The last post on my SVP 2011 talk took us to the point where I said that modeling a dinosaur made me realize that Alexander’s formula can’t be applied to typical dinosaurs. How did this come about?
Diplodocus non-running for its life
To test if Alexander’s formula made any sense when applied to dinosaurs I couldn’t use tracks. Those depend on the behavior of a specific individual in a specific situation, with that situations very likely not being the one I was interested: an all-out attempt to get the hell out of Dodge. So my only other option was using a 3D model of a dinosaur. Determining hip height, one of the main problems of the Alexander method, is then not a problem. The stride length, however, remains problematic, because it is well possible that many dinosaurs were able to run, thus have unsupported phases (all feet off the ground) during locomotion. Getting a stride length from the skeleton of a runner is at best guesswork, at worst pure fantasy. Sure, you can extrapolate from living animals, but it was the point of my test to see if we are allowed to do so in this case. Thus, I had to turn to the one group of dinosaurs were the skeleton and especially its size tells us that “no, most certainly this dinosaur was unable to run”. And that’s Sauropoda.
Why am I so certain that sauropods could not trot or run? It’s the shape of the limb bones! They indicate a fully erect and pillar-like limb posture (caution, however: that’s true when standing, not when going fast!), as seen in elephants today (or, in fact, probably even more straight).
Loxodonta africana skeleton from wikipedia. Note the straight femur shaft, lack of pronounced crista cnemialis, straight humerus shaft, long humerus and femur,
large hands and feet.
Elephants can’t really run in the sense of the word that most laypeople think of: they do not use unsupported phases. What they do manage is an odd-looking shuffle that is very close to a tölt, albeit with always at least one foot on the ground. That does mean that for each limb pair unsupported phases happen, and the hip does a up&down motion pattern that is normally seen in running gaits – the shoulder, however, does the pattern seen in walking. Lots of research has been done on this, I’ll just point you to two pages by John Hutchinson; check sources given there. And that is the best run elephants can achieve. Researchers call it a “run”, but it does not suffer from the problem of making maximal stride length determination that true gallops or fast-hopping gaits have.
Thus I stole another of Scott Hartman’s cool reconstruction drawings, this time of Diplodocus, and built a 3D CAD model based on it. (Can you smell another How-to post in the making?) That model I used to determine the maximum possible stride length in the forelimbs, which are a lot shorter than the hind limbs. Obviously, I didn’t simply pose my model, but checked out the motion range in the shoulder as well. Then, all it took was making the model walk (more How-to to come, I fear), to see if the determined stride length allowed for a sensible walk cycle. If the animal bobs all over the place, it wastes a lot energy, and the gait cylce is probably nonsense.
In the end, this came out of it:
These are a sequence of stills from a video exported to show the main simulation window. I’ll refrain from posting a video because I need to keep enough back to have a paper with “novel content” one day; I hope you all understand. As I hope you can see the body motions stay within acceptable limits, so this walk is OK.
Now I had a stride length and a hip height; what’s that web address again? Oh, yeah, http://www.sorbygeology.group.shef.ac.uk/DINOC01/dinocal1.html. Plug in the data and……
Wow – a measly 9 mph? That’s the best Diplodocus could do? Now, you can argue that data for extant animals scatters a lot, and (says Alexander 2006),the real speed may be 1.5 times the calculated. OK, under 15 mph…. and we have to consider the possibility that the real speed was as much lower. erhm…. That would mean I can outWALK a Diplodocus….. can you say Meals on Wheels???
So this speed is really really low. To put it into perspective let’s compared to the World records for marathon runners:
Women‘s marathon world record: av. speed 5.18 m/s
Men‘s marathon world record: av. speed 5.69 m/s
and even more obvious, let’s limit the human to a true walking gait:
Men‘s racewalking 20km world record: av. speed 4.33 m/s
Women‘s racewalking 20 km world record: av. speed 3.96 m/s
Wow, the women’s World record holder walks faster (and that is an endurance race!) than an adult Diplodocus could move if in extreme danger! To make it more obvious how utterly absurd this is, let me give you a little additional information on the good lady. She is 1.68 m tall! In fact, it seems my source (wikipedia page on racewalking – ouch) gave an outdated record; the real record holder is even smaller at 1.51 m! And just to reiterate: she used a walking gait, too!
You can “get it” if you really want…
I didn’t. For quite a long time I still didn’t get, even though the comparison suggested the solution to everything. And then, one day, walking quickly to catch a train I had my Eureka! moment. What if dinosaurs did not just use stride frequencies (SF) that we see within the spread of extant animals, but rather spooled the same gait up to much higher ones? I mean, not 1.5 times the calculated speed in the Alexander formula, but 2 times? 3 times? 4? That would make them a lot faster but still give the same track stride length! Alexander’s formula would thus massively underestimate the speed.
But what about the moment arm thingy? Think it through, I told myself: if stride length remains constant, at a comfortable length, what happens to joint torques if the frequency goes up?
First of all, the hip will see a massive torque increase. After all, the entire limb has to be accelerated forward a lot faster, going way above its own frequency (which is determined by the distance of the center of mass from the rotation point, think metronome), then it must be kept from going too far, and then it must be retracted with enormous force to bring the body forward. This is especially tough while accelerating, because you do not have momentum going for you.
In order to make the most of a SF increase the leg should be as long as possible, so you don’t want to flex it a lot. That’s good, because it keeps torques in the knee and ankle low. Lower than in a run, where you need knee flexion for two tasks: cushioning the impact when the foot takes the weight, and for keeping the hip from lifting up when you are at mid-stance, which would result in reduces traction (baaaad idea!). In fact, for the latter reason the up&down motion of the center of mass differs between waling and running: it goes up at midstance and down at maximum limb pro- and re-traction in a walk, and vice versa for a run. Also, the lower protraction and retraction angles of the limb lead to a more compressive force exerted by the mass of the animal than during a run, where there is a lot of bending moments. These will tend to flex the knee when the limb is protracted, and flex the ankle when it is retracted and creates the forward/upward thrust for the next jump in a run. And these flexing moments need to be countered. So the straighter your limb, the lower the torques, and if you don’t run a major reason for extensor torque creation (jumping) is totally gone.
This would mean that “kinematic similarity between dinosaurs and living birds and mammals” (Biewener 2002 about Hutchinson and Garcia 2002) was not given! Therefore, extrapolating from maximal forces in mammal or birds limbs to see if dinosaurs scaled accordingly would not be a valid approach to determine their maximum speed.
Plateosaurus racewalking. This is the maximum stride length I think
reasonable (pubes block larger protraction angles). Check out the very
straight limb posture! Knee and ankle are barely flexed.
It seemed to me that this might work, but that was just me reasoning. I needed to check this, and thus went in search for suitable publications on the biomechanics of racewalking. Sadly, I did not find anything I could understand that gave solid support. Few studies seem to really look at joint torques or at least measure the data I would need to easily calculated them. So I turned to my trusted (and well-hated) kinetic/dynamic modeling once more, and simply made a dinosaur model walk at different speeds using the same motion pattern. This means that I altered only the TIMING, not the joint MOTIONS. At SVP I had a long chat with Stephen Gatesy, and he jokingly asked if I simply used EXCEL to change the “time” column of the data table – in fact, that’s exactly what I did! I copied the time vs. joint orientation tables from my modeling porgram into EXCEL, added a column between them, and used =PRODUCT(A1;x) formula to create differing sequences. For “x” I used values like 1/2, 2/3, 1/4, etc. so that the new time series was shorter then the original one. Then, I altered the frame per time setting of the program so that the sequence was split into the same number of frames for all speeds (means I can compare by frame number and don’t get rounding discrepancies).
The models were ugly, at first. In fact, it was a year of playing with them until I had eliminated all problems that stem from the mathematical methods used. For example, the program can’t distribute forces across supernumerary joints. The simplest example is door hinges: in a gravity-free world you can model them with one perfect rotation axis, and no other motion. If you use two of them, the program is unable to split the forces between them, and just assigns it to one of them at random. A more complicated example is a walking animal. Here, there is a closed loop while two feet are on the ground, if the limb joints and the interactions between foot and ground are too simple in structure. If you model them as complex contacts (6-axis bushings, i.e., a spring/damper system for each sliding and rotational degree of freedom), however, all kinds of ugly things happen, not least an explosion of computing time. It took me an eternity, but I managed to make models that computed in a reasonable time and did not suffer from any of this.
My models aren’t fully done yet. I used Plateosaurus, and I will need to repeat this for Diplodocus and other dinosaurs, and ideally for a human. And I will need to create running models to see if the torque pattern in the simulation behaves as we know it does from experiments. Otherwise my results on extreme dinosaurian racewalking aren’t to be trusted.
But overall, so far, I see what I rpedicted: that torques in the distal joints would rise less, but those in the hip more, when the SF was increased without the stride length, compared to when both are increased. There are a few odd effects, and there is a ton of stuff to check (not least dreaded muscle physiology!), but so far it works. The models require much higher forces and moment arms in the hip, where, as we have seen, these are available in dinosaurs, and do not require as large forces and moment arms in the ankles.
Does this mean that John Hutchinson and colleagues screwed up? Not at all! Their method of checking if dinosaurs scaled as they should in order to run like chicken (which they don’t) tells us exactly what they concluded: T. rex was not a fast runner! It could probably run at the speed of a human at most. The problem is that people automatically take this to mean that it could “go” at most as fast as a human. But that’s not what the SIMM modeling tested. If you use base data from animals that experience the highest torques in their limbs while running, then you check for a motion pattern (running), not for a velocity. There are other ways to “go fast” than running. The studies do not say anything about how fast T. rex was able to roll, brachiate (swing from branch to branch using its arms only), fly, swim, drive a bike – or racewalk! (I supposed they could be used to check the latter, and we will certainly do it.)
Fast Forward Dinosaurs
So what would a dinosaur going really fast have looked like? Pretty much like one walking slowly, just faster. To us, so used to the typical mammalian gait changes from walk to trot and gallop, it would have seemed as if the animal had been filmed and that film was now replayed on fast forward. Quite unspectacular, we would just be surprised how quickly the critter got from one place to another. And because this was true of the vast majority of dinosaurs (with varying degree), a Jurassic hunt would have looked quite boring! In fact, this is so counterintuitive that some people manage not to get any of the stuff that is in my abstract and the Nature News article about it (another post to come, and soon, too).
I’ll end this here, with a last post (tomorrow?) looking at how this related to sauropod gigantism. I won’t discuss anything that goes beyond what I presented at SVP, in order to keep things “novel” for the paper, so please feel free to ask questions in comments, but don’t be disappointed if I refuse to reply.
R. M. Alexander 2006. Dinosaur biomechanics. Proceedings of the Royal Society of Biological Sciences. 273(1596):1849–1855, doi:10.1098/rspb.2006.3532.