# RE: Centripetal Forces on a Horizontally Grazing Sauropoda

```How might the sauropod get blood *back* to the heart in this system? The
centripetal acceleration might work to get blood away from the thorax, but
wouldn't it also keep it from getting back? I don't know if it'd be as
simple as setting up a venous "siphon" system between the tail and neck, as
blood from the tail and blood from the neck empty into the heart via
different veins (posterior vena cava and anterior vena cava, and the whole
complication of the hepatic portal system, etc.).

Andy

> -----Original Message-----
> From: owner-dinosaur@usc.edu [mailto:owner-dinosaur@usc.edu] On Behalf Of
> Mike Milbocker
> Sent: Tuesday, April 13, 2004 10:33 AM
> To: dinosaur@usc.edu
> Subject: 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.

```