Biomechanics

May 5, 2005Dr. Kelsey Jordahl

Size

Factor of 108 in sizeFactor of 1024 in mass!

Bacterium ~0.3m

Whale ~30 m

Scaling Surface Area to Volume ratio

V l3 Volume to lengthm l3 mass to length

S l2 Surface to volumeso S/V l m1/3

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 106 in mass(only 100 in size)

Elephant ~6000 kg

Shew ~6 g

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 numbersMechanical advantage

MA=Fo/Fi

Flatness indexFI=S1.5/V

Strainx/x0

Froude numberFr=v2/gl

Walking on water/l2g

Final ExamThursday, 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