11_FeathSize1W11

11_FeathSize1W11 - Flight Size and Scaling • Evolution of...

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Unformatted text preview: Flight, Size, and Scaling • Evolution of flight – Feathers – Limb Length • Size & Scaling – Surface Area to Volume Ratios – Isometry & Allometry Feathers: What Do They Do? • Multiple Functions – Display – Insulation – Flight • Feather form follows function Feathers: Insulating • Downy feathers – loose, fibrous – no central support. • Semiplume feathers – strengthening support, called a rachis, runs up the center Feathers: Contour • Barbs come off of central rachis • Small Barbules interconnect • Feather is strong and flexible • Colorful plumage • Streamlining in flight Feathers: Flight • Asymmetrical – Leading edge is narrower and more tightly packed than the trailing edge. Feathers: Flight • Overlap each other – stronger leading edge of one feather to overlies weaker but more flexible trailing edge of another. – Form solid surface on downstroke, Feathers: Filamentous • Found in fossils • Loose structure Fossils: Feathers • Look at Theropods only • Map on a few more species Fossils: Filamentous Feathers Beipiaosaurus Fossils: Insulating Feathers Caudipteryx Fossils: Contour Feathers or Microraptor Archaeopteryx: Feathers Fossils: Flight Feathers Wing Features • Large surface area compared to body size – Feathers – Length • Flying birds have relatively long arms as compared to their legs – Note this is a relative measure Fossil: Long Limbs Phylogeny: Flight Characters Length in meters 100=1m 103 103=1km 101 10-1 10-3=1mm 10-3 10-6=1µm 10-5 10-9=1nm 10-7 Let’s Examine Imaginary Simple, Cube Organisms Length =1m Using Formulas for Cubes, where length =L Surface Area=SA=6L2=6*12=6m2 Volume=V=L3=13=1m3 Let’s Examine Imaginary Simple, Cube Organisms They can “breathe” across their skin, anywhere there is contact with the outside, and have no circulatory system What happens if we double length without changing shape? SA=6L2 V=L3 SA=6m2 V=1m3 SA=24m2 V=8m3 SA increased only 4-fold, while V increased 8 fold The big critter has less surface to use to breathe in relation to its interior size This is true for all 3d shapes! Some processes scale with SA, others to V Plot Change in SA & V 20000 Surface Area or Volume 15000 10000 V=L3 SA=6L2 5000 0 0 6 13 19 25 Length Plot Change in SA & V 10000000 Surface Area or Volume 1000000 100000 10000 1000 100 10 1 Volume slope=3 Surface Area slope=2 1 10 100 Length 10000000 7 10 On a log-log graph, the slope=the exponent Volume slope=3 Surface Area or Volume 1000000 6 10 100000 5 10 10000 4 10 10 1000 3 10 100 2 101 10 100 1 100 1 101 10 Surface Area slope=2 102 100 Length Slope of SA vs Length is always 2 on loglog plot, if shape does not change with size 1E+06 106 105 104 103 102 101 100 100 1 1E+05 Cylinder=4πr2 Sphere=4πr2 Cube SA=6L2 SA in Units2 1E+04 1E+03 1E+02 1E+01 1E+00 101 10 102 100 Length in Units (m, ft, cm, etc) Slope of Volume vs Length is always 3 on log-log plot, if shape does not change with size 1E+07 106 Volume in Units3 1E+06 105 1E+05 Cylinder=πr3 Sphere=4πr3/3 Cube SA=L3 104 1E+04 103 1E+03 1E+02 102 101 100 100 1 1E+01 1E+00 101 10 102 100 Length in Units (m, ft, cm, etc) Slope of Length vs SA/V=-1, if shape does not change with size 10.0000 101 Cylinder SA/V 1.0000 100 Cube Sphere 10-1 0.1000 10-2 0 10 0.0100 1 101 10 102 100 Length Ways to Counter SA/V Problems Examples • Gas Exchange in Leaves – Takes place in channels within leaves – Orange tree with 2000 leaves • Outer SA of leaves ≅ 200 m2 • Internal SA for Gas Exchange ≅ 6000 m2 • Human Lungs – Aveoli in lungs increase SA • Lung Volume ≅ 6 Liters (0.006 m3) • Lung internal SA ≅ 50-100 m2 – Blood pumped across aveoli to increase – Air pumped in and out of lungs Examples • Gas Exchange in Leaves – Outer SA of leaf ≅ 0.1 m2 – Internal SA for Gas Exchange ≅ 3 m2 • Aveoli in lungs increase SA – Lung Volume ≅ 6 Liters (0.006 m3) – Lung internal SA 50-100 m2 – Blood pumped across aveoli to increase – Air pumped in and out of lungs • Microvilli of intestines (projections) • Lamellae of fish gills (flattening) • Capillaries (branching) Figure 41-13 ...
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