# RE: 4ped vs. 2ped maneuverability (was Re: A fundimental conundrum ...)

```From:   Betty Cunningham[SMTP:bettyc@flyinggoat.com]

>sorry I didn't do that.  It's not a biped thing but a vertical weight
>mass distribution thing.  Less area to move around the area of spin
>means easier spins.

The technical term for this is polar moment of inertia.  You calculate
it as the sum of the mass times radius of that mass squared, divided by
the sum of the mass.   Radius is measured from the axis along which you
want to turn - in the case a vertical axis through the center of
gravity. It is very important to engineers designing race cars, for
example because it directly measures the difficulty of turning.

Humans have low PMI.  Bipedal dinosaurs have very high PMI, due to the
long tails and necks - they are horizonal plan bipeds, quite different
in mass distribution from the vertical plan that humans use. I have been
working on physically simulating the turning dynamics of dinosaurs.
Their high PMI might actually be an advantage because they can
manipulate it dynamically by swinging their tails (like a ballerina does
pulling her arms in during a spin).  I don't have full results yet so
its hard to comment further.

to be missing a fundamental point.  Animals of either biped or
quadraped locomotion have undergone a wide range of secondary
evolutionary adaptations to specialize from a basic body plan.
[That's the sort of thing I was talking about when I said that Rob's
analysis was too superficial. -- MR ] Thus the cheetah has one set
(flexible spine etc.), ostriches quite another.  The various theropods
under discussion were highly modified versions of ancestral bipeds.

Evolution can take EITHER body plan and (given enough time) make a set
of adaptations which optimize it for a given niche - including either
high or low speeds.   The relative sucess of the cheetah and ostrich
endless) or slow bipeds (wading birds, flightless birds like the dodo)
show each plan can be adapted the other way too. I doubt that you find
any inherent advantages in biped versus quadraped by this direct line of
inquiry because in each case evolution can compensate through other
mechanisms, as the various examples show.

In any event, bipedalism and quadrapedalism evolved long before these
secondary adaptations took place. It might be possible to categorize the
class of such adaptations and draw some general conculsions but this is
difficult.   Also it is irrelevant to the origins of bipedalism, since
it evolved in various organisms for a set of specific reasons that made
sense at the time, not a broad generalization of what their decendants
might later make of it.

Nathan

```