Sauropod Dinosaur Neck Analysis
Regarding the subject whether the really large dinosaurs, the sauropods,
lived on land or in a water swamp, I have never seen a decent
analysis if the Physics involved in the neck. If these huge
animals lived on land, then the weight of their head and neck
would have been cantilevered out forward from their front
shoulder bone structures. (We have already discussed (from 1997) in the main
dinosaur discussion that the
hearts and heart valves could not have been strong enough to
pump blood up to the head and brain if the popular "grazing
from the tops of trees where there was no competition"
had been valid. The strength of biological tissues limits the
height of the brain above the hear to be slightly over 2 meters
(7 feet), as in giraffes or T. Rex.) That means that a land-dwelling
sauropod would always (and probably continuously) have to hold
the head and neck cantilevered out in front of the body, never higher
than about the height of the hump of the back, around 4 meters (15
feet) above the ground.
Therefore, a standard Engineering analysis is needed to determine the
structural integrity of the muscles and bones of the neck. When
Engineers design a new construction crane, IF it is intended to
have the capability of ever being horizontal, such an analysis is
a standard procedure requirement.
A Diplodocus neck skeleton, roughly 8 meters (24 feet) long
Where the forces and stresses in a crane structure are relatively
complicated due to all the angled gusset crossmembers, an analysis
of the cervical structure of a sauropod is actually much simpler.
Each cervical vertebra (neck bone) has an upward (anterior) extension
which is called a "spinous process". This upward extension
is always prominent in any skeleton of any larger animal, whether it
is a human, a dog or a dinosaur. The spinous process exists to be
the attachment point for an elastic ligament, the Ligamentum nuchae
(or Ligamentum nuchæ ) a fibrous membrane which is the supraspinous
ligaments which connect the tops of those spinous extensions
together, which therefore forms a relatively smooth
top line along the very top of the cervical vertebra. There are actually
two parallel Ligamenta nuchae, which connect the appropriate
places on the bifid spinous processes. In general, each
spinous process is bifid (split into two separate ends) so that there
are areas available for connection to these extremely important
ligaments. If even one ever failed, the head would certainly crash to the
ground and never again be lifted, which would allow smaller predators
to easily attack and kill it, so that is not an option!
A Diplodocus neck skeleton, showing part of the Ligamentum nuchae in red
One might imagine a series of short pieces of steel cable joining the
adjacent spinous processes. This would act to squeeze the vertebrae
"main bodies" together while also levering the two against
each other. Of course there was a cushion, a spinal disk between the
main bodies of the vertebrae, which allowed flexibility of the neck.
But the significant point here is that if we simply know the
"radius arm" of the tension and the cumulative weight of the
head and neck beyond that vertebra, we can easily determine the
tension that would have to exist in that "cable" The weight
involved is reasonably accurately known by the volume of the head
and neck and the assumption that the average density was close to 1.0
gm/cc, like all modern animals. The distance for a specific vertebra
between the center of the main body and the muscle attachment points
on the spinous process is simply measured from a fossil.
A human neck (cervical) vertebra, with front at top, from Gray's Anatomy
Say, as an example, possibly for a moderate sized Diplodocus,
the measured distance is 30 cm (around 12 inches).
Say also that the head and neck forward of that vertebra had a
probable total volume of 5 m3 (or around 50 cubic feet).
The weight involved (for that vertebra) would then be around 1,000 kg
(or 2,200 pounds). It is also important to determine how far forward
of this vertebra the "center-of-gravity" of this weight is.
In our example, we are going to say that it is at 3.5 meters (around
11 feet) forward of the vertebra.
Using standard Engineering practices and equations, this 1,000 kg at
a 3.5 meter arm distance means that the "moment" the product
of these two numbers, or 3,500 kg-m. Now, the muscles connecting
the vertebra spinous processes MUST provide this moment. Since
the tension in those muscles TIMES the effective radius arm must now
equal 3,500 kg-m, and we have measured the arm as being 30 cm (or 0.3 meter)
we can easily calculate the required tension in that muscle. It must
be 3,500/0.3 or around 12,000 kg-force of tension. The only question
then is whether the estimated cross-sectional area of that muscle
could provide this amount of tensile strength reliably. If we
measure-estimate that a Diplodocus had muscle attachment points which
allowed connection of an 8 cm (around 3 inch) diameter muscle, then we would
have a cross-sectional muscle area of around 50 cm2 (or 7
square inches). This would then require a fiber tensile strength of
around 12,000/50 or 240 kg-force/cm2. For reliability,
a "factor of safety" is always involved to minimize
spontaneous failures, so in this example, we would expect a need
of around 1,200 kg-force/cm2 muscle tensile strength.
The bottom, largest human neck vertebra, showing the large spinous process, from Gray's Anatomy
When we consider an analysis for a much larger and heavier Apatosaurus,
much greater muscle tensile strength appears to be necessary.
Really careful measurements and estimates of sizes and weights and
dimensions are needed to determine WHETHER an Apatosaurus' neck
muscles could have supported the weight of a cantilevered head and
neck. If this turns out to require muscle fiber tension greater than
that possible with biological tissues, then it would seem to REQUIRE
an aquatic environment, such that partial flotation would then support
the head and neck easily.
This presentation was first placed on the Internet in June 2005.
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C Johnson, Physicist, Physics Degree from Univ of Chicago