Size comparison scale

[theropod]

The problem is, this won’t impact the head mass overall, but its shape.

[Grey]

I've indicated Bianucci's opinion regarding the most likely shape of the head, no matter if that still allows to get a weight estimate.
Not sure about the bone density though.

[theropod]

And what phase of the spermaceti chamber does it refer to?
Bone density is the least of our concerns (overall density is near-impossible to estimate though, without a ct-scan at least)

[Grey]

Please pay attention : theworldofanimals.proboards.com/post/18481/thread

The c) option (source : Bianucci pers. comm with Jaime Bran).

[theropod]

So? That doesn’t answer the question, it is a speculative restoration of a Livyatan head in lateral view, but for its density it is important to know what impact the spermaceti chamber has on it.

[theropod]

Or, differently phrased, what’s the specific gravity of spermaceti in liquid and solid state respectively, and how much of the head is occupied by it in this reconstruction.

[Grey]

The restoration is speculative but in anycase, the variation is rather minor. For the density, we'd just need the density of Physeter.

[theropod]

Nope, the ratio between various components is going to be very different in Livyatan (way more bone, smaller spermaceti chamber…).
As regards the spermaceti, perhaps the difference is minor, perhaps it is not. If it serves to regulate bouyancy in an animal as humungous as Physeter, it must have quite some impact there at least.

[Grey]

Well, I don't see how it would impossible to make, given all the GDI estimates I've seen for others taxa with less complete remains and less reliable proxys to use.

[LeopJag]

Elephant seal. guess that they can get even bigger....

[theropod]

Oct 19, 2014 22:52:41 GMT 5 Grey said:

Well, I don't see how it would impossible to make, given all the GDI estimates I've seen for others taxa with less complete remains and less reliable proxys to use.

Then, how would you suggest to estimate the density of Livyatan’s head?

There are estimates for the density of those other taxa, and those, for the most part, are actually very complete (e.g. T. rex, Diplodocus, Brachiosaurus…) and well-described–and often studied in detail by the people who made those GDIs.
These estimates base on volumetric estimates, 3d-scanning (Hutchinson et al. 2011, Bates et al. 2009ab) and modeling and/or calculations involving crosssectional proportions (e.g. Wedel 2005) of that very taxon. Of course if you are reasonably certain that two things are very close in density, you can assume they are the same, but that isn’t the case here.
In this case, the tissue composition is certainly quite different from Physeter, the latter having a huge spermaceti chamber of variable density and relatively slender jaws and jaw muscles, while Livyatan has massive jaws and jaw muscles and a smaller spermaceti chamber.

If what you want is a mere estimate of volume, that’s way easier of course, as one can disregard the internal built.

[Grey]

It's not about what I want but about what's possible. That's just an idea, if you can try it the most accurately possible.

[theropod]

I’ve made a rough, GDI-like model with elliptical cross-sections for the cranium. Not sure how much soft-tissue there should be lateral to the maxillae and dentaries though, hence, this one is somewhat conservative. What I only really realised now is how extremely wide and flat this head is, quite the opposite of physeter with its relatively narrow head!

I got a volume of 4.8062m³ if my measurement is correct (though there’s some chance that the plugin I’m using isn’t working properly), measured as if the head was cut off clean at the condyle.
Does that sound reasonable?

Just for contrast, the skull of Sue turned out at 392kg in Hutchinson et al. 2011. Assuming it had a density of ~0.8, that translates to a volume of ~0.49m³, but that’s because theropod skulls are inflated and filled with air.
That of Livyatan is certainly closer to an entire T. rex than to its head.

See the attached files for details. I’ve attached the 3d model too, in case someone wants it. The background images aren’t included though, so if you need those, best just send me an email.

EDIT: See a revised version here→

Attachments:

livcranium2.blend (408.18 KB)

[Grey]

4.800 kg seems reasonnable, that's an idea already.

[theropod]

Not necessarily 4800kg.
The entire whale likely has a density similar to that of water, but that includes the lungs (at least when its not diving deep) and a lot of blubber. Likely that the heavy skull and teeth serve as ballast.

I’ve found this: plymsea.ac.uk/2029/1/Physical_properties_of_spermaceti_oil_in_the_sperm_whale.pdf
liquid spermaceti at a temparature has a specific gravity of about .853 (but it does get significantly denser at lower temperatures and higher pressures). Compact bone has a density of 1.5-1.9 according to various sources, and that of skeletal musculature is 1.09 (Snively et al. 2013, but I believe to have read that elsewhere as well). The brain and air spaces are probably neglegible but the tricky part is where it comes to the relative volume of the skull bone itself (which is still a very complex shape), and the surrounding skin, fat and fascia.

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References:
Clarke (1978): plymsea.ac.uk/2029/1/Physical_properties_of_spermaceti_oil_in_the_sperm_whale.pdf
Hutchinson, John R.; Bates, Karl T.; Molnar, Julia; Allen, Vivian; Makovicky, Peter J.: A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth. Vol. 6 (2011); 10; pp. 1-20
Snively, Eric; Cotton, John R.; Ridgely, Ryan; Witmer, Lawrence M.: Multibody dynamics model of head and neck function in Allosaurus (Dinosauria, Theropoda). Palaeontologia Electronica, Vol. 16 (2013); 2; pp. 1-29