Estimating Dinosaur Sizes

One repeating theme of my research is the evolution of gigantism. Not just why or how some animals got to huge sizes but also answering questions about how they functioned. But what concerns me here is estimating the size of an animal based on what is frequently a little more than a few fragmentary remains. It’s something I think is rarely taken into account.

Of couse we first have to establish what we mean by ‘size’. Lets take a fairly obvious example – Brachiosaurus. We can talk about how big he was in 3 main ways – length, height, and weight (mass).

Although Brachiosaurus was a tall animal, no-one really uses height nowadays as a serious measure of overall size. After all, many dinosaurs were long but relativly ‘short’ in comparison to Brachiosaurus, like a typical *Mamenchisaurus*. Allthough height is, of course, it is still usefull for comparing some animals – notably hominids, but also for determining what browsing competitors Brachiosaurus is likely to have. So already we are down to two, but now it all starts to get a bit serious.

Onto length then. Although the Brachiosaurus in Berlin is probably one of the most famous dinosaur mounts going (and is certainly the largest bone-based mount rather than a cast or restoration) it is actually a chimera. Of course it is almost certainly all Brachiosaurus – there’s no stray dicraeosaur vertebrae in there (probably), but depending on quite who you believe, the dinosaur is made up of bits from anywhere from 3 to 5 individuals. This means that immediatley we are actually a bit uncertain as to the true length of the beast – if there is one or two too few, or two many, vertebrae then at 30-50 cm each, we could be quite a way out in our estimation. And just how did the tail taper (the end of the tail never seems to survive fossilisation) – in many taxa the caudal vertebrae taper pretty regularly so even if most of the tail is missing you should be able to come up with an estimate thats going to be out by about 10% at worst. Of course in something like a diplodocid where the tail degenerates into the long whiplash you could easily end up adding or subtracting a few metres or more of total length if you guess the number and length of the individual vertebrae wrong. All a bit trying really.

Of course like the good palaeontologists we are, we take a look around and try to compare our skeleton to some close relatives to see if we can work out how many vertebrae each bit of the skeleton should have. But oh, Brachiosaurus IS the most complete brachiosaur we have, so we have to move outside the clade and compare it to some less closely related sauropods, some of whom show great differences in the number and arrangement of their vertebrae. Damn. Still, we can look at how the individual vertebrae we DO have vary (and some of those form part of a series) and from that we can put up a guesstimate of how the whole vertabral column will change down its length and give us a decent idea of how big it is.

If that looked a bit daunting, now we have a decent length estimate (around 25 m) we can try and calculate the weight of the animal. Of course we immediately have to take into account all the potential errors that have already crept into our length estimates. If our brachiosaur is 2 or 3 metres too long then inevitably our esitmate will make it too heavy. Reconstructions can vary too: Greg Paul favours very light theropod reconstructions for example. In his figures the animals tend to look emaciated, with very thin bodies and light frames. Of course he might be right, but compare that to a fat, well-fed heavy theopod and you may end up adding about 20-30% onto you mass estimates! This ‘gracile vs robust’ problem gets worse when we consider lungs and air sacs. Theropods and sauropods (saurischians) are long known to have hollowed out many of their vertebrae in order to reduce their mass, but many now also thing that these would have been augmented by air sacs analogous to those of birds (see Matt Wedel’s superb stuff on this for more info). This means that even the biggest, fattest sauropods (like our Brachiosaurus) may have had a very significant portion of its volume taken up by light, hollow bones, lungs and air-sacs and may not be half as hefty (Ok, maybe 20-30% less hefty) than we would otherwise have predicted.

Early methods relied on using Archimedes’ princliples to determine the volumes of various dinosaur models to determine thier mass (as was done by the biomechanics legend Mc Neil Alexander). Most animals are pretty much the same density as water (1g/cm3) so this normally works out quite well – but of course saurischians do their best to confound this!

Later on various allometric and scaling methods were used with varying degrees of success, but now two methods have emerged as the front runners in the War on Dinosaur Mass Estimates. The first is using bone dimensions to work out how heavy the animal was. The heavier the animal, the thicker its limb bones in order to support its weight. In fact they have to support not only the weight, but also the extra weight when the animal stands on less than 4 (or 2) legs, and more so for the forces travelling through the bone when it moves. This all adds up pretty quickly and heavy animals need strong bones, or are limited to how fast they can move to reduced these stresses and forces. Normally all of this scales quite well and so measuring the diameter of a femur should give you a pretty fair estimate as to the mass of the animal. As ever though, this comes with a few catches! Bones might deform during fossilisation and you might not be measuring the ‘true’ diameter. The animal might not distibute its weight evenly (most sauropods put most of their weight on the back feet, but Brachiosaurus is front heavy!). Or they animal might move alot, even a heavy one, so its limbs are thicker than you might expect. Finally, big animals might be unique. Although smaller animals scale well, we run out of decent examples of big terrestrial animals after elephants – and dinosaurs were a lot bigger, and maybe they were different for reasons we don’t understand or don’t know about.

Alternatively we can go down the hi-tech route. Don Henderson, (now at the Tyrrell) created a series of wonderful 3-D reconstructions in his compuer for his PhD and beyond. The great thing is that Don can allow for differentials in bone mass, lung volume etc. etc. to really build up the detail, and therfore the accuracy of his results. Plus he can do the same analysis on living animals to see if he’s on track. Turns out he is! His reconstructions and their follow ups (how some animals, including sauropods, float in water) are wonderful to look at, but more importantly are clearly well thought through and based on 1st principles of matematics and physics.

Well, thats a helluva big post, but hopefully provides some food for thought for those with an interest in all these ‘X metre long, Y ton’ estimates we see with every new dinosaur in the media. Of course there are lots of little exceptions, other methods, and often downright disagreements between palaeontologists about all of this, and many ‘gospel’ measurements should be taken with a pinch of salt. Still, we have drastically improved over the last 5-10 years and than can only be good for the rest of us when we want to try and calcuate speeds, metabolism, food intake or the rest. But for now, watch out for 1 ton T.rexes and 75 ton Diplodocuses and wonder if maybe the authors should think again as to how ‘big’ they really were.

This is a revised version of a Mk.1 post, to see the original with comments etc. go here.