How Fast Could They Run? Estimating Speed From Bones and Footprints

The first approach uses a relationship established from living animals between stride length, hip height and speed, which holds across a remarkable range of species because it follows from the physics of a pendulum-like limb rather than from anatomy. Measuring the distance between successive prints of the same foot gives stride length directly. Hip height is estimated from footprint length, using a ratio that varies between groups and introduces the main uncertainty. Putting both into the relationship returns a speed. The method has real strengths, since it measures an animal that was actually moving rather than one that might have, and real limits, since a trackway records one moment at whatever pace that animal chose, and the overwhelming majority of preserved trackways record walking rather than running.

The second approach builds the animal and asks what it could do:

• •A digital skeleton is assembled from scans and missing parts are reconstructed
• •Muscles are added with volumes estimated from attachment sites and from comparison with living animals
• •Body mass and its distribution are calculated, which determines the forces involved
• •Simulation finds the fastest gait the model can sustain without the legs failing or the animal falling
• •Results are validated by applying the same method to living animals whose speeds are known
• •The output is an upper limit rather than an observed speed, which is a different quantity from the track method

Modelling work has consistently produced lower figures for the largest predators than earlier estimates assumed. Studies of the biggest theropods return maximum speeds in the range of a fast human jog rather than anything approaching a vehicle, with the constraint being that leg muscle mass required to accelerate a several-tonne body rises faster than an animal can carry, and that bones and tendons would fail under the loads running would generate. Smaller theropods come out considerably faster. The famous scene of a large predator pursuing a moving vehicle is not supported by any current analysis and was not supported when the film was made. Track-derived speeds for large animals cluster at walking pace, which is consistent with the modelling and reflects both that the animals walked most of the time and that soft ground preserving tracks is poor ground for running.

The reason large animals are slow follows from scaling and applies to living animals as much as to extinct ones. Body mass rises with the cube of linear size while the cross-sectional area of bone and muscle, which determines the force they can bear and produce, rises with the square, so a larger animal has proportionally less strength available to support and accelerate itself. Living land animals reflect that, with the fastest being medium-sized and both smaller and much larger animals being slower, which produces a hump-shaped relationship between mass and top speed rather than a steady increase. An elephant cannot run in the ordinary sense, never having all feet off the ground, and the same reasoning predicts the same for the largest extinct predators. That relationship is one of the better-supported generalisations in the study of animal movement.

Both approaches leave real uncertainty and stating it is part of reporting a figure. Soft tissue is unknown, so muscle volumes and tendon properties are estimated from living animals that may not be good models for body sizes far outside the living range. Gait is assumed, and an animal may have used a gait the model did not consider, with recent work suggesting some large forms may have used a grounded running gait that never has both feet off the ground. Substrate affects track measurements, since soft mud both records prints and slows the animal making them. Maximum speed is rarely the interesting quantity, since endurance, acceleration and turning matter more for predation and are harder to estimate. And a maximum a model permits is not evidence the animal ever reached it.

Stride length and estimated hip height give a speed from a trackway, which records what an animal actually did, and modelling gives an upper limit for what its body allowed. Modelling puts the largest predators at around a fast jog, since the muscle needed rises faster than a multi-tonne animal can carry. Most preserved trackways record walking, and the famous film chase was never supported.