Sauropod Dinosaur Neck Physics Analysis

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.

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Extensive Research regarding dinosaur physiology was performed from 1996 through 2005. This presentation was first placed on the Internet in June 2005.

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.

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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
a Diplodocus neck structure
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
a Diplodocus neck - some of the connecting muscles drawn in
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
a human cervical (neck) vertebra
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
seventh, lowest cervical vertebra in humans

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