So I'm interested in sauropod size, and I was wondering how Ken Carpenter got his mass and length estimate in his paper on Amphicoelias fragillimus
since I'm kinda a numbers guy. This is what I found, if you're interested, and I posted this stuff on the DML (Dinosaur Mailing List) a week or so ago (slightly edited):
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 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 of the CMNH 84 specimen of D. carnegii lists the 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 mass of over 247 tonnes. I find this mass estimate of nearly 250 tonnes difficult to swallow. Paul uses a density of 0.9 for the body excluding the neck, even if we assume that 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.
Then I got this reply (and the only reply) from Dr. Mark Witton:
Your comments reminded me of this blogpost, which you may already have seen:
Mike Taylor's closing statement sums it all up nicely:
'Folks please remember, the punchline is not Amphicoelias fragillimus only weighed 78.5 tonnes rather than 122.4 tonnes. The punchline is when 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.'
To which, I replied:
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 rains a few years back 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 canal is missing. So, Mike's estimate for the height of the dorsal 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.
So yes, Amphicoelias fragillimus
was indeed BIG and probably bigger than any other sauropod for which we have evidence (as far as I am aware) and probably much bigger than commonly thought.
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). Taxonomic status of Seismosaurus hallorum
, a Late Jurassic sauropod dinosaur from New Mexico. 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. 149161. 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.