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*To*: augustoharo@gmail.com*Subject*: Re: Sauropod browsing energetics*From*: Mike Taylor <mike@indexdata.com>*Date*: Thu, 24 Mar 2011 22:42:45 +0000*Authentication-results*: msg-ironport2.usc.edu; dkim=neutral (message not signed) header.i=none*Cc*: skeletaldrawing@gmail.com, david.marjanovic@gmx.at, DML <dinosaur@usc.edu>*In-reply-to*: <AANLkTinv6aK2vgsWXqhx0YmxKWcu4XRUV1zpBQB3O0xw@mail.gmail.com>*References*: <380-220113323161828668@M2W142.mail2web.com> <4D8A4D95.9070800@gmx.at> <AANLkTik=dP+aZZWRW2_9Emb2QkyzaQyx8Z+RZgF6Fy_8@mail.gmail.com> <AANLkTinv6aK2vgsWXqhx0YmxKWcu4XRUV1zpBQB3O0xw@mail.gmail.com>*Reply-to*: mike@indexdata.com*Sender*: owner-DINOSAUR@usc.edu

On 24 March 2011 22:22, Augusto Haro <augustoharo@gmail.com> wrote: >> plus mechanically speaking >> simply having the longer neck necessitates greater muscle exertion >> _all the time_ (less so if held upright, but still extra work >> regardless), > > At equal mass, wouldn't be necessary also greater muscular exertion to > support an equivalent mass in other parts of the body of the similarly > massive animal? If you isometrically increase the size of a sauropod by a linear factor of x, then its mass scales with x^3 and the cross-sectional area of its muscles scale with x^2, so that mass/area scales with x. However, the neck and tail suffer worse because they are cantilevered out from the body. Not only does their mass scale with x^3, but the distance out from the fulcrum at which this mass acts scales with x, so that the moment to be countered scales with x^4. Does this mean that it's hard for necks to scale isometrically with the rest of the body? Well, not really -- because the height above the fulcrum at which the epaxial tension members acts is ALSO increased by a factor of x, so that the counter-moment goes with x^3 (i.e. x^2 for the force generated by muscles with cross-sectional area proportional to x^2, times the moment arm x). So the increases in the moment arms cancel out. So using this very simple (read: grossly oversimplied) model, it seems that the difficulty of scaling necks and tails as animals grow isometrically is exactly the same as that of scaling legs and other body parts, i.e. that stresses grow linearly with x. (Of course, larger animals are not in general isometrically similar to smaller ones.)

**References**:**Sauropod browsing energetics***From:*"bh480@scn.org" <bh480@scn.org>

**Re: Sauropod browsing energetics***From:*David Marjanovic <david.marjanovic@gmx.at>

**Re: Sauropod browsing energetics***From:*Scott Hartman <skeletaldrawing@gmail.com>

**Re: Sauropod browsing energetics***From:*Augusto Haro <augustoharo@gmail.com>

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