Bernoulli's Principle: As fluid (air) moves faster, the pressure drops.
Newton's Third Law: Equal and opposite reaction. This relates to how air is directed downwards, resulting in an upward force (lift).
Alula feathers play a role (details not specified).
Power Output
Power output is either aerodynamic or biomechanical.
Accelerometry (DBA - Dynamic Body Acceleration) is a method used (details not specified).
Downstroke and upstroke are phases of wing movement.
Example speed: 5 ms−1
Power Equations
Power=Force×distancepersecond
Power=Workpersecond
Power=Joulespersecond=Watts
Powered flight:Power=Force×Velocity=F×V
The units of Work is Joules.
Power Calculation
Power=mass×acceleration×ms−1
Power=(kg×ms−2)×(ms−1)=kgm2s−3
Power=Force×Velocity=F×V
Relates to powered flight
Measuring Wing Bending Forces
Dial et al. (1997) used strain gauges on the humerus bone of the wing to measure bending forces during flight.
Black-billed magpies exhibit an “L-shaped” curve in their mechanical power output.
Mechanical power output.
Bird Size Extremes
Teratorns: Huge, vulture-like birds.
Early forms had wingspans up to 8 m and body mass of 100 kg, e.g., Argentavis magnificens in Argentina.
Hummingbirds: Very small.
Range from 3 to 20 g.
Little and Large variations in size.
Kori Bustard
Kori Bustard (Ardeotis kori) is mentioned.
Scaling or effect of differences in size is a factor.
Experimental Questions
Why is it harder to sustain flight as birds get larger?
What limits the maximum performance of flying animals and how close do they get to them in the wild?
Power required vs. power available.
FlightPower=a×Mb
M probably refers to Mass and a & b are constants.
Mechanical Power (Power output).
Metabolic Power (Power input).
Muscle Efficiency?
Aerodynamics vs. biomechanics.
Wing Length Variation
Why do birds have different wing lengths?
Absolute Lift: Proportional to wing area (S). This is good for carrying loads, maneuvering, and landing.
Wing Length and Shape
Why do birds have different wing lengths?
Longer & thinner wings (higher aspect ratio): Help to reduce power required, increasing the Lift to Drag ratio (L/D).
AspectRatio=L2/S
L is possibly Length and S is surface area.
Wing Length and Flight Style
Why do birds have different wing lengths?
Long-distance fliers & gliders: Tend to have longer wings.
Larger birds: Tend to have long & thinner wings in proportion to their area.
Experimental Questions (Repeated)
Why is it harder to sustain flight as birds get larger?
What limits the maximum performance of flying animals and how close do they get to them in the wild?
Power required vs. power available.
FlightPower=a×Mb
Mechanical Power (Power output).
Metabolic Power (Power input).
Muscle Efficiency?
Aerodynamics vs. biomechanics.
Allometry of Body Shape
Allometry relationships:
L=a×M1/3or0.33
A=a×M2/3or0.67
VolorMass=a×M1
L=L1
A=L2
VolorMass=L3
Pennycuick (1982) - Antarctic Petrel Wing Shape
Looked at wing shape for 9 species of Antarctic petrel.
a) Wing span isometry = 0.33. L increases slightly faster than expected, but not significantly.
b) Wing area isometry = 0.67. S increased slightly slower (NS - not significant).
c) Aspect ratio (AR) is significantly greater with body mass.
This reduces induced power and increases L / D ratio so that power is proportional to less than M1.17.
Slope = 0.37
Slope = 0.627
Slope = 0.116
Timeline
Timeline shows appearance of different flying creatures.
Includes Pterosaurs, Quetzalcoatlus (15 m), Teratorns, Archaeopteryx (155 mya), Bats, Birds, and Pteranodon (10 m).
Time is in MYBP (millions of years before present).
Flight Summary
Low cost of transport (COT - energy per unit distance).
Relative flow of air over the wing is what matters; dropping down or running can help relative air flow.
Angle of glide is related to Lift to drag ratio (independent of mass).
Speed of flight is proportional to the square root of wing loading - bodymass/wingarea.
Long thin wings have a high Aspect Ratio (AR=L2/area) and, therefore, a higher lift to drag ratio (L/D).
Flight Summary (Continued)
Lift is a result of suction from above (Bernoulli Principle), pushing from below, and direction of air downwards (Newton’s 3rd law of motion).
Total amount of lift is proportional to wing area (S).
Overall shape of aerofoil and wing area determines lift coefficient of wing (aerodynamic effectiveness).
Power for flight is required to support weight (induced power) and overcome drag (parasite and profile power) + physiological costs.
Yields a U-shaped power/speed relationship.
Metabolic Power and Size Limits
To sustain flight, a bird must supply sufficient oxygen and ATP to the working muscles.
The amount of oxygen supplied to muscles depends on the rate of blood flow (ml min-1) that the bird’s heart can pump.
This scales around M0.82.
Metabolic power from oxygen?
Aerodynamic Power output vs. Metabolic Power input.
Power Input
Power input:
Metabolic rate (ATP) (Metabolism).
Carbon dioxide (DLW).
Oxygen consumption.
Heart rate?
Mitochondria are involved.
Various values stated
30
5
2000
Oxygen Consumption of Birds in Wind Tunnel
sVO<em>2=173×M</em>b−0.224
R2=0.848
Graph shows mass-specific rate of oxygen consumption (ml min-1 kg-1) versus body mass (kg) for various birds.
Birds listed include budgie, starling, kestrel, fish crow, laughing gull, pigeon, white-necked raven, barnacle goose, and bar-headed goose.
Metabolic Power Input Measurements
Various authors have measured oxygen consumption of birds (converted to Watts).
In general, there is a requirement for between 60 to 300 W kg-1, with smaller birds requiring larger relative costs per unit body mass.
Graph shows Power input (W kg-1) vs Air speed (m s-1) for various birds including budgerigar, white-necked raven, laughing gull, pigeon, fish crow, cockatiel, barnacle goose, starling, bar-headed goose, Allen's hummingbird.
Maximum Power Available
Maximum power available from oxygen and ATP?
Fick Equation:
VO<em>2=f</em>e×V<em>s×(C</em>aO<em>2−C</em>V02)
VO<em>2=V</em>b×(C<em>aO</em>2−C<em>V0</em>2)
VO2 = oxygen consumption
Vb = cardiac output
Heart Rate and Size
Maximum rate (beats min-1) that a heart can contract decreases as animal size increases.
Volume of blood pumped each beat is proportional to heart mass (Mh1).
The maximum cardiac output (ml min-1) will decline as the animal increases in size if heart mass scales isometrically.
Graphs
Graphs of heart mass (%) vs flight muscle mass (%) and heart mass (%) vs body mass (kg).
Heart Size and Aerobic Abilities
We can use the size of the heart of different families of animals to investigate their aerobic flight abilities.
Heart (%).
Muscle and Heart Size
Some birds have large flight muscles but small hearts (anaerobic fliers) (e.g., tinamous & pheasants).
Some have smallish flight muscles but large hearts (aerobic fliers) (e.g., kingfishers, swallows, tits & warblers).
Some have large flight muscles and large hearts (good aerobic & anaerobic) (e.g., pigeons & sandpipers).
Flight Muscle (%).
Muscle Fiber Types
Illustrates FG (fast glycolytic/anaerobic) fibre and FOG (fast oxidative glycolytic/aerobic) fibre.
M = mitochondria, C = capillary, L = lipid
Sustained vs Burst Power
Concept of sustained and burst power output defined: