If you really want to know how fast dinosaurs could run, there's one thing you need to do right off the bat: forget everything you've seen in movies and on TV. Yes, that galloping Gallimimus herd in Jurassic Park was impressive, as was that rampaging Spinosaurus on :Terra Nova. But the fact is that we know virtually nothing about dinosaur locomotion, except for what can be extrapolated from preserved footprints or inferred by comparisons with modern animals.
Galloping Dinosaurs? Not So Fast!
Physiologically speaking, there were three major constraints on dinosaur locomotion: size, body plan and metabolism. Size can be dispensed with easily: there's simply no way a hundred-ton titanosaur could have moved faster than a humvee driver looking for a parking space. (Yes, modern giraffes are vaguely reminiscent of sauropods, and can move speedily when provoked--but giraffes are orders of magnitude smaller than the biggest dinosaurs). By the same token, lighter plant-eaters--picture a wiry, 50-pound ornithopod--ran significantly faster than their lumbering cousins.
The speed of dinosaurs can also be inferred from their body plans--that is, the relative sizes of their arms, legs and trunks. The short, stumpy legs of Ankylosaurus, combined with its massive, low-slung torso, point to a dinosaur that was only capable of "running" as fast as an average human being can walk. On the other side of the dinosaur divide, there's some controversy about whether the short arms of Tyrannosaurus Rex would have vastly constrained its running speed (if an individual stumbled while chasing its prey, it might have fallen down and broken its neck!)
Finally, and most controversially, there's the issue of whether dinosaurs possessed endothermic ("warm-blooded") or ectothermic ("cold-blooded") metabolisms. In order to run fast for extended periods of time, an animal must generate a steady supply of internal energy, which necessitates a warm-blooded physiology. Most paleontologists now believe that carnivorous dinosaurs were endothermic, and that the smaller, feathered varieties may have been capable of leopard-like bursts of speed.
What Dinosaur Footprints Tell Us About Dinosaur Speed
Paleontologists do have one strand of forensic evidence for dinosaur locomotion: preserved footprints, or "ichnofossils," One or two footprints can tell us a lot about any given dinosaur, including its type (theropod, sauropod, etc.), its growth stage (hatchling, juvenile or adult), and its posture (bipedal, quadrupedal, or a mix of both). If a series of footprints can be attributed to one individual, it may be possible, based on the spacing and depth of the impressions, to draw conclusions about that dinosaur's running speed.
The problem is that even isolated dinosaur footprints are phenomenally rare, much less an extended set of tracks. There's also the matter of interpretation: for example, an interlaced set of footprints, one belonging to a small ornithopod and one to a larger theropod, may be construed as evidence of a 70-million-year-old chase to the death, but it may also be that the tracks were laid down days, months or even decades apart. (On the other hand, the fact that dinosaur footprints are virtually never accompanied by dinosaur tail marks indicates that dinosaurs held their tails off the ground when running, which must have slightly boosted their speed.)
What Were the Fastest Dinosaurs?
Now that we've laid the groundwork, we can come to some tentative conclusions about which dinosaurs were the flat-out fastest. With their long, muscular legs and ostrich-like builds, the clear champions were the ornithomimids ("bird mimics"), which may have been capable of reaching top speeds of 30 to 40 miles per hour. (If ornithomimids like Gallimimus and Dromiceiomimus were covered with feathers, as seems likely, that would be evidence for the warm-blooded metabolisms necessary to sustain such speeds.) Next in the rankings would be the small- to medium-sized ornithopods, which, like modern herd animals, needed to sprint quickly away from encroaching predators, and after them would come feathered raptors and dino-birds, which could conceivably have flapped their proto-wings for additional bursts of speed.
What about everyone's favorite dinosaurs, large, menacing theropods like T. Rex, Allosaurus and Giganotosaurus? Here, the evidence is more equivocal. Since these carnivores often preyed on relatively pokey ceratopsians and hadrosaurs, their top speeds would have been well below what's been advertised in the movies: 20 miles per hour at most, and perhaps even significantly less. In other words, the average large theropod may have been incapable of running down a grade-schooler on a dirt bike!