When you walk along a beach, you leave tracks with a particular stride length (the distance from one foot-fall to the next by the same foot). If you begin to run, the stride length increases, and the faster you go, the longer the stride length. An English expert in biomechanics, R. McNeil Alexander, spotted something more: there was a constant relationship between stride length and speed, providing you took account of the size of the animal (measured by the height of the hip from the ground), and it did not matter whether you made the calculation for a two-legged animal like a human, or a four-legged animal like a horse.
Alexander (1976) presented his evidence and his formula, and he suggested it could also be used for estimating the speed of movement of extinct animals, such as dinosaurs:
u = 0.25 g-0-5d1'67h-1-17, where u is velocity, g is the acceleration of free fall (gravity), d is stride length and h is hip height (Fig. 19.11). The formula can be simplified to:
u = 1.4 (1/h) - 0.27, for rough calculations. The hip height has to be measured from a skeleton of the dinosaur that is supposed to have made the tracks. If that cannot be done, there is a fairly predictable relationship
Figure 19.11 Diagram showing how to measure stride length (SL) and foot length (FL) on a dinosaur track.
between hip height and foot length for each major dinosaur group (hip height is 4 to 6 times the foot length, depending on the group), so all measurements can be made from the footprint slab if necessary.
Many paleontologists applied the Alexander formula to dinosaur tracks, and many subtle corrections have been suggested, but it seems to work pretty well. Typical calculated speeds range from 1 to 4 m s-1 for walking dinosaurs (about human walking speeds), with high values of 10-15 m s-1 for some smaller, flesh-eating dinosaurs that were in a hurry to catch their lunch. The maximum calculated speed of 15 m s-1 is equivalent to 54 km h-1, or 35 miles per hour, equivalent to a fast racehorse, or just faster than town driving speeds. Faster speeds have been claimed from some dinosaur tracks, but these are unlikely.
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