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Re: Airbagged(was Dive!Dive!Dive!)



Jeff Martz wrote:

>Tom Holtz wrote:

>> T. rex's metatarsi are proportionately as long as those of Dryosaurus and
>> Deinonychus, in an animal 100x or more their mass.
>> 
>     Again, I think this gets back to the decreasing stress sustaining 
>limitations of bone as you increase overall mass.

We're talking about two different types of proportion here, and it's best not to
mix them up. Metatarsal/femoral LENGTH proportions are commonly used as
indicative of an animal's "fleetness of foot", notwithstanding the THICKNESS
of the limbs. The THICKNESS proportions are allocated by evolution as mass
varies, to meet the demands of the formulae I will mention (not for the
first time)
here:

        Increasing the dimensions of an animal will multiply its strength (both
muscular and structural) by the square of the factor of increase (cross-
sectional area). The same increase will multiply its MASS by the CUBE 
of the factor of the increase (volume). So if you double the dimensions, the
strength increases by a factor of four, but the mass increases by a factor
of eight -- so the strength/mass ratio is actually halved, UNLESS the cross-
sectional area is increased relative to the overall mass. 
        This is why legs on animals are stouter than those of their smaller 
cousins (e.g., T.rex vs Deinonychus vs Compsognathus). The proportionate 
length of the legs may be the same, joint to joint, but the diameter must 
increase to support adjust the strength/mass ratio.
        Then there's the cumulative effect of the increased mass of the 
stronger limbs -- this puts a very real size limit on ground-walking animals,
if they expect a survivable degree of mobility.

He followed that post with a direct response to my own, including:

>> Fighter pilots routinely sustain forces well in excess of 6g for
>> periods of seconds at a time, rather than just a momentary
>> impact. 

>      "Momentary" is the important thing.  Fighter pilots build up the 
>gs more gradually.  I think if they were to go from 1 to 6 gs in an instant, 
>they would be massively smushed.  With a T.rex impact, we are talking 
>about a virtually intantaneous deceleration (someone with a little more 
>physics knowledge let me know if the build up acceleration and 
>deceleration is really relevant, or if there is more to it).     

Well, a "g" is a "g". It's a measure of acceleration (including
deceleration, using the strict definition of physics), and that takes
into account the duration involved. If the event, in this case the
impact of a dinosaur on the ground, takes twice as long, then the "g"
forces will be reduced. 

[ You missed Jeff's point which was about the derivative of
  acceleration with respect to time.  That could be important
  actually, especially since biological materials are highly
  visco-elastic.  I can't do more than arm wave about it or I'd have
  responded to him directly. -- MR ]

I understand that Farlow et al figured Rex was falling on moderately
soft ground, but not mushy -- entirely reasonable. This means that
during impact the ground would undergo some degree of deformation,
reducing the impact forces somewhat -- I'm sure they figured this into
it, or they would not have mentioned the softness of the surface.  On
impact, the two impacting surfaces would both give somewhat -- the
dino's body would flex, bending and, if the forces are sufficient,
breaking.
        Farlow et al obviously considered the forces involved
sufficient to pose a real danger of exceeding the breaking strength of
the bones. While I am in no position to dispute their calculations, I
simply think the beast will take measures to instinctively minimize
the impact, rather than just dropping like a sandbag.
        As for buildup of g forces, the aforementioned fighter pilots
use the fore- knowledge to tighten certain muscle groups and do a
"primal grunt", which, in combination with a special g-suit (which
pressurizes the lower parts of the body), helps to keep blood from
pooling in the legs and feet. With these, they can often sustain up to
9g before G-LOC (Gravity-induced Loss Of Consciousness, pronounced
"gee-lock"). But the load of the g forces is actually MORE than if it
were momentary, since the skeletal structure is not allowed to absorb
the load by flexion and rebound.

>>         And, instincts being what they are (and presumably were),
>> don't you think Rex would use its tremendous neck muscles to begin
>> decelerating its head as soon as its torso hit? You can't just
>> "seperately" drop torso and head -- they're still connected.  The head
>> may have avoided impact entirely.

>      An interesting point.  I wonder how well the neck musculature 
>could have resisted the impact forces.  

        Given the loads T.rex probably routinely lifted with its neck
muscles, I suspect it could handle the forces pretty well.

        It also occurs to me that, besides a "side roll" maneuver,
T.rex could have used its tail to very good advantage to minimize a
fall:
 
        I propose that the tail can balance the forebody, using the pelvis
as a fulcrum. 
        I further propose that, in keeping with accepted modern
theory, these dinos did not drag their tails on the ground, but
carried it aloft as a counterbalance.
        Finally, I propose that they would learn how to effectively
control the dynamics of their own balance, either by instinct or as
young (when falls are unlikely to be damaging.

        Now let's knock the legs -- even both of them -- out from
under Rex. By snapping his tail -- equal in leverage to the torso and
head -- downward, he can create a relative "lifting" force. This would
not, of course, keep him aloft (!), but it would have the effect of
reducing the impact force significantly -- very much the way judoka
(judo players) "slap the mat" to break their falls. For a creature
that uses its tail every day as a balance, this can easily be
instinctive.

        ...but I don't expect that to be the last word on this
topic!!!

Wayne Anderson