# Centripetal Forces on a Horizontally Grazing Sauropoda

```Centripetal Forces on a Horizontally Grazing Sauropoda

It has been presented that sauropods kept their head and neck coplanar with
the body and tail, and swung the neck, out-stretched in a circular path,
called the browse plane, centered on the shoulder region.

Assuming the neck length to be L, and the head makes one 180 degree transit
in time t then the force, F, that would push blood toward the head is given
by

F = mar = m V2/L   where V = pL/t

To give

F = mp2L2/t2

And

ar = p2L2/t2

Let L= 10m, then ar = 973/t2

For ar to equal the acceleration of gravity (ar = 9.8 m/s2)

t = 10 seconds

This is not an unreasonably short period of time if the head were to be
involved in warning the sauropod of danger.

If the sauropod were raising its head in a circular trajectory perpendicular
to the browsing plane, this would be the maximum time allowed in order for
gravity not to impede blood flow, i.e., at this rise rate the blood would be
?weightless?.

For faster motion, the head could actively fill with blood while rising. The
table below gives the g?s of force at various rise times:

Rise Time               g?s of force

10 s                    0.99
9 s                     1.23
8 s                     1.55
7 s                     2.03
6 s                     2.76
5 s                     3.97
4 s                     6.21

Thus, the rapid motion of the head in a circular arc can create sufficient
blood pumping forces.

If the head and tail were swept asynchronously, the animal could create an
efficient blood pumping system, independent of a heart. Combining feeding
and defensive strategies with blood pumping may have allowed this class of
animals to achieve their great size.

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