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Biomechanics May 5, 2005 Dr. Kelsey Jordahl Size Bacterium ~0.3m Whale ~30 m Factor of 108 in size Factor of 1024 in mass! Scaling Surface Area to Volume ratio so V l3 m l3 Volume to length mass to length S l2 S/V l m1/3 Surface to volume Example for cube Consequences of falling for organisms of difference sizes >100 kg: serious injury possible even at one’s own height (cows, horses, elephants, very large humans) 100 g – 100 kg: may be injured if fall from greater than own height (dogs, cats, squirrels, most humans) 100 mg – 100 g: no injury from any height (mice, insects, baby birds) <100 mg: never really fall at all; airborne (pollen, spores, very small animals) “You can drop a mouse down a 1000 yard mine shaft and, arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, and a horse splashes.” Scaling Land Mammals Shew ~6 g Elephant ~6000 kg Factor of 106 in mass (only 100 in size) Scaling factors for mammals y a Surface area 1.95 Skeletal mass (terrestrial) 3.25 Skeletal mass (cetacean) 3.07 Muscle mass 3.00 Metabolic rate 2.25 Effective lung volume 3.09 Frequency of breathing -0.78 Heart mass 2.94 Frequency of heartbeat -0.75 Kidney mass 2.55 Liver mass 2.61 Brain mass (nonprimates) 2.10 Brain mass (humans) 1.98 y la l=m1/3 Example of isometry and its consequences Example of allometry: bone proportions in pelycosaurs Example of allometry: shape change in human ontogeny Dimensionless numbers Mechanical advantage MA=Fo/Fi Flatness index FI=S1.5/V Strain x/x0 Froude number Fr=v2/gl Walking on water /l2g Final Exam Thursday, May 14 (same time & location) Chapters 22, 25, & 29 (sections 26.7, 26.8, & 26.9 also helpful) S. Vogel, Life’s Devices, chapters 3 & 4, on reserve in library Handout from today