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.



Clash of the Titans from above

Here’s the “Clash of the Titans” exhibit at the Sam Noble Oklahoma Museum of Natural History, featuring the reconstructed skeletons of the giant Oklahoma Apatosaurus – which I guess should now be called the giant Oklahoma apatosaurine until someone sorts out its phylogenetic position – and the darn-near-T. rex-sized Saurophaganax maximus, which may be Allosaurus maximus depending on who you’re reading.

Now, I love this exhibit in both concept and execution. But one thing that is more obvious in this view from the upper level balcony is that despite its impressive weaponry, a lone 3-to-5 ton Saurophaganax had an Arctic ice cap’s chance in the Anthropocene of taking down a healthy 30-meter, 40-50 ton apatosaur (which is to say, none). I like to imagine that in the photo above, the apatosaur is laughing at the pathetically tiny theropod and its delusions of grandeur.

Clash of the Titans from behind

In this shot from behind, you get a better look at the baby apatosaur standing under the big one, and it hints at a far more likely target for Saurophaganax and other large Morrison theropods: sauropods that were not fully-grown, which was almost all of them. I am hip to the fact that golden eagles kill deer, and some lions will attack elephants – as Cookie Monster says, “Sometime food, not anytime food” – but not only were smaller sauropods easier prey, they were far more numerous given the inevitable population structure of animals that started reproducing at a young age and made more eggs the bigger they got (as essentially all egg-laying animals do).

In fact, as discussed in our recent paper on dinosaur ontogeny (Hone et al. 2016), there may have been times when the number of fully-grown sauropods in a given population was zero, and the species was maintained by reproducing juveniles. The giant Oklahoma apatosaurine is a unique specimen today – by far the largest apatosaurine we have fossils of – but it may also have been an anomaly in its own time, the rare individual that made it through the survivorship gauntlet to something approaching full size.

Amazingly enough, there is evidence that even it was not fully mature, but that’s a discussion for another day. Parting shot:

Oklahoma Apatosaurus neck and head


Is that your flexor tubercle, Saurophaganax, or are you just hungry to see me?

Is that your flexor tubercle, Saurophaganax, or are you just hungry to see me?

Up top there is a commercially obtained cast sculpture of a thumb claw of Megaraptor. Down below is an unpainted urethane cast of one of my favorite inanimate objects in the universe: OMNH 780, a thumb claw of Saurophaganax. I dunno how much of the Megaraptor claw is real [none, it turns out, but it’s based on a true story]; certainly the cast is faithful enough to record some tool-marks in the rugose part near the base. But I know how much of OMNH 780 is legit, and that is all of it. I would have put in a photo of the actual specimen but irritatingly I forgot to take any during my recent visit, and I didn’t have the Megaraptor claw back then anyway. Hopefully I’ll get back to the OMNH this summer, and then it is ON.

The kaiju-loving fanboys of CarnivoraForum undoubtedly want to know how these two compare. Well, much to my disappointment, the Megaraptor claw is a shade longer (28.7 cm max straight-line distance) than the Saurophaganax claw (26.3 cm). But the Saurophaganax claw is about twice as thick and way more robust, and the flexor tubercle which anchored the tendon that powered the claw’s movement is friggin’ immense. It’s like pitting an NBA forward against an NFL linebacker: one is a little taller, but the other one will pound you like a tent stake.

If anyone’s wondering, these claws are both waaay shorter than those of Therizinosaurus (half a meter and up), which still holds the longest-claws-of-anything-ever title. The problem for fans of excessive violence is that Therizinosaurus probably wasn’t doing terribly exciting things with its claws–grooming its feathers, making veggie kabobs, and scratching its ample behind, most likely.

Mmmmmm...suffering. OM NOM NOM NOM!!

Mmmmmm…suffering. OM NOM NOM NOM!!

The same was not true for Saurophaganax, which the unbelievers call Allosaurus maximus, a red-blooded all-American murder machine with a triple PhD in kicking your ass. When it wasn’t drinking camptosaur blood straight from the jugular, it was eating mud-mired diplodocids butt first while they were still alive. And what about those rumors that Saurophaganax was completely feathered in $100 bills, or that it was the direct linear ancestor of Charles Bronson and Steven McQueen? It’s probably too soon to say, since I just made them up, but I’ll bet your mind is blown nonetheless.

How dangerous was Saurophaganax? Let me put it this way: it’s still dangerous. Thanks to the high concentration of heavy elements in Morrison dinosaur bones, you’re supposed to air out the specimen cabinets before you start working so the radon can escape. Otherwise you might breathe in freakin’ radioactive gas and get cancer (in contrast to some “facts” in the previous paragraph, this is actually true). That’s right, Saurophaganax can kill you, just by lying around in a drawer. After 145 million years, it’s still reaping souls for Hades. By god, that’s giving them what for!

In short, the thumb claw of Saurophaganax is the most impressive instrument of dinosaurian destruction I’ve yet laid eyes on. If you want to see it in context, check out the mounted skeleton at the Oklahoma Museum of Natural History in Norman.

This idiot is going to die.

This idiot is going to die.