# dinosaur trackway speed estimates

Hi there,

I agree with Emma Rainforth and others that speed estimates of dinosaurs from fossil tracks need to be taken with caution, and are often more informative qualitatively than quantitatively.  Based on experiments with living animals that I've done or others have published, the factor of error can easily be 50-100%.  So a track showing "10 meters/second" might be anywhere from less than 5 m/s to 20 m/s for all we know.  I wish we could put confidence limits on these estimates or at least do some rudimentary statistics, but so far the science hasn't advanced to that point.  Most people just use Alexander's 1976 equation without questioning it, and report one value of speed.

The key problem is that the equations of Alexander, Thulborn, and others (as they have admitted explicitly if you read the papers) have a lot of assumptions built into them, and the principles that underlie these assumptions are generally true for all animals but there is much variation.  The equations may seem simple: input footprint length (or hip height; FL*4 usually) and stride length and the output is velocity in m/s.  But there are a lot of hidden variables that are represented as constant values in these equations.  These variables (e.g. stride frequency, limb joint angles and effective limb length, etc.) are poorly understood for living animals, and that's why we often get erroneous speed estimates for living animals based on tracks.

A good commentary by Alexander on the use of his speed estimates is in this article:
Alexander, RMcN. 1991. Doubts and assumptions in dinosaur mechanics. Interdisciplinary Science Reviews 16(2): 175-181.
In particular, one insightful comment is that he worries that:
"[A]re people taking it too seriously?  Are paleontologists being deceived by the apparent precision of physical arguments into believing that my conclusions are firmer and more accurate than they really are?"

That being said, there are published accounts of some interesting trackways of small and large theropods, some of which show potentially fast speeds.  The faster ones (reviewed by Irby, 1999 in Museum of Northern Arizona Bulletin 160: 109-112) from smaller theropods should represent running gaits IF they are 11m/s.  I think more empirical data from living animals needs to be incorporated into these speed equations, though, before I'd read much quantitatively into these "speeds."

Kuban (1989 in Dinosaur Tracks and Traces; pp.57-72 and pp. 57-58 in particular) briefly notes that one trackway "exhibits unusually long paces relative to track length (8.48 mean pace/track length ratio), indicating an exceptional speed of about 10 m/s."  He illustrates the trackway in Fig 7.2 but to my knowledge no more data have ever been published on this trackway.  It does seem to have been made by a medium-largish theropod, similar in size to the one recently published in Nature by Day et al., and of grossly comparable relative stride length.

Whether either of these animals was truly running, or moving 8-10 m/s for that matter, is not clear to me from the published data.  It is particularly problematic that the actual data (footprint lengths, pace/step lengths, etc.) for each track are not readily available in the literature yet (as far as I know), and few of the trackways are well illustrated.  That makes it harder to evaluate what these tracks mean.  Most importantly, more sensitivity analysis of the many unknown parameters in these equations needs to be conducted before the quantitative estimates will have much rigor.

Nonetheless, I think the speed estimate methods are a great tool for teaching students about locomotion, biomechanics, mathematics, dinosaurs, and science.  A good example of how this can be used is at this excellent webpage: