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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 OF GROUND EFFECT IN FLAPPING FLIGHT By Horacio Jesus de la Cueva Salcedo  B.Sc., The University of British Columbia, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept this thesis as conforming to the required standard  Signature(s) removed to protect privacy  THE UNIVERSITY OF BRITISH COLUMBIA May 1991  ©  Horacio de la Cueva, 1991  In  presenting  this  thesis  in  partial  fulfilment  of the  requirements for an  advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by  his  or  her  representatives.  It  is  understood  that  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Signature(s) removed to protect privacy  (Signature)  Department of  c’ >1  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  q,  ,  ?  Abstract. a surface that increases Ground effect (GE) is an interaction between a wing and and maximum range speeds lift and reduces induced drag, stalling, minimum power, g GE during flapping flight were (Vataii, Vmp,Vmr, respectively). Four bird species utilisin ) at Mandarte Island B.C., studied: Double-Crested Cormorants (Pholacrocoraz auritus , Black Skimmers (Rynchops Brown Pelicans (Pelecarius occideniali.s) at Ensenada Méico a) at Ladner, Williams niger) at San Diego California, and Barn Swallows (Hirundo rstic Hz in nature and digitised Lake, and English Buff, B.C. Films were taken at 60—64 swallows and cormorants were for vertical wing displacement analysis. Flight speeds of measured with a Doppler radar. periodic ANOVA Best-fit sinusoids of dicular-linear regression (Batschelet 1981), were used to describe (Bliss 1970), and Fourier series (Lighthill 1958, Bloomfield 1976) vertical wing displacement vertical wing movement. Linearised sinusoids were used to show evaluating GE for fixed wings and average height of wings above the surface. Methods of for flapping flight. Average were compared to determine simple, realistic calculations of GE, utilising the theory of interference coefficients were used to evaluate the influence (Katz 1985 ) and banking Reid (1932). Results were compared to those for oscillating wings (at an angle to the horizontal) (Binder 1977). evaluated in cormorants. The effect of GE on the daily energy balance (DEB) was uctive, and fight costs. Power DEBs were constructed considering GE, metabolic, reprod namic theory (Pennycuick curves were constructed using fixed-wing quasi-steady aerody effect (OGE), 6 m•s, in GE 1975). Thght speeds Vmp=10.9 ms out of ground OGE of 1 OGE, 15.4 ms IGE and flight costs IGE and (IGE), arid Vmr16.3 ms the 1987 and 1988 reproductive cormorants were compared to speeds measured during savings of up to 40% of total seasons. Cormorants observed at Mandarte Island obtain a fixed cargo per trip (0.3 kg) from power when flying in GE. If cormorants fly with Ii  trips per day is 3—4 as observed by the feeding site to the nest the predicted number of unit weight a unit distance) was Robertson (1971). Cost of Transport (cost of moving a load. Foraging radius (Pennycuick, compared for flights IGE and OGE, with and without a le energy. Foraging radii ICE and 1979) calculates maximum distance travelled on availab sources. Flight IGE is significantly OGE of double-crested cormorants limit potential food cheaper than OGE for the double-crested cormorant. . Swallows and skimmers Flight energy expenditures were compared for the four species s are obtained only at speeds <8 show savings of up to 50% when IGE, but most saving s going from 5% at speeds > 15 m•s’. Cormora.nts and pelicans showed energy saving . 1 m•s’to 20% at speeds <8 ms  111  Table Of Contents Abstract List of Tables  ii  .  List of Figures  ix  List of Symbols Acknowledgements  xv  Chapter 1. Introduction.  1  Introduction  1  Bird Flight  1  Passive Flight  3  Active flight  4  Flight Behaviours  9  Ecology and Flight  11  Perspective of the current study  12  Chapter 2. Materials and Methods  13  Study Areas  13  Materials, Methods, and Preliminary Analysis  13  Filming  13  .Digitisimg  15  Morp hornetrics  19  Speed Measurements  20  Observations  21 iv  24  Chapter 3. Preliminary Statistical Analysis of Wing Movement.  24  Introduction Description of analytical methods  •  .  Linea.risation  •  .  Results  •  26 31 .  32  Reliability of the statistical tests  • 32  Comparison of analytical methods  • 32  Statistical results and equations  • 33 • 40  Conclusions Chapter 4. The Power Curve and Ground Effect  •  49  .  Introduction  49  The Power Curve  50  Maintenance Costs  50  Aerodynamic Costs  55  The Power Curve of the double-crested cormorant  59  Ground Effect in Flapping Flight  65  Conclusions  74 77  Chapter 5. Flapping flight in ground effect Introduction  •  .  .  .  Metabolic arid Maintenance Costs  •  .  .  .  77 80 80  Reproductive Costs  V  Cost of gonadal growth  81  Cost of egg production  81  Cost of incubation  82  Cost of chick rearing  82  Energy Input  83  .  85  Field Observations Flight records  85  .  Power curves and flight records for the double-crested cOrmOTard  .  • 86  Penalty curves for the double-crested corrrtorant  • 86  Cost of 2’ransport  .94  Daily Energy Balance  • 97  Foraging radius  105  Conclusions  107 108  Chapter 6 General Discussion Introduction  .  .  108  .  Aerodynarriics of GE  109  Ecology of GE Conclusions  •  •  .  114  •  .  117  Appendix A  120  References  140  V  List of Tab’es I. Time IGE whilst flying for four bird species  2  II. Flight ifim sequences, species, and codes  16  III. Correlation between stopwatch and radar speeds  22  IVa. Circular-linear regression of best fit data from Po 3  30  lVb. Periodic ANOVA for Po 3  30  Va. Areas under Po 3 and its least-square fitted curves  35  Vb. Equations of two different algorithms for Po 3  35  Via. Summary of linearisation of circular-linear regression of Po 3  36  VIb. Summary of linearisation of periodic ANOVA of Po 3  36  VIc. Correlation between periodic AN OVA and circular-linear regression.  36  VII. Summary of best-fit circular-linear regression equations  37  VIII. Summary of best-fit periodic AN OVA equations  38  DC Summary of first two terms of Fast fourier transforms  39  X. Mean monthly temperatures at Victoria International Airport (1988).  52  XI. Maintenance rates of double-crested cormorantsin Joules  53  XIIa. Anatomical characteristics of dissected double- crested cormorants.  60  vi’  XIIb. Pectoralis and total muscle mass of dissected double-crested cormorants. XIII.  ‘  .  .  60  .  71  values for raw data and best-fit equations of wing movements on GE  XIV. Characteristic speeds of double-crested cormorants  76  XV. Prey species fed to nestling double-crested cormorants  84  XVI. Flight speeds (m.s’), OGE for double-crested cormorant (August 1987).  .  .  .  , ICE for double-crested cormorant (August 1987). (m.s ) XVII. Flight speeds 1  .  .  .  87 88  XVIII. Flight speeds (m.s), OCE for the double-crested cormorant (August 1988). 89 XIX. Flight speeds (m.s’), ICE for double-crested cormorant (August 1988).  .  .  .  90  XX. Two-way Anova of flight speeds for summer 1987 and 1988  91  XXI. Flight type, speed, time and power of double-crested cormorants.  99 100  XXII. Mldmonth day arid night lengths of the reproductive period XXIII. Characteristic speeds and powers ICE and OGE for four bird species.  viii  .  .  .  118  List of Figures Figure 1. Time span of film sequences selected for analysis  17  Figure 2. Correlations and differences between radar and stopwatch speeds  23  Figure 3. Best fit, residuals, linearizations, correlations, and components for Po 3. Figure 4.  2 x  34  .  41  probability levels at 2 degrees of freedom.  Figure 5. 2-tailed t significance levels of intercepts from circular linear regression.  .  .  Figure 6. 2-tailed i significance levels of slopes from circular linear regression.  .  .  .  42 43  2 of multiple regression from circular linear regression Figure 7. F,  44  2 of multiple regression from ANOVA curves Figure 8. F,  45  Figure 9. Two-tailed  i  46  significance levels of intercepts from ANOVA curves  Figure 10. Two-tailed i significance levels of slopes from ANOVA curves  47  Figure 11. F,., 2 of multiple regression of from ANOVA  48  Figure 12. Maintenance rates of double-crested cormorant during reproductive season. 54 0 used in this study. Figure 13. Ratio between Pennycuick’s pro=l and the P,.  .  .  .  61  Figure 14. Power curve for the double-crested cormorant at Mandarte Island Figure 15. Characteristic speeds of the double-crested cormorant power curve. Figure 16. Power ratios at different speeds through the reproductive season  x  57  .  .  .  63 64  67  Figure 17. Reid’s (1932) interference coefficient u and h/b Figure 18. Wing shape of a double-crested cormorant during the downstroke. Figure 19. Raw data and best-fit regression, GE incurred, and GE range for Pa 1 Figure 20. Summary of range and mean us for the double-crested cormorants.  •  •  .  .  •  .  Figure 21. F 0 and Find curves for the double-crested cormorant Figure 22. Box plots of IGE and OGE speeds of the double-crested cormorants. Figure 23. Fight cost and speed of double-crested cormorant ICE and OGE.  69 72 73 75  •  .  92 93  Figure 24. Penalty curves for the double-crested cormorant IGE and OGE. Figure 25. Cost of Transport for the double-crested cormorant Figure 26. DEBs for the double-crested cormorant  101  Figure 27. Required daily fish catch of the double-crested cormorant.  102  Figure 28. Proportion of daylength spent flying  104  Figure 29. Double-crested cormorant foraging radii  106  Figure 30. Power and penalty curves for double-crested cormorants.  110  Figure 31. Power and penalty curves for brown pelicans  110  Figure 32. Power and penalty curves for barn swallows  110  Figure 33. Power and penalty curves for black skimmers  110  x  Figure 34. DEBs of barn swallow using GE.  110  Figure 35. Raw data and best-fit regression, GE incurred, and GE range for Pa 2.  121  Figure 36. Raw data and best-fit regression, GE incurred, and GE range for Pa 3  .  122  Figure 37. Raw data and best-fit regression, GE incurred, and GE range for Po 1  .  Figure 38. Raw data and best-fit regression, GE incurred, and GE range for Po 2  .  Figure 39. Raw data and best-fit regression, GE incurred, and GE range for Po 3  .  123 124 125  Figure 40. Raw data and best-fit regression, GE incurred, and GE range for Rn 1  .  126  Figure 41. Raw data and best-fit regression, GE incurred, and GE range for Rn 2  .  Figure 42. Raw data and best-fit regression, GE incurred, and GE range for Rn 3  .  Figure 43. Raw data and best-fit regression, GE incurred, and GE range for Rn 5  .  127 128 129  Figure 44. Raw data and best-fit regression, GE incurred, and GE range for Rn 6.  130  Figure 45. Raw data and best-fit regression, GE incurred, and GE range for Rn 7  .  131  Figure 46. Raw data and best-fit regression, GE incurred, and GE range for Rn 8  .  132  Figure 47. Raw data and best-fit regression, GE incurred, and GE range for Rn 9.  133  Figure 48. Raw data and best-fit regression, GE incurred, and GE range for Hr 1  134  .  Figure 49. Raw data and best-fit regression, GE incurred, and GE range for Hr 2.  135  Figure 50. Summary of range and mean o-s for the brown pelicans  136  Figure 51. Summary of range and mean as for the black skimmer sequences 1 to 5.  137  Figure 52. Summary of range and mean as for the black skimmer sequences 6 to 9.  138  Figure 53. Summary of range and mean as for the barn swallows  139  List of abbreviations, symbols, and their units. (dimensionless symbols are followed by a blank)  Symbol 2 a A Ap b bapp  BMR c CDb CDpro CDpara  1 C CLmaz  CT DEB D DIT Dpa,’  e Eday  f FR g(t) G GE IGE OGE h h/b  j k 1 K 2 K  Definition Fourier coefficient amplitude of wingbeat frontal plate area aspect ratio (b/c) wingspan apparent wing span Fourier coefficient basal metabolic rate wing chord body drag coefficient proffle drag coefficient parasite drag coefficient lift coefficient maximum lift coefficient Cost of Transport daily energy balance portion of day not spent flying induced drag total D in a two wing system parasite drag aerofoil efficiency diurnal maintenance energy nocturnal maintenance energy total energy input energy output replicates per sampling interval foraging radius function of trigonometric polynomial energy content of egg ground effect in ground effect out of ground effect height of wing above surface height to wingspan ratio energy available number of sampled points parasite & profile powers constant induced power constant induced power constant IGE 11  Units m 2 m m m W m m  s N N N W  W J J km W  m  kg.m’ 3s kg.m 1 .s 3 kgm cont...  L m M n p Pam Pchick Find Pme Pmp Pmr Pnoc Ppar Fpara Ppro 0 F  Q r Re 1 R s S d 0 Sb Sd  T  V V Vga in Vmp Vmr 01 V , Vataii w W Wapp Y  lift mass inesor or mean wing height number of points in sequence period of egglaying cycle absolute minimum power chick growth and maintenance induced power metabolic power minum fight power maximum range power night maintenance power parasite power Fpar+ Fpro proffle power total power wing loading correlation value Reynold’s number W & Dpar resultant variance wing area maximum cross sectional area of body wing disk area wing angle during flapping acrophase = maximum angle of wing period sum of all sampled values cos(wi) sin(wt) forward figh speed induced velocity maximum energy gain speed minimum power speed maximum range speed optimal flight speed stalling speed angular velocity of wing weight apparent weight under GE height of wing above water  N kg m days W W W W W W W W W W W 2 N•m  N 2 in 2 in 2 in  rad rad s  1 m.s ms 1  m.s ms 1 1 m•s N N in  cont...  xli’  a  r , j 8 ic  p o  ö  4’ w  wing’s angle of incidence air circulation around wing metabolic to mechanical efficiency wing angle during flapping energy spent per distance flown air density GE interference coefficient average CE interference coefficient acrophase=maximum angle of wing angular frequency  xiv  rad  rad J/m 3 kg.m  rad rads’  Acknowledgments I would like to thank my supervisor RW Blake for his encouragement and helpful suggestions and discussions that made the completion of this project possible. The inem bers of the thesis committee: CL Gass, J Gosline, DJ Randall, and JNM Smith provided  many suggestions for improvement of the manuscript and refinement of ideas. M Ksha triya helped polish many of the ideas presented here. B Kolotylo helped with the field work. 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. This work is dedicated to Horacio de la Cueva M, Teresita, Tere, Gerardo, and la vdg, and the anarchists of the world.  xv  Chapter 1. Introduction. Introduction  This study describes the use of ground effect (GE) for birds in flapping flight. It focuses 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 skimmer is 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 using periodic equations (Lighthill 1958, Batschelet 1981, Bliss 1970, Bloomfield 1976). GE in ) 1 flapping flight is discussed in chapter 4, in the context of reductions in induced drag (D and increases in lift (L) on the total power consumption during flight. Chapter 5 discusses the role GE plays in the energy balance and reproductive strategies of the birds studied focusing on the double-crested cormorant. Finally, in Chapter 6 the use of GE by the birds (Table I) is compared and contrasted.  Bird Flight  The study of bird flight has involved the development of aerodynamic theories applied to both aircraft and birds and the measuring instruments necessary to test them. For example, high speed photography and cinematography (e.g.  Brown 1948, Pennycuick  1968b, Spedding e a!. 1984) has been used to describe wing movements. The accurate measurement 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,  1  Table I. Time IGE whilst flying for the four birds species. Species Double-crested cormorant Brown pelican Black skimmer Barn swallow  Time Use 1OO o and from nest to and from nest whilst foraging foraging occasionally foraging  2  1983) and has been used to test predictions of optimal flight speeds. Traditionally bird flight has been dassified into active and passive forms. Passive Flight. Passive ffight does not imply the absence of energy expenditure by birds. This type of flight (gliding and soaring) involves an energy expenditure of approximately 2 times the basal metabolic rate (Baudlinette and Schmidt-Nielsen 1974) to hold the wings in flight position.  9 Gliding and soaring flight patterns were understood in principle in the l  century (Rayleigh 1883). Walkden (1925) developed models of soaring to predict optimal flight patterns of albatrosses. Gliding. In gliding birds travel forward and loose altitude at a rate dependent on the forward speed (V), maximum lift coefficient (CLmar (CDpara), lift to drag ratio, and wing loading  (Q,  1.5), body or parasite drag  unit weight per unit area of wing, N  ) (Pennycuick 1975). The study of gliding based on fixed winged models has been 2 •m extensive (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 (Vulur gryphus), and common crane (Grus grus) (Kerlinger 1989). Tucker (1987) calculates the performance and polar areas of a loggar falcon (Falco jugger) and a black vulture from wind tunnel measurements, considering the variable geometry of the wing. Spedding (1987a) investigated the vortex wake of a bird whilst gliding and compared the performances measured 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 and a black vulture by following the bird with the plane. He concluded that the bird needed little power to stay aloft, because it had a large lift coefficient (1.57) and dosed the top 3  slots 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 to remain in flight. Slope aring Bird use updrafts of air deflected by a prominent geographic feature, such as sea cliffs, mountains, and buildings (e.g.  Peruiycuick and Webbe 1959,  Pennycuick 1960, Kerlinger 1989). Thermal waring The birds exploit thermals created by the differential warming of the air in contact with the surface of the ground. Ti a thermal is to be used by a bird to gain altitude, the lift component of the forces created by the thermal must 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 gain altitude from which to initiate a glide (e.g. Rayleigh 1883, Cone 1964, Wood 1973, Wilson 1975). Soaring and gliding are not discrete activities. A bird will change from soaring to gliding and vice versa, depending on the instantaneous environmental d.rcumstances, and on its purpose for flying. For this reason most of the literature on passive flight incorporates elements of soaring and gliding (e.g. Newman 1958, Pennycuick 1972). Active Flight In contrast to passive fight the energy expenditure required by powered flight has been estimated to be from 6 to 23 times the basal metabolic rate (Utter and LeFebvre 1970, 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 camera to obtain records of the slow flight of a pigeon (Columba. livia). Brown discussed wing movements in relation to the action of the muscles and made inferences about fast forward 4  fight. Brown (1953) furthered his study by analysing films of pigeons and gulls at different fight speeds and assessed aerodynamical properties of various wing configurations. Walker (1925, 1927) employed numerical analysis to show that rooks could generate enough force to fly horizontally or climb, provided that they generated lift during both up and down strokes by the inner portion of the wing. He also concluded that flapping flight compared favourably with the efficiency of a screw propeller. To date three aerodynamicai theories have been used for the study of fight mechan ics 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; Norberg  a Ellington 19 9 1976b,c) and quasi-steady vortex theory (e.g. Weis-Fogh 1973, Rayner 7 1983, Pennycuick 1988b). Nachtigafl and Dreher (1987) clearly differentiated between the momentum jet and vortex models: “momentum jet is often used for rapid and useful es ti.rnating calculations, as for example the performance of helicopters. This does not mean however, that the principles of the fluid dynamics of vertical sustaining force creation can be explained by this method.” In other words momentum jet is a predictive theory only whilst vortex theory is both explanatory and predictive. In momentum jet theory a bird engaged in active flight flaps its wings, sweeping out a 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 pressure on the dorsal and forward side of the disk. This results in the air attaining a downward 2 as it passes through the disk. The air is accelerated further since there induced velocity V is a region of increased pressure behind and below the disk which is a mirror image of the area of reduced pressure ahead and above the bird. After leaving the disk the air continues to accelerate downward until, far behind the bird, it reaches an eventual downward velocity 2V(Pennycuick 1975). Blade element theory divides the wing into small chordwise wing L of the total lift L. This method segments of area S that must generate a proportion 1 5  calculates the angular velocity of the wing w necessary to generate a lift force equal to half 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, combining high speed photography with neutrally buoyant helium bubbles. Rayner and co-workers trained different animals to fly through the bubbles, allowing them to test some of the assumptions and predictions of the theoretical models of bird flight. Their flow visualisation method is based on the approach of Kokshaysky (1979) who employed clouds of small light particles to construct a qualitative model of the general configuration of the wa)e. Rayiier and colleagues (Spedding 1982, Spedding ci ci. 1984, Rayner ci ci. 1986) concluded that the differentiation of flight gaits between slow and fast flight is given by the iole of the upstroke in the flapping cycle and the shape of the wing. In slow flight there is a small forward speed component while the wings are beating at a relatively fast rate (i.e. the average speed of the wing tips is much greater than that of the body) (Cone 1968). In this gait the upstroke generates no thrust or lift and the wingtips are expected to come close to the body to minimise friction drag and inertial forces. Here transverse vortices are shed at the top and bottom of the downstroke, and the upstroke is flexed and inactive (Rayner ci a.?. 1986). This form of flight generates a vortex ring waice. Fast flight implies a slower wing movement relative to the forward speed (Cone 1968). In this gait the vortex sheets shed from the wings’ trailing edges roll into a pair of discrete vortex lines. For long winged species, e.g. kestrel (Spedding 1987b) in fast flight the upstroke is considered active, as it generates lift and thrust. The study of the mechanics of flapping flight has also examined other aspects of fight such as coordination of breathing movements and the storage of elastic energy in  6  the wishbone. Goslow et al. (1990) linked the use of the pectoralis muscle, wing, and bones of the shoulder and thorax.  The movements of these bones seem to serve as a  secondary pumping system between the air sacs and the lungs that is capable of operating independently of inhalation and exhalation and that might serve the increased metabolic demands of flight. Dial el al. (1987, 1988) demonstrated the relationship between flight muscles and wing movements. Both studies also established that the wishbone of the starling acts as a spring (Jenkins ci  iii.  1988).  Studies of bird flight have also focused on wing morphology and the aflometric rela tionships of flying animals. Savile (1957) discussed wing shape and the evolution of bird flight classifying them into four shapes: elliptical wing adapted to operation in confined spaces; high-speed wing for birds feeding aereafly or involved in long migration flights; high aspect ratio wing for oceanic soarers; and slotted high-lift wing for terrestrial soarers and predators that must carry heavy loads. Further studies on the relation of wing morphology and the relation to the biology of the bird include those of UM Norberg (1979) who stud ied 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 Cerihia  familiaris). She correlated the morphology with locomotor patterns and feeding station selections, and concluded that the differences in feeding station selection require different structural adaptations of the locomotor apparatus. Chari ci al. (1982) compared the flight characteristics, moment of inertia and flight behaviour of two aerial insectivores (Dirusus a.dsimilis and Merops orientalis), concluding that the low wing-loading and low aspect ratio values give these birds high manceuvrabllity. Also, the similarities in certain flight parameters appear to be convergent adaptations for catching insects during flight. Alatalo ei 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, whereas adult wings are better for faster flight. Kerlinger (1989) makes the same suggestion for  7  young and adult hawks. Greenwalt (1962, 1975) compiled data on the dimensional re lationships of flying animals and linked them to aerodynamical properties in relation to bird body type (duck, shorebird, or passerine), providing allometric relationships between mass, wing size, fight muscle mass, and power requirements for fight. Warham (1977) assessed the flight capabilities of procelariiformes based on their wing loading and wing shapes. Amongst the 48 species studied, wing loading and aspect ratio increase with body weight. Pennycuick (1987), studying flight in seabirds, divided the requirements of pow ered 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 that neither migration nor feeding, except for the use of wings underwater, are major factors in flight adaptations. Flight adaptations in seabirds seem to be determined mainly by the requirements of foraging and access to nests. Power consumption during fight is dependent on speed, giving a characteristic curve predicts U-shaped curve (Pennycuick 1969, 1975; Tucker 1973, Rayner 1979ab). This optimal speeds at which birds ought to fly if they are to maximise the amount of time spent flying (minimum power speed Vmp), or the amount of distance covered (maximum range speed Vmr) on a given amount of fuel, or the maximum rate of energy brought back to the nest  (1’9(Lm)  (RA Norberg 1981, Pyke 1981). Flight speed measurements have used  stopwatches and theodolites or car speedometers (Cooke 1933, Allen 1939, Cottam et al. 1942, Brown and Goodwin 1943, Meinertzhagen 1955, Tucker and Schmidt-Koening 1971, 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).  Speed  measurements with ornithodolites or Doppler radar units provide large and precise samples that allow statistical tests of the fight speeds of birds.  8  Flight Behaviours Flight is an energetically expensive activity, and it is assumed that birds have evolved strategies that would minimise this expenditure. Active flight strategies that minimise energy expenditure when compared to constant flapping flight include: Intermittent ffight: Periods of wing flapping alternate with periods when the wings are 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 stored temporarily in the bird’s body in the form of potential or kinetic energy during the passive phase 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 by muscular efficiency, and the optimum power output for steady flight. This flight strategy is further divided into: Undulating flight: birds glide and then regain altitude with a few strokes, typical of good gliders that are bigger than woodpeckers. Undulating flight reduces energy expenditure at most flight speeds, permitting a bird to fly slowly but economically (Rayner 1985). The need for musculature to operate at or dose to conditions of optimum thermodynamic efficiency appears to be a factor controffing the proportion of total flight which is devoted to the powered phase in undulating flight and can be achieved only at minimum drag speed (Vmp) (Ward-Smith 1984ab). Bounding flight: the wings are folded during the unpowered phase. This type of intermittent flight is typical of the smaller birds. Bounding ffight saves energy only at higher speeds and does not reduce the mechanical cost of transport (Rayner 1985). This type of flight can be seen as a strategy for increasing flight speed without incurring the penalty of increased energy expenditure associated with increased flight speed under the conditions of steady horizontal flight (Ward-Smith 1984b). Rayner (1985) concluded that both bounding and undulating flight have evolved as compromise adaptations between the strenuous and confficting constraints imposed by the physiology and mechanics of flying birds. Bounding flight in birds has been 9  accompanied by reduction in body size and widening of adaptability to trophic conditions, while undulating ffight permits larger birds to accommodate the power economy of gliding with efficient flapping flight. Formation flight. Formation flight is a mechanism for reducing energy expenditure during long migration flights that is available to flocking birds.  In this type of flight  the induced drag of the flock is reduced. Lissaman and Shollenberger (1970) developed a model for formation flight. Assuming birds had fixed wings, and they concluded that the typical vee formation, with a determined spacing between the wings, would result in energy savings. Heppner (1974) classified the flight formations by their shape. Higdon and Corrsin (1978) examined the induced drag of the flock and Haimmel (1983) examined how dissimilarity 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 the ground effect (GE). GE is a reduction in induced drag (Di) accompanied by an increase in lift (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 1.5 wingspans of the surface. The advantages of GE to the energy budget of certain fish and birds have been shown for the mandarin fish, and the gliding and flapping flight of the black skimmer 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 that for the case of flapping flight the qualitative wake structure described is probably not significantly affected by GE, although, particularly towards the end of the downstroke, the induced velocities behind the wing trailing edge may be. Hainsworth (1988) showed that for brown pelicans flying in ground effect (IGE) the average height of the body above the  10  water was higher for flapping (0.52m) than gliding birds (0.33rn). He estimates the D savings for gliding flight averages 49% and for flapping birds, calculating the savings at the average height of the body, would give a saving of 36%. Ecology and Flight The cost of flight and other energetic demands imposed on birds whilst foraging during and outside the reproductive season can give rise to predictions such as which form of transportation they should use to gather food (Houston 1990), or at what speeds birds ought to fly if they are to exploit patches efficiently (RA Norberg 1977), or bring the most energy back to the nest (RA Norberg 1981) An important question being asked by 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 and carrying their food (RA Norberg 1977). Energetic cost of foraging will be higher during the nesting and brooding seasons (RA Norberg 1981, Blake 1983). Factors determining how a bird maximises its net energy intake will depend on morphological characteristics such as aspect ratio  (), wing loading (Q), maximum power  available from the flight muscles, the structure of the environment (a seashore and a dense forest require different flight behaviours), the spatial and temporal distribution of resources (patchiness) and the resource utilisation overlap with other species (e.g. 1981).  UM Norberg  For example, the vultures in the Serengeti plains, using the morning’s narrow  thermal 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 flies  close to the surface of the water. This bird cannot rely on thermals, and employs GE as a way or reducing its energy expenditure whilst flying (Chapter 5).  11  Perspective of the current study  The present study assesses GE in flapping flight and examines how this ffight strategy is used by different birds. Four species of birds were chosen: double-crested cormorant Phalacrocorax auritus, barn swallow Hirundo rustica, black skimmer Rynchops nigra, and brown pelican Pelecanus occidenialis. The birds chosen represent a range of morphological types and life styles. Double-crested cormorants are sea birds that nest colonially (Lewis 1929, van Tets 1959, Drent ci a!. 1961, Drent ci a!. 1964, Robertson 1971), have a high  Q  and fly at high  speeds IGE most of the time. They are known to fly long distances between nests and foraging areas (up to 42 km round trip, P Arcese, W Hochachka, pers. comm, pers. obs.) IGE. Double-crested cormorants bring large loads (chapter 5). Barn swallows have low  (  Q, fly  (  20% body weight) back to the nest  at high speeds (Blake ci a!. 1990), bring small  1% body weight) loads back to the nest, and may utilise GE whilst foraging. Black  skimmers, first birds for which any work in GE was done (Withers and Timko 1977; Blake 1983, 1985), use GE during their foraging and prey capture episodes and carry small loads back to the nest. Brown pelicans like the double-crested cormorants carry large loads back to the nest, whilst flying IGE to and from the foraging sites and taking advantage of other energy saving devices such as formation flight (Hainsworth 1988).  12  Chapter 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 River Delta, 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 Diego Bay in San Diego, California, USA 32° 15’ N Brown pelicans:  At Todos los  ,  117° 07’ W.  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 with a Paiflard Bolex variable speed camera model H16 Sbm, powered by a Bolex EMS 12V DC motor, set at 50Hz. The camera was fitted with a Kern Vario-Smitr fl.9, 16-100mm Bolex H16RX lens with a through the lens automatic exposure meter.  13  Films taken at Vanier Park (barn swallows) and Brunswick Point (double-crested cormorants) were taken with a Paillard Bolex variable speed hand-winding camera at 60Hz. The camera was fitted with either a Kilar f3.5, 150mm lens or a Century Tele Athenar f5.6, 500mm lens. Film exposure was determined with either Sekonic Studio Deluxe or Gossen Lunasix 3 exposure meters adjusted for the proper film and camera speeds. Both cameras were used at their maximum nominal ifiming speeds, 64Hz for the Palllard Bolex hand-winding camera and 50Hz for the Bolex H16 Sbm electric motor driven camera. To determine the ciné cameras’ “real” speed a digital stopwatch (Professional Quartz Timer Sports Timer) was filmed at each camera’s maximum speed. At least five sequences of one second length each were used to find the average maximum filming speed of each camera. The manufacturer specified rate for the motor driven camera was found to be 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 and light conditions.  Eastman Ektrachrome 80 ISO/ASA (colour) and Plus-X Reversal 50  ISO/ASA (black and white) films were used under bright light conditions.  Eastman  Ektachrome 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 commercially by 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 fishing boat, and the films of the black skimmers were taken from the bank of a channel in San Diego. All these films were taken with a handheld camera. The filming was done with the motor off and the boat drifting in currents <1 knot. For the films of the double-crested cormorants at Brunswick Point and the barn swallows at Vanier Park the cameras were mounted on a tripod. 14  llax problems that must be accounted for Filming under field conditions creates para and the camera are not necessarily in sing the data. The flight of the subject  whilst analy  ective of the flapping wing movement, and the same horizontal plane, distorting the persp water. The problem of wing perspective is the perceived distance from the wing to the bring about symmetry to the flapping sequence overcome by using best-fit algorithms that ysis for more details). The problem of wing to (see Chapter 3, Preliminary Statistical Anal looking for a point of contact between the wing water distance was determined by either wing the wing and its reflection in the water and and the water in the sequence, or, by follo in a sequence, assuming that that. distance was finding the closest point between the two and the water. On a boat the camera is not fixed the minimum distance between the wing h will alter periodically the perspective from whic in the horizontal plane and the waves problem was solved by partitioning the sequence the wing movement is being filmed. This r the median height of the wingtip above the wate being analysed into segments in which was equal. Digitising. sequences were analysed. A selected sequence, All films were previewed, then selected shows at least one complete wingbeat cycle in for both in and out of ground effect flight, an object, the water, or the body of the bird sharp focus, with no visual obstruction by The film sequences of each species selected for and no undetermined wingtip locations. duration of each sequence is shown on Figure digitising are listed and coded (Table II). The water show a calm sea ranging from almost still 1. All sequences selected for digitising 1 knot, (double-crested cormorants n waves (barn swallow films) to small current drive filmed at Mandarte Island).  15  Table II. Film flight sequences, species, and codes. Sequence Code  Species double-crested cormorant Phalacrocoraz aurius  black skimmer Rynchops  Pa 1 Pa2 Pa3 Rn 1 Rn2 Rn3 Rn4 Rn5 Rn6 Rn7 Rn8 Rn9  nigra  brown pelican Pelecanws occidentalis  1 Po2 Po3  P0  barn swallow Hirundo rustica  Hr 1 Hr 2  16  Figure 1. Time span of film sequences selected for analysis, codes as in Table II.  Pa3 Pa2 Pal Rn9 Rn8 Rn7 Rn6  C.)  a)  Rn5  D  Rn4  —  C) Cl) .  C,  I  Rn3 Rn2 Rnl Po3 Po2 Pol Hr2 Hrl  0.0  0.5  1.5  1.0 Time, s  17  2.0  2.5  The selected film sequences were projected with a Photo Optical Data Analyser Elm projector, (Model 224A MKV The Athena Co., USA) capable of variable speed, frame by frame, and forward and reverse film motions. The projector was equipped with a Super Sankor-16  f 1.3,  38mm lens. The sequences’ frame numbers were determined with a  Photographic Analysis Ltd. (Canada) electronic frame counter. The images were projected to 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 above the 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 set at 100 units. The vertical (Y) axis scaling control was then calibrated so that equal length displacements of the digitiser’s eyepiece in the X and Y directions would give an equal number of displacement units. This procedure was carried out to standardise digitising procedures by making the projected image size of the whole bird equal to 100 units. These measures were then converted to real size based on my own data or literature values (van Tets 1959, Hartman 1961, Withers and Timko 1977, Dunn 1973, Blake 1983, Dunning 1984) for the determination of wing motion and the aerodynamic power requirement curves for each bird. To determine the movement of the wing tip with respect to a fixed origin when digitisiug flight sequences, the coordinates’ origin was placed at either the most distal point of the beak of the bird or at the water surface immediately below the wingtip at the end of the downstroke. If the first method was used, the distance between the water and beak was also measured. To determine the minimum height of the wing above the water in the case of the origin being located at the beak, the minimum wing to water distance was determined by subtracting the maximum observed wing length during the downstroke of the sequence 18  being analysed from the beak to water distance. In the case of the origin being located on the water, the distance between maximum observed wing length at the end of the downstroke of the sequence and the water was measured to obtain minimum distance between the wing and the water. Morph ometrics. For measurements of wing length, wing area, total weight, and weight of the pectoralis and supracoracoides (flight) muscles, specimens of double-crested cormorants, browii peli cans, and barn swallows were photographed, dissected, and weighed as described in detail below. No specimens of black skimmers were available and morphometric data are taken from the literature (Withers and Timko 1977, Blake 1983  ,  Dunning 1984). Additional  data for brown pelicans, double-crested cormorants, and barn swallows was taken from van Tets (1959), Hartman (1961) and Dunning (1984). Four frozen double-crested cormorants were obtained from Dr. David Jones, Univer sity of British Columbia. One frozen brown pelican was obtained from San Diego State University (San Diego, California, USA), four brown pelicans mounted in flight positions were 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. (permit No. PC BC 86/11), killed, placed in plastic bags, and frozen for later dissection in the laboratory. One brown pelican wing, one black skimmer wing, one barn swallow wing, and two double-crested cormorant wings were photographed at the Washington State Museum at the University of Washington in Seattle, Wa., USA. To determine wing area, the frozen double-crested cormorants were thawed and placed with their wings fully extended and fixed. All birds and wings were photographed and 8 x 10” black and white prints were prepared. The photographs were digitised on an Apple graphics tablet with an Apple II Plus computer. The area was determined by using an  19  area calculation programme that requires one known distance (a 30cm or a 15cm graded ruler in the specimens’ photographs). To minimise dessication the birds were weighed and their right and left supracora coides 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 muslce power output.  Speed Measurements. The flight speeds of double-crested cormorants and barn swallows were measured with a 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 from objects as small as a sparrow at distances up to 10 m The radar gun was powered by a 12 V rechargeable gel cell or a 12 V car battery. It was calibrated against ahsolute time on a Professional Quartz Timer Sports Timer (Honk Kong) digital sports watch, known distances, and fixed or random speeds of vehicles passing at different angles of incidence which 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 cormorants  10°. Therefore any reflected bird signal is  nor barn swallows were detected at angles  accurately recorded with E thcos 10° of the displayed speed, or  2% error. There was  no significant difference between the stopwatch speed and the cosine corrected radar speed at either 10° (1  =  1.714, p  =  0.09, n  =  25) or 20° (i  =  .135, p  =  0.89, n  25). Recorded  flight 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 are  20  shown on Table III. Figure 2 presents the regression lines between cosine corrected radars speeds and stopwatch speeds. Wind speeds when filming and recording flight speeds were measured with a Deuta . 1 Anemo (W. Germany) wind meter. All wind speed measurements were l m•s  Observations. Daily activities of cormorants in Mandarte Island were observed with binoculars or telescope. To avoid detection by cormorants observations were made whilst lying down on an inflatable boat near Mandarte Island. For further details of the reproductive behaviour of the double-crested cormorant. colony on Mandarte Island see Drent et a!. (1964).  21  Table III. Correlation between stopwatch and cosine corrected radar speeds at a 100 angle of incidence between radar and subjects. Component Intercept Slope  Coefficient 0.926 0.977  Multiple r = 0.827 n 2  Standard Error 1.838 0.0932 =  25 F 23 , 1  22  t value  Probability  0.504 10.482  0.622 0.001  <  109.876 df, p< 0.01  Figure 2. Best fit correlations and differences between radar cosine corrected speeds and stopwatch speeds. Panels a, c, and e for 10, 20, and 30°, respectively. The differences between cosine corrected radar speeds and stopwatch speeds are shown in panels b, d for 10, and 20°, respectively. In panels a, c, and e, regres sion lines are solid, dashed lines’ slopes=1.  7 ” 4 U> 16  18  20 22 radar, rn/s  24  26  b 16  18  20 22 radar rn/s  24  26  28  c’J CO  c’J  0 0  •0  d ‘12  14  radar rn’s LC)  c’J  C 0  E 2Lc, 0 U)  Ii’)  10  15  20 radar rn/s  25  30  23  16  18 20 22 radar rn’s  24  26  28  Chapter 3. Preliminary Statistical Analysis of wing movements. Introduction. GE increases as the wing approaches a surface (Reid 1932  ,  Kücheman 1978  Mc  Cormick 1979, Houghton and Carruthers 1972), and miriimises loss of altitude when birds glide near surfaces (Blake 1983). Birds in forward flapping flight are IGE as long as the wing or a part of it is  1.5 wingspans(b) in height above the ground during some portion  of the downstroke phase of the flapping cycle (Reid 1932, Withers and Timko 1977, Blake 1985). 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 horizon tal 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 while foraging by skimming the water in horizontal forward flight. Brown pelicans ifimed at Bahfa de Todos Los Santos, Ensenada, Mexico, and double-crested cormorants filmed at Mandarte Island flew not only in horizontal forward flight, but also in both ascending and descending powered flight ICE. To understand how GE affects birds during flapping flight it is important to determine not only the GE in level forward flight but also its overall effect during ascending or descending powered flight. GE during flapping flight is analysed by considering changes in height through the wingspan during the downstroke phase of the wing-beat cycle. This is the phase of the wingbeat cycle in which most of the lift is generated, although lift can also be generated during the upstroke in large flying vertebrates (UM Norberg 1975, 1976; Rayner 1981). To analyse the wing movement during the downstroke it is essential to find accurate, reliable and mathematically manipulable descriptions of the movement of the wing on the vertical (Y) axis.  24  Movement 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 described by time series analysis. Bloomfleld (1976) defines a time series as a collection of numerical observations arranged in a natural order, usually associated with a particular instant or interval of time. He defines the Fourier analysis of a time series as a decomposition of the series into a sum of sinusoidal components. Fourier series can be used to describe any data-analysis procedure that describes or measures the fluctuation in a time series by comparing the series with sinusoids (Bloomfleld 1976). So, the changes in height above the ground in the vertical (Y) axis of a flapping wing, can be described by their Fourier series. 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 to  an extent limited by the analytical technique used and the sample size (Broch 1981). Three statistical methods were chosen to describe the periodic sinusoidal vertical wing movement. Circular-linear (periodic) regression and correlation (Batschelet 1981), periodic Analysis of Variance (ANOVA) (Bliss 1970). and discrete Fourier analysis of time series (Bloomfield 1976). The circular-linear regression and periodic ANOVA algorithms calculate the mean height of the wingtip (mesor, M) and the first two terms of a Fourier series that describes the particular flight sequence analysed. The discrete Fourier transform analysis renders a number of harmonics equal to the half the number of points sampled in the flight sequence being analysed. Both circular-linear regression and periodic ANOVA require random and independent sampling. Neither of these two conditions are met by the sampling technique and sampling apparatus 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 by the previous one. Nethertheless, Batschelet (1981) recommends the use of circular-linear 25  regression techniques for the description of periodic phenomena, such as the vertical wing movements. The strength of these techniques is demonstrated by the highly significant results obtained here, by the fit of the calculated curves to the points and by independent test of areas under the original and calculated curves. A Fourier series is a representation of a periodic function  f(x)  as a linear additive  combination of cosine and sine functions (Lighthill 1958). Fast Fourier transforms produce where  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 that describes the vertical wing movement is directly proportional to sample size (Bloomfield 1976), it is important to establish the statistical significance of any particular harmonic and its corresponding physical reality. While carrying out the analysis I found that the statistically most significant Fourier coefficients of any flapping sequence were the mean height of the wingtip (M), which also represents the bird’s body height, and the first two harmonics, which represent the movement of the wing. In all sequences the sum of the additional terms contributed <<0.01% towards explaining the original wave. Description  of Anaiyticai  Methods.  Circular linear regression and periodic ANOVA describe phenomena of the general form: (I.)  (i—t 0 Y=M-fAcosw )  where t is the independent time variable. The other parameters of the equation are: M mean level or mesor, A  =  amplitude (A  ). 0 0), (mamum distance between M and t  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()  =  1 cos(w M+A  —  2 cos(2w1 +A 26  —  )+  ...  + A. cos(kwt  —  4k)  (2)  Batschelet’s (1981) algorithm requires a minimum of n  =  6 equally spaced time instants  for a good fit. Bliss’ (1970) algorithm requires at least one and a half wavelengths and a minimum 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  2 s 1 (z,y)/s  where coy and s and  1  (x  (x,y) =  —  Z)(yj  —  y)  are the variances.  2  He then sets the correlation coefficients as:  rs  =  corr (y,cos  ),  =  corr (y, sin  4),  rcs =  where  4’ = wt  corr (cos qS, sin  ),  to define the correlation coefficient between y and  4’ for  the first term in the  Fourier series as: 2 = (rc r  where y and  4’  +  s  —  rcrsrcs)/1  —  TS)  (3)  are independent and when n is large:  (4)  2 ni’  Eq. (4) is Batschelet’s (1981) test statistic.  27  Since the sine and the cosine are orthogonal and additive transformations of time, the significance of the Fourier factors eq. (1) can be expressed as:  Y  =  0 + a  1 cos(w) + b1 sin(wt) a  (5)  (Bliss 1970) aflows the constants in eq. (1) to be determined from the regression coefficients 1 . If we let u 1 1 and b a  =  1 cos(wi) and v  =  sin(wi) then eq. (5) may be written as:  (6)  biv 1 Y=a0+ajuii+  where  1 u  =  =  E(ui vi)  =  1 0. The regression coefficients a  and  1 have the b  same denominator, k, for all uniformly spaced series of Ic intervals, so that Eu Ev?  k. When f(number of replicates per sampling interval)= 1 at each time  ,  they  are computed as: 1 a  -  (uay) V’  L.  2 1  E(viy)  -  [uiy]  —  —  1  [viy]  Evk where the square brackets  []  means of the variates. With  designate the sums of squares or products measured from the  f replicated  ys at each i, totaling T, the regression coefficients  are computed directly from 2 as:  = 1 a  [u 2’.] fk  and  = 1 b  [v1 T] ‘fk  T is the sum total of all values, k is the sampling frequency. The same rules apply for the second and any subsequent harmonics (Bliss 1970). Sequence Po3 (a pelican in descending flapping flight) was chosen to test the reliability and statistical significance of the algorithms that describe the travel of the wingtip. The 28  null hypothesis states that there is no periodic relationship between time and the vertical location of the wing tip. The sequence consists of 3.5 wingbeat cycles with an average of 19 recorded points per cycle, thus fulfilling all the requirements of both the circularlinear regression (Batschelet 1981) and periodic ANOVA (Bliss 1970) algorithms. All other sequences chosen were analysed with either or both methods. The AN OVA test is performed by comparing the mean square of each harmonic and the mean square of the scatter in the curve against the error mean sum of squares. The statistical gniflcance is determined by standard F-distribution tables or by the method described in the results section of this chapter.  Table Wa presents the results of the  circular-linear regression and Table IVb the results of the periodic AN OVA for Po3. Both methods provide statistically gniflcant results.  29  Table IVa. Circular-linear regression of the best fit data from Po3. 2 r 0.703713  ulue 2 v ) 2 (ri * r 53.4822  p <0.001  Table lVb. Periodic Analysis of Variance for the digitized sequence Po 3 of a pelican flying in ground effect. Source a b 1 b 2 a scatter error TOTAL  Sum of Squares  D. F.  M. S.  F-ratio  7.916 0.002 0.088 3.297 11.302  2 2 15 56 75  3.958 0.001 0.006 0.059  67.232 0.017 0.099  30  p <  0.001 .998 .906  Lin ear.isaüon.  The nusoids representing wingtip movements were linearised to provide a measure ment of A and M that would allow comparisons both between and across species. By defining:  z  where  =  wi and ç  =  =  (cos ç — 5  (7)  =  (cos bj  (8)  0 and i —  then s— 0 g()=M+Ai(co )  (9)  x 1 Y=M+A  (10)  xk. AIZ -A ...-FAk Y=M+ H 1 + 2 z  (11)  becomes  and eq. (2) becomes  (Batschelet 1981). Standard linear regression and correlation techniques can then be applied. The algorithms for both circular-linear regression and circular-linear AN OVA were written, tested and calculated at Biosciences Data Centre (BDC) of the University of British Columbia. The regression of the linearisation and the correlation between tests were done using the ‘S’ data analysis and graphics package. The Fast Fourier Transforms were done with the ‘S’ statistical package enhancements designed at the University of Washington and installed in the BDC’s computer.  31  Results.  Reliability of the statistical tests.  The aim of the chapter is to find mathematical expressions that describe the vertical wing movement of birds IGE. The wingtip movements of Po 3  ,  the best fits by rcular  linear regression, periodic ANOVA and Fast Fourier transforms, ther residual plots of circular-linear correlation and periodic ANOVA, the correlation between these two meth ods, and the componets of the Fast Fourier transforms are presented in Figure 3. Both the circular-linear regression and the ANOVA algorithms calculate least square curves that do not 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, an independent test of the reliability of the algorithms is obtained. Also, if the area under the curves 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 under Po 3 and its best fit curves employing the digitiser and area determination software of the BDC. Given the small differences in areas between the raw data and the best fit curves, the areas can be considered identical. The best fits given by the algorithms developed in the present study are an accurate representation of the data, and their results can be used to describe the GE during forward horizontal, ascending, or descending flight. Comparison of analytical methods. Although circular-linear regression and periodic ANOVA give different equations (Ta ble Va), they differ by less than 10%. Table Vb presents the equations resulting from the use of the circular regression and periodic ANOVA algorithms on Po3. The results of  32  the linearisation of the circular-linear regression and the periodic AN OVA can be seen of Tables Via and b, respectively. The residual plots of circular-linear regression and periodic AN OVA (Fig. 3b, top and center, respectively) show that nce the algorithms find the least square lines, the largest differences occur in those points further away from the best fit curve, i.e. beginning and end of the descent. Note that the residuals between the algorithms and the original data set are not random but periodic. 11 the circular-linear regression and the periodic AN OVA algorithms produced the same best-fit curve, the plot of the resulting points of one algorithm against the resulting 2 points of the other would produce a line of b (slope)=l and r  =  1. The scatter plot of  the 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-linear regression. Statistical results and equations. All data sets that fulfilled the requirements described for each of the tests described in the section of Materials, Methods and Preliminary Analysis of chapter 2 were analysed by the appropriate method (circular-linear regression, circular AN OVA, or Fourier trans forms). The statistical results of the circular-linear regression analysis are reported on Figure 4, and the statistical results of the its linearisation on Figures 5 to 7. The statis tical results of the periodic ANOVA analysis are reported on Figure 8 and the statistical results of its linearisation in Figures 9 to 11. Table VII summarises the equations for circular-linear regression, for the sequences analysed with this method. Table VIII summarises the equations for the sequences anal ysed with the periodic AN OVA. Table IX presents the first two terms of the discrete Fourier transforms for all sequences used in the present study. 33  Figure 3. Best fit curves, residual plots, and linearizations; correlation be tween circular ANOVA and circular-linear regression; and Fast-Fourier transform components for Po 3 wing-tip pattern. Panel a presents the best fit curves for drcular-linear regression (top), periodic ANOVA (centre), and Fast-Fourier trans form (bottom). Panel b presents the residuals for circular-linear regression (top), and periodic AN OVA (centre). Panel c presents the linearization of circular-linear regression (top), and periodic ANOVA (centre). Panel cs the correlation between circular-linear regression and periodic ANOVA. The Fast-Fourier transform com ponents are: periodogram (e), amplitudes (i), and acrophases (g).  a  b  d  C  >  0  z  0.0  0,4  06  12  1.6  0.0  0.4  0.1  12  1.6  -0.6  5  10152020  Feq.eoy  0  0.6  -0.6  -0.2  04  02  XA o)  c.,La-6n. re  f  g  e  0  04  02  -02  The s  20  10  T r.zn*r  34  30  40  0  10  20 Turn  30  06  40  Table Va. Areas under Po 3 and its least-square fitted curves. The areas are used to compare the fit of both circular-linear regression and periodic ANOVA to the raw data of Po 3 a pelican flight sequence. Curve Po 3 Regression ANOVA  Difference  Area 2 units 72.198 69.854 67.084  Percentage  2 units  2.344 5.114  3.36 7.62  Table Vb. Equations obtained with the two different algorithms employed for describing Po 3 Method  Equation  Regression ANOVA  —0.019 + 0.463 —0.040 + 0.456  *  1 (t  *  —  —  35  0.044) + 0.024 0.133) + 0.007  * (2 *  2 (t  —  —  (_0.027)) (—1.220))  Table Via. Summary of the linearization of the aErcular linear regression of Po3. Component  Coefficient  -0.026 Intercept 1st sinusoid 0.992 2nd sinusoid 1.019 0.710 2 Multiple r  i Value  Standard Error 0.0244 0.0743 0.9595 73 , 2 n= 76 F  -1.060 13.350 1.062 89.184 p=O  =  p 0.854 < 0.001 0.292  Table VIb. Summary of the linearization of the periodic ANOVA of Po 3 Component  Coefficient  -0.026 Intercept 1.002 1st sinusoid 2nd sinusoid 4.708 2 0.699 Multiple r  Value  Standard Error 0.0248 0.0769 4.9468 73 , 2 n= 76 F  =  -1.064 13.018 0.952 84.776, p0  p 0.291 < .001 0.342  Summary of the correlation between periodic AN OVA Table Vic. and circular-linear regression algorithms. Component Intercept Slope  Coefficient -0.020 0.981  2 Multiple r  =  Standard Error  t  Value  p  0.0027 0.0083  -7.285 118.020  < <  4 F 7 , 0.998 n= 76 1  36  =  13928.8, p=O  .001 .001  Table VII. Summary of best-fit circular-linear regression equations 2 cos(2wi 1 cos Y = M±A i) + A —  —  Sequence Pa 1 Pa 2 Pa 3 Po 1 Po 2 Po 3 Rn 1 Rn 2 Rn 3 Rn 5 Rn 6 Rn 7 Rn 8 Rn 9 Hr 1 Hr 2  k  2 A  0.334 0.430 0.387  A 1 0.100 0.089 0.0837  4.641 0.176 0.677  0.0278 0.0103 0.007  3.417 3.881 -1.501  9 10 10  0.913 0.303 -0.040  0.681 0.493 0.458  0.361 0.679 O.709  -1.362 -0.483 1.062  17 18 19  0.285 0.333 0.790 0.889 0.857 0.113 0.059 0.340 0.146 0.008  0.270 0.274 0.385 78.663 68.640 0.301 0.184 0.244 0.043 0.098  0.510 1.276 -0.920 1.066 0.248 0.096 -0.366 0.837  0.082 0.048 0.046 0.021 0.072 0.074 9.615 7.555 0.029 0.020 0.023  10 8 13 12 13 17 22 12  -0.785 1.086  0.039 0.025  -0.115 1.548 2.962 0.102 -0.687 4.337 4.688 -0.337 2.284 2.509  Mesor  37  7 6  Table VIII. Summary of best-fit periodic ANOVA equations ). s—i)+A wt— +Aio os(2 Y=M c 2 Sequence  Mesor  Pa Pa Po Po  1 2  0.334 0.430  1 3  0.879 -0.040  Rn Rn Rn Rn Rn Rn Rn Hr Hr  1 2 5 6 7 8 9  0.282 0.022 0.055 0.022 0.102 0.042 0.346  1 2  0.146 0.008  A 2 0.022 2.788 0.010 0.176 0.098 0.549 0.007 0.133 0.024 0.244 0.025 0.274 -0.186 0.023 0.087 0.290 0.373 0.274 -0.186 0.022 0.043 0.283 0.127 0.164 -0.297 0.010 0.029 0.267 0.831 0.043 -0.785 0.039 0.025 0.098 1.086  A 1 0.124 0.089 0.602 0.456  38  k 1.830 3.880  10 10  3.039 -1.220  17 20  2.958 1.814 2.961 1.814 3.547 2.568 0.733  11 9 15 14 17 22 12  2.283 2.510  7 6  Table IX. Summary of the first two terms of Fast fourier data selected on performed transforms cos(2wi-). 2 Y=M+Aicosw—4i)+A Sequence  Mesor  Pa 2 Pa 3 Po 1 Po 3 Rn 1 Rn 2 Rn 3 Rn 5 Rn 7 Rn 8  0.430 0.387  A 1 0.025 0.042  0.879 -0.040 0.282 0.351 0.777 0.055 0.102 0.0421  2 A .793 1.481  0.110 0.207  -1.102 -1.284 3.770 4.686  0.022 0.035 0.211 0.097  2.380 3.754  0.056 0.075 0.396 0.230 0.081 0.057  -1.173 1.287 1.187 0.400 3.431 4.139  0.118 0.285 0.061 0.227 0.030 0.087  -1.174 -0.0595 0.326 -1.543 3.421 3.469  39  Figures 4 to 11 present a novel method for summarising statistical results through significance level curves.  By locating the appropriate calculated statistic in the figure  with the probability plane corresponding to the appropriate distribution  , i, 2 (x  or F) and  degrees of freedom it is possible to ascertain its significance level without having to consult a standard statistical table. A  distribution probability plane for 2 degrees of freedom  is presented in Figure 4. Figures 5, 6, 9, and 10 are two-tailed Student’s t probability planes. Figures 7, 8, and 11 are one-tailed F distribution probability planes for 2 degrees of freedom in the numerator. Conclusions. The aim of this chapter was to find mathematical expressions that describe the vertical wing movement of birds IGE. Both circular-linear regression and periodic AN OVA describe to an statistically highly significant level the vertical displacement of the wing, as long as the appropriate prerequisites of sample size for the algorithm are fulfilled. These estimates tend to obscure ascent or descent manceuvres of the bird by building the best-fit sinusoid around the median height of the wing (M) during the sequence and modifying the overall amplitude by taking into account the highest and lowest points of the sequence when constructing the sinusoid.  Nontheless the general trend of the flight sequence can be  obtained. Fast-Fourier transforms describe precisely the recorded vertical movement of the wing. These transforms can be cumbersome to manipulate given that the number of Fourier terms is directly proportional to the number of data points. Also, such a precise description masks any trends on the data, precluding generalisations of the film sequence being analysed. Despite the particular limitations of any of the three methods used in this study for describing the vertical wing movements of a bird in flapping flight, any of them can be used with coafidence. To analyze the film sequences I selected the method that provided a statistically significant result and was easiest to manipulate.  40  Figure 4. x 2 probability levels at 2 degrees of freedom for of the best fit curves for the circular-linear regression algorithm. The horizontal represent standard rejection levels (p = 0.05, p = 0.01, and p = 0.001), The Y axis represents value and the ordinate gives the exact probability of obtaining the calculated 2 the calculated x • The diagonal dotted line is an exact probability line for x 2 standard rejection represent lines horizontal The freedom. values for 2 degrees of levels indicated in the box. x 2 values falling below any of the horizontal lines are statistically significant at an a level smaller than the probability value of the line.  C  C C > C C 0 0  Q  C  C C C 0 C  0  5  10  15  20  Chsquared values  41  25  30  35  Figure 5. Two-tailed Student’s significance levels of the intercepts resulting from the linearisation of the circular-linear regression algorithm. The abscissa represents degrees of freedom and the ordinate obtained i values. The lines rep 0.05, 0.01, and 0.001. To find the significance level resent rejection levels of c of a calculated for the appropriate number of degrees of freedom, the obtained value is plotted on the graph. i values falling above any of the lines are statisti cally significant at an c level smaller than the probability value of the line.  * V  **  0)  2  CO >  —  IC)  0 \  —--—  V  C  x  0 I  I  0  20  40  60  Degrees of Freedom  42  80  100  Figure 6. Two tailed Student’s i slgaificance levels of the slopes resulting from the linearisation of the circular-linear regression algorithm. See Figure 5 for ex planation.  0  I-fr Rn 0.01  ———  0.001  ———-  C C  V  Po Pa  T  C I1  C) D CC >  V  0  V  0  0  I’ 0 *  .‘  0  20  40  60  Degrees of Freedom  43  80  100  Figure 7. F-distribution significance levels at 2 degrees of freedom numera tor of the multiple regression analysis of the linearisation of the circular lin ear regression algorithm. The abscissa represents degrees of freedom and the ordinate obtained F values. The parabolic lines represent rejection levels of a 0.05, 0.01, and 0.001. To find the significance level of a calculated F for the appropriate number of degrees of freedom, the obtained value is plotted on the graph. F values failing above any of the lines are statistically significant at an a level smaller than the probability value of the line.  C L() -  -  -  V  ——  005  X  H  *  p  0.01 0.001  V C C  V 0 0 C) > L1  0 \ C  —  \  \  ‘•-_.  0  20  I  I  I  40  60  Degrees of freedom denominator  44  80  100  Figure 8. F-distribution significance levels at 2 degrees of freedom numerator of the best fit curves for the periodic AN OVA algorithm. See Figure 7 for explana tion.  0 0  IL,  -  I  h——  X  0.05 0.01  V  0.001  *  Hr Rn Pc Pa  0  C  V  V  C)  .2 > U  \  \  \  —  ..---  It,  —  •.  -  x I  20  0 -  I  40  60  Degrees of freedom denominator  45  80  100  Figure 9. Two-tailed Student’s i gniflcance levels of the intercepts resulting from the linearisation of the periodic AN OVA algorithm. See Figure 5 for expla  nation.  0 L)  0  a) > It,  0  0  20  40  60  Degrees of Freedom  46  80  100  Figure 10. Two-tailed Student’s t significance levels of the slopes resulting from the linearisation of the periodic AN OVA algorithm. See Figure 5 for explanation.  0 C U,  Hr Rn ——-—  ———-  C C  I  C U,  1  0.01  V  0.001  Po Pa  a) V  >  U,  0  20  40  60  Degrees of Freedom  47  80  100  Figure 11. F distribution gnificance levels at 2 degrees of freedom numerator of the multiple regression analysis of the linearisation of the periodic ANOVA algorithm. See Figure 7 for explanation.  0 C  It, X  0.05  0 ——  0.01 0.001  E  Hr Rn P0 Pa  0 0  V 0  It,  C) >  o  \ -\  \  x  \ N  It)  -  .  0-  20  40  60  Degrees of freedom denominator  48  80  100  Chapter 4. The Power Curve and Ground Effect.  Introduction.  Flapping flight requires a large energy output when compared to the basal metabolic rate or the maintenance energy. The calculation of a bird’s flight power requirements has been approached from two perspectives. The first approach has been to measure the physiological power expenditure whilst flying (e.g. Tucker 1966, 1972; Torre-Bueno and Larochelle 1978; Tatner and Bryant 1986; and Rothe e al. 1987). Although this approach gives a physiological estimate of the power consumed during active flapping flight, it does not directly reflect the aerodynamic forces that must be overcome in flight. The second approach directly considers aerodynamic forces and the power requirements of active (flapping) flight for birds and other flying vertebrates. These forces have been assessed via fixed wing aircraft quasi-steady aerodynamics theory and momentum jet theory with modifications 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 1979a b 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 through the momentum jet theory does not explain these forces. Vortex theory does provide an explanation for the creation of the aerodynamic forces (Nachtigail and Dreher 1987), but it is computationafly complex. To assess aerodynamic forces generated during forward flapping flight a power curve which takes into account the the different aerodynamic drag components must be created. The mechanical energy available from flight muscles and the energy required to fly impose an upper limit to the size of a bird engaged in flapping flight and to its payload 49  (Pennycuick 1975). Limitations imposed by a bird’s morphology and energy available for flight and maximum payload, and stalling speed 8 (V t a) can be overcome by using GE. GE reduces induced drag (D ) and stalling speed (V 2 ) 1 a 8 1 whilst increasing lift (L).  The Power Curve.  The assessment of the total power requirements for flapping flight must take into ac count both the aerodynamic forces that must be overcome by the bird and the physiological requirements that the bird must meet in order to fly. The assessment presented here fol lows Pennycuick (1975) by considering the maintenance metabolism and the aerodynamic forces. It then combines these two components and adds an estimate of the energy required by 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 mea sure of metabolic rate is employed. Metabolic rate can be measured by calculating the difference 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 by measuring the amount of oxygen used in the oxidation process, provided information about which substances have been oxidised (Schmidt-Nielsen 1979). The metabolic rate (W) of a non-passerine bird can be estimated by the allometric equation: 723 Fme = 3.79m°  (12)  (Pennycuick, 1975 based on Lasiewski and Dawson, 1967), where Pmet is the metabolic rate and m the mass (kg). Metabolic power (Pmet) gives a good indication of the minimal energetic requirements of a bird. By taking this assessment into account and converting the metabolic energy into a mechanical power equivalent by multiplying with an efficiency 50  factor q of 0.23 (Pennycuick 1975). A 1.88kg double-crested cormorant should have a metabolic 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 maintenance energy.  Henneman (1983) measured maintenance energy of double-crested cormorants  under different environmental conditions recreated in the laboratory. He discovered that the birds had a higher basal rate than that predicted by the equation of Aschoff and Pohl (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, and Enight = (1.25  —  0.0290°C)5.58,  (14)  for night. In these equations E is the rate of metabolism in cm 3 02 g’ hr’ and .  .  °  C is  the environmental temperature. These figures were converted to W by multiplying by a factor of 5.58 to express them in SI units compatible with the calculations of aerodynamic power. The temperatures used here to calculate metabolic rates for the double-crested cor morants are those registered at the Victoria International Airport, near Mandarte Island, for the summer of 1988. The temperatures (provided by the Canadian Atmospheric Envi ronment Service) are shown in Table X. The calculated mechanical maintenance energies (Pme) of the double-crested cormorants for night and day during the reproductive season  are calculated using the masses of the double-crested cormorants of Table XIIa and are plotted in Figure 12 as a ratio of the metabolic rate calculated via eqn. (12). The ac tual values of the mechanical equivalents of maintenance rates can be seen in Table XI. Eq. (12) underestimates energy expenditures. The seasonal (temperature) dependence of metabolic cost (Fig. 12) will be accounted for when calculating the energy expenditures of the double-crested cormorants. 51  Table X. Mean monthly temperatures of the Victoria International Airport for 1988. Month April May June July August September  Mean max  Mean mm  oc  oc  13.6 16.3 19.1 22.5 21.5 17.8  4.2 6.4 8.3 10.1 10.2 6.8  52  C.3  CD  cn  II3c)11  II  II  III)C?3 II  ,  CD  a-I.  CI  PC)  Figure 12. Ratios of day and night maintenance rates of double-crested cor morants, eqs. (13) and (14), to Pme eq. (12), for the reproductive season at Mandarte Island.  +  +  + H+  H A  CD  C  day night  Mar  Apr  El  I  I  May  Jul  Jun  month  ‘54  Aug  Sep  Oct  Aerodynamic Costs.  air:  thrust itself through the Three forces must be overcome by a flapping flyer in order to ted power term. parasite, profile and induced drag forces. Each force has an associa me the drag generated Parasite OW (Ppar) is the power required by the bird to overco  by the shape of the body and is usually calculated as .Ppar = pVApCDpar  (15)  ) at a standard atmosphere, V is the 3 3 (1.256kg m where: p is the air density in kg m , A is the equivalent flat plate area of the body at its 1 forward speed of the bird in m•s .  widest point (Pennycuick 1975) and is calculated as: Sbody  Cij  (16)  of the body and can be estimated where Sb d is the cross sectional area of the widest point 0 from the allometric relationship: ° 66 m 3 d = 8.13 x 10 0 Sb  (17)  where m is the mass in kg. (Pennycuick 1975) ined by the Reynolds number (Re) CDb is the body drag coefficient which is determ ted as: at which the bird is flying (Pennycuick et al. 1988). CDb is calcula CDb  1.57  —  O.IOSln(Re)  (18)  where Re = 1.25 x iO/.  (19)  friction drag of the Profile power (Ppro) is the power required to overcome form and lt power to calculate (Pennycuick wings during the power stroke, and it is the most difficu 55  0 is constant (i.e. independent 1975, Rayner 1979a b). Pennycuick (1975) assumes that Pp. te minimum power (Pam). of speed) over median speeds and is equal to 1.1 times the absolu  Pam will be discussed later on this section. and it is calculated The present study assumes that Ppro is proportional to the speed,  Ppro = pSVCDpro  (20)  coefficient, assumed to have a where S is the wing area, and CDpro is the profile power value of 0.02 (Rayner 1979a). speeds higher than Estimating the power curve with eq. (20) results ii Vmp and Vmr d cormorants at Mandarte maximum values of flight speed recorded for the double-creste 0 used in this and the P,,. Island. Figure 13 illustrates the ratio between Pennycuick’s PprO study.  56  and the Ppro calcu  Figure 13. Ratio between Pennycuick’s (1975) constant lated in this study.  It) C  C  It)  0  Di  o  C  d  It)  Q  0  c  I  I  C  6  8  10  14  12  Vm!s  57  16  18  20  the  to generate the force required to support Induced power (Find) is the power required under vortex theory, by the shedding of weight of the bird. This force is generated,  entum jet theory assumes that a back and vortices from the wing tips of the bird. Mom This momentum is a product of the mass downward momentum is imparted to the air. arbitrarily defined wing disk (Sd). The wing flow (mass per unit time) passing through an (Pennycuick wingspan as diameter Sd disk is the area of a circular disk with the 1975). d of speed; as a direct consequence, at a forward spee Pd is inversely proportional to the case; Find is calculated nd would be infinite. This is not 2 zero the requirements for P ck Such calculations can be found in Pennycui m j€t and vortex theory, respectively and are (1975) and Rayner 1979a,c for momentu ts do not hover. Find at speeds higher than 0 not applicable to this study since cormoran  differently under those circumstances.  is calculated as:  2 R Find  (21)  = 2pVSde  airfoil efficiency factor of 1.0 and Rf is the where Sd is the wing disk area, and e is an nycuick, 1989a) and is calculated as: resultant of the weight and body drag (Pen Rf = JW2 + Dar  (22)  is the body or parasite drag: where W is the weight in Newtons N and Dpar .Dpar = .pv2A  (23)  1 = PSCDpro + pApCpar K  (24)  Following Blake (1983) let:  and = 2 K  R 2 2pSde 58  (25)  then Ppara  3 1 V K  (26)  V’  (27)  and 2 Pind = K  The sum of the aerodynamic power requirements produces the characteristic U-shaped curve, but leaves aside physiological considerations. The lowest point of the curve reflects the speed at which a bird should fly for minimum power consumption, or minimum power velocity (Vmp). It is this “absolute minimum power” (Pam) that Pennycuick (1975) uses to generate his estimate of .Ppro. Pennycuick (1975) considers P,.o to be 1.1 times P,. A more realistic curve (Pennycuick 1975) is generated if the metabolic or the maintenance power (expressed in a mechanical currency) is added.  Lastly, the cost of ventilation  and blood circulation necessary to provide the oxygen to the flight muscles must to be considered. Pennycuick (1975) uses a factor of 1.1 based on Tucker’s (1973) estimates of power expenditure by the heart and ventilation during exercise (5% each), and the same standard will be used here.  The power curve for the double-crested cormorant. To calculate the power requirements for double-crested cormorants some of their  anatomical characteristics must be known. The necessary measurements were obtained by dissecting 4 cormorants (for details see chapter 2, Materials and Methods). The results of 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 of the aerodynamic power components give a characteristic  U  shaped curve which includes  maintenance power. For more details see the legend to Figure 14.  59  t:’3  cDCD  L’3  H-P  L’3C)  coc’  CD DC  DcD  PP  C)1  i-”  ‘1  0  ci)  C)  1  0  ci ci,  C) CD  CD OCD —  I.  k)  H-P  -,  J)1  C3  -(D  PPP  t.) C.)’ C’:)  HDOPC  bC)l  C)  C)  H-PPPP x y  CD  -  t3  ci’  Jq  Cl)  q  I  0  ‘-  I  8  CD  ci,  CD  CD  CD  CD  ci,  ci)  CD  i-  0  CD  Figure 14. Power curve for double-crested cormor&nts at Mandarte Island. a to which the muintenance and exercise and d is the is Find, b Ppar, c expenditures (e) have been added in mechanical equivalents.  Cr)  C) 0  e I  0  —  I  I  I  5  10  15  V(m/s)  61  20  Figure 15 illustrates the two characteristic speeds of the power curve: the speed at which the least amount of energy is consumed, allowing the greatest time in air, (i.e. the minimum power speed, Vmp, and the maximum range speed (Vmr), the speed at which a bird flies the longest distance for a given amount of fuel). Vm,. is found by drawing a tangent line from the origin to the power curve or by finding the minimum ratio between total power and speed. As shown in Figure 12, P, in the double-crested cormorant varies with ambient temperature. Power consumption ratios based on minimum calculated mail)tenance power are presented in Figure 16. It can be seen that the energy consumption during flight by a double-crested cormorant changes by about 5% for the range of temperatures recorded during the reproductive season of 1988.  62  Figure 15. Characteristic speeds of the double-crested cormoraiit power curve for the month of July.  Vmr  C)  Vmp  15.1  11 .1  c’J  0) 0  ci-  I  I  0  5  10  V(m/s)  63  15  20  Figure 16. Ratios of power consumption at different speeds throughout the re productive season of the double-crested cormorants at Mandarte Jsland. The X axis represents flight speeds, the Y axis power ratios.  L()  q  q 1  C 1  0 •1-  0 cJ  c  1  c  c q  .1 ii 6  8  10  12  I  I  I  I  14  16  18  20  Vm/s  64  Ground Effect in Flapping Flight. to the reduced GE explanations fall into two separate categories. The first effect is due tends to increase the mass flow under the wing in the presence of the ground where it (a), resulting in an pressure at the wing’s lower surface for a positive angle of incidence effect is due to overall gain in the lift of the two dimensional wing section. The second —Ii) that can be (y the velocity induced by an imaginary reflected wing at a height wing experiences an explained by the lifting line model. In the case of a positive a, the around the wing) additional forward velocity (V = F/47rh) (where F is the circulation extension of the that reduces the free stream velocity and thereby decreasing lift. The sion that the wing vortex line model on a three dimensional finite wing leads to the conclu tip vortices will always increase the lift of the wing ICE (Katz 1985). to the ground Reid (1932) explains ground effect by saying that “a wing flying close a limitless expanse e behaves as though it were one wing of a certain imaginary biplan in its mirror image in the of fluid; the hypothetical biplane is composed of the real wing and biplane has the gap 2h.’ ground plane. If the height of the wing above the ground is h, the and of opposite sign, ‘Since the lifts of the wing and its image are equal in magnitude also have opposite the self induced and mutually induced vertical velocities at each wing y give a new vertical signs. The vector sum of the self-induced and mutually induced velocit velocity.” The total induced drag of the two-wing system is: DIT  =  2 D 2 +2 D 1 +1 D 1  (28)  2 the mutual induced D is the induced drag experienced by the real wing, 1 experienced by 22 the induced drag experienced by the image wing. The part drag, and D  where  the real wing is:  LL’ + 4pirV2bbt pirV2b 2 2 L  =  65  (29)  since b  =  b’ and L Di=  L 2 p7rb 2(1  (30)  Reid (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 wing tip of a bird during flapping flight. The present chapter considers the vertical displacement of the whole wing through the downstroke phase of flapping flight and how these changes play a role in the amount of GE experienced by the bird. Previous studies of GE during flight in birds have been based on fixed-wing aircraft aerodynamic models and have not considered other existing aerodynamic models of GE. For example, these studies have assessed GE for black skimmers in gliding flight without explaining changes in altitude loss (Withers and Timko 1977  ),  gilding without loss of altitude (Blake 1983 ), or have  considered that the average height of the wing during the downstroke is sufficient to estimate GE during flapping flight (Blake 1985). Employing the model of Reid (1932), a quasi-steady approach is taken here, where the 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 changes in its angle with respect to the horizontal. The wing obtains its highest absolute angular values at the beginning and end of the downstroke and its minimum angle (0 radians) at the instant the wing is parallel to the ground. These changes in height through time are expressed by the sinusoids of chapter 3. To date no detailed study of the biomechanics of flapping wings in GE exists. Neither is there an aerodynamic model that can describe wings with both variable geometry and large oscillations (Prof. J Katz pers. comm.). The biomechanicai approach to the study of 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). 66  Figure 17. Reid’s (1932) interference coefficient for GE, o, plotted against the ‘wingspan to wing height to wingspan ratio (h/b).  0  E  0) U)  0  0  0 0  0.0  02  0.4  0.6  0.8  1.0  hib  67  1.2  1.4  1.6  Blake’s (1983) model indicates that GE is important in the daily energy balance of the black 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 of Binder (1977) on GE for fixed wings at banking angles from 0 to 20c found a reduction in D dependent on the banking angle. Katz (1985) studied GE on plunging (rapidly ascending and descending) wings subject to oscillations of 0.1 of the chord (the chord is the distance from the leading edge to the trailing edge of the wing) concluding that the 1 was reduced and L increased. Neither Blake’s time to reach a steady lift coefficient C (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 is characterised by large amplitude and low frequencies. Both the Binder (1977) and Katz 1 for oscillating and banking wings, respectively. (1985) models indicate a reduction in D Any model that attempts to predict GE in flapping flight should agree at least qua)itatively with the results of Binder (1977) and Katz (1985). The wing shape during downstroke was determined by filming birds flying towards or away from the camera. It was found that the wing can be described as a rigid spar hinged at the wing root (Fig. 18). Since GE can be assessed through lifting line theory models employing only the wingspan (b) and its height above the ground (h), GE is assessed by assuming that the wing behaves like a straight hinged spar and that the flapping cycle is symmetrical around the longitudinal axis of the body, allowing an averaging of the interference coefficient cr over the whole cycle.  68  Figure 18. Front view of a downstroke by a double-crested cormorant ifimed at 60 Hz. The lines indicate wing positions at different frame numbers.  1  2  3 4  6  69  u is assessed at 0.7b at each measured and calculated best fit point of the downstroke portion of the wing flapping cycle. These series of us are then averaged and a mean u,  a is  reported. The ãs for all the sequences are shown in Table XIII. Table XIII also shows that although 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 underestimates  a 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 19 and 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 coef ficient 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 53 for the barn swallow. nd: 2 To calculate the power curve IGE u is incorporated into the calculation of P  (31)  (1 —u).V’ —K . 2 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: 2 c-L  =  (32)  then the apparent b (bapp) IGE is: bapp  (33)  =  1 i.e. V Changes to bapp should be reflected in changes in wing area and consequently in 1 =  2W t.F_,  ‘—‘Lmaz  70  (34)  Table XIII. Mean u values for the raw data and best-fit equations of wing movements on ground effect. Data set Pa 1 Pa 2 Pa 3  Raw data 0.38 0.29 0.29  Best-fit 0.38 0.29 0.29  Po 1 Po 2 Po 3  0.20 0.29 0.33  0.16 0.38 0.29  Rn Rn Rn Rn Rn Rn Rn Rn  1 2 3 5 6 7 8 9  0.45 0.38 0.17 0.38 0.45 0.38 0.45 0.38  0.45 0.38 0.17 0.15 0.16 0.45 0.57 0.38  Hr 1 Hr 2  0.57 0.76  0.76 0.76  71  Figure 19. Raw data and best fit, and incurred GE for Pa 1 Panels a (raw data) and d (best fit) represent wing movement through time and space seen from the root towards the wingtip. Time goes from left to right along the X axis, the position of the different wing segments go ‘into the page” along the Z axis from body (front) to wingtip (back), height of the wing increases from bottom to top of the page along the Y axis. Panels b (raw data) and e (best fit) represent the us experienced. The X axis is time of flight in s, u is on the Y axis. Panels c (raw data) 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 axis represents the h/b ratios, and the Y axis plots u. .  d  a 0  0 Lq 0  )C I0  0 c’J  0  00.0  0.1  0.2  0.3  Time s  0.5  0.4  0.6  0  0  C  0  \  .1;  \  C  0  00.0  \  0.2  0.4 0.6 0.8  1.0  1.2  1.4  1.6  000  0.2 0.4 0.6  0.8  h/b  hJb  72  1.0  1.2 1.4  1.6  Figure 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 encoun tered is the solid line segment. The dashed line represents possible us and + a for the sequence. The X axis represents the h/b ratios, and the Y axis plots u.  Palgt  Pal 0  \  a) 0  0  \  \  \  \  \  (‘S  c  0  . 0 a  0.4 0.6  0.2  1.0  0.8  00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 h/b  1.2 1.4 1.6  h/b  Pa8gt  Pa8  o  0  \  \  Cr1  CD  \ C)  0)  \  0  o 0 a 0  0.2  0.4  0.6 0.8  1.0  1.2  1.4  0  .1;  \  Pa99gt \  \  1.2 1.4  1.6  \  CD  \  c:;  \  .  \ C..J  (‘S  a  - .—---  —.  —  0  0  000  1.0  Pa99  0  \  0.8  h/b  \ \  0.2 0.4 0.6  00.0  1.6  h/b  0.2  0.4 0.6 0.8 1.0 h/b  1.2  1.4 1.6  00.0  0.2 0.4 0.6  73  0.8 1.0 h/b  1.2  1.4 1.6  where S is the wing area, arLd CLmz is the maximum lift coefficient, assumed to have a value of 1.5 (Pennycuick 1975). , related to the wing span of the dissected double-crested 2 S is the wing area in cormorants by the regression equation: S = 0.6412b  —  0.006714  (35)  ) = 26.3600 and p = 0.0068). Based on both apparent wing span (bapp) 4 2 = 0.931 and F(l, (r and its calculated S, Vsaii can be recalculated. The power curves IGE are calculated with the bapp corresponding to the calculated  a.  Figure 21 shows the power curves IGE and OGE and their respective Pds, using an interference coefficient o = 0.29. Observe that ICE Vgtaii=Vmp. Table XIV shows the characteristic speeds of the double-crested cormorant ICE and OGE.  Conclusions  Analysis of the metabolic and aerodynamic components of the power curve show that total power consumption will vary by  5% during the cormorants breeding season. Also  2 and increasing bapp, the apparent wing GE reduces power consumption by reducing D span, consequently decreasing  tal1,  Vmp, and Vmr.  The effect of the energy savings  reflect on the foraging strategies of the cormorants as shown in chapter 5.  74  and Find curves for the double-crested cormorant. The dashed lines represent power consumption ICE; solid lines represent power consumption OGE. Figure 21.  C)  / /  Ptot,OGE  / / / / / / / / / / I I / F I /  C  Ptot,.  Pind,IGE N. S. N.  S  -  0  _7  --  10  5  V(m/s)  75  --  -1------------  15  I  20  Table XIV. Characteristic speeds of double-crested cormorantbased on anatomical characteristics of dissected birds. Speed 1 ms  Month May  Jun  Jul  Aug  Sept  out of Ground effect 11.1 11.1 Vmp 15.4 15.4 Vmr  11.1 15.4  11.1 15.4  11.1 15.4  11.1 15.4  in Ground effect 9.7 9.7 V,, 14.0 14.0 Vmr  9.7 14.0  9.7 14.0  9.7 14.0  9.7 14.0  Apr  76  Chapter 5. Ground effect in flapping flight. Introduction Energy savings during ICE flight produce a downward displacement of the power curve and a change in its shape (Fig. 21). All the birds studied here: double-crested cormorant (Phalacrocorax auritu.s), brown pelican (Pelecarus occidenialis), barn swallow (Hirundo rzLstica), and black skimmer (Rynchops niger) utilise GE but under different circumstances and for different reasons. This chapter considers GE in the daily energy balance (DEB) of the double-crested cormorant in detail, summarizes the aerodynamics of GE for the four species, and concludes with a general discussion of the use of GE in flapping flight. Table XIII, chapter 3 (Preliminary Statistical Analysis) and Appendix A coefficients is different for different species. The value of  indicates that the range of and W,  a  Q, b, and Ap determine the shape of the power curve and the energy saved by the  bird. These savings have direct consequences on the daily energy balance (DEB) of the birds, as shown here. Cheverton et al. (1985) state that “in order to construct an optimality model of behaviour, one has to identify constraints, and to identify constraints one has to know something about the mechanisms controlling behaviour. Thus optimality modelling implies a knowledge of mechanisms”  .  Most studies concerning optimal foraging theory and daily  energy balances (DEBs) of birds and other flying animals have assumed that the energetic cost of flying can be treated as a constant (e.g. Bryant and Westerterp 1980, Stalmaster and Gessaman 1984, Westerterp and Bryant 1984, Cheverton e a?. 1985, and Leopold ei a?.  1985). This assumption may not hold true in nature and its bases can be evaluated  under 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 either 77  an ornithodolite (Pennycuick, 1982a) or a Doppler radar unit (Schnell 1965, 1974; Schnell and Hellack 1978, 1979; Kolotylo 1989; Blake et al. 1990). DEB (Blake 1985) is the ratio of the energy available to an animal from foraging to its energy expenses. Some workers have 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, and nestling rearing periods using time budgets for the different activities, estimating flight speeds 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 black skimmer with a kinematic and aerodynamic analysis of its flight ICE. Flight speed was calculated 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 considering the energy costs of flight and other activities during the reproductive season, taking into account the effect of GE in the DEE He predicted flight speeds IGE and OGE at which the 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 skimmer incorporate the flight speed and its associated cost. Their method lacks flexibility when calculating the DEB, since they deal with only the average speed. Blake (1985) predicted the 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 the birds were observed flying (e.g. Kolotylo 1989, Blake e l. 1990). Even when flight speeds and their associated costs are known, the construction of a DEB or the proposal of an optimal foraging strategy requires careful consideration of the biomechanical constraints. Flight is a metabolically expensive activity, varying with the speed, load, and wind conditions. I overcame these limitations by constructing DEBs that use the range of observed flight speeds and associated energy costs for the double-crested cormorants at Mandarte Island.  This approach predicts flight and feeding behaviours  under which the birds can maintain their DEB. 78  the  to , and increases the lift (L) on a wing flying close (D ) GE reduces induced drag 1 s both minimum power (Vmp) ground (see chapter 4). As a consequence GE decrease  all cost of flight. These reductions and maximum range (Vmr) speeds and reduces the over and Vmr) can translate into ds both in the cost of flight and on the characteristic spee (Vmp ested cormorants can fly slower than the two major foraging strategies. ICE the double-cr cost, or they can fly at a given high optimal predicted speeds OGE at a greatly reduced r speed OGE. Also, due to the increase speed IGE for the same cost than flying at a lowe r load of food back to the nest relative in L generated by GE, the birds could carry a large to OGE at the same speed.  time  tructed, where the costs and the Here a DEB for the double-crested cormorant is cons as maintenance, reproduction, spent flying are major components. Other costs such  gy are taken from previous studies incubation, and chick rearing, and the sources of ener Robertson 1971; Dunn 1973, 1975, on these birds (Bartholomew 1942a,slb; van Tets 1959; g 1973). 1976; Henneman 1983), or of birds in general (Kin le-crested cormorants at Mandarte The present knowledge of needs and habits of doub in the DEB and foraging strategy Island leaves, for the purpose of this thesis, two areas cost of flight and the cost of foraging of the double-crested cormorant unexplored. The ductive season fly between the nest (diving). Double-crested cormorants during the repro the foraging site are done on an empty and the foraging site. Flights from the nest to a loaded one. The changes in weight stomach, whilst flights back to the nest are done with be reflected in changes in flight strategy of the bird whilst flying from and to the nest could t flying. As it will be shown in this that could optimise the amount of energy or time spen Island seem to have a wide variety of chapter, the double-crested cormorants at Mandarte d make use of them to meet their DEBs. speeds and load capabilities available, and coul site when feeding their young, they Although the birds fly to and from the foraging fish to pass and then dry their plumage. search for bottom fish or wait for schools of 79  This makes time spent flying to and from the nest an important variable in their foraging strategy. The last important consideration for the DEB and foraging strategy of the double aested 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 left over after having taken into account all other known energetic expenditures. Assuming all other costs remain constant, the amount of energy left for foraging depends on the amount of energy spent flying. Here it is assumed that adult double-crested cormorants carry a load of 0.3 kg of fish per trip back to the nest, which is within the boundaries of loads reported and weight of stomach contents found for cormorants (Robertson 1971, Dunn 1973). I will assume that the birds can vary the number of trips between Mandarte Island and Active Pass from 1 to 8 per day. Under these assumptions a larger number of trips increases the total amount of food (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 presented in Table XI, chapter 4 and used here.  Reproductive Costs. Double-crested cormorants are a monogamous species in which both parents share incubation and chick feeding duties (Lewis 1929). Birds that establish a nest incur the costs of reproduction.  80  rants. Cost of gonadal growth in male arid female double-crested cormo uction by the male to be negli.. King (1973) considers the physiological cost of reprod not considered here. The female, gible (0.04 % of BMR) and for this reason this cost is uctive season. King (1973) however, must &st develop gonads for the oncoming reprod in quail and estimates establishes a cost of maximal growth rate of an ovary at .072W that “it is questionable that that such cost will not exceed 10% of BMR. He further states ]” (King 1973 p.87). sexual activation is a significant caloric burden [for the female  Cost of egg production in the female. l growth. Although “the Egg production is a more expensive activity that gonada ncy of synthesis combined assumptions regarding caloric content of an egg and the efficie it possible to estimate the total with data on average egg weight and clutch size make eggs, there is no simple way to h energy requirements for production of an egg or a dutc of the laying of the clutch, or the estimate the temporal cause of energy expenditure daring g concurrently “(King 1973). peak energy required when several ovarian follicles are growin for one egg as Nevertheless King (1973) assumes a peak daily expenditure 2G/p  Wpeak  (36)  where C = Joule/egg, and p period of the cycle in days. kg (Lewis 1929) (n=50, The average mass of a double-crested cormorant egg is 0.0465 an egg mass of the double-crested range 0.033.5-0.050 kg), whereas van Tets (1959) found kg (n=143). Assuming the caloric cormorants at Mandarte Island with a mean of 0.040 and assuming a conversion efficiency of 0.77 (King 1973), value of an egg to be 4.4kJ a typical size 5.7lkJ.g for an egg. The cost of producing 4 eggs, the cost of production is 1 rte Island (van Tets 1959, Robertson brood for the double-crested cormorants in Manda and 0.046 kg egg, respectively. 1971) varies between 0.81 and 0.83 W for a 0.040 81  Cost of incubation.  both  No generalisations can be made of the energetic costs of incubating eggs due to the variation in methodologies and measurement techniques and to the changes in  cost induced by microclimate, dutch mass, nest construction and insulation, and adult ues physiology and behaviour (Walsberg 1983). Grant (1984) describes a variety of techniq s. used to measure energy spent during the incubation period and discusses the finding ss and While some seabirds like the macaroni and tockhopper penguins, the laysan albatro ss had the benin petrel had incubation costs lower than resting levels, the wandering albatro an kestrel, barn a higher cost. Also measurements within the thermoneutrai zone for americ level. owl, great tit, starling, and zebra finch showed no cost of incubation above resting the Given these findings and the fact that double-crested cormorants feed regularly during iture to incubation period, we will assume that incubation adds no extra energy expend the incubating parent. Cost of thick rearing. from The double-crested cormorant is an aitriciai bird. Chicks are fed by their parents described birth to about 50 days of age (Robertson 1971). The growth of the chicks can be Robertson by fitting a logistic carve to the growth measurements of the chicks (Dunn 1975, peak in energy 1971), with a peak energy intake around 25 days of age (Dunn 1975). This back to each consumption is reflected in the amount of food that the parent must bring 1 day’ for this age, which will chick. Dunn (1973) gives a peak figure of 550g chick cormorant rearing provide the chick with 29W. Given what is known about double-crested assumed that: habits (Lewis 1929, van Tets 1959, Dunn 1973, Robertson 1971), it can be in Mandarte both parents provide an equal share of the feeding effort, a common broods r of birds in Island consists of 3 chicks (van Tets 1959, Robertson 1971 ), and the numbe With the above such brood that reach the fledging period is over 90% (Robertson 1971). per day or 5SWof assumptions and requirements each parent must supply 1.1 kg of food .  82  its maintenance and foraging energy during the peak period, in addition to providing for expenses.  Energy Input. exclusively on fish. Robertson The double-crested cormorants of Mandarte Island feed rearing capabilities of double(1974) during a 3 year study at Mandarte Island on the brood pelagicus) gathered data on the crested cormorants and pelagic cormorants (Phalo.crocoraz . He found that most of the type and quantities of fish ingested by the growing chicks ing that double-crested prey species are characteristic of the littoral benthic zone, indicat rn coast of B.C., contrary to the cormorants are bottom dweller feeders along the southe -crested cormorants as feeding conclusions of Ainley et a!. (1981) who characterise double not on, flat bottoms. Table on schooling fish that occur from the surface to near, but found fish remnants in doubleXV, based on Robertson (1974), shows the most commonly crested cormorant chick regurgit ations. tic value of the fish as Dunn (1975), using a bomb calorimeter, calculated the energe to estimate 1 of fresh weight fish. By employing a bomb calorimeter 4.75 x 106 Joziles kg digestive efficiency of 0.82 or the energy content of the excreta she also established a estimated that an adult double3.9 x 106 Jo’u.les kg’ of fish ingested. Dunn (1973) per day. Considering that the crested cormorants eats between 20 and 30% of their weight d that the adult double-crested dissected cormorants weighted 1.88kg, it will be assume day. These assumption translates to cormorants consume at least 25% of their weight per .  . 10 J less than 1.76 x 6 a minimum of 0.470kg of fish per day, providing no  83  Table XV. Prey species fed to nestling doublecrested cormorant, based on chick regurgitation data from Robertson (1971). Species  % by number  % by weight  penpoint gunnel crescent gunnel pacific sandlance shiner seaperch snake prickleback others  23.8 22.8 20.5 15.5 11.5 5.9 100  35.7 15.9 4.6 20.5 10.2 13.1 100  84  Field Observations. Observations were carried out during 28-31 August 1987 and 29-31 August 1988 at the 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 nesting after first failures. In the summer of 1987 either no chicks hatched from the second dutch or all 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 corrnorants chicks were seen in late September 1988. All observation at Mandarte Island and surrounding area were done under sunny conditions 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 population history see Drent ci aL, (1964). Flight Records Bird flight speeds were measured with the Doppler radar gun with the methods described in chapter 2, Materials and Methods. Double-crested cormorants flying over the surface of the water spent most of their time near the surface of the water and on occasions at heights <5  in.  Flights IGE and OGE were recorded as the double-crested  cormorants flew from Mandarte Island to the feeding grounds in the morning or as they returned 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 sample size was large (N=224). Two way ANOVA was used to determine if the recorded speeds changed from year to year and to determine any differences in the mean speeds ICE and OGE. The results of the analysis are shown in Table XX. The speeds were not significantly 85  different from year to year, but there was a statiticafly significant difference between speeds IGE and OGE(Fig. 22) The non-overlapping notches in the box-and-whisker plots show a significant difference at c = 0.05 between the median speeds IGE and OGE. Power curves and Flight Records for the double-crested cormorants at Mandarte Island. Figure 22 shows that the flight speeds at which the double-crested cormorants were flying near Mandarte Island both IGE and OGE occur over a wide range. OGE maximum recorded speed is > 2.8 times higher than the minimum, and IGE the maximium is > 2.5 times the minimum. Figure 23 shows the predicted power consumtion for loaded and unloaded flight ICE and OGE. Panels a and c show the power consumed by an unloaded double-crested cormorant (i.e.one with an empty stomach). Panels b and d show the power consumed by a double-crested cormorant IGE and OGE, respectively. The box-and-whisker plots are the same as those in Figure 22 for flights IGE and OGE and correspond to the power curve presented in the panel. Note that the power curves are not very steep in their ascending arms. The ICE curve was calculated utilizing b. This and the reduction of I), cause a slowly increasing curve at the lower speeds. the observed speeds seem to correspond to the flatter part of the curve, and the median observed speed is slightly lower than the calculated 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 be compared to the power associated with Vmp and Vmr. To make this comparison a flight speed and its corresponding aerodynamical power are divided by one of the characteristic speeds, either Vmp or Vmr, and its associated aerodynamical power. The result is a “penalty curve” for each characteristic speed. Penalty curves are unit free and index the speeds and 86  Table XVI. Stem-and-leaf table of the dis , OGE 1 tribution of flight speeds, in ms at Mandarte Lsland for the double-crested cormorant in August 1987. The numbers on the leftmost column represent the speed class. The numbers, on the right represent the number of readings for each speed class and the appropriate decimal. N  =  111 Median  Decimal 6 7 8 9 10 11 12 13 14 15 16  =  10 Quartiles  =  point is at the space 0000 000000000000000000 000000000000000 000000 000000000000000000000 0000000000000000 000000000000000000 000000 000 000  87  8, 12  Table XVII. Distribution of flight speeds, , IGE at Mandarte Island for the 1 in ms double-crested cormorant in August 1987. For explanation see table XVI. N  =  64 Median  Decimal 7 8 9 10 11 12 13 14  =  11 Quartiles  point is at the space 0000 0000 0000000 00000000000000 000000000 000000000000 00000000 0000  88  10, 12  , 1 Table XVIII. Distribution of flight speeds, ms d double-creste the for OGE at Mandarte Island cormorant in August 1988. For explanation see table XVI. N  =  34 Median  9.75 Quartiles  Decimal point is at the space 9 6 22224579 7 012 8 01337899 9 012267 10 27 II 14 12 25 13 12 14  89  7.9, 10.7  Table XIX. Distribution of flight speeds, in , imder the IGE at Mandarte Island 1 m•s for the double-crested cormorant in August 1988. For explanation see table XVI. N  =  16 Median  Decimal 7 8 9 10 11 12 13 14 15 16  11.75 Quartiles  point is at the space 2 4 177 47 4 1 037 34 2 0  90  =  9.7, 14  Table XX. Two-way AN OVA for the Eight speeds of double-crested cor morants recorded at Mandarte Island during the summers of 1987 and 1988. Source: grand mean Year  n 4  Mean 10.60  sd 0.930  se 0.465  Source: Year Year 87 88 Factor: Levels: Type:  n 2 2 Flight type 2 Random  Mean 10.44 10.76 Year 2 Within  sd 0.612 1.457 Speed 4 Data  se 0.433 1.031  Source  SS  cu  MS  F  p  mean F/ Year YF/  449.3972 2.1419 0.0992 0.3570  1 1 1 1  449.3972 2.1419 0.0992 0.3570  209.816  0.044  0.278  0.691  91  *  Figure 22. Box-and-whisker plots of IGE and OGE speeds of the double-crested cormorants at Mandarte Island. The top and bottom horizontal lines represent the upper and lower ranges, respectively, of the recorded flight speeds. The bottom of the box represents the lower (25%) quartile, the dotted line the median, and the top of the box the third quartile (75%). The notches give the 95% confidence interval for the median. Box width is proportional to the square root of sample size.  GD  CD  1  Cl)  >  C  CD  OGE  IGE 92  rant IGE Figure 23. Cost of flight and speed range for the double-crested cormo and OGE with an empty (uld) stomach or a full load (id).  In ground effect (unloaded)  Out of ground effect(unloaded  It) C.)  C.,  —  It)  It) C’j C)  C)  o  Q_  0 C%  c.’1 It)  It)  6  8  10  14  6  18  8  10  14  18  V rn/s  V rn/s  Out of ground effect (loaded)  In ground effect (loaded)  If) C.)  d  C., It)  c\J  c’J C)  C)  o -  0  ‘  c%J  C’  :  If)  6  8  10  14  6  18  8  10  14 V rn’s  V rn/s  93  18  their corresponding aerodynamic powers to the selected characteristic speed. Figure 24 is a group of penalty curves for the double-crested cormorants at Mandarte Island for flights with and without loads to the nest. From the penalty curves an understanding of the range of the observed speeds can be at least partiafly developed. None of the observed speeds seem to be 1.3 times more expensive than flight at V,, or 1.2 times more expensive than Vmr. It seems therefore that the double-crested cormorants have a wide range of speeds at which they are able to fly without having to incur in a large energy expenditure when compared to the power associated with the characteristic aerodynamic speeds Vmp and Vmr, flight IGE can be 20% cheaper at the lower speed range and at the observed median speeds.  Cost of Transport Cost of Transport (CT) was defined by Tucker (1970) as the ratio of metabolic rate to the product of speed and body weight, and is expressed as:  CT=  (37)  1 0 is the total power spent flying at any given speed, V is the velocity, in ms where P and W is the body weight. It is a dimensionless index that allows direct comparison of the 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 comparison of travelling with or without a load IGE and OGE. Figure 25 shows the CT curves for the double-crested cormorants.  CT is always a minimum at Vmr. Figure 25 shows that changes in CT are higher when the animal is loaded, similar for most speeds ICE, at a minimum for unloaded flights ICE, and are relatively high at the lower speeds. The decrease of Cost of Transport ICE is associated with the reduction in D and the increase in bapp. If the birds flight strategy is to minimise Cost of Transport thesy should be observed flying near Vmr. 94  Figure 24. Penalty curves for the double-crested cormorant IGE and OGE. In a penalty curve the point with the coordinates (1,1) represents the characteristic aerodynamical speed (Vmp or Vmr) and its associated power. Any point along the X axis, the speed index, will indicate how much lower or higher the speed is relative to the characteristic speed. On the Y axis, the power index, a Y < 1 corresponds to an energy expenditure smaller than the energy associated with the characteristic speed of the given penalty curve. The case of Y < 1 is, by definition, non existent for the penalty curve associated with Vmp. When Y > 1 the power index gives an indication of how much higher the power is than the power associated with the characteristic speed. The solid lines represent costs with respect to Vmp the dashed lines represent costs with respect to Vmr. a and b are for empty stomachs, c and d for full stomachs.  In ground effect no load  No ground effect no load 0  -ø  LC)  C’J 0 Cu  0 Cu  ‘4,  0.0  0.5  1.0  1.5  2.0  1.0  0.0  2.0  V ratio  V ratio  No ground effect loaded  In ground effect loaded  0 -F  to  I  c’.i  0 Cu  0 Cu  a)  ‘4, 0  0  CD ‘4,  0.0  0.5  1.0  1.5  0  2.0  1  2 V ratio  V ratio  95  3  Figure 25. Cost of Transport for the double-crested cormorant on an empty ), 1 stomach and carrying a 0.3 kg load both ICE and OGE. X axis, velocity (m.s Y axis, Cost of Transport  loaded  0  c’J 0  0  T  6  8  10  14  12 V rn/s 96  16  18  20  Daily Energy Balance. orant raising young occurs The peak energy demand period on a double-crested corm rearing in this chapter for more when the chicks are 25 days old (see section Cost of chick g at their maximal rate during details). Nestling double-crested cormorants can be growin t in July will be considered. ther July or September. A DEB for a chick rearing adul double-crested cormorants at Table XXI presents some of the measured speeds of the closest 100 seconds, it takes the Mandarte Island, the approximate time, rounded to the est feeding grounds at Active Pass birds to reach the commonly used and probably furth and the power it takes to fly at that 21 km away, assuming constant speed and no wind, stomach (0.3 kg). The calculation speed both ICE and OCE on an empty and loaded into account the differences in of the total daily energy expenditure by the birds takes ers the length of the daylight maintenance rates between day and night and also consid by the birds on their daily hours in each month. To calculate the actual energy spent ated with Hennemann’s (1983) activities the maintenance rates for day and night are estim day and night lengths of the equations (13), night, respectively. For this calculations the the Canadian Atmospheric months during the reproductive season were acquired from and night lengths in seconds on Environmental Service. Table XXII presents the day . This date was chosen arbitrarily the l5 day of each month of the reproductive season month. These times along with as representative of the night and day lengths of that 4 are used to compute the nightly the temperature data presented in Table X of chapter during flight and the maintenance maintenance costs (29.8kJ), the total power consumed the non-flying periods of the energy consumed by the double-crested cormorants during ively of the maintenance rate (Pmet). day. These periods are assumed to consist exclus i.e. diving. There are no estimates of This estimate leaves out the energy spent foraging rants whilst foraging, and the energy the energy consumed by the double-crested cormo  97  available for this activity can be obtained from the difference between the energy required by all other activities and the maximum recorded energy input. Figure 26 shows a series of DEBs for the double-crested cormorants at Mandarte Island during the month of July. For a bird to have an adequate supply of energy its total expenditures must be below the horizontal line at 1.0. Only the birds that make 3 or more trips have enough energy to account for all expenses, including foraging. If energy requirements 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 27 shows the total food (in kg of sh) required and the amount of food gathered with different number of trips. Robertson (1971) established that at the height of the double-crested cormorant chicks growth season the parents travel between 3 and 4 times per day between the nest and the feeding site. The minimum number of trips recorded might be determined by the stomach capacity of the birds, or their available aerodynamicai power. Dunn (1973) estimates the stomach capacity to be 20 to 30% of the weight of the bird or 0.36 to 0.54 kg for the cormorants used in this study. The number of trips that an adult double-crested cormorant can take between the nest 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 0.3 kg of fish per trip, based on load capacity (above, and Fig 27). The energy left after flying to and from the nest should leave enough energy to carry out other activities such as foraging and feeding the chicks. ii) A maximum time an adult double-crested cormorant can spend in all of its diurnal activities determined by the hours of daylight. Time spent flying to the feeding site and back to the nest is time not spent doing other activities. 98  c  ø c  00 1Q tn  cD  c, c c  c.i  CL  j0 eni  L J  I*  -.L  i--)L’3  c  t,  en  CD  d  CD  CD  0  CD  .  H3  tf2  ‘  CD  Cl)  CD  CD  -a  CD  cl)  CD  0  CD  CD  CD  r,)  CD  e-  CD  Table XXII. Day and night durations for the middle of the month for the reproductive pe riod of the double-crested cormorants (Cana dian Atmospheric Environmental Service). Month April 15 May 15 June 15 July 15 August 15 September 15  Day length  Night length  8  S  49320 54960 58880 56700 51720 45360  37080 31440 27520 29700 34680 41040  100  at Mandarte Island during Figure 26. DEBs for the double-crested cormorants presents the ratio on July. The X axis shows fight speeds, the left vertical axis number of foraging trips energy gathered (E) to energy spent (EotL) for a different the solid lines flights to Active Pass. The dashed lines represent flights OGE and The vertical axis on the right assumes ICE. A value of 1.0 indicates numbers above each pair energy expenditures are double of those calculated. The of lines indicates the number of trips taken.  6  1 Lf)  -4  2 uJ  3 4 LC)  8  -o I  I  I  I  I  6  8  10  12  14  Vm/s  101  I  16  18  20  Figure 27. Energy requirements for the double-crested cormorants during the month of July expressed in kg of fish. The X axis shows flight speeds, the Y axis presents the daily amount of fish required. The horizontal lines indicate the total amount of food gathered during the number of trips shown in right margin assuming 0.3 kg fish per trip. The number-lines indicate intake of fish requirements for total number of trips per day, OGE (above) IGE (below). Any number-line above its corresponding horizontal line indicates an energy deficit for the day.  8  a,  c3) -  o  0  oc\J  40  2  1 I  I  6  8  10  I  I  I  I  I  12  14  16  18  20  Vm/s  102  Figare 28 shows the proportion of daylight spent by the bird flying if it commuted at day different speeds and for different number of trips. TI the birds were to fy 8 times a to Active Pass it would consume 0.5 to 0.98 of the total daylight hours. Considering that feeding of the chicks is shared by both parents, less than 0.5 of the daylight should be spent by each parent travelling to and from the foraging tes. The longer a double-crested cormorant spends at a rich feeding place, the greater the chance of it encountering food, thus, again, minimising the time spent flying to and from the foraging site to the nest increases the time the double-crested cormorant can spend foraging. It seems likely then, that time spent flying is one of the limiting factors for the . double-crested cormorants at Mandarte Island at the peak period of the chicks’ growth  103  Figure 28. Proportion of daylight spent travelling between Mandarte Island and Active Pass. The X axis indicates flight speed, the Y axis the proportion of daylight spent flying. The lines indicate proportion of time spent flying for the shown number of trips.  1  0:!  o  0) >  Cl) V 0  o tc 0  0  0  C  q C  6  8  10  12  14  Vm/s  104  16  18  20  Foraging radius sites. DoubleThe availability of food for the young might restrict the choice of nest as far as Active Pass crested cormorants from Mandarte Island have been observed to fly should be enough (21 kin) to obtain food for their young. In order to reach the site there Pennycuick (1979), energy left over from the previous day to reach this site. Following foraging radius (FR) is:  FR=  where  j is  Pmet, and  iv D(Pmet +  +  PflOC  the energy available (J), V flight speed  Pcjjcç)  + 2kV  (38)  D total time not spent flying (s),  the energy spent in maintenance day and night, respectively (W), Ph1k  maintenance energy of the chicks (W), and  the cost of moving a unit distance (J/m).  ed speeds assuming the The FR shown in Figure 29 were calculated for the range of observ birds fly 1-8 foraging trips the previous day. te to supply It was shown that I or 2 feeding trips per parent per day are not adequa me if the amount of food the total energy needed (Fig. 27). This restriction could be overco of the double-crested per trip brought back to the nest was increased. Field observations daily number of trips cormorants at Mandarte Island Robertson (1971) indicate that the been shown that the per parent is 3 or 4, which corroborates my prediction. It has also left for other activities upper number of trips per day is constrained by the amount of time such as feeding the chicks, diving, thermoregulation after dives, etc. other times of the From the model employed here flight and foraging behaviours for demands of feeding chicks year can be predicted. Outside the nesting season the energy be those of thermoregu disappear. Under those circumstances the higher demands could other activities were known lation during the winter, for example. TI the costs of these and 105  I-a  0  3  o  0)  -&  o  a)  -  -  -  t’b3 P1.3 P13 F’I I’,  •  -  -  -  -.  -. -.  = —  —  _a  -a  -a ..a  —  ..a  K  -a —  -  -  -a  (f)  -o  (V  g  1.  .-  ‘.b  V0-4  (0)  0) a,  a,  3’4’  cn  (0) 0 (03 (0) Ca)  (03 (0)  (43 (6)  .-.  (4.) (.4.3 (4) (4) (4.) (A.)  (.  (.U (A.)  (.3.3  (.1.) (.1.,  C.t.3 (.Z.3  (0) P03 P0)-I  (4) (0) (03 P0.) (0)  N)) N), Pa, (4) Pa)  P4) P43 ro,  b  4..b.  .  ( ( 3  ()  (X.3 C.X3  I  ‘4  (.X.) (3W C.3W  (,X.)  N)  rso., fl3 P43  3 3 )3 p13 P03 N)) P43  .  C,3W (.X.3  C.X..3 (.3W (.3W (.3W  50 I  (1)  03  90.  44 44. 94  44 44  V  0 0  0)  0)  cocCi 0(0 003 0)0) 03CC) coo, CXC)  coo 0)0 0303 00  0) CD (00 00) 0303 coo, 0)03  °‘0 00  (0 00 03 03 00 0)0 03 0  COW  a, a,  0)03  003  00  00  003 00  q  ,  Q  Cl)  Ci)  Ct>  ‘-C  C  ,  ‘-C  ‘  Ct>  Ci,  4  rj  (b  03 00 0)0) (0 0) 00) 0) 0) 0) 0)  ti  -  ‘-l  ‘-1  8  Cti  e4-  ‘-C  e  o  ,  .  CD  150  ti  .  PP  0)  0)  100 I  Foraging radius km  (e.g. Henneman 1983), the total energy that must be gathered could be predicted. Under less restrictive drcumsta.nces the number of trips, speeds, and time spent flying might not be restrictive. Under these circumstances the double-crested cormorants should be observed flying at aerodynamically optimal speeds (Vmp and Vmr).  Conclusions  It can be concluded that 1 or 2 trips per day to Active Pass yield to little energy for the cormorants to meet the DEB. On the other hand 8 trips per day use most of the available daylight time. By constructing DEBs of the double-crested cormorants during the breeding season that include food intake and known energy expenditures I demonstrate that the cormorants incur substantial time and energy savings whilst traveling ICE to and from the nest, thus showing the importance of GE to their DEB.  107  Chapter 6. General Discussion Introduction  Aerodynamic energy savings obtained IGE will impact on the DEB of a bird in proportion to flight time IGE. The birds chosen for this study use GE under a variety of circumstances as shown if Table I, chapter 1. This chapter will summarize the methods on this work used to study GE in flapping flight for the double-crested cormorant, look at the aerodynamic energy savings in GE and relate them to the flight ecology of the four birds species chosen for this study. I have shown that detailed analysis of flapping flight IGE can predict fight strate gies that a double-crested cormorant should follow during the breeding season if it is to maximise time spent foraging and at the nest, and reduce the overall cost of flight. The analysis consisted of three parts: description of wing movements, construction of power curves IGE and OGE, and the role of GE in the DEB. To obtain an accurate description of the vertical wing movement during flapping fight IGE I employed three methods, circular linear regression, periodic ANOVA, and Fourier transforms. The first two methods proved to be statistically significant and easy to manipulate. Fourier transforms, although accurate, provided more detailed than neccesary for the purposes of my analysis. The work on power consumption during flight took into account aerodynamic and metabolic costs, assessed the reduction that GE produces on 811 V and the apparent increase in wing span (b) with its consequent reduction in .  108  Aerodynamics of GE acteristic speeds, power ratios, and Figures 30 to 33 show the power curves, char lated ãs of Table XIII, chapter 3. A penalty curves for each species based on the calcu power consumptions can be seen in reduction in Vmp and Vmr and their corresponding show that the overall savings decrease Figures 30 to 33 and Table XXIII. All Figures est calculated speeds there are energy ‘with increasing speed. Nonetheless even at the high and brown pelican (Fig. 31). savings for the double-crested cormorant (Fig. 30)  el b in Figs. 30 to 33) is a function The ratio in power consumed IGE and OGE (pan power curves of the double-crested of a and the shape of the power curve. The U-shaped a) give rise to sigmoid power ratios (b in cormorant (Fig. 30 a) and brown pelican (Fig. 31 all speeds. The J-shaped power curves of both Figs.) which reflect power savings IGE at . 33 a) give rise to rapidly accelerating the barn swallow (Fig. 32 a) and black skimmer (Fig r flight speeds. The penalty curves (c curves that reflect large savings ICE only at the lowe le-crested cormorant and the brown pelican in Figs. 30 to 33) show that for both the doub t at both V and Vmr OGE. For the barn IGE flight at most speeds is cheaper than fligh 1 than flying for speeds of up to 8 ms swallow and black skimmer it is cheaper to fly ICE of flight speeds reported by Withers and at either Vmp or Vmr OGE i.e. the lower range Timko (1977) and Blake ci a!. (1990).  109  Figure 30. Power and penalty curves 1GB and 0GB, and characteristic speeds for the double-crested cormorant (mass=1.8 kg). X axis, speed ( m.s’). Panel a shows the power curves 1GB and 0GB top and bottom, respectively. Power curves both 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 speeds 1GB and OGE. Symbols as in a, Vmp and Vmr 0GB. Panel c presents penalty curves for 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 than travel at the corresponding characteristic speed. .  Cr)  a  b co  0  o 5  10  15  20  6  V (mis)  C  0 /  a) 0  0  ‘4, cD  6 8  12  16  12 Vm/s  q c%J  8  20  Vm/s 110  16  20  Figure 31. Power, penalty curves ICE and OGE and characteristic speeds for the brown pelican (mass=3.3 kg). See Figure 30 for explanation of curves.  b  a LU  CD  0 LU  0  o  cJ LC)  5  10  15  20  25  5  V (mis)  LC)  0 C,,  Li  10  15  15 Vmis  C  5  10  20  25  V rn/s  111  20  25  Figure 32. Power, penalty curves [GE and OGE and characteristic speeds for the barn swallow (mass=0.03 kg). See Figure 30 for explanation of curves.  Q  a  b  a) 0  0 LU  0  i0 G)  0 LU  0_c  —  c.J  0 CD 0  0  q  It. 0  0  02468  12  16  2  (0  C  4-.  LCI)  ccj  0  246810  6  8 10 V rn/s  V rn/sec  U)  4  14  Vrn/s  112  14  Figure 33. Power, penalty curves ICE and OGE and characteristic speeds for the black skimmer (mass= 0.36 kg). See Figure 30 for explanation of curves.  b Co  a Co  it)  b  0) LU  x  Q uJ  C’)  S28  C.j  it)  ‘  68810  1214  ‘  V(m/s)  0  Vm/s  (Y)  I 68 810  68 810  1214  Vm/s  113  1214  Ecology 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 importance of GE in the flight and DEB of a bird. The most important characteristic of flights IGE might be how much less expensive they are when compared to the power required to fly at 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 lifestyle of many birds excludes the use of GE. There can also be disadvantages to the reliance on GE such as time spent away from cover. TI far away visual reference points are used for orientation, GE is not a good flight strategy as these points disappear when  flying  close to  a surface. The shape of the curv both ICE and OGE and the corresponding savings for each bird can be used to gain some insight into the foraging and feeding behaviours with respect to CE. The barn swallow is not an obligate GE flyer, although it does sometimes come near the ground to feed (Kolotylo 1989, Blake e al. 1990, pers. ohs.). The utilisation of GE by the barn swallow at the speeds at which it has been observed foraging has no major impact in its energetic expenses (Fig. 34), and GE might be a consequence of feeding near the ground where a number of flying insects can be found and not necessarily an energy saving foraging behaviour. Barn swallows skim the water surface, and during this behaviour GE might be utilised to reduce  Vaiaii,  allowing the birds to reduce flight speed.  Black skinimers feed by submerging their lower mandible in the water whilst gliding without loss of altitude or flapping their wings (Blake 1983, 1985). GE presents an energy saving of 10—20% whilst foraging at the range of speeds reported by Withers and Tirako 1 due to GE might help the capture of prey whilst skimming. V (1977). The decrease in 8  114  Figure 34. DEBs of the barn swallow using GE for different proportions of the total time spent flying. X axis, speed (m.s’), Y as, proportion of energy gathered IGE. Box-and-whisker plot of speeds observed in the field.  c’Jj  Lr T  1 0  0  .5  LU  C  C  Q  to  a?  I  I  I  2  4  6  I  I  I  10  12  14  0  0  8 Vm/s  115  16  Both 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’ total mass so as to modify substantially their power curve and overall flight expenses. The major savings from GE are found at those speeds at which both birds have been observed foraging and not at a speed  >  Vmr at which they would be expected to fly to and from  the nest maximising energy intake (RA Norberg 1981). Both double-crested cormorants and brown pelicans save energy whilst flying ICE at most of the calculated and observed speeds. Both birds travel considerable distances to and from the nest and are known to carry large  ( 20% body weight)  loads (e.g. Robertson  1971 for the double-crested cormorant). Energy savings for the double-crested cormorant are in the order of 10—20%, and these savings accumuiate through the time spent travelling favouring a small number of trips at high speeds between the nest and the foraging site. A similar argument can be made for the brown pelican which is expected to travel to and from the nest in a similar fashion. In the cases of the double-crested cormorant and the brown pelican the shape of the power curves and their overall flight expenses are substantially affected by the load carried back to the nest. It has been shown in chapter 5 that the double-crested cormorant incurs substantial time and energy savings by travelling at high speeds (> 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 the four species. Reductions  iii  Vmp are larger than reductions in Vmr since the influence of GE  is inversely proportional to flight speed. The size of the changes is larger for the smaller species (barn swallow and black skimmer) than for the larger species. In more general terms it can be suggested that morphological and behavioural traits that determine the shape of the power curve will determine the extent of energy savings IGE at a given speed. It has been shown for the birds in this study that those with high A. and low  Q  (barn swallow and black skimmer) carrying light loads GE saves energy only 116  at the lower range of flight speeds. Neither barn swallow nor black skimmer travel to and from the nest IGE. On the other band birds with lower  and higher  Q like double-crested  cormorants and brown pelicans utilise GE over a larger range of speeds and travel ICE to and 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 of their 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 axe high.  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 reduce in birds as a function of the h/b ratio; the closer a bird is to the ground the less energy demanding takeoff will be.  Conclusions  This is the first study that details vertical wing movement and power consumption in order to assess the importance of GE in the DEB of the double-crested cormorant. It also considers the use of GE by brown pelicans, barn swallows, and black skimmers. These four species were classified according to morphological characters that influence the power curve (b,  .,,  and  Q).  This classification allowed me to divide the birds into those that  obtaind gniflcant energy savings from GE at all speeds even when carrying loads of 20% of their weight (double-crested cormorant, brown pelican), and those that benefit from GE only at the lower speeds and carry loads approz 1% body weight (barn swallow, black skimmer). Double-crested cormorants and barn swallows present extremes of morphology and feeding strategies. The cormorant has high to the nest. The swallow has low  Q,  high  ,  Q,  low A and carries large loads back  and carries light loads. As I have shown  these birds use GE under different conditions. Pigeon guillemots at Mandarte Island with 117  Table 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), brown pelican (B, 3.30 kg), black skimmer (C, 0.36 kg), and barn swallow (D, 0.03 kg).  Vmp A B C D  %  OGE  IGE  11.1 9.5 5.1 4.2  9.7 9.6 4.3 2.9  14 0.9 17 43  Pmp  %  OGE  IGE  16.3 21.5 1.3 0.2  12.5 14.6 1.0 0.9  30 47 30 70  118  Vmr  %  OGE  ICE  15.1 13.3 7.6 6.2  14.0 12.2 6.9 5.0  8 8 10 24  Pmr  %  OGE  ICE  18.7 25.1 1.5 0.2  14.8 16.1 1.2 0.1  26 55 28 64  intermediate characteristics (high  Q,  low A, and small loads) and short flights between  the nest and the foraging site should fly IGE at speeds close to those predicted by Ri Norberg’s 1982 model of maximum energy gain. This first attempt at the understanding the ecological significance of GE in flapping flight points at two areas that should be studied in more detail: 1. Accurate measurements of flight speeds accompanied by detailed analysis of flight behaviours, 2.  A detailed  aerodynamical account of GE in a wing with periodic changes in both geometry and height above the surface.  119  Appendix A Graphs of GE calculations for raw and best fit data  120  Figure 45. Raw data, best-:fit regression, GE ixcurred, and GE range forPa 2 For explanation see Figure 29.  d  a  Time s  Time s 0  \  C \  \  \ E0  \  \  \  (V 0 0  0  LO 0.2 0.4 0.6 0.8  1.0  1.2  1.4  1.6  °0.0 0.2 0.4 0.6  h/b  121  0.8 1.0 1.2 1.4 1.6 h/b  Figure 46. Raw data, best-fit For explanation see Figure 29.  regression,  GE incurred, and GE range for Pa 3.  d  a  CD 0 0 0  0  C’.J  U)  0  C U) C., 0  It,  CD  0  C  0  CD  o0.0  0.2  0.6  0.4  0.8  oQ.Q  0.4  Time s  Time s C  0  \  \  0 0  00.0  0.2  0.4 0.6 0.8  1.0  1.2  1.4 1.6  h/b  122  0.2 0.4 0.6  0.8  h/b  1.0  1.2  1.4  1.6  for Po 1 Figure 47. Raw data, best-fit regression, GE incurred, and GE range For explanation see Figure 29.  d  a  U,  c 0  u. 0 0  Ec t,) 0 U)  cJ 0  0  00.0  0.2  0.6 0.4 Time s  1.0  0.8  1\’ *•J1< 1 \1 0.6  0.4  0.2  00.0  Time  0.8  1.0  s  0  \  C  000  0.2 0.4  0.6 0.8 1.0 h/b  1.2  1.4  0  1.6  000  123  \  IF \  \  \  \  \  0.2 0.4 0.6  0.8 h/b  1.0  1.2  1.4  1.6  2. Figure 48. Raw data, best-fit regression, GE incurred, and GE range for Po For explanation see Figure 29.  a  0  0  d  0  0  00.0 0.2 0.4 0.6  124  0.8 1.0 bib  1.2 1.4 1.6  Figure 49. Raw data, best-fit regression, GE incurred, and GE range for Po 3. For explanation see Figure 29.  “V a  d  Time s C  0  0.2  0.4  0.6  0.8  hk  125  1.0  1.2  1.4  1.6  Figure 50. Raw data, best-fit regression, GE incurred, and GE range for Rn 1 For explanation see Figure 29.  a  d 0  0  0  o  C  F,-. 0 )0  C C’)  0 0  C  c’J 000  0.1  0.2  0.3  0.5  0.4  00.0  0.1  0.3  0.2  Time s  Time s 0•  P  0  •11.0 0.4 0.6  0.8 1.0 h/b  1.2  1.4  1.6  00.0  0.2  0.4 0.6  0.8  h/b  126  1.0  1.2  1.4  1.6  Figure 51. Raw data, best-fit regression, GE incurred, and GE range for Rn 2 For explanation see Figure 29.  a  d 0  0 0  E  EL  0  o c’J  0  0 —  °0.0  C\j  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 0.35  Time s  Time s 0  0  0  c  \  P \  0  c..J 0  0.2  h/b  127  0.4 0.6 0.8 hlb  1.0  1.2  1.4  1.6  0)  0  C)  p  p  0  to  -k  -a  r0  0)  p  0  jo  0.2  0.2  0.4  0.6  sigma  sigma 0.4 0.6  0.8  C)  —  0.8  1.0  1.0  Cl)  3 CD  zic’  p  p  sigma 0.10 0.15 0.20 0.25 0.30 0.35  ci  I  0  L  0  0  CD  oq  1p.1  -  0)  I’)  C  0)  p  C  )  o  0.8  0.8  sigma 0.4 0.6  sigma 0.4 0.6  0.2  0.2  F’  1.0  1.0  CD  01  0  0  0  Wj\)  I  C)  ‘-1  LrJ  0  C  0  C  1.  CD  ‘1  (D  Ii:  l,1  C  0  p  01  0  p  zl 301  zi  sigma 0.4 0.6  C3  •0)  0  0  0  p  0  0.2  0.2  0.6  0.4  0.6  sigma  0.4  sigma  0.8  0.8  1.0  1.0  0  0 •0’  0  30 Co C) Cl,  0 r%)  p  0 0  0.0  0.1  0.2  0.2  0.3  sigma  0.6  sigma 0.4  CD  0.4  0.8  0.5  1.0  I  C)  CD  C)  ei  C)  0  C,)  Ct,  o  -a  C  Figure 55. Raw data, best-fit regression, GE incurred, and GE range for Rn 7 For explanation see Figure 29.  a  d  0  0  0.0  0.2  0.4 0.6 Time s  0.8  1.0  .i.  131  Figure 56. Raw data, best-fit regression, GE incurred, and GE range for Rn 8 For explanation see Figure 29.  a  d  Time s  Time s  \ C  C  .i. a 00.0  hlb  132  0.2 0.4  0.6  0.8 1.0 hf  1.2  1.4  1.6  Figure 57. Raw data, best-fit regression, GE incurred, and GE range for Rn. 9. For explanation see Figure 29.  d  a 0  Time s  Time s c  Ii  00.0  P  0  0  -,  0.2 0.4 0.6 0.8 1.0 hlb  1.2  1.4 1.6  °0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6  133  Figure 58. Raw data, best-fit regression, GE incurred, and GE range for Hr 1. For explanation see Figure 29.  a  d  o a?  0 0  Eh  )0  c 0  0.3 0.2 Time s  0.5  Time s  \ 0  N c..J 0 0  C  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  h/b  h/b  134  1.2 1.4  1.6  Figure 59. Raw data, best-fit regression, GE incurred, and GE range for Hr 2 For explanation see Figure 29.  o  C  0  C) 0  0  E 5  Er—  C)  C) 0  0  CD 0  CD  ir:  c’  C  00.0  0.1  0.3 0.2 Time s  0.5  0,4  0  0 .-  \ 0  0  C)  C)  a  a  e.j  a  a C  °O.O 0.2 0.4 0.6 0.8 1.0 h/b  1.2  1.4 1.6  135  C 0•  0.2 0.4  0.6  0.8 h/b  1.0  1.2  1.4  1.6  C)  -  0  -.  •03  o  o  6 -u  0.6  sigma 0.4  0.8  0.8  1.0  1.0  (0 ...+  9.0  0  a  ‘3  a  a  3  -  (0  “I -.1  0  -  Oro  °  a  4.  a  -.  0  .  Oo tOcyco  3  a  0  rs.)  0  0.2  0.6  sigma 0.4  c  1.0  0.2  0  0.8  1.0  o  0.6  sigma 0.4  0.8  o  0.2  0.6  sigma 0.4  0  “3  o  a  0.2  0.2  0.2  0.4  0.6  sigma  0.6  sigma 0.4  0.8  0.8  1.0  1.0  (Q  0  o  e  0  er  Ct,  q  CD  oq  (t  0  C?3  •0  0.2 0.4 0.6 0.8 1.0  sigma  C;’ (0  D  33  1’.)  •0  0  C  •r\)  o  o /  /  /  0.2 0.4 0.6 0.8 1.0  sigma  0.2 0.4 0.6 0.8 1.0  sigma  0  p  0  F’)  -A  0  0  •0  -A  D (*) a  (0 _4.  :3 (*3  0 0)  p  0  I I  0.2 0.4 0.6 0.8 1.0  sigma  0.2 0.4 0.6 0.8 1.0  sigma  (0  I  0.2 0.4 0.6 0.8 1.0  sigma  0.2 0.4 0.6 0.8 1.0  sigma  (0  —  :3  —.  (t  0.’  I  ‘r  p, 0  (t  Cl)  Ct  ‘  p1  Figure 62. Summary of range and mean us for the black skimmer sequences 6 to 9. For explanation see Figure 30.  Rn6gt  Rn6  N  I 000  I  0.2  0.4 0.6  0.8 1.0 h/b  1.2  1.4 1.6  00.0  0.2 0.4 0.6  0.2  0.4 0.6  0.8 1.0 h/b  1.2 1.4  1.6  00.0  .iI.  00.0 0.2 0.4  1.6  Rn8gt  0.6 0.8 1.0 h/b  1.2  1.4  1.6  Rn9  0.6 0.8  1.4  h/b  ii 0.4  1.2  0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6  Rn8  000 0.2  1.0  Rn7gt  Rn7  00.0  0.8 h/b  1.0  1.2 1.4  1.6  .I .iI  00.0  0.2 0.4 0.6  0.8  1.4 1.6  \\  0.2  0.4 0.6  0.8  bib  138  1.2  Rn9gt  00.0  h/b  1.0  h/b  1.0 1.2  1.4  1.6  0.0  0.2  I II  0.6  sigma  /7  0.4  0.8  1.0  a)  ‘3  -&  crö,  o o  0  7  7  /  //  /7  0.0 0.2 0.4 0.6 0.8 1.0  0)  \)  —&  o / 1 co  a  0  sigma  I  /  /  /7  0.2  0.6  sigma  /7  0.4  1.0 ——  0.8  // / I\3/  n  0  a /  0.0 0.2 0.4 0.6 0.8 1.0 0  0)  0  0.0  0  sigma  Co  L  I  p  Il)  0  I-i  CD  CD  .  0  References Alatalo RV, L Gustaisson and A Lundberg 1984 Why do young passerine birds have shorter wings than older birds? 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