T. rex mechanix

[ngear@gvtc.com]

It almost seems like the more I think about the physics of being a rex, the
less I understand how this animal worked.  Here are some of the things I am
currently pondering.

Locomotion/maneuverability:  Polar moment of inertia.  
Anyone who has ever tried to make a turn with a 20 foot ladder on his/her
shoulder can understand the problem here, except the rex body got up to
double that length and had, quite literally, tons of momentum.  It would
have taken a while to get that body pivoting, and nearly the same time and
energy would have been required to stop it pivoting.  While striding, most
of the time only one foot would have been in contact with the ground, so all
turning torque would have had to have been transmitted to the ground through
a single contact patch that was, what, thirty-something inches across?  The
rex could have exerted torque more effectively during the time both feet
were in contact with the ground, but while striding, this would have been a
very brief interval.

So, was there something else the rex could have done to pivot that body, or
are we forced to conclude that its lifestyle simply did not require quick turns?

(Incidental to this, I have occasionally heard it suggested that the rex
inhabited forests or jungles.  I've tried to navigate a 30 foot beam through
a thicket of trees before, and I can assure you it was a major pain.  I have
a much easier time imagining the rex inhabiting open range.)

Locomotion/conservation of energy:  The sprung beam.  
Most bipeds we have experience with have vertical or compact torsos, but the
rex body and tail functioned, essentially, like a long horizontal sprung
beam.  If you've ever walked with a long pole resting horizontally on your
shoulder, you've probably noticed that the natural periodicity of the pole
tends to favor certain sympathetic paces.  The main two are a quick pace
where the pole is out of phase (ends go up with each footfall) and the load
on the shoulder is fairly constant, and a slower cadence where the pole is
in phase (ends go down with each footfall) and there is very little load
between steps.  I suspect the long-bodied rex would also have favored
certain cadences.  What I find intriguing to contemplate is the long cadence
mode where the load decreases between footfalls (the mode kangaroos exploit
so well--except without the alternating gait).  If the rex were able to get
completely off the ground between footfalls when running, I think this must
have been how they did it.

Standing:  It is almost unthinkable that a full-grown rex would not have
been able to lie down occasionally or recover from a fall, but how the rex
got up off the ground seems to me to be an interesting problem.  I can
imagine how it might have rolled from lying on its side up into a deep squat
position using its tail and head pushing against the ground, but then how to
get up out of the deep squat?  I only have pictures to work from, but the
mechanical disadvantage of a rex knee looks like it would have been too
great when the knee was fully bent for the rex to have used brute force to
stand out of a deep squat.  (I'm getting load estimates approaching 100,000
pounds tension on the knee tendon, but I think I could be more accurate if I
had a better picture of a rex leg in profile to work from.  I've seen a
steel cable rated for 50 tons load and it was nearly four inches in
diameter, so I doubt the tendon that could take this sort of load would have
had the flexibility needed to wrap under a fully bent knee.)  However, the
load drops off considerably if the rex leg is only half bent (a crouch, in
other words), so could the rex have reduced the load somehow when the knee
was fully bent to enable it to get up into a crouch?  I could only think of
a couple of mutually incompatible ways of accomplishing this.  One being
that the rex used its long body to generate upward momentum by flexing its
tail and trunk upward abruptly, followed immediately by a sharp downflex to
get the pelvis up as high as possible before the upward momentum was lost.
(This one seemed a tad too energetic to me.)  The other being that the rex
used its long body to leave a significant portion of its weight bearing
directly on the ground until the legs were up straight enough to be able to
take the full load.  If the rex could have humped its pelvis up by pressing
down with its tail in back and with its chest or chin in front, every pound
loaded directly to the ground would have meant several pounds reduction in
the tension in each knee tendon.  I also liked this four-point lift scenario
because it simplified the problem of how to balance while standing.
Unfortunately, I have been informed that the rex spine was not flexible
enough to have permitted it to do this (a beautiful theory shot down by a
pesky little fact), so now I'm looking for a third offload scenario. 
Any suggestions?


Nicholas Wren
Kenocephalosaurus