Method 1 is obviously succeptible to the interpretation of the model-maker. The ``classic'' mass estimate of 80 tons for Brachiosaurus comes from Colbert's 1962 application of method 1 to a model which Matt Wedel describes as ``morbidly obese. It looked like a freakin' Macy's parade balloon. The limb muscles go well beyond the boundaries of the girdles, a sure sign that someone was just throwing clay on an armature without doing a musculoskeletal reconstruction first.''
R. McNeil Alexander applied the same technique to rather better Brachiosaurus model from the British Museum of Natural History, arriving at an estimate of 46 tons; and Greg Paul has done something similar with his own bones-and-muscle reconstruction and reached an estimate of ``only'' 32 tons.
There is another difficulty with method 1: we don't know the density of dinosaurs. Colbert estimated a density close to 1 (i.e. the same as water) based on that of crocodiles, because they are related to dinosaurs. But sauropods are morphologically very distant from modern crocodiles! While limb bones are typically very solid (no marrow cavity), sauropod vertebrae, particularly those of larger species, tend to be extensively pneumatic. To cite Matt Wedel again, his guess at Argentinosaurus density (and so, I imagine, most large sauropods) is 70-75% - but that's based on the assumption of a much more extensive air-sac system than most people seem prepared to believe in. Still, any figure in the range 70-100% seems credible.
Method 2 has its own obvious problem - real animals don't stay on or even very close to the ``best line'' through the points you get by plotting limb-bone cross-sectional area vs. mass. For example, on the basis of such a ``best line'', you'd expect elephants to have thicker leg bones than they actually have, and rhinos to have thinner bones. This variation reflects the fact that different animals have different degrees of athletic ability. So method 2 is probably not good for much better than a within-a-factor-of-two estimate. For what it's worth, Anderson et al. used this method to estimate a Brachiosaurus mass similar to Greg Paul's 32 tons.
Method 3 is succeptible to the same kind of artist's-impression problems as 1, plus it seems inherently less reliable, as it depends more on guesswork concerning the third dimension. The truth is, I don't fully understand Christiansen's explanation of this method, but it does seem to involve a lot of intuition.
Finally, to clear up the 180-ton Brachiosaurus estimate: this is actually for ``Ultrasauros'', which at the time of the estimate was thought to be a large brachiosaurid[1]. In his otherwise wonderful book Dinosaurs, Spitfires and Sea Dragons, Christopher McGowan's reaches this staggering number by considering the classical 80-ton estimate for vanilla Brachiosaurus, observing that the ``Ultrasauros'' bones are 1.3 times the size of those in well-known Brachiosaurus specimens, and multiplying 80 tonnes by 1.33, which is about 2.2.
Notes
This left Jensen in the strange position that his own animal couldn't be known by its own name, which was preoccupied by Kim's sauropod. Faced with this situation, he simply shrugged and named his animal Ultrasauros (1985) instead.
So far so weird. But wait - there's more! Then it became apparent that the holotype of the new taxon - a dorsal vertebra - was in fact from Supersaurus, the diplodocid discovered at the same time. Which meant that ``Ultrasauros'' because a junior synonym of Supersaurus.
The remaining ``Ultrasauros'' material - a scapulocoracoid - is now thought to represent merely a large Brachiosaurus - about 15% larger than the specimen in the Humbolt museum (although that's a composite.) Apparently, it's no larger than the biggest of the Tendaguru Brachiosaurus specimens. [back]