Re: Amphicoelias size

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

Thanks Mark. I have indeed read that post. However, it mainly is dealing with 
the proposed dimensions of the vertebrae. I am more concerned with being unable 
to replicate Carpenter's work, which as I noted, is due to apparently faulty 
assumptions as to the dimensions of *Diplodocus*. If we instead accept Mike 
Taylor's estimate of the height at about 2.29 meters, we still get that *A. 
fragillimus* was 2.29/.966=2.37 times as long as *D. carnegii* which means an 
extrapolated length of over 58 meters, which compares well to Carpenter's 
original estimate of 58 meters. However, I get this by assuming *D. carnegii* 
was 24.8 meters long; if we instead assume Carpenter's length for the latter 
species of 26.25 meters, we get an extrapolated length of just over 62 meters. 
Compare this to Mike's length estimate of around 49 meters. So, by my 
calculation, we're still off by 9-13 meters from Mike's estimate.


Also, *A. fragillimus* would be (2.37)^3=13.3 times as voluminous, for a 
resulting mass estimate of 151.6 tonnes (assuming *D. carnegii* was 11.4 
tonnes). Compare this to Mike's reduced mass estimate of 78.5 tonnes. So I'm 
still off by over 73 tonnes from Mike's estimate. This is because Mike assumed 
Carpenter's original math was right, but, as far as I can tell, it is not. So 
we're still talking a sauropod in the 150-250 tonne range, which is still 
larger 
by at least 50 tonnes than the next biggest sauropod (excluding the problematic 
*Bruhathkayosaurus* whose material has now been lost in heavy according to Dr. 
Kumar Ayyasami, so it's unlikely we'll ever get a better description, esp. 
since 
he apparently has no other photos or drawings of the material) and still around 
30 tonnes larger than Carpenter originally estimated.

I should point out that Mike probably underestimates the height of *A. 
fragillimus* anyways. If you notice, the neural arch in *A. fragillimus* is a 
lot longer than in the scaled up *A. altus* photo--and we are still missing a 
good part of the neural arch since the neural cana
 of *A. fragillimus* is probably at least 
10 cm too short, probably more, for a more probable (IMO) height of 2.39+ 
meters. That would imply a mass of around 84-85 tonnes using Mike's method 
based 
off Carpenter. However, using the real dimensions of *D. carnegii* we would 
actually get an implied mass of  around 172 tonnes give or take a few kilos. 
This is more than double Mike's estimate of 78.5 tonnes for a 2.29 meters 
dorsal 
and for the adjusted mass of 84 tonnes for a 2.39 meter dorsal.

Obviously, there are ways to get the numbers down. Greg Paul's original mass of 
*D. carnegii* might be too high because he used a density of 0.9 instead of the 
more likely 0.8 for the average density of the body and the tail, and 0.6 for 
the neck instead of a more likely 0.3. This means we could comfortably reduce 
all the mass estimates above by about 10-12%. This still gives us an equally 
plausible range of 152-221 tonnes and easily over 60 meters depending on the 
exact restored dimensions of the vertebrae, and still indicates an animal the 
size of your average Blue Whale and maybe heavier. Whatever, *Amphicoelias* was 
BIG.


----- Original Message ----
From: Mark Witton <Mark.Witton@port.ac.uk>
To: zach.armstrong64@yahoo.com
Cc: dinosaur@usc.edu
Sent: Tue, January 11, 2011 4:09:44 AM
Subject: Re: Amphicoelias size

Zach, 

Your comments reminded me of this blogpost, which you may already have seen:

http://svpow.wordpress.com/2010/02/19/how-big-was-amphicoelias-fragillimus-i-mean-really/


Mike Taylor's closing statement sums it all up nicely: 

'Folks â please remember, the punchline is not âAmphicoelias fragillimus only 
weighed 78.5 tonnes rather than 122.4 tonnesâ.  The punchline is âwhen you 
extrapolate the mass of an extinct animal of uncertain affinities from a 
132-year-old figure of a partial bone which has not been seen in more than a 
century, you need to recognise that the error-bars are massive and anything 
resembling certainty is way misplaced.â'

Mark

--

Dr. Mark Witton

Palaeobiolo
y of Portsmouth
Burnaby Building
Burnaby Road
Portsmouth
PO1 3QL

Tel: (44)2392 842418
E-mail: Mark.Witton@port.ac.uk

If pterosaurs are your thing, be sure to check out:

- Pterosaur.Net: www.pterosaur.net
- The Pterosaur.Net blog: http://pterosaur-net.blogspot.com/
- My pterosaur artwork: www.flickr.com/photos/markwitton 

>>> Zach Armstrong <zach.armstrong64@yahoo.com> 10/01/2011 20:44 >>>
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 e
t 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 spec
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
tural 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.