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Biomechanics

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Scaling Surface Area to Volume ratio. V l3 Volume to length. m l3 mass to length ... injured if fall from greater than own height (dogs, cats, squirrels, most humans) ... – PowerPoint PPT presentation

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Title: Biomechanics


1
Biomechanics
  • May 5, 2005
  • Dr. Kelsey Jordahl

2
Size
Factor of 108 in size Factor of 1024 in mass!
3
Scaling Surface Area to Volume ratio
V ? l3 Volume to length m ? l3 mass to
length S ? l2 Surface to volume so S/V ? l ?
m1/3
4
Example for cube
5
Consequences of falling for organisms of
difference sizes
  • gt100 kg serious injury possible even at ones
    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)
  • lt100 mg never really fall at all airborne
    (pollen, spores, very small animals)

6
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.
7
Scaling
8
Land Mammals
Factor of 106 in mass (only 100 in size)
9
Scaling factors for mammals
y ? la lm1/3
10
Example of isometry and its consequences
11
Example of allometry bone proportions in
pelycosaurs
12
Example of allometry shape change in human
ontogeny
13
Dimensionless numbers
  • Mechanical advantage
  • MAFo/Fi
  • Flatness index
  • FIS1.5/V
  • Strain
  • ?x/x0
  • Froude number
  • Frv2/gl
  • Walking on water
  • ?/?l2g

14
Final ExamThursday, May 14(same time location)
  • Chapters 22, 25, 29 (sections 26.7, 26.8,
    26.9 also helpful)
  • S. Vogel, Lifes Devices, chapters 3 4, on
    reserve in library
  • Handout from today
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