Re: T. rex mechanix

[ngear@gvtc.com]

Bill Adlam wrote:
>This whole analysis only applies to standing creatures.  When running or 
>even walking, it is easy to turn by stepping slightly differently.  If the 
>force you exert on the ground (and therefore the force the ground exerts on 
>you) does not act through your centre of mass, you will experience a moment 
>or torque...

>The important factor in T. rex's manoeuvrability is how far apart its feet 
>could tread while running.  I know the feet would normally have been very 
>close together, but how far could it have widened the gap without losing 
>too much speed?


Although the first line isn't quite right (since the energy it takes to get
a body rotating is the same whether that body is standing or moving) Mr.
Adlam does raise an issue I did consider for a while.  Here was my thinking
on the matter:

If T. rex could have put on the brakes, so to speak, on the inside leg and
hit the accelerator on the outside leg when going into a turn (and the
reverse when coming out of the turn), this would indeed have contributed to
rotating (and halting the rotation) of the rex body and might have assisted
foot torque or reduced the need for it.  So how much could this have
assisted?  There are actually two factors to consider to determine the
effectiveness of this strategy.  One is how far to the side of the point
directly below the center of gravity the rex could plant its foot, and the
other is how much braking and accelerating force it could exert.

As to the first factor, it should be obvious that the further to the side of
your center of gravity you plant your foot, the faster you will fall toward
your other foot, so the slower the cadence the closer to directly beneath
the center of gravity you must step and the less effective this strategy
becomes.  I originally was going to try to figure out in absolute distance
how far to the side the rex could have planted for a given cadence, but then
I realized that's not what matters.  What matters is the angle from the
center of the plant up through the center of gravity.  At slow paces this
was probably only a few degrees off vertical.  I'm not sure what the maximum
angle could have been, but I would think 20 degrees off vertical (or more
accurately, off effective vertical, since the rex probably did bank a bit in
turns) would be a very generous figure.  At 20 degrees the rex would have
been wasting a lot of energy throwing its mass from side to side and it
would have greatly increased the likelihood of foot slippage on the outside leg.

The second factor strongly favors medium speeds.  The rex has to be going
fast enough for braking to have an effect, but slow enough that the outside
leg can still accelerate.  I should probably point out that the braking and
accelerating forces have to be of the same magnitude, and here's why:
Remember that angle up to the center of gravity?  That sets your plane of
rotation and the rex nose would slew down at about the same slope when
braking (eg. down at roughly 10 degrees off vertical for a lean angle of 10
degrees off vertical), so there must be a compensating acceleration adding
just as much speed as the braking leg took off in order to get the nose back
up.  Note that this slew angle means there would have been several times the
effect in pitching the body fore and aft (or the nose up and down) as
rotating the body about the vertical axis.

So, if the rex could have used this strategy at all, it would not have been
at slow speeds because the lean angles would have been too slight, and it
would not have been at top speeds because 1) the rex would have had to have
been going slow enough that the outside leg could add just as much extra
thrust energy as the braking leg took off, 2) braking on the inside leg
would have slowed the rex even further and 3) because this strategy would
have scrubbed off a lot of forward speed by converting it into side-to-side
motion.  Even in its most effective speed range, this strategy's
contribution to rotating the body would have been modest, at best, and I
suspect its energy demands would not have made it cost-effective.

It was for these reasons I ultimately concluded this was not the solution to
the foot torque problem.

-------------
Nicholas Wren