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Comparative Vertebrate-Bio Design and Mechanics

Comparative Vertebrate-Bio Design and Mechanics -...

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Biomechanics and Biophysics Physics and Math -Body size and constraints -Gravity is important to big animals -Smaller animals are not affected as much by gravity; are affected though by surface forces or tension (example: ant in the rain) Size ???? Can an elephant run???? Never run impact on limbs is too great We define running as a form of locomotion as all limbs must leave the ground at sometime Absolute vs Relative Absolute size increase is equal to the direct increase in length, volume/mass, and surface area (example: head as adult gets larger) Relative size increases is equal to the differential increase in length, volume/mass, and surface area (example: head as adult-smaller) Surface area and Volume SA: L^2 V: L^3 -Volume increases faster than surface area ???? Is the blue whale the largest organism to inhabit the earth ever???? No, fungus Armillaria ostoyae (honey mushroom) 2200 acres 3.5 miles in diameter 2400-7200 years old Located in Oregon Surface Area SA=4* h *r^2 Problem: Blue whale=2438 cm long=1.86e7 cm^2 Shrew=8cm long=201 cm^2 V=4/3*h*r^3 Whale=7.59e9 cm^3 Shrew=268 cm^3 300 time increase in size (smallest to largest)
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93000 folds increase in surface area 28 million-fold increase in volume SA: V=1:300 Metabolism=VO 2 Y=bx^a (Allometric scaling) o Allometry is the proportion of things o “b” and “a” are constants o Forms a parabola Log y=Log b+ Log x^a Log y=Log b + a Log x (forms a straight line) o Absolute (see graphs) o For every increase in mass, there is a small increase in metabolism o Slope of line=0.738 o Relative (see graphs) o Amount of Oxygen consumed per hour per given gram of animal o As we increase in size, you increase in efficiency, such that each gram of
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