Re: Sloping terrain Re: Woman against Abelisaur

["Habib, Michael" <MHabib@Chatham.edu>]

On Jul 25, 2011, at 10:40 AM, Don Ohmes wrote:
> The assumption that the disadvantage of weight overwhelms the advantages 
> of absolute power, power relative to surface area, and leg length is not 
> supported by observation of extant animals. Not supported by the physics 
> either.

Actually, the physics (as best we can apply them with several unknowns) predict 
that sauropods would do poorly in extremely deep mud.  I feel that you are 
exaggerating the role of swamps and compliant terrain in the ecology of 
Elephants, as well - yes, they can and do move through deep mud, and some of 
them enjoy swampy habitats, but there is little evidence that they particularly 
escape predation in this manner or that deep soft sediments are their primary 
habitat.  The videos you supplied are very cool, and they show that elephants 
can move over soft terrain with heavy loads if required (and trained).  
However, even taking the concept that elephants are "mud adapted", this is a 
case where the elephant to sauropod analogy is weak on the point of functional 
morphology (see below).

Theoretically, during walking, quadrupedal animals can indeed be more stable 
than bipedal ones (both quads and bipeds are passively unstable during running, 
of course).  However, the accommodation of compliant substrates is not merely a 
matter of stability.  Propulsive efficiency is also of great importance, and 
that depends (in part) on how much the substrate deforms.  A biped with wide 
feet can have much greater propulsive efficiency on compliant substrates than a 
quadruped with narrow feet, for example.  

Basic physics/mechanical modeling implies that sauropods would have had low 
propulsive efficiency on extremely compliant substrates, and some of them would 
have been prone to miring on account of having very heavily loaded foot 
sections.  Despite having passing similarities to elephants, the substrate 
stress per foot in most sauropods was many times greater.  Elephants actually 
have relatively broad feet, while sauropods did not.  Elephants also have more 
potential flexion in their limbs (even though they usually walk with columnar 
limbs).  Despite their bipedality, large theropods would be expected to move 
more effectively on compliant substrates and sink into them less.

That trend holds (mechanically speaking) until we move to a substrate that is 
so compliant that all of the animals in question sink in it deeply, regardless 
of foot area (i.e. theropods sink fully, as well).  At that point, the most 
effective way to move is be able to touch harder sediment below, and that means 
simple height becomes the best determinate of propulsive ability - giving an 
advantage to tall animals like sauropods as long as they can, indeed, reach a 
less compliant medium below the "quick sand", as it were.  As the sediment 
becomes even more compliant, it effectively becomes a full fluid, at which 
point propulsion is swimming, and theropods again become more efficient, though 
I doubt they hunted while swimming very often.

I can describe that all in mathematical terms, of course, but I'm not sure 
anyone here wants to read that...

--Mike


Michael Habib
Assistant Professor of Biology
Chatham University
Woodland Road, Pittsburgh PA  15232
Buhl Hall, Room 226A
mhabib@chatham.edu
(443) 280-0181