It is now high time I finally write up my own SVP talk. The title was a bit boring:
Fast moving dinosaurs: why our basic tenet is wrong
Abstract: Locomotion speeds of dinosaurs are often calculated from ichnofossils, using Alexander’s formula that is based on data mainly from mammals and birds. Results indicate that dinosaurs were rather slow compared to mammals. Inaccuracies due to errors in hip height estimates and other factors are expected, but the method is generally accepted to deliver at least “ballpark figures”. However, in nearly all dinosaurs except theropods the hind limbs differ significantly from both mammals and birds in the distribution of maximal joint torques possible. Is it biomechanically sound to apply the formula under these circumstances?
A detailed assessment of dinosaur limbs, using musculoskeletal modeling in SIMM and Computer Aided Engineering (CAE) kinetic/dynamic modeling, taking gravity, mass distribution and inertia into account, indicates that a basic tenet of Alexander’s formula, the proportional relationship between stride length (SL) and stride frequency (SF) seen in mammals and birds, is unlikely to have existed in non-theropod dinosaurs, and may have had an unusually low slope in theropods. This means that speeds calculated from tracks are the slowest speeds at which the animals have moved, but may be significantly too low. We may therefore not expect to gain information on the top speeds of dinosaurs from tracks at all.
Skeleton-based analyses can suffer from similar uncertainties, because large limb excursion angles as seen in quickly moving mammals create high forces in the limbs. Usually, similar limb kinematics are assumed for dinosaurs. However, if dinosaurs combined high SFs with short SLs, they were able to move far faster for given maximal forces in the joints than previous models suggest. The modeling results from SIMM and CAE suggest that dinosaurs used much higher SF/SL ratios than mammals, achieving absolute speeds in walking gaits that force same-size mammals into running gaits.
OK, what’s that to mean?
Let’s start with the title image of my talk.
Plateosaurus engelhardti GPIT/RE/7288
CT-scan based digital skeletal mount.
This image has a distinct Paulian feel to it, I am afraid. I didn’t copy the Paul pose, especially because Paul drew Plateosaurus running on all fours and even galloping (both of which is nonsense). However, the picture shows an agile animal, which apparently derives a lot of its forward speed from extending the knee and ankle. That’s what today’s mammal look like, and how they get much of their speed. They also typically use large femur excursions (the thigh goes back and forth in the hip across a large angle), and flexion and extension of the back if they are quadrupedal and going really fast (=galloping). Humans, as the sole large bipeds among mammals, typically run like the Plateosaurus in the picture: we lean forward and use a digitigrade position at toe-off (just before the foot leaves the ground).
There’s a number of big problems with the picture above.I’ll list them below. For now, let’s talk about dinosaur speeds.
Dinosaur speeds – how do we determine them?
There are two basic way (sensible ways, that is) that are commonly used to determine how fast dinosaurs could run. Ok, you can use WAGs (wild ass guesses) and do vague estimates of muscle forces and moment arms. If you want to do it properly and without too much “human input” (i.e., your personal guesses influencing important parameters) there really are only “speed from tracks” and biomechanical modeling.
The speed-from-track method was invented up by the famous biomechanics researcher R. McNeil Alexander (sigh – another wikipedia page to fix). In 1976 he came up with a deceptively simple formula (Alexander 1976): if you know the stride length and the hip height of an animal you can calculate its speed. Hip height, Alexander said, can be estimated from foot length.
Now why should that work? Alexander measured stride length (the distance between two successive imprints of the same(!) foot) in various animals, and the speeds at which the tracks were made. And he found that there seemed to be a direct relation between them: “The faster an animal walks or runs, the longer, in general, are its strides. […] I have now obtained a relationship between speed, stride length and body size from observations of living animals and applied this to dinosaurs to achieve estimates of their speeds.” (Alexander 1976: p. 129)
Here’s the graph that goes with it; it shows (top) that for the animals tested the relative stride length is linked to Froude number (a dimensionless parameter related to speed, this way size is taken out of the equation). And (bottom), it shows that the sediment the animal runs on doesn’t matter.
Ok, that’s a regression one can work with, right?
and here’s the formula:
v = 0.25*g0.5*SL1.67*h-1.17
Now all you have to do is measure a track, and plug the data into the formula. For the lazy there even are websites:
Dinosaur Speed Calculator online at Sheffield University.
The problems are legion. First of all, the data for mammals scatters widely. Alexander tested a number of animals: humans, horses, jirds, elephants and ostriches. None of these are really that similar to typical dinosaurs. Then, estimating the hip height from footprint length is a really tricky issue (see Rainforth and Manzella 2007). And then there is an inverse relationship between a sediment’s suitabilities for speedy locomotion and track preservation. (Just a fancy way of saying that surfaces that will likely preserve tracks well are usually not good for running on them, e.g., because they are slippery). Also, animals don’t spend all their time at full throttle. So most of the tracks they make are slow walks to begin with. Thus we are likely to receive only the lower and middle end of typical dinosaurian locomotion speeds.
So what about the other approach? Biomechanical modeling? I’ll save that for the next post.
Alexander, R.M. 1976.
Rainforth, E.C. and M. Manzella. 2007. ‘Estimating speeds of dinosaurs from trackways: a re-evaluation of assumptions.’ Pp. 41-48 in Rainforth E.C. (ed.), Contributions to the Paleontology of New Jersey (II): Field Guide and Proceedings, Geological Association of New Jersey 24th Annual Conference and Field Trip.