Amphicoelias size

[Zach Armstrong <zach.armstrong64@yahoo.com>]

Ok, so this has been bugging me for a while, so I decided to see if anyone can 
help me out here.

Carpenter (2006) in his review of *Amphicoelias fragillimus* reconstructed a 
height of 2.7 meters for the posterior dorsal based off comparisons to *A. 
altus*. Now he estimated a length of 58 meters and a mass of 122,400 kg. This 
is 

his method for these calculations: "Assuming that the mega-diplodocids are 
scaled up versions of Diplodocus, then the volume (hence mass) changes in 
proportion to the third power of the linear dimension (Schmidt-Nielsen, 1984). 
Thus, if Diplodocus carnegii had a length of 26.25 m and mass of 11,500 kg 
(Paul, 1994), then A. fragillimus had a mass of around 122,400 kg, which is 
still within the hypothesized maximum mass for a terrestrial animal (Hokkanen, 
1986)." Now, the mass follows if we assume that *A. fragillimus* was 58 meters, 
and *D. carnegii* was 26.25 meters. This means *A. fragillimus* was 
58/26.25=2.2 

times as big in linear dimensions. This means it should be (2.2)^3=10.648 times 
as voluminous and thus presumably that many times more heavier than *D. 
carnegii*. So 11,500*10.648=122,452 kg. So that makes sense.

However, where did Carpenter get the length estimate  for *A. fragillimus*? He 
based it off of *D. carnegii*, as mentioned above and cited the stats for the 
latter from Paul (1994). However, Paul (1994) did not list a mass of 11,500 kg 
and a length of 26.25 meters for *D. carnegii*. He listed a mass of 11 tonnes 
and a length of 24.8 meters. So where did the mass estimates that Carpenter 
cited come from? I don't know. Am I missing something here? Maybe someone else 
on the list can help me out here.

But that's not all. If *A. fragillimus* is supposed to be 2.2 times larger in 
linear dimensions, then going backwards from the estimated height of 2.7 meters 
estimated for the lone preserved dorsal in *A. fragillimus* means that the 
dorsal vertebrae of *D. carnegii* should 2.7/2.2=1.22 meters tall. Now, my 
digital copy of Hatcher's (1901) description o
9th dorsal as 94.6 cm tall and the 10th dorsal as 96.6 cm 
tall (even the supposed "11th dorsal" was only 105.1 cm tall). So, somehow 
Carpenter thought that the comparable dorsal in *D. carngeii* was somewhere 
between 25.4 and 27.4 cm taller than it actually was. In fact, Lucas et al.'s 
(2006) taxonomic revision lists the 9th dorsal as about 1.2 meters tall for the 
"seismosaur" specimen. So Carpenter in essence assumed that an individual 
*Diplodocus* with seismosaur-sized vertebrae only massed about 11.5 tonnes and 
was 26.25 m long, even though more recent estimates of the seismosaur's size 
are 

around 30 tonnes in mass and 30-32 meters in length.

So what happens if we scale off the actual measurements listed for the CMNH 84 
*D. carnegii* specimen? Well,  assuming the dorsal in *A. fragillimus* was the 
10th dorsal, then it was 2.7/0.966=2.79 times larger in linear dimensions than 
that *Diplodocus* specimen. If that specimen was indeed 24.8 meters as Paul 
(1994) says, than an estimated length for *A. fragillimus* is around 69 meters, 
a full 11 meters longer than Carpenter originally estimated. The disparity is 
even worse if we assume a 26.25 m *Diplodocus* individual which gives us an 
estimated length of around 73 meters.

What about mass? Well, if *A. fragillimus* was 2.79 times larger in linear 
dimensions than *D. carnegii*, then it was (2.79)^3=21.7 times more voluminous 
and therefore more massive. So, assuming that the CMNH 84 specimen was indeed 
11.5 tonnes, then *A. fragillimus* should be 21.7*11.5=249.55 tonnes (!). This 
is almost 130 tonnes heavier than estimated by Carpenter, and is larger than 
the 

largest Blue Whale specimens that I have heard about, the largest of which may 
have been at least 200 tonnes in mass based off oil yield. Even using Greg 
Paul's more precise estimate of 11.4 tonnes listed on his website for the CMNH 
84 

*Diplodocus* still gives a mas of  over 247 tonnes. I find this mass estimate 
of 

nearly 250 tonnes difficult to swallow. Paul uses a density of 0.9 fo
t this should be about 0.8 as indicated 

by work done on pneumaticity in sauropods done by Matt Wedel, this would mean 
we 

could reduce the mass to be about 88% of of the original mass which reduces it 
only
to 219 tonnes, which is still fairly unbelievable. So, here's the big question: 
is there 

some major flaw in my reasoning here?

For the record, I think Carpenter's estimated height for *A. fragillimus* is 
reasonable. I did a similar scaling technique using GIMP's measuring tools and 
got an estimated height of 2.65 meters for the vertebrae based off of *A. 
altus*. Using this slightly reduced measurement, you still get a mass estimate 
of around 235-237 tonnnes (depending on how many decimal places you want to 
truncate) which is still around 110 tonnes heavier than estimated by Carpenter 
and is still heavier the heaviest known Blue Whales.

Best regards,

Zach

Refs--

Paul, G.S., 1994, Big sauropods - really, really big sauropods: The Dinosaur 
Report, The Dinosaur Society, Fall, p. 12-13.

Lucas, S.G., Spielman, J.A., Rinehart, L.A., Heckert, A.B., Herne, M.C.,  Hunt, 
 

A.P., Foster, J.R., and Sullivan, R.M. (2006). âTaxonomic status  of  
Seismosaurus hallorum, a Late Jurassic sauropod dinosaur from New Mexicoâ. In  
Foster, J.R., and Lucas, S.G.. Paleontology and Geology of the Upper Morrison 
Formation. New Mexico Museum of Natural History and Science (bulletin 36). pp. 
149â161. ISSN 1524-4156.

Carpenter, Kenneth.  2006.  Biggest of the big: A critical re-evaluation of the 
mega-sauropod Amphicoelias fragillimus Cope, 1878.  pp. 131-137 in J. Foster 
and 

S. G. Lucas (eds.),  Paleontology and Geology of the Upper Jurassic Morrison 
Formation.  New  Mexico Museum of Natural History and Science Bulletin 36.

Hatcher, J.B. 1901. Diplodocus (Marsh): its osteology, taxonomy  and probable 
habits, with a restoration of the skeleton. Memoirs of the  Carnegie Museum 1: 
1-63 and plates I-XIII.