Leg Bone Optimization

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Leg Bone Optimization A long bone is a hollow
tube that may fail by buckling, bending or
compression. for a bending moment M
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• Figure 7.3 The area A, section modulus Ze and
  fully plastic modulus Zp
• for three simple sections.

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For a moment M and a strength ?max the minimum
mass of a bone that will not break can be
calculated from the buckling equation mass of
the bone without marrow Radius ratio of tube
k (r1/r0) K ??max/4 Density ? The
best air-filled bone would be very thin-walled,
but if it contains bone marrow, then it gets
heavy again.
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Mass/length and radius ratio of bones with and
without marrow for the same bending
strength. Best ratio for inner/outer is 0.63
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Actual k-values, for animals
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Bone air (birds). As the thickness goes down,
k up, the weight for a given break strength in
bend decreases but the weight for failure in
buckling goes up. Bird bones are hollow with
k0.9
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Can optimize further by tapering the bone or
otherwise changing it along the length. Dog bones
get larger as you move away from the distal end
of the tibia (ankle) to the proximal end (knee).
You can also get clever with shape.
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