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

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By contrast to the very delicate pelican humerus and ulna in the previous post, here is the left femur of Aepyornis OUMNH 4950 — an “elephant bird” from Antolanbiby, Madagascar. It’s just a couple of meters away from the pelican, in the same Oxford gallery:

This is of course a ludicrously robust bone, as befits a gigantic ground-dwelling bird. But the fun thing is that it, too, is very pneumatic. You can see this in lots of ways: the foramina up at the top, the little patch of stretched texture at mid-length, and most of all in the honeycomb structure of the inside of the bone, which we can see where the cortex has broken off at both proximal and distal ends.

Birds: they’re made of air.

Several drinks later, they all die and somehow become skeletonised, and that’s how they all land up on a table in my office:

2016-04-14 11.12.52

Top left: pieces of monitor lizard Varanus exanthematicus. Cervical vertebrae 1-7 on the piece of paper, femora visible above them, bits of feet below them. Awaiting reassembly. The whole skeleton is there.

Top right, on a plate on top of some lizard bits: skull, cervicals and feet of common pheasant Phasianus colchicus. The skull has come apart, and I can’t figure out how to reattach the quadrates. One of the feet is cleanly prepped out and waiting to be reassembled, while the other retains some skin for now.

Bottom left: skull and anterior cervicals of red fox Vulpes vulpes. Lots of teeth came out during the defleshing process, and will need to be carefully relocated and glued after the skull has finished drying out.

Bottom right: skull and anterior cervicals of European badger Meles meles. The skull is flat-out awesome, and by far my favourite among my mammal skulls. If tyrannosaurs were medium-sized fossorial mammals, they’d have badgers’ skulls for sure. A few teeth that came out have been glued into place; once the glue is dry, this skull is done.

 

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 feel 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 if interest was this segment that followed immediately:

How long it was depends on whether you think it held its neck out horizontaly 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

Continuing with what seems to have turned out to be Brachiosaur Humerus Week here on SV-POW! (part 1, part 2, part 3), let’s consider the oft-stated idea that brachiosaurs have the most slender humeri of any sauropod. For example, Taylor (2009:796) wrote that:

Discarding a single outlier, the ratio of proximodistal length to minimum transverse width (Gracility Index or GI) in humeri of B. brancai [i.e. Giraffatitan] varies between 7.86 for the right humerus HMN F2 and 9.19 for the left humerus HMN J12, with the type specimen’s right humerus scoring 8.69, slightly more gracile than the middle of the range […] For the B. altithorax type specimen, the GI is 8.50, based on the length of 204 cm and the minimum transverse width of 24 cm reported by Riggs (1904:241). However, the B. altithorax humerus looks rather less gracile to the naked eye than that of B. brancai, and careful measurement from Riggs’s plate LXXIV yields a GI of 7.12, indicating that the true value of the minimum transverse width is closer to 28.5 cm. As noted by Riggs (1903:300-301), the surface of the distal end of this humerus has flaked away in the process of weathering. Careful comparison of the humeral proportions with those of other sauropods (Taylor and Wedel, in prep.) indicates that the missing portion of this bone would have extended approximately a further 12 cm, extending the total length to 216 cm and so increasing the GI to 7.53 – still less gracile than any B. brancai humerus except the outlier, but more gracile than any other sauropod species except Lusotitan atalaiensis (8.91), and much more gracile than the humerus of any non-brachiosaurid sauropod (e.g., Diplodocus Marsh, 1878 sp., 6.76; Malawisaurus dixeyi Jacobs, Winkler, Downs and Gomani, 1993, 6.20; Mamenchisaurus constructus Young, 1958, 5.54; Camarasaurus supremus Cope, 1877, 5.12; Opisthocoelicaudia skarzynskii Borsuk-Bialynicka, 1977, 5.00 – see Taylor and Wedel, in prep.)

Implicit in this (though not spelled out, I admit) is that the humeri of brachiosaurs are slender proportional to their femora. So let’s take a look at the humerus and femur of Giraffatitan, as illustrated in Janensch’s beautiful 1961 monograph of the limbs and girdles of Tendaguru sauropods:

Janensch1961-tendaguru-limbs--plates-AJ--giraffatitan-limb-bones

The first thing you’ll notice is that the humerus is way longer than the femur. That’s because Janensch’s Beilage A illustrates the right humerus of SII (now properly known as MB R.2181) while his Beilage J illustrates the right femur of the rather smaller referred individual St 291. He did this because the right femur of SII was never recovered and the left femur was broken, missing a section in the middle that had to be reconstructed in plaster.

(What’s a Beilage? It’s a German word that seems to literally mean something like “supplement”, but in Janensch’s paper it means a plate (full-page illustration) that occurs in the main body of the text, as opposed to the more traditional plates that come at the end, and which are numbered from XV to XXIII.)

How long would the intact SII femur have been? Janensch (1950b:99) wrote “Since the shaft of the right femur is missing for the most part, it was restored to a length of 196 cm, calculated from other finds” (translation by Gerhard Maier). Janensch confused the left and right femora here, but assuming his length estimate is good, we can upscale his illustration of St 291 so that it’s to SII scale, and matches the humerus. Here’s how that looks:

Janensch1961-tendaguru-limbs--plates-AJ--giraffatitan-limb-bones-scaled

Much more reasonable! The humerus is still a little longer, as we’d expect, but not disturbingly so.

Measuring from this image, the midshaft widths of the femur and humerus are 315 and 207 pixels respectively, corresponding to absolute transverse widths of 353 and 232 mm — so the femur is broader by a factor of 1.52. That’s why I expressed surprise on learning that Benson et al (2014) gave Giraffatitan a CF:CH ratio (circumference of femur to circumference of humerus) of only 1.12.

Anyone who would like to see every published view of the humeri and femora of these beasts is referred to Taylor (2009:fig. 5). In fact, here it is — go crazy.

Taylor (2009: figure 5). Right limb bones of Brachiosaurus altithorax and Brachiosaurus brancai, equally scaled. A-C, humerus of B. altithorax holotype FMNH P 25107; D-F, femur of same; G-K, humerus of B. brancai lectotype HMN SII; L-P, femur of B. brancai referred specimen HMN St 291, scaled to size of restored femur of HMN SII as estimated by Janensch (1950b:99). A, D, G, L, proximal; B, E, H, M, anterior; C, K, P, posterior; J, O, medial; F, I, N, distal. A, B, D, E modified from Riggs (1904:pl. LXXIV); C modified from Riggs (1904:fig. 1); F modified from Riggs (1903:fig. 7); G-K modified from Janensch (1961:Beilage A); L-P modified from Janensch (1961:Beilage J). Scale bar equals 50 cm.

Taylor (2009: figure 5). Right limb bones of Brachiosaurus altithorax and Brachiosaurus brancai, equally scaled. AC, humerus of B. altithorax holotype FMNH P 25107; DF, femur of same; GK, humerus of B. brancai paralectotype HMN SII; LP, femur of B. brancai referred specimen HMN St 291, scaled to size of restored femur of HMN SII as estimated by Janensch (1950b:99). A, D, G, L, proximal; B, E, H, M, anterior; C, K, P, posterior; J, O, medial; F, I, N, distal. A, B, D, E modified from Riggs (1904:pl. LXXIV); C modified from Riggs (1904:fig. 1); F modified from Riggs (1903:fig. 7); GK modified from Janensch (1961:Beilage A); LP modified from Janensch (1961:Beilage J). Scale bar equals 50 cm.

Notice that the femur of Giraffatitan, while transversely pretty broad, is freakishly narrow anteroposteriorly. The same is true of the femur of Brachiosaurus, although it’s never been shown in a published paper — I observed it in the mounted casts in Chicago.

Weird.

Calculations

So let’s take a wild stab at recalculating the mass of Giraffatitan using the Benson et al. formula. First, measuring the midshaft transverse:anteroposterior widths of the long bones gives eccentricity ratios of 2.39 for the femur and 1.54 for the humerus (I am not including the anterior prejection of the deltopectoral crest in the anteroposterior width of the humerus) . Dividing the absolute transverse widths above by these ratios gives us anteroposterior widths of 148 for the femur and 150 mm for the humerus. So they are almost exactly the same in this dimension.

If we simplify by treating these bones as elliptical in cross section, we can  approximate their midshaft circumference. It turns out that the formula for the circumference is incredibly complicated and involves summing an infinite series:

0a1f9b3824382486507885622ddcf283

But since we’re hand-waving so much anyway, we can use the approximation C = 2π sqrt((a²+b²)/2). where a and b are the major and minor radii (not diameters). For the femur, these measurements are 176 and 74 mm, so C = 848 mm; and for the humerus, 116 and 75 mm yields 614 mm. (This compares with FC=730 and HC=654 in the data-set of Benson et al., so we have found the femur to be bigger and the humerus smaller than they did.)

So the CF:CH ratio is 1.38 — rather a lot more than the 1.12 reported by Benson et al.  (Of course, if they measured the actual bones rather than messing about with illustrations, then their numbers are better than mine!)

And so to the mass formula, which Campione and Evans (2012) gave as their equation 2:

log BM = 2.754 log (CH+CF) − 1.097

Which I understand to use base-10 logs, circumferences measured in millimeters, and yield a mass in grams, though Campione and Evans are shockingly cavalier about this. CH+CF is 1462; log(1462) = 3.165. That gives us a log BM of 7.619, so BM = 41,616,453 g = 41,616 kg.

Comparison with Benson et al. (2014)

Midshaft measurements and estimates for SII long bones (all measurements in mm)
SV-POW! Benson et al.
Femur Humerus Femur Humerus
Transverse diameter 353 232 240
Transverse radius 176 116 120
Anteroposterior diameter 148 150 146
Anteroposterior radius 74 75 73
Circumference 848 614 730 654
Total circumference 1462 1384
Mass estimate (kg) 41,616 34,000

My new mass estimate of 41,616 kg is is a lot more than the 34,000 kg found by Benson et al. This seems to be mostly attributable to the much broader femur in my measurement: by contrast, the humerus measurements are very similar (varying by about 3% for both diameters). That leaves me wondering whether Benson et al. just looked at a different femur — or perhaps used St 291 without scaling it to SII size. Hopefully one of the authors will pass by and comment.

More to come on this mass estimate real soon!

References

 

Actually we had the Jurassic talks today, but I can’t show you any of the slides*, so instead you’re getting some brief, sauropod-centric highlighs from the museum.

* I had originally written that the technical content of the talks is embargoed, but that’s not true–as ReBecca Hunt-Foster pointed out in a comment, the conference guidebook with all of the abstracts is freely available online here.

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Like this Camarasaurus that greets visitors at the entrance.

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And this Apatosaurus ilium ischium with bite marks on the distal end, indicating that a big Morrison theropod literally ate the butt of this dead apatosaur. Gnaw, dude, just gnaw.

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And the shrine to Elmer S. Riggs.

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One of Elmer’s field assistants apparently napping next to the humerus of the Brachiosaurus alithorax holotype. This may be the earliest photographic evidence of someone “pulling a Jensen“.

Cary and Matt with Brachiosaurus forelimb

Here’s the reconstructed forelimb of B. altithorax, with Cary Woodruff and me for scale. The humerus and coracoid (and maybe the sternal?) are cast from the B.a. holotype, the rest of the bits are either sculpted or filled in from Giraffatitan. The scap is very obviously Giraffatitan.

Matt with MWC Apatosaurus femur

Cary took this photo of me playing with a fiberglass 100% original bone Apatosaurus femur upstairs in the museum office, and he totally passed up the opportunity to push me down the stairs afterward. I kid, I kid–actually Cary and I get along just fine. It’s no secret that we disagree about some things, but we do so respectfully. Each of us expects to be vindicated by better data in the future, but there’s no reason we can’t hang out and jaw about sauropods in the meantime.

Finally, in the museum gift shop (which is quite lovely), I found this:

Dammit Nova

You had one job, Nova. ONE JOB!

So, this is a grossly inadequate post that barely scratches the surface of the flarkjillion or so cool exhibits at the museum. I only got about halfway through the sauropods, fer cryin’ out loud. If you ever get a chance to come, do it–you won’t be disappointed.

You know the drill: lotsa pretty pix, not much yap.

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Our first stop of the day was the Fruita Paleontological Area, which has a fanstastic diversity of Morrison animals, including the mammal Fruitafossor and the tiny ornithopod Fruitadens.

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Plus it’s a pretty epic landscape, especially with the clouds and broken light we had this morning.

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I found a bone! Several bits, actually, a few meters away from the Fruitadens type quarry. I’d like to think that this proximal femur might be Fruitadens, but I don’t know the diagnostic characters and haven’t had time to look them up. Anyone know how diagnostic this honorary shard of excellence might be?

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After lunch, John Foster took us on a short hike to the quarry where Elmer Riggs got the back half of the Field Museum Apatosaurus. The front half came from a site in southern Utah, several decades later.

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The locals brought Riggs out in the 1930s for the dedication of two monuments–this one at the Apatosaurus quarry, and another like it at the Brachiosaurus quarry some miles away. Tragically, both monuments have the names of the dinosaurs misspelled!

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In the afternoon we visited the Mygatt-Moore Quarry and the Camarasaurus site in Rabbit Valley. Can you see the articulated Camarasaurus neck in this photo?

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Here’s a hint: the neural arches of two posterior cervical vertebrae in transverse horizontal cross-section.

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This Camarasaurus is apparently a permanent feature. If you’re wondering why no-one has excavated it, it’s because it’s buried in sandstone that is stupid-dense. The expenditure of time and resources just isn’t worth it, when right down the hill dinosaurs are pouring out of the much softer sediments of the Mygatt-Moore Quarry like water from a hydrant. This is the lesson I am learning about the Morrison: finding dinosaurs is easy. Finding dinosaurs you can get out of the ground and prepare–that’s something else.

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Our last stop of the day was Gaston Design, where Rob Gaston showed us how he molds, casts, and mounts everything from tiny teeth to good-sized skeletons.

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Like this Deinosuchus that is about to chomp on Jim Kirkland. Jim doesn’t look too worried.

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Here’s a nice cast of a busted sauropod dorsal, probably from Apatosaurus or Diplodocus, showing the pneumatic internal structure. Compare to similar views of dorsals in this post and this one. This is actually one half of a matched set that includes both halves of the centrum. I left with one of those sets of my own, a few dollars poorer and a whole lot happier.

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The end–for now.