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Re: Stego/Ankylo limbs (long)



In a message dated 96-02-04 12:50:55 EST, Robert.J.Meyerson@uwrf.edu (Rob
Meyerson) writes:

>Sorry, your wrong on this one.  Set this one up as a physics problem
>regarding
>the justification of stresses (I can't think of the real term, but this is
>close
>enough).  With the feet under the body, the stress diagram looks like this:
>
>         1
>         1 w
>         1
>         V
>
>In this case, the force on the feet (w) equals the mass times the
>acceleration due to gravity (simple Newtonian stuff).
>
>With the forelimb held off to the side, the diagram looks like this:
>
>        --------->1
>         \ A      1
>          \       1
>           \      1
>            \     1 x
>          H  \    1
>              \   1
>               \  1
>                \ 1
>                 >V
>
>Where:
>        H = Hypotenus (with a value equal to w).
>
>        A = The angle between hypotenuse and horizontal.
>
>        X = Total load applied to the feet.
>
>Trigonometry says that X = H.cos A.  Since the cosine of any angle (provided
>A < 90) is always less than one, then X < H.  Therefore, the total load
>applied
>to the feet is less with the feet held out to the side.
>
>

Oops. This ain't right at all. The _load on the feet_ is the same regardless
of where they are placed on the ground, and it depends mainly on the weight
of the body and how it is distributed therein. What the hypotenuse of the
above triangle measures, in how much longer it is than the vertical vector,
is the _extra_ force that needs to be distributed along the leg muscles in
order to hold the leg out at the specified angle from the sides. The vertical
leg minimizes the difference between the length of the hypotenuse and the
vertical (effectively to zero), which is why it's the "preferred" stance of
graviportal animals.