Norwescon 41 Guests of Honor: Ken Liu, Galen Dara, and, er, me. Mike would like to remind you that you can get your own ‘Kylo Stabbed First’ t-shirt here.

The week before last I was fortunate to be the Science Guest of Honor at Norwescon 41 in Seattle (as threatened back when). I had a fantastic time. I got to give talks on binocular stargazing and the sizes of the largest sauropods and whales (ahem), participate on panels on alien biology and creature drawing, and meet a ton of cool people, including my fellow Guests of Honor, multiple-award-winning author Ken Liu and multiple-award-winning artist Galen Dara, both of whom turned out to be humble, easygoing, regular folks (if frighteningly talented).

I also had a lot of great conversations with folks who were attending the con, which is exactly what I wanted. One of the most interesting was a hallway conversation with a fellow DM named Shawn Connor. He had a great question for me, which I liked so much I wanted to answer it here on the blog. Here’s his question, copied with permission from a follow-up email:

I run tabletop RPGs, and in my current game one of the characters is a caveman type who naturally grew up hunting dinosaurs. As one does. His weapon is a dinosaur bone, customized and used as a club. I have attached the picture that he came up with [below]. Now understanding the picture is obviously not of a real dinosaur bone – it’s probably a chicken bone or a cow bone or something – let’s assume for the sake of this exercise that it is and that it is four feet long stem to stern. Given that, two questions: discounting the extra bling attached how heavy would such a bone be, and what kind of dinosaur could it have come from?

I’m going to answer those questions out of order. Advance warning: this will be a loooong post that will go down several rabbit holes that are likely of more intense interest to me, personally, than to anyone else on the planet. Read on at your own risk.

Whose femur is in the image?

First, Shawn is correct in noting that the femur in the image provided by his player is not a dinosaur femur. The prominent trochanters and spherical head offset on a narrow neck clearly make it a mammal femur, and if it’s four feet long, it could only have come from an elephant or an indricothere. Or a giant humanoid, I suppose, which is what the anatomy of the bone in the image most closely resembles. (It also appears to be foreshortened to make the distal end look bigger, or deliberately distorted to enhance the clubby-ness.)

Mounted elephant at the Museum of Osteology in Oklahoma City, with Tyler Hunt for scale.

But let’s play along and assume it’s from a non-human mammal. How big? Back in 2016 I was fortunate to get to measure most of the mounted large mammal skeletons at the Museum of Osteology in Oklahoma City, along with Tyler Hunt, then a University of Oklahoma undergrad and now finishing up his MS thesis under my mentor, Rich Cifelli.* The mounted elephant at the Museum of Osteology has a shoulder height of 254 cm (8 ft, 4 in) and a femur length of 102 cm (3 ft, 4 in). Assuming isometric scaling, a world record elephant with a shoulder height of 366 cm (12 ft) would have a femur length of 147 cm (4 ft, 10 in). So a four-foot (122 cm) femur would belong to an elephant roughly in the middle of that range, about ten feet (3 m) tall at the shoulder. That’s the size of the big bull elephant mounted at the Field Museum in Chicago.

The big mounted bull elephant at the Field Museum is 10 feet tall at the shoulder and weighed 6 tons in life. Note Mike for scale on the lower right. He and the elephant are about equidistant from the camera, so he should make a roughly accurate scale bar. Photo from our visit in 2005!

* Two further notes: first, I have roughly a zillion awesome photos from that 2016 visit to the Museum of Osteology, both of the specimens and of Tyler and me measuring them – not having posted them yet is one of the things I was whingeing about in the post that kicked off our return-to-weekly-posting thing this year. And second, I owe a belated and public thanks to the folks at the Museum of Osteology for accommodating Tyler and me. They helped us with ladders and so on and basically gave us free rein to play with collect data from their mounted skeletons, which was incredibly generous and helpful, and fortunately reflects the pro-research and pro-researcher attitude of most museums.

Which dinos had four-foot femora?

As for what kind of dinosaur a four-foot femur could have come from, we can rapidly narrow it down to a handful of clades: sauropods, ornithopods, theropods, and stegosaurs.

  • Sauropods. The longest complete femora of Patagotitan are 238 cm (7 ft, 10 in; Carballido et al. 2017), and an incomplete femur of Argentinosaurus has an estimated complete length of 250 cm (8 ft, 2 in; Mazzetta et al. 2004). So a four-foot femur would not be from a particularly large sauropod – something about elephant-sized, as you might expect from the elephant comparison above. Our old friend Haplocanthosaurus will fit the bill, as we’ll see in a bit.
  • Ornithopods. Femora of 172 cm (5 ft, 8 in) are known for the hadrosaurs Shantungosaurus (Hone et al. 2014) and Huaxiaosaurus (Zhao and Li 2009), and Zhao et al. (2007) reported a 170 cm (5 ft, 7 in) femur for Zhuchengosaurus (Huaxiaosaurus and Zhuchengosaurus may be junior synonyms of Shantungosaurus). But those are all monsters, well over 10 metric tons in estimated mass. So a four-foot femur would be from a large but not insanely large hadrosaur.

Mmmmmm…suffering. OM NOM NOM NOM!!

  • Theropods. Among the largest theropods, the holotype of Giganotosaurus has a femur length of 143 cm (4 ft, 8 in; Coria and Salgado 1995), and ‘Sue’ the T. rex (a.k.a. FMNH PR2081) has a right femur 132 cm long (4 ft, 4 in; Brochu 2003). So a four-foot femur from a theropod would definitely be from one of the monsters. The femur of Saurophaganax was 113.5 cm long (Chure 1995), just under four feet, which I only note as an excuse to use the above photo, which I adore.
  • Stegosaurs. I don’t know the longest femur that has been recovered from a stegosaur, but getting in the ballpark is easy. NHMUK PV R36730 has a femur 87 cm long, and the whole animal was approximately 6 m long (Maidment et al. 2015). Partial bits and bobs of the largest stegosaurs suggest animals about 9 m long, implying a femur length of about 130 cm (4 ft, 3 in), or just over the line.

I think that’s it. I don’t know of any ceratopsians or ankylosaurs with femora long enough to qualify – I assume someone will let me know in the comments if I’ve forgotten any.

How much would a four-foot femur weigh?

There are a couple of ways to get to the answer here. One is to use Graphic Double Integration, which is explained in this post.

Limb bones are not solid – in terrestrial tetrapods there is virtually always a marrow cavity of some sort, and in marine tetrapods the limb bones tend to be cancellous all the way through. Estimating the mass of a limb bone is a lot like estimating the mass of a pneumatic bone: figure out the cross-sectional areas of the cortex and marrow cavity (or air space if the bone is pneumatic), multiply by the length of the element to get volumes, and multiply those volumes by the density of the materials to get masses. I piled up all the relevant numbers and formulas in Tutorial 24, a move that has frequently made me grateful to my former self (instead of cussing his lazy ass, which is my more usual attitude toward Past Matt).

Currey and Alexander (1985: fig. 1)

Sauropod limb bones are pretty darned dense, with extremely thick cortices and smallish marrow spaces that are not actually hollow (tubular) but are instead filled with trabecular bone. My gut feeling is that even a four-foot sauropod femur would be almost too heavy to lift, let alone wield as a club, so in the coming calculations I will err in the direction of underestimating the mass, to give our hypothetical caveman the best possible chance of realizing his dream.

Some of the proportionally thinnest cortices I’ve seen in sauropod limb bones are those of the macronarian Haestasaurus becklesii NHMUK R1870, which Mike conveniently showed in cross-section in this post. I could look up the actual dimensions of the bones (in Upchurch et al 2015: table 1 – they passed the MYDD test, as expected), but for these calculations I don’t need them. All I need are relative areas, for which pixels are good enough.

First, I took Mike’s photo into GIMP and drew two diameters across each bone, one maximum diameter and a second at right angles. Then I drew tick marks about where I think the boundaries lie between the cortex and the trabecular marrow cavity. Next, I used those lines as guides to determine the outer diameters (D) and inner diameters (d) in pixels, as noted in the image.

For the radius, on the left, the mean diameters are D = 891 and d = 648. I could divide those by 2 to get radii and then plug them into the formula for the area of a circle, etc., but there’s an easier way still. For a tubular bone, the proportional area of the inner circle or ellipse is equal to k^2, where k = r/R. Or d/D. (See Wedel 2005 and Tutorial 24 for the derivation of that.) For the Haestasaurus radius (the bone, not the geometric dimension), d/D = 0.727, and that number squared is 0.529. So the marrow cavity occupies 53% of the cross-sectional area, and the cortex occupies the other 47%.

For the ulna, on the right, the mean diameters are D = 896 and d = 606, d/D = 0.676, and that number squared is 0.457. So in this element, the marrow cavity occupies 46% of the cross-sectional area, and the cortex occupies the other 54%.

(For this quick-and-dirty calculation, I am going to ignore the fact that limb bones are more complex than tubes and that their cross-sectional properties change along their lengths – what I am doing here is closer to Fermi estimation than to anything I would publish. And we’ll ground-truth it before the end anyway.)

Left: rat humerus, right: mole humerus. The mole humerus spits upon my simple geometric models, with extreme prejudice. From this post.

You can see from the photo (the Haestasaurus photo, not the mole photo) that neither bone has a completely hollow marrow cavity – both marrow cavities are filled with trabecular bone. By cutting out good-looking chunks in GIMP and thresholding them, I estimate that these trabecular areas are about 30% bone and 70% marrow (actual marrow space with no bone tissue) by cross-sectional area. According to Currey and Alexader (1985: 455), the specific gravities of fatty marrow and bone tissue are 0.93 and 2.1, respectively. The density of the trabecular area is then (0.3*2.1)+(0.7*0.93) =  1.28 kg/L, or about one quarter more dense than water.

But that’s just the trabecular area, which accounts for about one half of the cross-sectional area of each bone. The other half is cortex, which is probably close to 2.1 kg/L throughout. The estimated whole-element densities are then:

Radius: (0.53*1.28)+(0.47*2.1) = 1.67 kg/L

Ulna: (0.46*1.28)+(0.54*2.1) = 1.72 kg/L

Do those numbers pass the sniff test? Well, any skeletal elements that are composed of bone tissue (SG = 2.1) and marrow (SG = 0.93) are constrained to have densities somewhere between those extremes (some animals beat this by building parts of their skeletons out of [bone tissue + air] instead of [bone tissue + marrow]). We know that sauropod limb bones tend to have thick cortices and small marrow cavities, and that the marrow cavities are themselves a combination of trabecular bone and actual marrow space, so we’d expect the overall density to be closer to the 2.1 kg/L end of the scale than the 0.93 kg/L end. And our rough estimates of ~1.7 kg/L fall about where we’d expect.

Femur of Haplocanthosaurus priscus, CM 572, modified from Hatcher (1903: fig. 14).

To convert to masses, we need to know volumes. We can use Haplocanthosaurus here – the femur of the holotype of H. priscus, CM 572, is 1275 mm long (Hatcher 1903), which is just a hair over four feet (4 ft, 2.2 in to be exact). The midshaft width is 207 mm, and the proximal and distal max widths are 353 and 309 mm, respectively. I could do a for-real GDI, but I’m lazy and approximate numbers are good enough here. Just eyeballing it, the width of the femur is about the same over most of its length, so I’m guessing the average width is about 23 cm. The average width:length ratio for the femora of non-titanosaur sauropods is 3:2 (Wilson and Carrano 1999: table 1), which would give an anteroposterior diameter of about 15 cm and an average diameter over the whole length of 19 cm. The volume would then be the average cross-section area, 3.14*9.5*9.5, multiplied by the length, 128 cm, or 36,273 cm^3, or 36.3 L. Multiplied by the ~1.7 kg/L density we estimated above, that gives an estimated mass of 62 kg, or about 137 lbs. A femur that was exactly four feet long would be a little lighter – 86.6% as massive, to be exact, or 53.4 kg (118 lbs).

I know that the PCs in RPGs are supposed to be heroes, but that seems a little extreme.

But wait! Bones dry out and they lose mass as they do so. Lawes and Gilbert (1859) reported that the dry weight of bones of healthy sheep and cattle was only 74% of the wet mass. Cows and sheep have thinner bone cortices than sauropods or elephants, but it doesn’t seem unreasonable that a dry sauropod femur might only weigh 80% as much as a fresh one. That gets us down to 43 kg – about 95 lbs – which is still well beyond what anyone is probably going to be wielding, even if they’re Conan the Cimmerian.

Picture is unrelated.

I mentioned at the top of this section that there are a couple of ways to get here. The second way is to simply see what actual elephant femora weigh, and then scale up to dinosaur size. According to Tefera (2012: table 1), a 110-cm elephant femur has a mass of 21.5 kg (47 lbs). I reckon that’s a dry mass, since the femur in question had sat in a shed for 50 years before being weighed (Tefera 2012: p. 17). Assuming isometry, a four-foot (122 cm) elephant femur would have a dry mass of 29.4 kg (65 lbs). That’s a lot lighter than the estimated mass of the sauropod femur – can we explain the discrepancy?

 

Femora of a horse, a cow, and an elephant (from left to right in each set), from Tefera (2012: plate 1).

I think so. Elephant femora are more slender than Haplocanthosaurus femora. Tefera (2012) reported a circumference of 44 cm for a 110-cm elephant femur. Scaling up from 110 cm to 122 cm would increase that femur circumference to 49 cm, implying a mean diameter of 15.6 cm, compared to 19 cm for the Haplo femur. That might not seem like a big difference, but it means a cross-sectional area only 2/3 as great, and hence a volume about 2/3 that of a sauropod femur of the same length. And that lines up almost eerily well with our estimated masses of 29 and 43 kg (ratio 2:3) for the four-foot elephant and sauropod femora.

A Better Weapon?

Could our hypothetical caveman do better by choosing a different dinosaur’s femur? Doubtful – the femora of ‘Sue’ are roughly the same length as the Haplo femur mentioned above, and have similar cross-sectional dimensions. Hadrosaur and stegosaur femora don’t look any better. Even if the theropod femur was somewhat lighter because of thinner cortices, how are you going to effectively grip and wield something 15-19 cm in diameter?

I note that the largest axes and sledgehammers sold by Forestry Suppliers, Inc., are about 3 feet long. Could we get our large-animal-femur-based-clubs into the realm of believability by shrinking them to 3 feet instead of 4? Possibly – 0.75 to the third power is 0.42. That brings the elephant femur club down to 12.3 kg (27 lbs) and the sauropod femur club down to 18 kg (40 lbs), only 2-3 times the mass of the largest commonly-available sledgehammers. I sure as heck wouldn’t want to lug such a thing around, much less swing it, but I can just about imagine a mighty hero doing so.

Yes, there were longer historical weapons. Among swing-able weapons (as opposed to spears, etc.), Scottish claymores could be more than four feet long, but crucially they were quite light compared to the clubs we’ve been discussing, maxing out under 3 kg, at least according to Wikipedia.

T. rex FMNH PR2081 right fibula in lateral (top) and medial (bottom) views. Scale is 30 cm. From Brochu (2003: fig. 97).

If one is looking for a good dinosaur bone to wield as a club, may I suggest the fibula of a large theropod? The right (non-pathologic) fibula of ‘Sue’ is 103 cm long (3 ft, 4.5 in), has a max shaft diameter just under 3 inches – so it could plausibly be held by (large) human hands, and it probably massed something like 8-9 kg (17-20 lbs) in life, based on some quick-and-dirty calculations like those I did above. The proximal end is even expanded like the head of a war club. The length and mass are both in the realm of possibility for large, fit, non-supernaturally-boosted humans. Half-orc barbarians will love them.

And that’s my ‘expert’ recommendation as a dice-slinging paleontologist. Thanks for reading – you have Conan-level stamina if you got this far – and thanks to Shawn for letting me use his question to freewheel on some of my favorite geeky topics.

References

“But wait, Matt”, I hear you thinking. “Every news agency in the world is tripping over themselves declaring Patagotitan the biggest dinosaur of all time. Why are you going in the other direction?”

Because I’ve been through this a few times now. But mostly because I can friggin’ read.

Maximum dorsal centrum diameter in Argentinosaurus is 60cm (specimen MCF-PVPH-1, Bonaparte and Coria 1993). In Puertasaurus it is also 60cm (MPM 10002, Novas et al. 2005). In Patagotitan it is 59cm (MPEF-PV 3400/5, Carballido et al. 2017). (For more big centra, see this post.)

Femoral midshaft circumference is 118cm in an incomplete femur of Argentinosaurus estimated to be 2.5m long when complete (Mazzetta et al. 2004). A smaller Argentinosaurus femur is 2.25m long with a circumference of 111.4cm (Benson et al. 2014). The largest reported femur of Patagotitan, MPEF-PV 3399/44, is 2.38m long and has a circumference of either 101cm (as reported in the Electronic Supplementary Materials to Carballido et al 2017) or 110cm (as reported in the media in 2014*).

TL;DR: 60>59, and 118>111>110>101, and in both cases Argentinosaurus > Patagotitan, at least a little bit.

Now, Carballido et al (2017) estimated that Patagotitan was sliiiiightly more massive than Argentinosaurus and Puertasaurus by doing a sort of 2D minimum convex hull dorsal vertebra area thingy, which the Patagotitan vertebra “wins” because it has a taller neural spine than either Argentinosaurus or Puertasaurus, and slightly wider transverse processes than Argentinosaurus (138cm vs 128cm) – but way narrower transverse processes than Puertasaurus (138cm vs 168cm). But vertebrae with taller or wider sticky-out bits do not a more massive dinosaur make, otherwise Rebbachisaurus would outweigh Giraffatitan.

Now, in truth, it’s basically a three-way tie between Argentinosaurus, Puertasaurus, and Patagotitan. Given how little we have of the first two, and how large the error bars are on any legit size comparison, there is no real way to tell which of them was the longest or the most massive. Still, to get to the conclusion that Patagotitan was in any sense larger than Argentinosaurus you have to physically drag yourself over the following jaggedly awkward facts:

  1. The weight-bearing parts of the anterior dorsal vertebrae are larger in diameter in both Argentinosaurus and Puertasaurus than in Patagotitan. Very slightly, but still, Patagotitan is the smallest of the three.
  2. The femora of Argentinosaurus are fatter than those of Patagotitan, even at shorter length. The biggest femora of Argentinosaurus are longer, too.

So all of the measurements of body parts that have to do with supporting mass are still larger in Argentinosaurus than in Patagotitan.

Now, it is very cool that we now have a decent chunk of the skeleton of a super-giant titanosaur, instead of little bits and bobs. And it’s nice to know that the numbers reported in the media back in 2014 turned out to be accurate. But Patagotitan is not the “world’s largest dinosaur”. At best, it’s the third-largest contender among near equals.

Parting shot to all the science reporters who didn’t report the same numbers I did here: instead of getting hype-notized by assumption-laden estimates, how about doing an hour’s worth of research making the most obvious possible comparisons?

Almost immediate UPDATE: Okay, that parting shot wasn’t entirely fair. As far as I know, the measurements of Patagotitan were not available until the embargo lifted. Which is in itself odd – if someone claims to have the world’s largest dinosaur, but doesn’t put any measurements in the paper, doesn’t that make your antennae twitch? Either demand some measurements so you can make those obvious comparisons, or approach with extreme skepticism – especially if the “world’s largest dino” claim was pre-debunked three years ago!

* From this article in the Boston Globe:

Paleobiologist Paul Upchurch of University College London believes size estimates are more reliable when extrapolated from the circumference of bones.

He said this femur is a whopping 43.3 inches around, about the same as the Argentinosaurus’ thigh bone.

‘‘Whether or not the new animal really will be the largest sauropod we know remains to be seen,’’ said Upchurch, who was not involved in this discovery but has seen the bones first-hand.

Some prophetically appropriate caution from Paul Upchurch there, who has also lived through a few of these “biggest dinosaur ever” bubbles.

References

I was a bit disappointed to hear David Attenborough on BBC Radio 4 this morning, while trailing a forthcoming documentary, telling the interviewing that you can determine the mass of an extinct animal by measuring the circumference of its femur.

We all know what he was alluding to, of course: the idea first published by Anderson et al. (1985) that if you measure the life masses of lots of animals, then measuring their long-bone circumferences when they’ve died, you can plot the two measurements against each other, find a best-fit line, and extrapolate it to estimate the masses of dinosaurs based on their limb-bone measurements.

AndersonEtAl1985-dinosaur-masses-fig1

This approach has been extensively refined since 1985, most recently by Benson et al. (2014). but the principle is the same.

But the thing is, as Anderson et al. and other authors have made clear, the error-bars on this method are substantial. It’s not super-clear in the image above (Fig 1. from the Anderson et al. paper) because log-10 scales are used, but the 95% confidence interval is about 42 pixels tall, compared with 220 pixels for an order of magnitude (i.e. an increment of 1.0 on the log-10 scale). That means the interval is 42/220 = 0.2 of an order of magnitude. That’s a factor 10 ^ 0.2 = 1.58. In other words you could have two animals with equally robust femora, one of them nearly 60% heavier than the other, and they would both fall within the 95% confidence interval.

I’m surprised that someone as experienced and knowledgeable as Attenborough would perpetuate the idea that you can measure mass with any precision in this way (even more so when using only a femur, rather than the femur+humerus combo of Anderson et al.)

More: when the presenter told him that not all scientists buy the idea that the new titanosaur is the biggest known, he said that came as a surprise. Again, it’s disappointing that the documentary researchers didn’t make Attenborough aware of, for example, Paul Barrett’s cautionary comments or Matt Wedel’s carefully argued dissent. Ten minutes of simple research would have found this post — for example, it’s Google’s fourth hit for “how big is the new argentinian titanosaur”. I can only hope that the actual documentary, which screens on Sunday 24 January, doesn’t present the new titanosaur’s mass as a known and agreed number.

(To be clear, I am not blaming Attenborough for any of this. He is a presenter, not a palaeontologist, and should have been properly prepped by the researchers for the programme he’s fronting. He is also what can only be described as 89, so should be forgiven if he’s not quite as quick on his feet when confronted with an interviewer as he used to be.)

Update 1 (the next day)

Thanks to Victoria Arbour for pointing out an important reference that I missed: it was Campione and Evans (2012) who expanding Anderson et al.’s dataset and came up with the revised equation which Benson et al. used.

Update 2 (same day as #1)

It seems most commenters are inclined to go with Attenborough on this. That’s a surprise to me — I wonder whether he’s getting a free pass because of who he is. All I can say is that as I listened to the segment it struck me as really misleading. You can listen to it for yourself here if you’re in the UK; otherwise you’ll have to make do with this transcript:

“It’s surprising how much information you can get from just one bone. I mean for example that thigh bone, eight feet or so long, if you measure the circumference of that, you will be able to say how much weight that could have carried, because you know what the strength of bone is. So the estimate of weight is really pretty accurate and the thought is that this is something around over seventy tonnes in weight.”

(Note also that the Anderson et al./Campione and Evans method has absolutely nothing to do with the strength of bone.)

Also of interest was this segment that followed immediately:

How long it was depends on whether you think it held its neck out horizontally or vertically. If it held it out horizontally, well then it would be about half as big again as the Diplodocus, which is the dinosaur that’s in the hall of the Natural History Museum. It would be absolutely huge.

Interviewer: And how tall, if we do all the dimensions?

Ah well that is again the question of how it holds its neck, and it could have certainly reached up about to the size of a four or five storey building.

Needless to say, the matter of neck posture is very relevant to our interests. I don’t want to read too much into a couple of throwaway comments, but the implication does seem to be that this is an issue that the documentary might spend some time on. We’ll see what happens.

References

I just gave an answer to this question on Quora, and it occurred to me that I ought to also give it a permanent home here. So here it is.


This is a great example of a question that you’d think would have a simple, clear answer, but doesn’t. In fact, as a palaeontologist specialising in dinosaur gigantism, I have an abiding fear of being asked this question in a pub quiz, and not being able to produce the name that’s written on the quizmaster’s answer sheet.

First, what do we mean by “biggest”? Diplodocus was longer than Apatosaurus, but Apatosaurus was heavier. Giraffatitan was taller than either. Let’s simplify and assume we want to know the heaviest dinosaur.

Second, estimating the masses of extinct animals is incredibly hard even when we have a pretty complete skeleton. For example, the gigantic mounted brachiosaur skeleton in Berlin (which used to be called “Brachiosaurus” brancai but is now recognised as the separate genus Giraffatitan) has been subject to at least 14 estimates in the published scientific literature, as summarised here. They vary from 13,618 kg to 78,258 kg — a factor of 5.75 for the same individual. That’s like looking at a human skeleton and not knowing whether its from Kate Moss or Arnold Schwazenegger. (There are reasons for this and I urge you to read the linked article.)

Third, the big dinosaurs tend to be very poorly represented. Giraffatitan is probably the heaviest dinosaur known from a more or less complete skeleton (though even that is put together from several different individuals) so I could give that as the answer to the hypothetical pub-quiz — though the answer sheet would probably be out of date and call it Brachiosaurus.

Fourth, which individual of a given species do we mean? I said Giraffatitan is known from a more or less complete skeleton. And my best guess is that that individual massed, say, 30,000 kg. But an isolated fibula of the same species is known that’s 12.6% longer than the one in the skeletal mount. That suggest an animal that masses 1.126^3 = 1.43 times as massive as the mounted skeleton — say 43,000 kg. There might be yet bigger Giraffatitan individuals. On the other hand, there is some evidence that Apatosaurus, which is usually thought of as not being so big, might have got even bigger.

Fifth, the very biggest specimens tend to be known from only a handful of bones. A good example here is the titanosaur Argentinosaurus, which is known from several vertebrae and a few limb bones, but not all from the same individual. It’s a good bet that it massed 60-70 tonnes — so maybe about twice as much as Giraffatitan, but much less than the often-cited 100 tonnes. Other, more recently discovered, titanosaurs seem to be in the same size class: Puertasaurus, Futalognkosaurus, Dreadnoughtus and more. They they are hard to compare directly due to the paucity of overlapping material, or at least described overlapping material. (Scientists are working on getting more of this stuff properly described in the literature, which will help.)

But, sixth, the very biggest dinosaurs tend to be apocryphal. There’s Amphicoelias fragillimus, known only from E. D. Cope’s drawing of the upper half of a single vertebra. This may have been 50 m long and massed 80 tonnes; but other published estimates say 58 m and 122 tonnes. We really can’t say from the very poor remains.

So if you get asked this question in a pub quiz, your best bet is to roll a dice, pick an answer, close your eyes and hope. Roll 1 for Giraffatitan, 2 for Brachiosaurus, 3 for Apatosaurus, 4 for Argentinosaurus, 5 for Dreadnoughtus and 6 for Amphicoelias fragillimus. Good luck!

 

I imagine that by now, everyone who reads this blog is familiar with Mark Witton’s painting of a giant azhdarchid pterosaur alongside a big giraffe. Here it is, for those who haven’t seen it:

Arambourgiania vs giraffe vs the Disacknowledgement redux Witton ver 2 low res

(This is the fifth and most recent version that Mark has created, taken from 9 things you may not know about giant azhdarchid pterosaurs.)

It’s one of those images that really kicks you in the brain the first time you see it. The idea that an animal the size of a giraffe could fly under its own power seems ludicrous — yet that’s what the evidence tells us.

But wait — what do we mean by “an animal the size of a giraffe”? Yes, the pterosaur in this image is the same height as the giraffe, but how does its weight compare?

Mark says “The giraffe is a big bull Masai individual, standing a healthy 5.6 m tall, close to the maximum known Masai giraffe height.” He doesn’t give a mass, but Wikipedia, citing Owen-Smith (1988), says “Fully grown giraffes stand 5–6 m (16–20 ft) tall, with males taller than females. The average weight is 1,192 kg (2,628 lb) for an adult male and 828 kg (1,825 lb) for an adult female with maximum weights of 1,930 kg (4,250 lb) and 1,180 kg (2,600 lb) having been recorded for males and females, respectively.” So it seems reasonable to use a mass intermediate between those of an average and maximum-sized male, (1192+1930)/2 = 1561 kg.

So much for the giraffe. What does the azhdarchid weigh? The literature is studded with figures that vary wildly, from the 544 kg that Henderson (2010) found for Quetzalcoatlus, right down to the widely cited 70 kg that Chatterjee and Templin (2004) found for the same individual — and even the astonishing 50 kg that seems to be favoured by Unwin (2005:192). In the middle is the 259 kg of Witton (2008).

It occurred to me that I could visualise these mass estimates by shrinking the giraffe in Mark’s image down to the various proposed masses, and seeing how credible it looks to imagine these reduced-sized giraffes weighting the same as the azhdarchid. The maths is simple. For each proposed azhdarchid mass, we figure out what it is as a proportion of the giraffe’s 1561 kg; then the cube root of that mass proportion gives us the linear proportion.

  • 544 kg = 0.389 giraffe masses = 0.704 giraffe lengths
  • 259 kg = 0.166 giraffe masses = 0.549 giraffe lengths
  • 70 kg =0.0448 giraffe masses = 0.355 giraffe lengths

Let’s see how that looks.

Arambourgiania vs giraffe vs the Disacknowledgement redux Witton ver 2 low res

On the left, we have Mark’s artwork, with the giraffe massing 1561 kg. On the right, we have three smaller (isometrically scaled) giraffes of masses corresponding to giant azhdarchid mass estimates in the literature. If Don Henderson (2010) is right, then the pterosaur weighs the same as the 544 kg giraffe, which to me looks pretty feasible if it’s very pneumatic. If Witton (2008) is right, then it weighs the same as the 259 kg giraffe, which I find hard to swallow. And if Chatterjee and Templin (2004) are right, then the giant pterosaur weighs the same as the teeny tiny 70 kg giraffe, which I find frankly ludicrous. (For that matter, 70 kg is in the same size-class as Georgia, the human scale-bar: the idea that she and the pterosaur weigh the same is just silly.)

What is the value of such eyeball comparisons? I’m not sure, beyond a basic reality check. Running this exercise has certainly made me sceptical about even the 250 kg mass range which now seems to be fairly widely accepted among pterosaur workers. Remember, if that mass is correct then the pterosaur and the 259 kg giraffe in the picture above weight the same. Can you buy that?

Or can we find extant analogues? Are there birds and mammals with the same mass that are in the same size relation as these images show?

References

  • Chatterjee, Sankar, and R. J. Templin. 2004. Posture, locomotion, and paleoecology of pterosaurs. Geological Society of America, Special Paper 376. 68 pages.
  • Henderson, Donald M. 2010. Pterosaur body mass estimates from three-dimensional mathematical slicing. Journal of Vertebrate Paleontology 30(3):768-785.
  • Witton, Mark P. 2008. A new approach to determining pterosaur body mass and its implications for pterosaur flight. Zitteliana 28:143-159.

How bigsmall was Aquilops?

December 12, 2014

Handling Aquilops by Brian Engh

Life restoration of Aquilops by Brian Engh (CC-BY).

If you’ve been reading around about Aquilops, you’ve probably seen it compared in size to a raven, a rabbit, or a cat. Where’d those comparisons come from? You’re about to find out.

Back in April I ran some numbers to get a rough idea of the size of Aquilops, both for my own interest and so we’d have some comparisons handy when the paper came out.

Archaeoceratops skeletal reconstruction by Scott Hartman. Copyright Scott Hartman, 2011, used here by permission.

Archaeoceratops skeletal reconstruction by Scott Hartman. Copyright Scott Hartman, 2011, used here by permission.

I started with the much more completely known Archaeoceratops. The measurements of Scott Hartman’s skeletal recon (shown above and on Scott’s website – thanks, Scott!) match the measurements of the Archaeo holotype given by Dodson and You (2003) almost perfectly. The total length of Archaeoceratops, including tail, is almost exactly one meter. Using graphic double integration, I got a volume of 8.88L total for a 1m Archaeoceratops. That would come down to 8.0L if the lungs occupied 10% of body volume, which is pretty standard for non-birds. So that’s about 17-18 lbs.

Archaeoceratops and Aquilops skulls to scale

Aquilops model by Garrett Stowe, photograph by Tom Luczycki, copyright and courtesy of the Sam Noble Oklahoma Museum of Natural History.

Archaeoceratops has a rostrum-jugal length of 145mm, compared to 84mm in Aquilops. Making the conservative assumption that Aquilops = Archaeoceratops*0.58, I got a body length of 60cm (about two feet), and volumes of 1.73 and 1.56 liters with and without lungs, or about 3.5 lbs in life. The internet informed me that the common raven, Corvus corax, has an adult length of 56-78 cm and a body mass of 0.7-2 kg. So, based on this admittedly tall and teetering tower of assumptions, handwaving, and wild guesses, Aquilops (the holotype individual, anyway) was about the size of a raven, in both length and mass. But ravens, although certainly well-known, are maybe a bit remote from the experience of a lot of people, so we wanted a comparison animal that more people would be familiar with. The estimated length and mass of the holotype individual of Aquilops also nicely overlap the species averages (60 cm, 1.4-2.7 kg) for the black-tailed jackrabbit, Lepus californicus, and they’re pretty close to lots of other rabbits as well, hence the comparison to bunnies.

Of course, ontogeny complicates things. Aquilops has some juvenile characters, like the big round orbit, but it doesn’t look like a hatchling. Our best guess is that it is neither a baby nor fully grown, but probably an older juvenile or young subadult. A full-grown Aquilops might have been somewhat larger, but almost certainly no larger than Archaeoceratops, and probably a meter or less in total length. So, about the size of a big housecat. That’s still pretty darned small for a non-avian dinosaur.

Although Aquilops represents everything I normally stand against – ornithischians, microvertebrates, heads – I confess that I have a sneaking affection for our wee beastie. Somebody’s just gotta make a little plush Aquilops, right? When and if that happens, you know where to find me.

References

In a comment on the last post, on the mass of Dreadnoughtus, Asier Larramendi wrote:

The body mass should be considerably lower because the reconstructed column don’t match with published vertebrae centra lengths. 3D reconstruction also leaves too much space between vertebrae. The reconstruction body trunk is probably 15-20% longer than it really was. Check the supplementary material: http://www.nature.com/srep/2014/140904/srep06196/extref/srep06196-s1.pdf

So I did. The table of measurements in the supplementary material is admirably complete. For all of the available dorsal vertebrae except D9, which I suppose must have been too poorly preserved to measure the difference, Lacovara et al. list both the total centrum length and the centrum length minus the anterior condyle. Centrum length minus the condyle is what in my disseration I referred to as “functional length”, since it’s the length that the vertebra actually contributes to the articulated series, assuming that the condyle of one vertebra sticks out about as far as the cotyle is recessed on the next vertebra. Here are total lengths/functional lengths/differences for the seven preserved dorsals, in mm:

  • D4 – 400/305/95
  • D5 – 470/320/150
  • D6 – 200/180/20
  • D7 – 300/260/40
  • D8 – 350/270/80
  • D9 – 410/ – / –
  • D10 – 330/225/105

The average difference between functional length and total length is 82 mm. If we apply that to D9 to estimate it’s functional length, we get 330mm. The summed functional lengths of the seven preserved vertebrae are then 1890 mm. What about the missing D1-D3? Since the charge is that Lacovara et al. (2014) restored Dreadnoughtus with a too-long torso, we should be as generous as possible in estimating the lengths of the missing dorsals. In Malawisaurus the centrum lengths of D1-D3 are all less than or equal to that of D4, which is the longest vertebra in the series (Gomani 2005: table 3), so it seems simplest here to assign D1-D3 functional lengths of 320 mm. That brings the total functional length of the dorsal vertebral column to 2850 mm, or 2.85 m.

At this point on my first pass, I was thinking that Lacovara et al. (2014) were in trouble. In the skeletal reconstruction that I used for the GDI work in the last post, I measured the length of the dorsal vertebral column as 149 pixels. Divided by 36 px/m gives a summed dorsal length of 4.1 m. That’s more than 40% longer than the summed functional lengths of the vertebrae calculated above (4.1/2.85 = 1.44). Had Lacovara et al. really blown it that badly?

Before we can rule on that, we have to estimate how much cartilage separated the dorsal vertebrae. This is a subject of more than passing interest here at SV-POW! Towers–the only applicable data I know of are the measurements of intervertebral spacing in two juvenile apatosaurs that Mike and I reported in our cartilage paper last year (Taylor and Wedel 2013: table 3, and see this post). We found that the invertebral cartilage thickness equaled 15-24% of the length of the centra.* For the estimated 2.85-meter dorsal column of Dreadnoughtus, that means 43-68 cm of cartilage (4.3-6.8 cm of cartilage per joint), for an in vivo dorsal column length of 3.28-3.53 meters. That’s still about 15-20% shorter than the 4.1 meters I measured from the skeletal recon–and, I must note, exactly what Asier stated in his comment. All my noodling has accomplished is to verify that his presumably off-the-cuff estimate was spot on. But is that a big deal?

Visually, a 20% shorter torso makes a small but noticeable difference. Check out the original reconstruction (top) with the 20%-shorter-torso version (bottom):

Dreadnoughtus shortened torso comparison - Lacovara et al 2014 fig 2

FWIW, the bottom version looks a lot more plausible to my eye–I hadn’t realized quite how weiner-dog-y the original recon is until I saw it next to the shortened version.

In terms of body mass, the difference is major. You’ll recall that I estimated the torso volume of Dreadnoughtus at 32 cubic meters. Lopping off 20% means losing 6.4 cubic meters–about the same volume as a big bull elephant, or all four of Dreadnoughtus‘s limbs put together. Even assuming a low whole-body density of 0.7 g/cm^3, that’s 4.5 metric tons off the estimated mass. So a ~30-ton Dreadnoughtus is looking more plausible by the minute.

For more on how torso length can affect the visual appearance and estimated mass of an animal, see this post and Taylor (2009).

* I asked Mike to do a review pass on this post before I published, and regarding the intervertebral spacing derived from the juvenile apatosaurs, he wrote:

That 15-24% is for juveniles. For the cervicals of adult Sauroposeidon we got about 5%. Why the differences? Three reasons might be relevant: 1, taxonomic difference between Sauroposeidon and Apatosaurus; 2, serial difference between neck and torso; 3, ontogenetic difference between juvenile and adult. By applying the juvenile Apatosaurus dorsal measurement directly to the adult Dreadnoughtus dorsals, you’re implicitly assuming that the adult/juvenile axis is irrelevant (which seems unlikely to me), that the taxonomic axis is (I guess) unknowable, and that the cervical/dorsal distinction is the only one that matter.

That’s a solid point, and it deserves a post of its own, which I’m already working on. For now, it seems intuitively obvious to me that we got a low percentage on Sauroposeidon simply because the vertebrae are so long. If the length-to-diameter ratio was 2.5 instead of 5, we’d have gotten 10%, unless cartilage thickness scales with centrum length, which seems unlikely. For a dorsal with EI of 1.5, cartilage thickness would then be 20%, which is about what I figured above.

Now, admittedly that is arm-waving, not science (and really just a wordy restatement of his point #2). The obvious thing to do is take all of our data and see if intervertebral spacing is more closely correlated with centrum length or centrum diameter. Now that it’s occurred to me, it seems very silly not to have done that in the actual paper. And I will do that very thing in an upcoming post. For now I’ll just note three things:

  1. As you can see from figure 15 in our cartilage paper, in the opisthocoelous anterior dorsals of CM 3390, the condyle of the posterior vertebra is firmly engaged in the cotyle of the anterior one, and if anything the two vertebrae look jammed together, not drifted apart. But the intervertebral spacing as a fraction of centrum length is still huge (20+4%) because the centra are so short.
  2. Transferring these numbers to Dreadnoughtus only results in 4.3-6.8 cm of cartilage between adjacent vertebrae, which does not seem unreasonable for a 30- or 40-ton animal with dorsal centra averaging 35 cm in diameter. If you asked me off the cuff what I thought a reasonable intervertebral spacing was for such a large animal, I would have said 3 or 4 inches (7.5 to 10 cm), so the numbers I got through cross-scaling are actually lower than what I would have guessed.
  3. Finally, if I’ve overestimated the intervertebral spacing, then the actual torso length of Dreadnoughtus was even shorter than that illustrated above, and the volumetric mass estimate would be smaller still. So in going with relatively thick cartilage, I’m being as generous as possible to the Lacovara et al. (2014) skeletal reconstruction (and indirectly to their super-high allometry-derived mass estimate), which I think is only fair.

References

 

How massive was Dreadnoughtus?

September 11, 2014

Dreadnoughtus published body outline - Lacovara et al 2014 fig 2

In the paper describing the new giant titanosaur Dreadnoughtus, Lacovara et al. (2014) use the limb bone allometry equation of Campione and Evans (2012) to derive a mass estimate for the holotype individual of 59.3 metric tons. This is presumably the “middle of the road” value spat out by the equation; the 95% confidence interval on either side probably goes from 40 to 80 metric tons or maybe even wider.

I decided to see if 59 metric tons was plausible for Dreadnoughtus by doing Graphic Double Integration (GDI) on the published skeletal reconstruction and body outline (Lacovara et al. 2014: fig. 2). The image above is the one I used, so if you like, you can check my numbers or try your hand at GDI and see what you get.

First up, I have to congratulate Lacovara et al. for the rare feat of having everything pretty much to scale, and a properly-sized scale bar. This is not always the case. Presumably having a 3D digital model of the reconstructed skeleton helped — and BTW, if you haven’t downloaded the 3D PDFs and played with them, you are missing out bigtime.

Here are my measurements of various bits in the picture and the scale factors they give:

Meter scale bar: 37 pixels – 1.0 meters – 37 px/m
Human figure: 66 pixels – 1.8 meters – 37 px/m
Scapula: 62 pixels – 1.7 meters – 36 px/m
Humerus: 58 pixels – 1.6 meters – 36 px/m
Femur: 70 pixels – 1.9 meters – 37 px/m
Cervical: 45 pixels – 1.1 meters – 41 px/m (not included in average*)
Neck: 407 pixels – 11.3 meters – 36 px/m
Post-cervical vertebral column: 512 pixels – 13.8 meters – 37 px/m
Total length: 922 pixels – 26.0 meters – 35 px/m
AVERAGE 36 px/m

* I didn’t include the cervical because when I measured it I sorta guessed about where the condyle was supposed to be. That was the odd measurement out, and I didn’t want to tar Lacovara et al. for what might well be my own observer error.

Dreadnoughtus decomposed for GDI - Lacovara et al 2014 fig 2

Here’s the chopped-up Dreadnoughtus I used for my estimate. Just for the heck of it, for the first time out I assigned all of the body regions circular cross-sections. We’ll come back to how realistic this is later. Here’s what I got for the volumes of the various bits:

Head: 0.2 m^3
Neck: 13.9
Body: 32.1
Tail: 4.0
Limbs: 6.8
TOTAL: 57.0 m^3

Okay, this is looking pretty good, right? Lacovara et al. (2014) got 59.3 metric tons using limb allometry, I got a volume of 57 cubic meters using GDI. If Dreadnoughtus was the same density as water — 1 metric ton per cubic meter — then my estimated mass would be 57 tons, which is crazy close given all of the uncertainties involved.

BUT there are a couple of big buts involved. The first is that a lot of sauropods had distinctly non-round body cross-sections (Diplodocus, Camarasaurus). So assuming circular cross-sections might inflate the body well beyond its likely volume. Second is that sauropods were probably much less dense than water (discussed here, here, and here, and see Wedel 2005 for the full scoop). What are the implications for Dreadnoughtus?

Round and Round

It turns out that circular cross-sections are probably defensible for some parts of Dreadnoughtus. By playing around with the 3D PDF of the assembled skeleton I was able to get these orthogonal views:

Dreadnoughtus 3D skeleton orthogonal views

I don’t remember what the pixel counts were for the max height and max width of the torso, but they were pretty close. I measured at several points, too: front of the pelvis, max extent of ribcage, mid-scap. This is probably not super-surprising as the fatness of titanosaurs has been widely noted before this. Here’s a cross-section through the torso of Opisthocoelicaudia at D4 (Borsuk-Bialynicka 1977: fig. 5) — compare to the more taconic forms of Diplodocus and Camarasaurus linked above.

Opisthocoelicaudia torso x-s - Borsuk-Bialynicka 1977 fig 5

Okay, a round torso on Dreadnoughtus I can buy. A round neck and tail, not so much. Look at the skeletal recon and you can see that even with a generous allowance for caudofemoralis muscles on the tail, and diapophyses on the cervical vertebrae, no way were those extremities circular in cross-section. Just off the cuff I think a width:height ratio of 2:3 is probably about right.

But there are some body regions that probably were round, or close enough as to have made no difference, like the head and limbs. So I actually toted up the volume three times: once with circular cross-sections throughout (probably too fat), once with a 2:3 width:height ratio in the neck, trunk, and tail (probably too thin, at least in the torso), and once with the 2:3 ratio only in the neck and tail (my Goldilocks version). Here are the numbers I got:

Dreadnoughtus Table 1 three volumes

 

Air Apparent?

Now, for density. Birds are usually much less dense than water — lotsa cited data in this hummingbird post, the punchline of which is that the average whole-body density of a bunch of birds is 0.73 g/cm^3. Why so light? In part because the lungs and air sacs are huge, and account for 15-20% of the whole-body volume, and in part because many of the bones are pneumatic (= air-filled). For a really visceral look at how much air there can be in the bones of birds, see this post, and this one and this one for sauropods.

In my 2005 paper (almost a decade old already — gosh!), I found that for Diplodocus, even a fairly conservative estimate suggested that air inside the bones accounted for about 10% of the volume of the whole animal in life. That may be higher than in a lot of birds, because sauropods were corn-on-the-cob, not shish-kebabs. And that’s just the air in the bones — we also have several lines of evidence suggesting that sauropods had air-sacs like those of birds (Wedel 2009). If the lungs and air sacs occupied 15% of the volume of the whole animal, and the air in the bones occupied another 10%, that would give a whole-body density pretty close to the 0.73 g/cm^3 found for birds. Sauropods might have been lighter still — I didn’t include visceral, intermuscular, or subcutaneous diverticula in my calculations, because I couldn’t think of any way to constrain their volumes.

What about Dreadnoughtus? As Lacovara et al. (2014) describe, the cervical, dorsal, and sacral vertebrae and sacral ribs are honeycombed with pneumatic camellae (small, thin-walled chambers). And the dorsal ribs have pneumatic foramina and were probably at least partly hollowed-out as well. The caudal vertebrae do not appear to have been pneumatic, at least internally (but diverticula going into the tail can be cryptic — see Wedel and Taylor 2013b). Diplodocus has a big, long, highly pneumatic tail, but Dreadnoughtus has a much longer neck, both proportionally and absolutely, and pneumatic dorsal ribs. So this one may be too close to call. But I also ran the numbers for T. rex way back when and found that air in its vertebrae accounted for 7% of its body volume (this abstract). Pessimistically, if we assume Dreadnoughtus had small lungs and air sacs (maybe 10% of whole-body volume) and not much air in the bones (7%), it’s whole-body density was probably still closer to 0.8 g/cm^3 than to 0.9. Optimistically, a lot of titanosaurs were radically pneumatic and they have may have had big air sac systems and extensive diverticula to match, so a bird-like 0.7-0.75 g/cm^3 is certainly not beyond the bounds of possibility.

Dreadnoughtus Table 2 twelve masses

This table shows a spectrum of masses, based on the three body volumes from GDI (columns) and some possible whole-body densities (rows). Note that the columns are not in the same order as in the first table — I lined them up from most t0 least voluminous here. The 57-ton estimate is the max, and that assumes that the neck and tail were both perfectly round, and that despite the lungs, air sacs, and air reservoirs inside the bones, the whole-body density of Dreadnoughtus was still 1.0 g/cm^3, neither of which are likely (or, I guess, that a real Dreadnoughtus was significantly fatter than the one shown, and that all of that extra bulk was muscle or some other heavy tissue). The 28t mass in the lower left corner is also unrealistic, because it assumes a tall, narrow torso. My pick is the 36t estimate at the bottom of the middle column, derived from what I think are the most defensible volume and density. Your thoughts may differ — the comment thread is open.

Roll Your Own

Dreadnoughtus Table 3 body region comparison

This last table is just a quick-and-dirty comparison of how the volume of the body breaks down among its constituent parts in Plateosaurus (from this post), Giraffatitan (from Taylor 2009), and Dreadnoughtus (based on my “tall neck and tail” GDI). Dreadnoughtus seems to have a more voluminous neck and a less voluminous trunk, proportionally, than Giraffatitan, but I think a lot of that is down to the very fat fleshy envelope drawn around the cervicals of Dreadnoughtus. We are fortunate to count some fearsomely talented paleoartists among our readers — I’ll look forward to seeing what you all come up with in your independent skeletal recons.

So, what’s the take-home? Based on the data available, I don’t think the holotype individual of Dreadnoughtus massed anything like 59 metric tons. I think 35-40 metric tons is much more defensible. But I’m happy to have my errors pointed out and new data and arguments brought to the fore. Your thoughts are most welcome.

References

We’ve touched on this several times in various posts and comment threads, but it’s worth taking a moment to think in detail about the various published mass estimates for the single specimen MB.R.2181 (formerly known as HMN SII), the paralectotype of Giraffatitan brancai, which is the basis of the awesome mounted skeleton in Berlin.

Here is the table of published estimates from my 2010 sauropod-history paper, augmented with the two more recent estimates extrapolated from limb-bone measurements:

Author and date Method Volume (l) Density (kg/l) Mass (kg)
Janensch (1938) Not specified `40 t’
Colbert (1962) Displacement of sand 86,953 0.9 78,258
Russell et al. (1980) Limb-bone allometry 13,618
Anderson et al. (1985) Limb-bone allometry 29,000
Paul (1988) Displacement of water 36,585 0.861 31,500
Alexander (1989) Weighing in air and water 46,600 1.0 46,600
Gunga et al. (1995) Computer model 74,420 1.0 74,420
Christiansen (1997) Weighing in air and water 41,556 0.9 37,400
Henderson (2004) Computer model 32,398 0.796 25,789
Henderson (2006) Computer model 25,922
Gunga et al. (2008) Computer model 47,600 0.8 38,000
Taylor (2009) Graphic double integration 29,171 0.8 23,337
Campione and Evans (2012) Limb-bone allometry 35,780
Benson et al. (2014) Limb-bone allometry 34,000

(The estimate of Russell et al. (1980) is sometimes reported as 14900 kg. However, they report their estimate only as “14.9 t”; and since they also cite “the generally accepted figure of 85 tons”, which can only be a reference to Colbert (1962)”, we must assume that Russell et al. were using US tons throughout.)

The first thing to notice is that there is no very clear trend through time, either upwards or downwards. Here’s a plot of mass (y-axis) against year of estimate (x-axis):

giraffatitan-mass-by-year

I’ve not even tried to put a regression line through this: the outliers are so extreme they’d render it pretty much useless.

In fact, the lowest and highest estimates differ by a factor of 5.75, which is plainly absurd.

But we can go some way to fixing this by discarding the outliers. We can dump Colbert (1962) and Alexander (1989) as they used overweight toys as their references. We more or less have to dump Russell et al. (1980) simply because it’s impossible to take seriously. (Yes, this is the argument from personal incredulity, and I don’t feel good about it; but as Pual (1988) put it, “so little flesh simply cannot be stretched over the animal’s great frame”.) And we can ignore Gunga et al. (1995) because it used circular conic sections — a bug fixed by Gunga et al. (2008) by using elliptical sections.

With these four unpalatable outliers discarded, our highest and lowest estimates are those of Gunga et al. (2008) at 38,000 kg and Taylor (2009)at 23,337. The former should be taken seriously as it was done using photogrammetrical measurements of the actual skeletal mount. And so should the latter because Hurlburt (1999) showed that GDI is generally the least inaccurate of our mass-estimation techniques. That still gives us a factor of 1.63. That’s the difference between a lightweight 66 kg man and and overweight 108 kg.

Here’s another way of thinking about that 1.63 factor. Assuming two people are the same height, one of them weighing 1.62 times as much as the other means he has to be 1.28 times as wide and deep as the first (1.28^2 = 1.63). Here is a man next to his 1.28-times-as-wide equivalent:

two-men

 

I would call that a very noticeable difference. You wouldn’t expect someone estimating the mass of one of these men to come up with that of the other.

So what’s going on here? I truly don’t know. We are, let’s not forget, dealing with a complete skeletal mount here, one of the very best sauropod specimens in the world, which has been extensively studied for a century. Yet even within the last six years, we’re getting masses that vary by as much as the two dudes above.

 

As promised, some thoughts on the various new brachiosaur mass estimates in recent papers and blog-posts.

Back in 2008, when I did the GDI of Giraffatitan and Brachiosaurus for my 2009 paper on those genera, I came out with estimates of 28688 and 23337 kg respectively. At the time I said to Matt that I was suspicious of those numbers because they seemed too low. He rightly told me to shut up and put my actual results in the paper.

More recently, Benson et al. (2014) used limb-bone measurements to estimate the masses of the same individuals as 56000 and 34000 kg. When Ian Corfe mentioned this in a comment, my immediate reaction was to be sceptical: “I’m amazed that the two more recent papers have got such high estimates for brachiosaurs, which have the most gracile humeri of all sauropods“.

So evidently I have a pretty strong intuition that Brachiosaurus massed somewhere in the region of 35000 kg and Giraffatitan around 30000 kg. But why? Where does that intuition come from?

I can only assume that my strongly held ideas are based only on what I’d heard before. Back when I did my 2008 estimate, I probably had in mind things like Paul’s (1998) estimate of 35000 kg for Brachiosaurus, and Christiansen’s (1997:67) estimate of 37400 for Giraffatitan. Whereas by the time the Benson et al. paper came out I’d managed to persuade myself that my own much lower estimates were right. In other words, I think my sauropod-mass intuition is based mostly on sheer mental inertia, and so should be ignored.

I’m guessing I should ignore your intuitions about sauropod masses, too.

References