Estimating dinosaur speed from footprints and biomechanical models

A dinosaur trackway preserves distances between successive contacts with the ground, not a clock reading. Researchers can measure the footprints and their spacing, but estimating speed requires a relationship between stride, body dimensions and movement. Skeletal models supply a different route: they simulate how muscles, joints and bones could support locomotion. Both approaches produce conditional estimates, and they do not necessarily answer the same question.

Measure stride before applying a formula

Stride length is the distance between successive prints of the same foot. It differs from the step between opposite feet, a distinction that matters in an alternating bipedal trackway. Researchers first need to identify a consistent sequence, assess which impressions belong together and determine the exposed level within the original track-bearing sediment. Erosion, later infilling and undertracks can obscure the actual contacts.

Hip height is then estimated from footprint dimensions or a proposed trackmaker's anatomy. A multiplier based on footprint length is a practical approximation rather than a universal conversion. Different limb proportions, postures and preservation can produce different hip-height estimates. The guide to two-legged and four-legged dinosaur movement explains why locomotor anatomy must be considered before applying one body-size relationship to unlike animals.

What the classic equation assumes

R. McNeill Alexander's 1976 method related speed to stride length and hip height using comparisons with living animals. In a widely used form, speed increases approximately with stride length to the power 1.67 and decreases with hip height to the power 1.17, while gravity is held constant. These relationships express an empirical model; they are not a timing device hidden inside the fossil.

The exponents show how measurement uncertainty propagates. Keeping everything else unchanged, a ten per cent increase in measured stride raises the calculated speed by about seventeen per cent. Increasing the assumed hip height by ten per cent lowers it by roughly eleven per cent. These are illustrations of the formula's sensitivity, not error bars measured for every trackway. Substrate effects and the appropriateness of the comparative relationship introduce additional uncertainty.

A 2025 experiment tested the calculation against living birds

Tash Prescott and colleagues filmed two helmeted guineafowl crossing mud of different consistencies and digitised the resulting tracks. Their Biology Letters study, published on 25 June 2025, compared speeds measured directly from video with speeds calculated from trackway measurements. Several formulae overestimated speed in their experimental conditions. Identical strides could also be produced at markedly different actual speeds.

The result challenges uncritical numerical precision, especially for freely moving animals on deformable ground. It does not measure dinosaur speeds directly, and a study of two birds cannot quantify the same bias for every extinct species or tracksite. Nevertheless, it tests a crucial assumption under conditions relevant to footprint formation: a trackmaker can change how it steps as the ground yields, without changing speed in the way a simple stride equation predicts.

Skeletons test mechanical feasibility

Biomechanical models reconstruct limb segments, joint ranges, muscle forces and body mass. They can then search for movements that satisfy balance and loading constraints. If a proposed gait requires unrealistic muscle force or imposes excessive stress on a supporting bone, the model provides a reason to question that gait. The strength of the result depends on how the missing soft tissues and mechanical properties were assigned.

William Sellers and colleagues included bone-stress constraints in a Tyrannosaurus model published in 2017. Under those assumptions, true running in a large adult would impose problematic skeletal loads. This is evidence against a particular high-speed running interpretation, rather than a direct observation of a living tyrannosaur. Body mass, muscle architecture, tendon behaviour and the definition of a running gait all affect how models should be compared.

Preferred Tyrannosaurus walking speed answers a different question

A 2021 study by Pasha van Bijlert and colleagues modelled the tail's natural oscillation frequency as a route to estimating a preferred walking rhythm. Their baseline Tyrannosaurus result was 1.28 metres per second, about 4.6 kilometres per hour, with modelled alternatives spanning 0.80–1.64 metres per second. The numerical interval describes variations within that modelling approach; it is not a stopwatch measurement or the complete possible speed range of the species.

Preferred walking pace concerns a rhythm that may reduce locomotor effort. Maximum performance concerns the upper mechanical and physiological limits under different circumstances. Confusing these quantities makes the same animal appear alternately sluggish and exceptionally fast depending on which number is quoted. The discussion of fast dinosaur candidates treats comparative claims separately from the method used to obtain each estimate.

Why a fastest-species league table remains uncertain

Long legs and a light body can support hypotheses about cursorial ability, but neither establishes an exact kilometre-per-hour maximum. Modern animals of similar mass can have very different locomotor specialisations. There is no general rule that an animal near fifty kilograms must outperform everything heavier or lighter, and incomplete fossils make rankings between extinct species still harder to standardise.

A defensible speed statement therefore identifies its basis: a particular trackway, a particular skeletal model or a model of preferred walking. It states the assumed body dimensions and the limits of the calculation. Comparisons are most useful when they match those quantities, rather than placing a trackway's walking episode beside another species' simulated maximum and calling the difference a race result.