Re: T. Rex mechanics

[ngear@gvtc.com]

Martin Baeker wrote:
>The recent discussion about the "kings" mechanics bothers me a bit: All
>posters were assuming that the T rex was a static thing.
>
>Sure, if you try to turn a large ladder around , which is completely
>rigid, you have to get all the torque into the ground through your feet.
>However, if you have two ladders, one in front of you and one behind you
>(o.k., you would need four arms to move them around, but this is only
>theory...) and turn both of them in opposite directions, the net torque
>through your feet is zero. See the following sketch:
>
>------0------      move to          0
>                                   / \
>                                  /   \
>                                 /     \
>
>You can try this experimentally the following way (I did!): Sit on a
>well-greased office chair and take some heavy weight into one of your
>outstretched arm. Move the arm quickly and, because of the torque you
>exert on the chair and conservation of angular momentum, the chair will
>rotate in the opposite direction (you might to have to do this quickly, to
>overcome friction.) Now, if you take two weights in each of your hands and
>move them simultaneously (see picture above) , the chair remains still.
>Short essence of long rambling: If you are a T rex and want to turn around
>a corner quickly, you may compensate the torque your body creates by moving
>the tail simultaneously.



I normally would not include this much of a post in a reply, but Mr. Baeker
here has actually done a first-rate job of showing why swinging the tail
would *not* have helped the rex rotate its body when making a turn.  Since I
can hardly improve on his demonstration, I will just pick up where he left
off.  Presumably the rex would not wish to remain bent after executing the
turn, so, to borrow Mr. Baeker's illustration and extend his logic:

------0------    move to        0        move to    ------0------
                               / \
                              /   \
                             /     \

Thus, when the rex straightened its tail back to in-line with its torso
after executing the turn, it would have found itself pointing in exactly the
same direction as before the turn.  So tail bending would not have helped
alleviate the foot torque problem at all.

>Now, it is for you experts to tell me whether T rex's weight distribution
>would allow this,

And here he indentifies an issue I almost included in the original mechanix
post.  (And I see now it was a mistake to edit that one out.)  Let's go back
to the ladder, except this time make it a folding ladder with you at the
hinge.  When straight, each side counterbalances the other, but if you let
that ladder bend, the ends will try to fall because each end will lose its
counterbalance.    I think that when T. rex shifted that heavy head to one
side of the centerline, it would have shifted the tail to the opposite side
to compensate.  Shifting both head and tail off to the same side of the
centerline would have had the undesireable effect of moving the center of
gravity off to that side.  Move the center of gravity to directly over one
foot, and you have a rex that can't walk.  Move the center of gravity even
further off to the side, and you have a rex that is falling over. 

While I'm at it--

Randy King wrote:
>Turning isn't always this simple.  By leaning into a turn, you can
>take some of the torque off of the foot.

Although I am picking on Mr. King here, I have received several similar
messages about leaning or banking, so I'd probably better say something
about this.  There is nothing about the act of banking into a turn per se
which will help a body rotate in the direction of that turn.  It still comes
back to torque transmitted through the ground contact(s).  In quadrupeds,
this generally means the front legs impart more centripetal force going into
the turn (ie, press out harder against the ground) than the hind legs.
Humans don't have front and hind legs, but with our vertical bodies, only
small and barely noticeable quantities of torque are needed to start and
stop us rotating, so foot torque is more than ample to the task.  Is it
actually obvious to most people that leaning over in a turn does not have
the effect of rotating the body into that turn, or should I explain this
further?

I guess I'd better head this one off too.  Someone out there is probably
thinking about how a rolling wheel will rotate into the turn when it banks
over.  This is a gyroscopic phenomenon and what you are observing is
precession.  It only applies to rotating bodies--which the rex pretty much
wasn't.  (If you cancel the gyroscopic effect of a rolling wheel by putting
a counter-rotating mass inside, the wheel will just fall over without
turning, the same way a stationary wheel does.)

Okay, so we still don't have anything that helps us reduce the foot torque
problem, but at least, if nothing else, we are making fine progress by
elimination, eh?

-------------
Nicholas Wren
Kenocephalosaurus