0.29 0.29Po 1 0.20 0.16Po 2 0.29 0.38Po 3 0.33 0.29Rn 1 0.45 0.45Rn 2 0.38 0.38Rn 3 0.17 0.17Rn 5 0.38 0.15Rn 6 0.45 0.16Rn 7 0.38 0.45Rn 8 0.45 0.57Rn 9 0.38 0.38Hr 1 0.57 0.76Hr 2 0.76 0.7671Figure 19. Raw data and best fit, and incurred GE for Pa 1 . Panels a (rawdata) and d (best fit) represent wing movement through time and space seen fromthe root towards the wingtip. Time goes from left to right along the X axis, theposition of the different wing segments go ‘into the page” along the Z axis frombody (front) to wingtip (back), height of the wing increases from bottom to top ofthe page along the Y axis. Panels b (raw data) and e (best fit) represent the usexperienced. The X axis is time of flight in s, u is on the Y axis. Panels c (rawdata) and f(best fit) present the range of u’s encountered (solid line segment).The dashed line represents possible us and + for the sequence. The X axisrepresents the h/b ratios, and the Y axis plots u.00Lq0) CI00c’J000.0a d0.1 0.2 0.3 0.4 0.5Time s00.1;0C0.6\\\000.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6hJbC000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b72Figure 20. Srimmary of range and mean us for the double-crested cormorants.The X axis represents the h/b ratio and the Y axis 0. The range of u’s encountered is the solid line segment. The dashed line represents possible us and + afor the sequence. The X axis represents the h/b ratios, and the Y axis plots u.0Pal Palgt0(‘Sc00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6\\\\CDc:;\ .\(‘S C..Ja —. - .—--- —0 0000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6a)00a0.\\\\\\0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b h/bPa8 Pa8gt\CD\C) \00a0oo0\Cr10)00.0 0.2 0.40.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/bPa99 Pa99gt\\\\0.6 0.8 1.0 1.2 1.4 1.6h/b0.1;0h/b h/b73where S is the wing area, arLd CLmz is the maximum lift coefficient, assumed to have avalue of 1.5 (Pennycuick 1975).S is the wing area in2, related to the wing span of the dissected double-crestedcormorants by the regression equation:S = 0.6412b — 0.006714 (35)(r2 = 0.931 and F(l,4) = 26.3600 and p = 0.0068). Based on both apparent wing span (bapp)and its calculated S, Vsaii can be recalculated. The power curves IGE are calculated withthe bapp corresponding to the calculated a.Figure 21 shows the power curves IGE and OGE and their respective Pds, usingan interference coefficient o = 0.29. Observe that ICE Vgtaii=Vmp. Table XIV shows thecharacteristic speeds of the double-crested cormorant ICE and OGE.ConclusionsAnalysis of the metabolic and aerodynamic components of the power curve show thattotal power consumption will vary by 5% during the cormorants breeding season. AlsoGE reduces power consumption by reducing D2 and increasing bapp, the apparent wingspan, consequently decreasing tal1, Vmp, and Vmr. The effect of the energy savingsreflect on the foraging strategies of the cormorants as shown in chapter 5.74Figure 21. and Find curves for the double-crested cormorant. The dashedlines represent power consumption ICE; solid lines represent power consumptionOGE.0 5 10 15C)Ptot,OGEC////////////IIPtot,./FI/Pind,IGEN.S.N.S- _7 -- -- -1------------ I20V(m/s)75Table XIV. Characteristic speeds of double-crested cormorant-based on anatomical characteristics of dissected birds.Speed Monthms1Apr May Jun Jul Aug Septout of Ground effectVmp 11.1 11.1 11.1 11.1 11.1 11.1Vmr 15.4 15.4 15.4 15.4 15.4 15.4in Ground effectV,, 9.7 9.7 9.7 9.7 9.7 9.7Vmr 14.0 14.0 14.0 14.0 14.0 14.076Chapter 5.Ground effect in flapping flight.IntroductionEnergy savings during ICE flight produce a downward displacement of the powercurve and a change in its shape (Fig. 21). All the birds studied here: double-crestedcormorant (Phalacrocorax auritu.s), brown pelican (Pelecarus occidenialis), barn swallow(Hirundo rzLstica), and black skimmer (Rynchops niger) utilise GE but under differentcircumstances and for different reasons. This chapter considers GE in the daily energybalance (DEB) of the double-crested cormorant in detail, summarizes the aerodynamicsof GE for the four species, and concludes with a general discussion of the use of GE inflapping flight. Table XIII, chapter 3 (Preliminary Statistical Analysis) and Appendix Aindicates that the range of coefficients is different for different species. The value of aand W, Q, b, and Ap determine the shape of the power curve and the energy saved by thebird. These savings have direct consequences on the daily energy balance (DEB) of thebirds, as shown here.Cheverton et al. (1985) state that “in order to construct an optimality model ofbehaviour, one has to identify constraints, and to identify constraints one has to knowsomething about the mechanisms controlling behaviour. Thus optimality modelling impliesa knowledge of mechanisms” . Most studies concerning optimal foraging theory and dailyenergy balances (DEBs) of birds and other flying animals have assumed that the energeticcost of flying can be treated as a constant (e.g. Bryant and Westerterp 1980, Stalmasterand Gessaman 1984, Westerterp and Bryant 1984, Cheverton e a?. 1985, and Leopold eia?. 1985). This assumption may not hold true in nature and its bases can be evaluatedunder field conditions. The energetic cost of flight can be calculated (e.g. Pennycuick 1975,1989a, Rayner 1979b), if the actual flight speed can be measured accurately with either77an ornithodolite (Pennycuick, 1982a) or a Doppler radar unit (Schnell 1965, 1974; Schnelland Hellack 1978, 1979; Kolotylo 1989; Blake et al. 1990). DEB (Blake 1985) is the ratioof the energy available to an animal from foraging to its energy expenses. Some workershave measured flight speeds and calculated the associated costs when calculating the DEB.Withers (1977) constructed DEBs for the cliff swallow for the nest building, nesting, andnestling rearing periods using time budgets for the different activities, estimating flightspeeds with a stopwatch and using aerodynamic theory to calculate the flight expenditures.Withers and Timko (1977) estimated the foraging efficiency and the DEB of the blackskimmer with a kinematic and aerodynamic analysis of its flight ICE. Flight speed wascalculated by measuring frame to frame displacements in the ciné record. Blake (1985)developed a model for the energetics of foraging in the black skimmer by consideringthe energy costs of flight and other activities during the reproductive season, taking intoaccount the effect of GE in the DEE He predicted flight speeds IGE and OGE at whichthe black skimmer should be observed flying in order to obtain a positive DEB.The studies of Withers (1977) and Withers and Timko (1977) on the black skimmerincorporate the flight speed and its associated cost. Their method lacks flexibility whencalculating the DEB, since they deal with only the average speed. Blake (1985) predictedthe flying speeds of black skimmers ICE but had no field records to test his predictions.A more comprehensive approach would be to incorporate the range of speeds at which thebirds were observed flying (e.g. Kolotylo 1989, Blake e l. 1990).Even when flight speeds and their associated costs are known, the construction of aDEB or the proposal of an optimal foraging strategy requires careful consideration of thebiomechanical constraints. Flight is a metabolically expensive activity, varying with thespeed, load, and wind conditions. I overcame these limitations by constructing DEBs thatuse the range of observed flight speeds and associated energy costs for the double-crestedcormorants at Mandarte Island. This approach predicts flight and feeding behavioursunder which the birds can maintain their DEB.78GE reduces induced drag (D1), and increases the lift (L) on a wing flying close tothe ground (see chapter 4). As a consequence GE decreases both minimum power (Vmp)and maximum range (Vmr) speeds and reduces the overall cost of flight. These reductionsboth in the cost of flight and on the characteristic speeds (Vmp and Vmr) can translate intotwo major foraging strategies. ICE the double-crested cormorants can fly slower than theoptimal predicted speeds OGE at a greatly reduced cost, or they can flyat a given highspeed IGE for the same cost than flying at a lower speed OGE. Also, due to the increasein L generated by GE, the birds could carry a larger load of food backto the nest relativeto OGE at the same speed.Here a DEB for the double-crested cormorant is constructed, where thecosts and thetime spent flying are major components. Other costs such as maintenance, reproduction,incubation, and chick rearing, and the sources of energy are taken fromprevious studieson these birds (Bartholomew 1942a,slb; van Tets 1959; Robertson 1971; Dunn 1973, 1975,1976; Henneman 1983), or of birds in general (King 1973).The present knowledge of needs and habits of double-crested cormorantsat MandarteIsland leaves, for the purpose of this thesis, two areas in the DEB and foraging strategyof the double-crested cormorant unexplored. The cost of flight and the cost of foraging(diving). Double-crested cormorants during the reproductive season fly between the nestand the foraging site. Flights from the nest to the foraging site are done on an emptystomach, whilst flights back to the nest are done with a loaded one. The changes in weightof the bird whilst flying from and to the nest could be reflected in changes in flight strategythat could optimise the amount of energy or time spent flying. As it will be shown in thischapter, the double-crested cormorants at Mandarte Island seem to have a wide variety ofspeeds and load capabilities available, and could make use of themto meet their DEBs.Although the birds fly to and from the foraging site when feedingtheir young, theysearch for bottom fish or wait for schools of fish to pass and thendry their plumage.79This makes time spent flying to and from the nest an important variable in their foragingstrategy.The last important consideration for the DEB and foraging strategy of the doubleaested cormorants is the actual cost of foraging. These birds forage by diving (e.g.Bartholomew 1942a), but the actual costs and time spent on this activity are unknown.In the present study it will be assumed that the energy spent foraging is equal to that leftover after having taken into account all other known energetic expenditures. Assuming allother costs remain constant, the amount of energy left for foraging depends on the amountof energy spent flying.Here it is assumed that adult double-crested cormorants carry a load of 0.3 kg of fishper trip back to the nest, which is within the boundaries of loads reported and weight ofstomach contents found for cormorants (Robertson 1971, Dunn 1973). I will assume thatthe birds can vary the number of trips between Mandarte Island and Active Pass from 1 to8 per day. Under these assumptions a larger number of trips increases the total amount offood (energy) brought back to the nest and also increases the amount of time spent flying.Metabolic and Maintenance Costs.The metabolic and maintenance costs of the double-crested cormorant are presentedin Table XI, chapter 4 and used here.Reproductive Costs.Double-crested cormorants are a monogamous species in which both parents shareincubation and chick feeding duties (Lewis 1929). Birds that establish a nest incur thecosts of reproduction.80Cost of gonadal growth in male arid female double-crested cormorants.King (1973) considers the physiological cost of reproduction by the male to be negli..gible (0.04 % of BMR) and for this reason this cost is not considered here. The female,however, must &st develop gonads for the oncoming reproductive season. King (1973)establishes a cost of maximal growth rate of an ovary at .072W in quail and estimatesthat such cost will not exceed 10% of BMR. He further states that “it is questionable thatsexual activation is a significant caloric burden [for the female]” (King 1973 p.87).Cost of egg production in the female.Egg production is a more expensive activity that gonadal growth. Although “theassumptions regarding caloric content of an egg and the efficiency of synthesis combinedwith data on average egg weight and clutch size make it possible to estimatethe totalenergy requirements for production of an egg or a dutch of eggs, there is no simpleway toestimate the temporal cause of energy expenditure daring the laying of the clutch, or thepeak energy required when several ovarian follicles are growing concurrently “(King 1973).Nevertheless King (1973) assumes a peak daily expenditure for one egg asWpeak 2G/p (36)where C = Joule/egg, and p period of the cycle in days.The average mass of a double-crested cormorant egg is 0.0465 kg (Lewis 1929) (n=50,range 0.033.5-0.050 kg), whereas van Tets (1959) found an egg mass of the double-crestedcormorants at Mandarte Island with a mean of 0.040 kg (n=143). Assuming the caloricvalue of an egg to be 4.4kJ and assuming a conversion efficiency of 0.77(King 1973),the cost of production is 5.7lkJ.g1 for an egg. The cost of producing 4 eggs, a typical sizebrood for the double-crested cormorants in Mandarte Island (van Tets 1959, Robertson1971) varies between 0.81 and 0.83 W for a 0.040 and 0.046 kg egg, respectively.81Cost of incubation.No generalisations can be made of the energetic costs of incubating eggs due toboth the variation in methodologies and measurement techniques and to the changes incost induced by microclimate, dutch mass, nest construction and insulation, and adultphysiology and behaviour (Walsberg 1983). Grant (1984) describes a variety of techniquesused to measure energy spent during the incubation period and discusses the findings.While some seabirds like the macaroni and tockhopper penguins, the laysan albatross andthe benin petrel had incubation costs lower than resting levels, the wandering albatross hada higher cost. Also measurements within the thermoneutrai zone for american kestrel, barnowl, great tit, starling, and zebra finch showed no cost of incubation above resting level.Given these findings and the fact that double-crested cormorants feed regularly during theincubation period, we will assume that incubation adds no extra energy expenditure tothe incubating parent.Cost of thick rearing.The double-crested cormorant is an aitriciai bird. Chicks are fed by their parents frombirth to about 50 days of age (Robertson 1971). The growth of the chicks can be describedby fitting a logistic carve to the growth measurements of the chicks (Dunn 1975, Robertson1971), with a peak energy intake around 25 days of age (Dunn 1975). This peak in energyconsumption is reflected in the amount of food that the parent must bring back to eachchick. Dunn (1973) gives a peak figure of 550g . chick1 day’ for this age, which willprovide the chick with 29W. Given what is known about double-crested cormorant rearinghabits (Lewis 1929, van Tets 1959, Dunn 1973, Robertson 1971), it can be assumed that:both parents provide an equal share of the feeding effort, a common broods in MandarteIsland consists of 3 chicks (van Tets 1959, Robertson 1971 ), and the number of birds insuch brood that reach the fledging period is over 90% (Robertson 1971). With the aboveassumptions and requirements each parent must supply 1.1 kg of food per day or 5SWof82energy during the peak period, in addition to providing for its maintenance and foragingexpenses.Energy Input.The double-crested cormorants of Mandarte Island feed exclusively on fish. Robertson(1974) during a 3 year study at Mandarte Island on the brood rearing capabilities of double-crested cormorants and pelagic cormorants (Phalo.crocoraz pelagicus) gathered data on thetype and quantities of fish ingested by the growing chicks. He found that most of theprey species are characteristic of the littoral benthic zone, indicating that double-crestedcormorants are bottom dweller feeders along the southern coast of B.C., contrary totheconclusions of Ainley et a!. (1981) who characterise double-crested cormorants as feedingon schooling fish that occur from the surface to near, but not on, flat bottoms.TableXV, based on Robertson (1974), shows the most commonly found fish remnants in double-crested cormorant chick regurgit ations.Dunn (1975), using a bomb calorimeter, calculated the energetic value of the fish as4.75 x 106 Joziles . kg1 of fresh weight fish. By employing a bomb calorimeter to estimatethe energy content of the excreta she also established a digestive efficiency of 0.82or3.9 x 106 Jo’u.les kg’ of fish ingested. Dunn (1973) estimated that an adult double-crested cormorants eats between 20 and 30% of their weight per day. Consideringthat thedissected cormorants weighted 1.88kg, it will be assumed that the adult double-crestedcormorants consume at least 25% of their weight per day. These assumptiontranslates toa minimum of 0.470kg of fish per day, providing no less than 1.76 x 106J.83Table XV. Prey species fed to nestling double-crested cormorant, based on chick regurgitationdata from Robertson (1971).Species % %by number by weightpenpoint gunnel 23.8 35.7crescent gunnel 22.8 15.9pacific sandlance 20.5 4.6shiner seaperch 15.5 20.5snake prickleback 11.5 10.2others 5.9 13.1100 10084Field Observations.Observations were carried out during 28-31 August 1987 and 29-31 August 1988 atthe time of the second incubation attempt for the double-crested cormorants for each year.Only a small portion of birds actually raise 2 broods per year, but, other birds are nestingafter first failures. In the summer of 1987 either no chicks hatched from the second dutch orall of the chicks died during their first few days of life (pers. ohs. and W. Rochachka pers.comm.). The 1988 reproductive season was successful, as many double-crested corrnorantschicks were seen in late September 1988.All observation at Mandarte Island and surrounding area were done under sunnyconditions and winds 1 knot. For details of location of Mandarte Island see chapter 2,Materials and Methods. For a full description of Mandarte Island and its bird populationhistory see Drent ci aL, (1964).Flight RecordsBird flight speeds were measured with the Doppler radar gun with the methodsdescribed in chapter 2, Materials and Methods. Double-crested cormorants flying overthe surface of the water spent most of their time near the surface of the water and onoccasions at heights <5 in. Flights IGE and OGE were recorded as the double-crestedcormorants flew from Mandarte Island to the feeding grounds in the morning or as theyreturned to the nest at Mandarte Island in the evening.The flight records for each year were divided into two classes per year, IGE and OGE.Although the distribution of the speed records is a truncated normal, (see Tables XVI,XVII, XVIII, and XIX) the results were analysed by two-way AN OVA, as the samplesize was large (N=224). Two way ANOVA was used to determine if the recorded speedschanged from year to year and to determine any differences in the mean speeds ICE andOGE. The results of the analysis are shown in Table XX. The speeds were not significantly85different from year to year, but there was a statiticafly significant difference between speedsIGE and OGE(Fig. 22) The non-overlapping notches in the box-and-whisker plots show asignificant difference at c = 0.05 between the median speeds IGE and OGE.Power curves and Flight Records for the double-crested cormorants at MandarteIsland.Figure 22 shows that the flight speeds at which the double-crested cormorants wereflying near Mandarte Island both IGE and OGE occur over a wide range. OGE maximumrecorded speed is > 2.8 times higher than the minimum, and IGE the maximium is > 2.5times the minimum.Figure 23 shows the predicted power consumtion for loaded and unloaded flight ICEand OGE. Panels a and c show the power consumed by an unloaded double-crestedcormorant (i.e.one with an empty stomach). Panels b and d show the power consumed bya double-crested cormorant IGE and OGE, respectively. The box-and-whisker plots arethe same as those in Figure 22 for flights IGE and OGE and correspond to the power curvepresented in the panel. Note that the power curves are not very steep in their ascendingarms. The ICE curve was calculated utilizing b. This and the reduction of I), causea slowly increasing curve at the lower speeds. the observed speeds seem to correspondto the flatter part of the curve, and the median observed speed is slightly lower than thecalculated Vmp.Penalty curves for the double-crested corinorants at Mandarte Island.The total amount of energy spent flying is more relevant to the DEB if it can becompared to the power associated with Vmp and Vmr. To make this comparison a flightspeed and its corresponding aerodynamical power are divided by one of the characteristicspeeds, either Vmp or Vmr, and its associated aerodynamical power. The result is a “penaltycurve” for each characteristic speed. Penalty curves are unit free and index the speeds and86Table XVI. Stem-and-leaf table of the distribution of flight speeds, in ms1, OGEat Mandarte Lsland for the double-crestedcormorant in August 1987. The numberson the leftmost column represent the speedclass. The numbers, on the right representthe number of readings for each speed classand the appropriate decimal.N = 111 Median = 10 Quartiles = 8, 12Decimal point is at the space6 00007 0000000000000000008 0000000000000009 00000010 00000000000000000000011 000000000000000012 00000000000000000013 00000014 0001516 00087Table XVII. Distribution of flight speeds,in ms1, IGE at Mandarte Island for thedouble-crested cormorant in August 1987.For explanation see table XVI.N = 64 Median = 11 Quartiles 10, 12Decimal point is at the space7 00008 00009 000000010 0000000000000011 00000000012 00000000000013 0000000014 000088Table XVIII. Distribution of flight speeds, ms1,OGE at Mandarte Island for the double-crestedcormorant in August 1988. For explanation seetable XVI.N = 34 Median 9.75 Quartiles 7.9, 10.7Decimal point is at the space6 97 222245798 0129 0133789910 012267II 2712 1413 2514 1289Table XIX. Distribution of flight speeds, inm•s1, imder the IGE at Mandarte Islandfor the double-crested cormorant in August1988. For explanation see table XVI.N = 16 Median 11.75 Quartiles = 9.7, 14Decimal point is at the space7 28 49 17710 4711 412 113 03714 3415 216 090Table XX. Two-way AN OVA for the Eight speeds of double-crested cormorants recorded at Mandarte Island during the summers of 1987 and 1988.Source: grand meanYear n Mean sd se4 10.60 0.930 0.465Source: YearYear n Mean sd se87 2 10.44 0.612 0.43388 2 10.76 1.457 1.031Factor: Flight type Year SpeedLevels: 2 2 4Type: Random Within DataSource SS cu MS F pmean 449.3972 1 449.3972 209.816 0.044 *F/ 2.1419 1 2.1419Year 0.0992 1 0.0992 0.278 0.691YF/ 0.3570 1 0.357091Figure 22. Box-and-whisker plots of IGE and OGE speeds of the double-crestedcormorants at Mandarte Island. The top and bottom horizontal lines represent theupper and lower ranges, respectively, of the recorded flight speeds. The bottom ofthe box represents the lower (25%) quartile, the dotted line the median, and the topof the box the third quartile (75%). The notches give the 95% confidence intervalfor the median. Box width is proportional to the square root of sample size.GD_____________________CDCl)>CCDIGE OGE192Figure 23. Cost of flight and speed range for the double-crested cormorant IGEand OGE with an empty (uld) stomach or a full load (id).Out of ground effect(unloadedC.)C.,—It)C’jC)oQ_ C%It)In ground effect (unloaded)It)It)c.’1It)6 8 10 14 18V rn/sIn ground effect (loaded)C)0C)06 8 10 14 18V rn/sOut of ground effect (loaded)If)C.)C.,c’JC)o ‘- c%JIf)dIt)c\JC’:6 8 10 14 18 6 8 10 1418V rn/s V rn’s93their corresponding aerodynamic powers to the selected characteristic speed. Figure 24 isa group of penalty curves for the double-crested cormorants at Mandarte Island for flightswith and without loads to the nest.From the penalty curves an understanding of the range of the observed speeds canbe at least partiafly developed. None of the observed speeds seem to be 1.3 times moreexpensive than flight at V,, or 1.2 times more expensive than Vmr. It seems thereforethat the double-crested cormorants have a wide range of speeds at which they are able tofly without having to incur in a large energy expenditure when compared to the powerassociated with the characteristic aerodynamic speeds Vmp and Vmr, flight IGE can be20% cheaper at the lower speed range and at the observed median speeds.Cost of TransportCost of Transport (CT) was defined by Tucker (1970) as the ratio of metabolic rateto the product of speed and body weight, and is expressed as:CT= (37)where P0 is the total power spent flying at any given speed, V is the velocity, in ms1and W is the body weight. It is a dimensionless index that allows direct comparison ofthe expenditures associated with carrying a unit weight a unit distance at a given speed.In the case of the double-crested cormora.nts at Mandarte Island it allows the comparisonof travelling with or without a load IGE and OGE. Figure 25 shows the CT curves for thedouble-crested cormorants.CT is always a minimum at Vmr. Figure 25 shows that changes in CT are higherwhen the animal is loaded, similar for most speeds ICE, at a minimum for unloaded flightsICE, and are relatively high at the lower speeds. The decrease of Cost of Transport ICEis associated with the reduction in D and the increase in bapp. If the birds flight strategyis to minimise Cost of Transport thesy should be observed flying near Vmr.94Figure 24. Penalty curves for the double-crested cormorant IGE and OGE. Ina penalty curve the point with the coordinates (1,1) represents the characteristicaerodynamical speed (Vmp or Vmr) and its associated power. Any point along theX axis, the speed index, will indicate how much lower or higher the speed is relativeto the characteristic speed. On the Y axis, the power index, a Y < 1 correspondsto an energy expenditure smaller than the energy associated with the characteristicspeed of the given penalty curve. The case of Y < 1 is, by definition, non existentfor the penalty curve associated with Vmp. When Y > 1 the power index givesan indication of how much higher the power is than the power associated with thecharacteristic speed. The solid lines represent costs with respect to Vmp the dashedlines represent costs with respect to Vmr. a and b are for empty stomachs, c and dfor full stomachs.0Cua)00CuIn ground effect no load-ø0.0 1.0 2.0V ratioIn ground effect loadedNo ground effect no load00.0 0.5 1.0 1.5 2.0V ratioNo ground effect loaded0-FCD0.0 0.5 1.0 1.5 2.0V ratio0Cu0Cu0LC)C’J‘4,toc’.i‘4,‘4,I0 1 2 3V ratio95Figure 25. Cost of Transport for the double-crested cormorant on an emptystomach and carrying a 0.3 kg load both ICE and OGE. X axis, velocity (m.s1),Y axis, Cost of TransportT6 8 10 12 14 16 18 20V rn/sloaded0c’J0096Daily Energy Balance.The peak energy demand period on a double-crested cormorant raising young occurswhen the chicks are 25 days old (see section Cost of chick rearing in this chapter for moredetails). Nestling double-crested cormorants can be growing at their maximal rate duringther July or September. A DEB for a chick rearing adult in July will be considered.Table XXI presents some of the measured speeds of the double-crested cormorants atMandarte Island, the approximate time, rounded to the closest 100 seconds,it takes thebirds to reach the commonly used and probably furthest feeding groundsat Active Pass21 km away, assuming constant speed and no wind, and the power it takes to fly at thatspeed both ICE and OCE on an empty and loaded stomach (0.3 kg). The calculationof the total daily energy expenditure by the birds takes into account the differences inmaintenance rates between day and night and also considers the length of thedaylighthours in each month. To calculate the actual energy spent by the birds ontheir dailyactivities the maintenance rates for day and night are estimated with Hennemann’s (1983)equations (13), night, respectively. For this calculations the day and night lengths of themonths during the reproductive season were acquired from the Canadian AtmosphericEnvironmental Service. Table XXII presents the day and night lengths in seconds onthe l5 day of each month of the reproductive season. This date was chosenarbitrarilyas representative of the night and day lengths of that month. These times along withthe temperature data presented in Table X of chapter 4 are used to computethe nightlymaintenance costs (29.8kJ), the total power consumed during flight and the maintenanceenergy consumed by the double-crested cormorants during the non-flyingperiods of theday. These periods are assumed to consist exclusively of the maintenance rate (Pmet).This estimate leaves out the energy spent foraging i.e. diving. There areno estimates ofthe energy consumed by the double-crested cormorants whilst foraging,and the energy97available for this activity can be obtained from the difference between the energy requiredby all other activities and the maximum recorded energy input.Figure 26 shows a series of DEBs for the double-crested cormorants at MandarteIsland during the month of July. For a bird to have an adequate supply of energy its totalexpenditures must be below the horizontal line at 1.0. Only the birds that make 3 ormore trips have enough energy to account for all expenses, including foraging. If energyrequirements were to double, or if calculations underestimated the actual cost by 100%,birds could fly only at a narrow speed range for 8 daily trips to Active Pass. Figure 27shows the total food (in kg of sh) required and the amount of food gathered with differentnumber of trips.Robertson (1971) established that at the height of the double-crested cormorant chicksgrowth season the parents travel between 3 and 4 times per day between the nest and thefeeding site. The minimum number of trips recorded might be determined by the stomachcapacity of the birds, or their available aerodynamicai power. Dunn (1973) estimates thestomach capacity to be 20 to 30% of the weight of the bird or 0.36 to 0.54 kg for thecormorants used in this study.The number of trips that an adult double-crested cormorant can take between thenest and the feeding site (Active Pass, 21 km away) can be limited by:i) The maximum amount of energy that can be gathered in a day. Assumed to be 0.3kg of fish per trip, based on load capacity (above, and Fig 27). The energy left afterflying to and from the nest should leave enough energy to carry out other activitiessuch as foraging and feeding the chicks.ii) A maximum time an adult double-crested cormorant can spend in all of its diurnalactivities determined by the hours of daylight. Time spent flying to the feeding siteand back to the nest is time not spent doing other activities.98CDj0en00eni1Q tntf2e-CDr,)c,CLH3‘CDt,øcc.iCD.ccccDcCDCDi--)L’3d CDCD 0LJI*-.L0 CDCD cl) CD -a CD CD Cl) CDTable XXII. Day and night durations for themiddle of the month for the reproductive period of the double-crested cormorants (Canadian Atmospheric Environmental Service).Month Day length Night length8 SApril 15 49320 37080May 15 54960 31440June 15 58880 27520July 15 56700 29700August 15 51720 34680September 15 45360 41040100Figure 26. DEBs for the double-crested cormorants at Mandarte Island duringJuly. The X axis shows fight speeds, the left vertical axis presents the ratio onenergy gathered (E) to energy spent (EotL) for a different number of foraging tripsto Active Pass. The dashed lines represent flights OGE and the solid lines flightsICE. A value of 1.0 indicates The vertical axis on the right assumesenergy expenditures are double of those calculated. The numbers above each pairof lines indicates the number of trips taken.61Lf)-42uJ34LC)8-oI I I I II6 8 10 12 14 16 18 20Vm/s101Figure 27. Energy requirements for the double-crested cormorants during themonth of July expressed in kg of fish. The X axis shows flight speeds, the Y axispresents the daily amount of fish required. The horizontal lines indicate the totalamount of food gathered during the number of trips shown in right margin assuming0.3 kg fish per trip. The number-lines indicate intake of fish requirements for totalnumber of trips per day, OGE (above) IGE (below). Any number-line above itscorresponding horizontal line indicates an energy deficit for the day.8a,c3)-o 0oc\J4021I I I I I I I6 8 10 12 14 16 18 20Vm/s102Figare 28 shows the proportion of daylight spent by the bird flying if it commuted atdifferent speeds and for different number of trips. TI the birds were to fy 8 times a dayto Active Pass it would consume 0.5 to 0.98 of the total daylight hours. Considering thatfeeding of the chicks is shared by both parents, less than 0.5 of the daylight should bespent by each parent travelling to and from the foraging tes.The longer a double-crested cormorant spends at a rich feeding place, the greater thechance of it encountering food, thus, again, minimising the time spent flying to and fromthe foraging site to the nest increases the time the double-crested cormorant can spendforaging. It seems likely then, that time spent flying is one of the limiting factors for thedouble-crested cormorants at Mandarte Island at the peak period of the chicks’ growth.103Figure 28. Proportion of daylight spent travelling between Mandarte Island andActive Pass. The X axis indicates flight speed, the Y axis the proportion of daylightspent flying. The lines indicate proportion of time spent flying for the shown numberof trips.10:!o0)>Cl)V0otc000CqC6 8 10 12 14 16 18Vm/s20104Foraging radiusThe availability of food for the young might restrict the choice of nest sites. Double-crested cormorants from Mandarte Island have been observed to fly as far as Active Pass(21 kin) to obtain food for their young. In order to reach the site there should be enoughenergy left over from the previous day to reach this site. Following Pennycuick (1979),foraging radius (FR) is:FR=iv (38)D(Pmet + PflOC + Pcjjcç) + 2kVwhere j is the energy available (J), V flight speed D total time not spent flying (s),Pmet, and the energy spent in maintenance day and night, respectively (W), Ph1kmaintenance energy of the chicks (W), and the cost of moving a unit distance (J/m).The FR shown in Figure 29 were calculated for the range of observed speeds assuming thebirds fly 1-8 foraging trips the previous day.It was shown that I or 2 feeding trips per parent per day are not adequate to supplythe total energy needed (Fig. 27). This restriction could be overcome if the amount of foodper trip brought back to the nest was increased. Field observations of the double-crestedcormorants at Mandarte Island Robertson (1971) indicate that the daily number of tripsper parent is 3 or 4, which corroborates my prediction. It has also been shown that theupper number of trips per day is constrained by the amount of time left for other activitiessuch as feeding the chicks, diving, thermoregulation after dives, etc.From the model employed here flight and foraging behaviours for other times of theyear can be predicted. Outside the nesting season the energy demands of feeding chicksdisappear. Under those circumstances the higher demands could be those of thermoregulation during the winter, for example. TI the costs of these and other activities were known105Foragingradiuskmtiti50100150II.a)-t’b3C.X..3.cna,-aP1.3(.3W0)03,,-P13(.3W1.a,0)-F’I(.3W(1)CD.-aI’,C,3W‘40)03(bqo—(.X.300K3I0)0)..a3(,X.).(00)—)3(.X.)00)rje-ap13(3W0)0)..aP03C.3W4..b.0)0)Cl)4N))(X.3b003-aP43C.X300‘-C()00e4-o0rso.,(00_afl3(3V0-400)P43003N)C.t.3‘.b0)03Q—P4)(.Z.3a,a,Ci,P43(.1.)COWI-a-ro,(.1.,0)(000N))(.3.30303N),3’4’003Pa,(.U0)0(4)(A.)030Cti0=Pa)(.Ct>—°‘08(4)(4.)00-.(0)(.4.30)CD‘‘-1-.(03(4)(00P0.)(4)00)‘-C(0)(4.)0303‘-l-&(A.)coo,0)-.-.PP0)03,-.(0)(43VP03(6)coo-P0)-I0)0C--g(03440303(0)4400-(V(0)44cocCi‘-C•044.0(0-o.-(0394003(0)0)0)Ca)03CC)Ct>(f)coo,(0)90.CXC)oCi)(e.g. Henneman 1983), the total energy that must be gathered could be predicted. Underless restrictive drcumsta.nces the number of trips, speeds, and time spent flying mightnot be restrictive. Under these circumstances the double-crested cormorants should beobserved flying at aerodynamically optimal speeds (Vmp and Vmr).ConclusionsIt can be concluded that 1 or 2 trips per day to Active Pass yield to little energyfor the cormorants to meet the DEB. On the other hand 8 trips per day use most of theavailable daylight time. By constructing DEBs of the double-crested cormorants duringthe breeding season that include food intake and known energy expenditures I demonstratethat the cormorants incur substantial time and energy savings whilst traveling ICE to andfrom the nest, thus showing the importance of GE to their DEB.107Chapter 6.General DiscussionIntroductionAerodynamic energy savings obtained IGE will impact on the DEB of a bird inproportion to flight time IGE. The birds chosen for this study use GE under a varietyof circumstances as shown if Table I, chapter 1. This chapter will summarize the methodson this work used to study GE in flapping flight for the double-crested cormorant, lookat the aerodynamic energy savings in GE and relate them to the flight ecology of the fourbirds species chosen for this study.I have shown that detailed analysis of flapping flight IGE can predict fight strategies that a double-crested cormorant should follow during the breeding season if it is tomaximise time spent foraging and at the nest, and reduce the overall cost of flight. Theanalysis consisted of three parts: description of wing movements, construction of powercurves IGE and OGE, and the role of GE in the DEB.To obtain an accurate description of the vertical wing movement during flappingfight IGE I employed three methods, circular linear regression, periodic ANOVA, andFourier transforms. The first two methods proved to be statistically significant and easy tomanipulate. Fourier transforms, although accurate, provided more detailed than neccesaryfor the purposes of my analysis. The work on power consumption during flight took intoaccount aerodynamic and metabolic costs, assessed the reduction that GE produces onand the apparent increase in wing span (b) with its consequent reduction in V811.108Aerodynamics of GEFigures 30 to 33 show the power curves, characteristic speeds,power ratios, andpenalty curves for each species based on the calculated ãs of Table XIII, chapter 3. Areduction in Vmp and Vmr and their corresponding power consumptions can be seen inFigures 30 to 33 and Table XXIII. All Figures show that the overall savings decrease‘with increasing speed. Nonetheless even at the highest calculated speeds there are energysavings for the double-crested cormorant (Fig. 30) and brown pelican (Fig. 31).The ratio in power consumed IGE and OGE (panel b in Figs. 30 to 33) is a functionof a and the shape of the power curve. The U-shaped power curves of the double-crestedcormorant (Fig. 30 a) and brown pelican (Fig. 31 a) give rise to sigmoid power ratios (binboth Figs.) which reflect power savings IGE at all speeds. The J-shaped power curves ofthe barn swallow (Fig. 32 a) and black skimmer (Fig. 33 a) give rise to rapidly acceleratingcurves that reflect large savings ICE only at the lower flight speeds. The penalty curves (cin Figs. 30 to 33) show that for both the double-crested cormorant and the brown pelicanIGE flight at most speeds is cheaper than flight at both V and VmrOGE. For the barnswallow and black skimmer it is cheaper to fly ICE for speeds of upto 8 ms1 than flyingat either Vmp or Vmr OGE i.e. the lower range of flight speeds reported by Withers andTimko (1977) and Blake ci a!. (1990).109Figure 30. Power and penalty curves 1GB and 0GB, and characteristic speedsfor the double-crested cormorant (mass=1.8 kg). X axis, speed ( m.s’). Panel ashows the power curves 1GB and 0GB top and bottom, respectively. Power curvesboth 1GB and 0GB were calculated assuming no changes in b with chages in . A= Vmp, X 1mr both IGE and 0GB. Panel b is the power ratio for equal speeds1GB and OGE. Symbols as in a, Vmp and Vmr 0GB. Panel c presents penalty curvesfor power consumption IGE with respect to Vmp (solid line), and Vmr (dashed line)0GB. A power ratio < 1 indicates that travel IGE at that speed is cheaper thantravel at the corresponding characteristic speed.00a)00qc%J6 8 12 16 20Vm/sCr) a bcoo6 8 12 16 20Vm/s5 10 15 20V (mis)C/‘4,cD110Figure 31. Power, penalty curves ICE and OGE and characteristic speeds for thebrown pelican (mass=3.3 kg). See Figure 30 for explanation of curves.5 10 15V rn/s20 25LU0LU0aCDbcJoLC)5 10 15 20 25V(mis)LC)5 10 15 20 25VmisC0LiC,,111a ba)0Figure 32. Power, penalty curves [GE and OGE and characteristic speeds for thebarn swallow (mass=0.03 kg). See Figure 30 for explanation of curves._____________Q_________0LUi0 0G) 0LU0_c —c.J0q002468 12 16V rn/sec V rn/s(00CD0It.02 4 6 8 10 14CU)4-.LCI)ccj0246810 14Vrn/s112‘ 68810V(m/s)1214 ‘ 68 810Vm/s12140I68 810Vm/s1214aFigure 33. Power, penalty curves ICE and OGE and characteristic speeds for theblack skimmer (mass= 0.36 kg). See Figure 30 for explanation of curves.bCoCo0)LUQuJS28it)it)C’)C.jbx(Y)113Ecology of GE.GE results in energy savings to a bird flying near a surface, but there are currencies,besides aerodynamical expenses, that must be considered when assessing the importanceof GE in the flight and DEB of a bird. The most important characteristic of flights IGEmight be how much less expensive they are when compared to the power required to flyat equal speeds OGE and how they affect other currencies.GE requires that birds fly over large, smooth and relatively uninterrupted surfaces.This habitat is restricted to open water bodies and open land. The habitat and lifestyleof many birds excludes the use of GE. There can also be disadvantages to the reliance onGE such as time spent away from cover. TI far away visual reference points are used fororientation, GE is not a good flight strategy as these points disappear when flying close toa surface.The shape of the curv both ICE and OGE and the corresponding savings for eachbird can be used to gain some insight into the foraging and feeding behaviours with respectto CE. The barn swallow is not an obligate GE flyer, although it does sometimes come nearthe ground to feed (Kolotylo 1989, Blake e al. 1990, pers. ohs.). The utilisation of GE bythe barn swallow at the speeds at which it has been observed foraging has no major impactin its energetic expenses (Fig. 34), and GE might be a consequence of feeding near theground where a number of flying insects can be found and not necessarily an energy savingforaging behaviour. Barn swallows skim the water surface, and during this behaviour GEmight be utilised to reduce Vaiaii, allowing the birds to reduce flight speed.Black skinimers feed by submerging their lower mandible in the water whilst glidingwithout loss of altitude or flapping their wings (Blake 1983, 1985). GE presents an energysaving of 10—20% whilst foraging at the range of speeds reported by Withers and Tirako(1977). The decrease in V81 due to GE might help the capture of prey whilst skimming.114Figure 34. DEBs of the barn swallow using GE for different proportions of thetotal time spent flying. X axis, speed (m.s’), Y as, proportion of energygathered IGE. Box-and-whisker plot of speeds observed in the field.0LUc’JjLrT0CCQtoa?00 2 4 6 8 10 12 14 16Vm/s1151.5I I I I I IBoth barn swallows and black skimmers feed their young by carrying light loads (1% body weight) back to the nest. The size of these loads does not alter the birds’ totalmass so as to modify substantially their power curve and overall flight expenses. Themajor savings from GE are found at those speeds at which both birds have been observedforaging and not at a speed > Vmr at which they would be expected to fly to and fromthe nest maximising energy intake (RA Norberg 1981).Both double-crested cormorants and brown pelicans save energy whilst flying ICE atmost of the calculated and observed speeds. Both birds travel considerable distances toand from the nest and are known to carry large ( 20% body weight) loads (e.g. Robertson1971 for the double-crested cormorant). Energy savings for the double-crested cormorantare in the order of 10—20%, and these savings accumuiate through the time spent travellingfavouring a small number of trips at high speeds between the nest and the foraging site. Asimilar argument can be made for the brown pelican which is expected to travel to and fromthe nest in a similar fashion. In the cases of the double-crested cormorant and the brownpelican the shape of the power curves and their overall flight expenses are substantiallyaffected by the load carried back to the nest. It has been shown in chapter 5 that thedouble-crested cormorant incurs substantial time and energy savings by travelling at highspeeds (> 15 m.s’) whilst travelling ICE to and from the nest.Table XXIII shows the changes in Vmp and Vmr and their respective powers for thefour species. Reductions iii Vmp are larger than reductions in Vmr since the influence of GEis inversely proportional to flight speed. The size of the changes is larger for the smallerspecies (barn swallow and black skimmer) than for the larger species.In more general terms it can be suggested that morphological and behavioural traitsthat determine the shape of the power curve will determine the extent of energy savingsIGE at a given speed. It has been shown for the birds in this study that those with highA. and low Q (barn swallow and black skimmer) carrying light loads GE saves energy only116at the lower range of flight speeds. Neither barn swallow nor black skimmer travel to andfrom the nest IGE. On the other band birds with lower and higher Q like double-crestedcormorants and brown pelicans utilise GE over a larger range of speeds and travel ICE toand from the nest in order to maxiinise overall energy savings.There are occasional GE flyers, i.e. birds that don’t use GE as a main component oftheir behaviour to reduce their DEB. These birds might use GE during their flight e.g.barn swallows and gulls.GE reduces energy constraints during takeoff, when induced power requirements axehigh. None of the studies that I found address GE during takeoff (Pennycuick 1969,Simpson 1983, Heppner and Anderson 1985, Marden 1987). GE during takeoff will reducein birds as a function of the h/b ratio; the closer a bird is to the ground the less energydemanding takeoff will be.ConclusionsThis is the first study that details vertical wing movement and power consumption inorder to assess the importance of GE in the DEB of the double-crested cormorant. It alsoconsiders the use of GE by brown pelicans, barn swallows, and black skimmers. Thesefour species were classified according to morphological characters that influence the powercurve (b, .,, and Q). This classification allowed me to divide the birds into those thatobtaind gniflcant energy savings from GE at all speeds even when carrying loads of20% of their weight (double-crested cormorant, brown pelican), and those that benefit fromGE only at the lower speeds and carry loads approz 1% body weight (barn swallow, blackskimmer). Double-crested cormorants and barn swallows present extremes of morphologyand feeding strategies. The cormorant has high Q, low A and carries large loads backto the nest. The swallow has low Q, high , and carries light loads. As I have shownthese birds use GE under different conditions. Pigeon guillemots at Mandarte Island with117Table XXIII. Vmp and Vmr (m.s’) IGE and OGE, their corresponding powers (W), and% changes from OGE to IGE for the double-crested cormorant (A, mass= 1.8 kg), brownpelican (B, 3.30 kg), black skimmer (C, 0.36 kg), and barn swallow (D, 0.03 kg).Vmp % Pmp % Vmr % Pmr %OGE IGE OGE IGE OGE ICE OGE ICEA 11.1 9.7 14 16.3 12.5 30 15.1 14.0 8 18.7 14.8 26B 9.5 9.6 0.9 21.5 14.6 47 13.3 12.2 8 25.1 16.1 55C 5.1 4.3 17 1.3 1.0 30 7.6 6.9 10 1.5 1.2 28D 4.2 2.9 43 0.2 0.9 70 6.2 5.0 24 0.2 0.1 64118intermediate characteristics (high Q, low A, and small loads) and short flights betweenthe nest and the foraging site should fly IGE at speeds close to those predicted by RiNorberg’s 1982 model of maximum energy gain.This first attempt at the understanding the ecological significance of GE in flappingflight points at two areas that should be studied in more detail: 1. Accurate measurementsof flight speeds accompanied by detailed analysis of flight behaviours, 2. A detailedaerodynamical account of GE in a wing with periodic changes in both geometry and heightabove the surface.119Appendix AGraphs of GE calculations for raw and best fit data120Figure 45. Raw data, best-:fit regression, GE ixcurred, and GE range forPa 2For explanation see Figure 29.a0°0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/bdTime s Time s0\C \\\\\(V00LOE0\0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b121Figure 46. Raw data, best-fit regression, GE incurred, and GE range for Pa 3.For explanation see Figure 29.a000U)It,00o0.00000.0CD00C’.JCU) C.,0CDCCD0.8 oQ.Qd0.2 0.4 0.6Time s0.4Time sC0\\0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b122000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/bFigure 47. Raw data, best-fit regression, GE incurred, and GE range for Po 1For explanation see Figure 29.a d0u.00Ect,) 0U)cJ0000.0U,c•1’*<11\J\1.0 00.0 0.2 0.4 0.6 0.8 1.00.2 0.4 0.6 0.8Time s Time sC000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b00\ IF\\\\\\123Figure 48. Raw data, best-fit regression, GE incurred, and GE range for Po 2.For explanation see Figure 29.0000.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6biba d00124Figure 49. Raw data, best-fit regression, GE incurred, and GE range for Po 3.For explanation see Figure 29.d“V0.2 0.4 0.6 0.8 1.0 1.2 1.4hkaTime sC01.6125Figure 50. Raw data, best-fit regression, GE incurred, and GE range for Rn 1For explanation see Figure 29.a d00oF,-.0) 0000.5 00.0 0.1 0.2 0.3Time s0CCC’)Cc’J000 0.10•0•11.00.2 0.3 0.4Time sP0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4h/b1.61260.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6hlbFigure 51. Raw data, best-fit regression, GE incurred, and GE range for Rn 2For explanation see Figure 29.a d000EL E0oc’J 00—C\j°0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 00.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35Time s Time s0________________________P\c \0c..J000h/b1271p.1 oq CD 0 0 L 0 Isigma0.20.40.60.81.0sigma0.100.150.200.250.300.35— C)pjo 0 p 0)r0 -a-k to 0 p p C) 0 0)sigma0.20.40.60.81.0cipzic’3 CD Cl)o ) C p 0)-C I’) 0)sigma0.20.40.60.81.0sigma0.40.6zisigma0.20.40.60.81.00p 0 01 p 0 Czl301 0Wj\) 0 0 01C l,1 Ii: (D ‘1 CD 1.C 0 LrJ ‘-1 CD C) IF’sigma0.20.40.60.81.0sigma0.20.40.60.81.0C3sigmasigma0.20.40.60.81.00.00.10.20.30.40.50__________________00 p 0 0 0 •0)C -a oCt, C,) 0 C) ei C) CD C) ICDp 0 r%)30CoC)Cl,0 0 •0’00.2 0.4 0.6 0.8 1.0Time sdFigure 55. Raw data, best-fit regression, GE incurred, and GE range for Rn 7For explanation see Figure 29.a000.0.i.131d0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6hfFigure 56. Raw data, best-fit regression, GE incurred, and GE range for Rn 8For explanation see Figure 29.aTime s Time sC.i.\Ca00.0hlb132Figure 57. Raw data, best-fit regression, GE incurred, and GE range for Rn. 9.For explanation see Figure 29.c0Ii00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6hlbda0Time s Time sP0-,°0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6133Figure 58. Raw data, best-fit regression, GE incurred, and GE range for Hr 1.For explanation see Figure 29.daoa?00Eh) 0c00.2 0.3Time s Time s0.50\NC00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/bc..J0000.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b134CC)0EC)50CDc’00.0Figure 59. Raw data, best-fit regression, GE incurred, and GE range for Hr 2For explanation see Figure 29.o00Er—C) 0CD0ir:C0.1 0.2 0.3Time s0,4 0.50 0.-\0 0C) C)a ae.ja aC C°O.O 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0•h/b h/b0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6135sigma00.20.40.60.81.0e0a(ta ‘3 aa0oo “3oq CDC)______________9.01.0o00qoc03rs.)oa04.oaaCt,•03-u°3OroOo0tOcyco(0(0(Q-.--...+.000er“I--.1-.sigma0.20.40.60.81.0sigma0.20.40.60.81.0sigmasigma0.20.40.60.81.00.20.40.60.81.0sigma0.20.40.60.86sigma0.20.40.60.81.0sigma0.20.40.60.81.0o o •r\)/C/ /0 •0 1’.)sigma0.20.40.60.81.00 p 0D (*)a(0 _4.-A•0sigma0.20.40.60.81.0p10.’—.(t‘Ct Cl) (t:3p,—0(0‘r Isigma0.20.40.60.81.0•0C?3:3 (*3sigma0.20.40.60.81.00 p 0 0) 0 0 -A F’)33 D C;’ (0(0sigma0.20.40.60.81.0 II IFigure 62. Summary of range and mean us for the black skimmer sequences 6 to9. For explanation see Figure 30.Rn6 Rn6gtNI______________I______________000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b h/bRn7 Rn7gt00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b h/bRn8 Rn8gtii.I000 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b h/bRn9 Rn9gt.iI. .iI \\00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6h/b bib1380sigmasigma0.00.20.40.60.81.00.00.20.40.60.81.00______________0______________——.a/7/7CDo0/7Ico1//L—&I/\)IICD0)0)sigmasigma0.00.20.40.60.81.00.00.20.40.60.81.00________________________0_________________________oaI-io0/7I///crö,7_//Co-&/n/0‘37I\3/Il)a)pReferencesAlatalo RV, L Gustaisson and A Lundberg 1984 Why do young passerine birds haveshorter wings than older birds? 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