Sauropod Dinosaur Neck Physics Analysis
Extensive Research regarding dinosaur physiology was
performed from 1996 through 2005. This presentation was first placed
on the Internet in June 2005.
Presented June 2005|
- A careful examination of the mechanical structure of neck
vertebrae of Sauropod Dinosaurs seems to require new perspectives
and conclusions regarding their lives.
- We know the dimensions of the neck structure of Sauropod Dinosaurs.
IF they were land-dwelling creatures and they carried their head
out ahead of the body, then the head was necessarily supported
in a cantilevered manner.
- Since most biological tissue has a density very similar to that
of water, we know pretty reliably that some Sauropods had heads
which weighed at least a metric tonne, or 2,200 pounds. Using standard
Mechanical Engineering formulas, we can determine the stress loads
on each neck vertebrae, neck disk, neck muscle and neck tendon.
- The results of such calculations indicate that many Sauropods COULD NOT
HAVE cantilevered their heads horizontally forward of their forelegs.
- In 1997, we provided the mathematical proof that heart muscles and
tissues, heart valves and artery tissues could not withstand the
fluid pressure loads for any situation where a Sauropod would have raised
its head high to eat from treetops.
- The fact that we now have eliminated BOTH possibilities regarding
land-dwelling Sauropods seems to force a necessary conclusion that
such large Sauropods could not have been land-dwelling animals.
They NEEDED to have some flotation effect, in order to support the
head, given the known neck vertebrae data. This seems to force
the conclusion that they were Swamp-dwelling or even swimmers.
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 of 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
Sauropod Dinosaur Physics Subjects 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 heart to be slightly over 2 meters
(7 feet), as in giraffes or African Elephants 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.
If the neck and head would have been lowered to the ground regularly,
meat-eating predators would certainly have attacked and killed them,
but they evidently lived for very long times to be able to grow
to such immense size and mass.
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 angled 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 more than 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.
This is realistically within the strength of modern muscle, ligament,
and tendon tensile strengths. It IS possible for the sauropod
to have held its head up cantilevered while on dry land.
However, if that sauropod spent most of its life in a swamp or pond,
the flotation effect would allow that head and neck to be nearly
completely supported by natural flotation, where no continuous
massive musculature exertion would have been required, as would
certainly be true as a land-based creature.
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.
Sauropod Dinosaur Physics Subjects. A logical discussion of several poor assumptions regarding dinosaurs
Sauropod Dinosaur Mouth Analysis Regarding Cold-/Warm-Blooded The size of dinosaurs' mouths and the capability to be warm-blooded
Sauropod Dinosaur Neck Physics Analysis The strength of neck bones, muscles and tendons in dinosaurs
This presentation was first placed on the Internet in June 2005.
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago