Biomechanics May 5, 2005 Dr. Kelsey Jordahl

Size Factor of 10 8 in size Factor of in mass! Bacterium~0.3m Whale~30 m

Scaling Surface Area to Volume ratio V  l 3 Volume to length m  l 3 mass to length S  l 2 Surface to volume so S/V  l  m 1/3

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 Factor of 10 6 in mass (only 100 in size) Elephant ~6000 kg Shew~6 g

Scaling factors for mammals ya Surface area1.95 Skeletal mass (terrestrial)3.25 Skeletal mass (cetacean)3.07 Muscle mass3.00 Metabolic rate2.25 Effective lung volume3.09 Frequency of breathing-0.78 Heart mass2.94 Frequency of heartbeat-0.75 Kidney mass2.55 Liver mass2.61 Brain mass (nonprimates)2.10 Brain mass (humans)1.98 y  l a l=m 1/3

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 = F o /F i Flatness index FI = S 1.5 /V Strain  x/x 0 Froude number Fr=v 2 /gl Walking on water /l2g/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