In our PeerJ neck-anatomy paper, we speculated on how long individual cervical vertebrae might have grown. Here is the relevant section:

Mere isometric scaling would of course suffice for larger animals to have longer necks, but Parrish (2006, p. 213) found a stronger result: that neck length is positively allometric with respect to body size in sauropods, varying with torso length to the power 1.35. This suggests that the necks of super-giant sauropods may have been even longer than imagined: Carpenter (2006, p. 133) estimated the neck length of the apocryphal giant Amphicoelias fragillimus Cope, 1878 as 16.75 m, 2.21 times the length of 7.5 m used for Diplodocus, but if Parrish’s allometric curve pertained then the true value would have been 2.21^1.35 = 2.92 times as long as the neck of Diplodocus, or 21.9 m; and the longest single vertebra would have been 187 cm long.

Now this speculation is shot through with uncertainty. As we’ve discussed before, at length, all estimates of Amphicoelias fragillimus length and mass are wildly speculative; and Parrish’s allometry result was extrapolated from an unconvincingly small data set. But still, these numbers are probably the best we can do with what we have.

In Diplodocus carnegii, C14 is the longest individual vertebra at 642 mm long (Hatcher 1901, p. 38). The Amphicoelias:Diplodocus size ratio of 2.21 from Carpenter and the neck allometry constant of 1.35 from Parrish suggest that the corresponding vertebra in the big boy would have been 2.92 times as long as that 642 mm, hence the 187 cm that we reported.

So what does a 187-cm long cervical vertebra look like? Scaling up from the Diplodocus carnegii C14 in Hatcher (1901: plate III) and using my good self as a scalebar, here it is:

I find that just a little bit frightening. In more ways than one.

References

• Carpenter, Kenneth. 2006 Biggest of the big: a critical re-evaluation of the mega-sauropod Amphicoelias fragillimus (Cope, 1878). New Mexico Museum of Natural History and Science Bulletin 36:131.
• Cope, Edward D. 1878. Geology and paleontology: a new species of Amphicoelias. The American Naturalist 12:563.
• Hatcher, Jonathan 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.
• Parrish, J. Michael. 2006. The origins of high browsing and the effects of phylogeny and scaling on neck length in sauropodomorphs. pp 201-224 in: Amniote paleobiology, University of Chicago Press, Chicago.