The running ability of

Some qualitative anatomical studies (^{−1}) and an overall high degree of athleticism for large theropods like

Biomechanical models inherently incorporate anatomical characters (e.g., limb proportions) on which more traditional qualitative assessments are based, but also require quantitative definitions for soft tissue parameters associated with mass distribution and muscle properties. These soft tissue parameters are almost never preserved in dinosaur fossils and therefore need to be estimated indirectly. Typically, minimum and maximum bounds are placed on such parameters based on data from living animals (

One solution is to find information in the preserved skeletal morphology that can be used to reduce the predictive dependence of biomechanical models on soft tissue. It has recently been suggested that bone loading can be used to improve the locomotor reconstruction of fossil vertebrates by excluding gaits that lead to overly high skeletal loads (

Ostrich bone cross sections parameters were scaled from the literature (

Muscle paths are in red and joints are in blue. The axes arrows are 1 m long.

However there are two main problems with approaches based on joint reaction forces. Firstly to accurately calculate the loads sustained

MBDA approaches to locomotor reconstruction require a linked segment model of the animal to be built based on its skeletal morphology and inferred myology (

Bone stress analysis was performed by treating the limb long bones as irregular beams and calculating the mid-shaft loading. The load was calculated directly from the multibody simulator by splitting each of the leg segments into two separate bodies that were linked by a fixed joint. The simulator was then able to calculate both the linear forces and rotational torques acting around this non-mobile joint using the full dynamic model and therefore including inertial forces as well as muscle forces and joint reaction forces. A full finite element analysis would have been preferable but this is currently too computationally expensive in this context and previous work has shown that the mean error in long bone loading is likely to be approximately 10% (_{compressive} is the normal stress in the beam due to compression (N m^{−2}). ^{2}). _{bending} is the normal stress in the beam due to bending (N m^{−2}). _{x} is the bending moment about the _{y} is the bending moment about the _{x} is the second moment of area about ^{4}). _{y} is the second moment of area about ^{4}). _{xy} is the product moment of area (m^{4}).

To calculate the dynamic loads, this simulation needs to be able to walk and run bipedally. This was achieved using our standard gait morphing methodology (

(A) maximum velocity; (B) Froude number; (C) stride length; (D) gait cycle duration.

Foot contact times are also shown (black is ipselateral limb, grey is contralateral limb). The time axis represents two complete gait cycles, and the dashed line is drawn at 100 MPa which is the nominal stress limit for a safety factor of 2.

^{−1} for the high stress limit conditions (>200 MPa). Lowering the peak stress limit has little effect on this maximum speed until it is reduced below 150 MPa when the maximum speed drops rapidly. This clearly shows that limiting the stress at high values has no effect on running speed and therefore the simulation is not stress limited in these conditions. At lower stress limits, the stress limit controls the maximum speed indicating that the simulation is stress limited at physiologically realistic peak stresses.

There are two definitions of walking and running that are commonly used when considering bipedal gait. The traditional definition is “progress by lifting and setting down each foot in turn, so as to have one foot always on the ground” (

In the

The velocity changes in

As with all attempts at reconstructing the locomotor capabilities of fossil animals it is important to be somewhat cautious with our interpretations. These results improve on those obtained by previous biomechanical work by excluding some of the previously plausible values and thereby reducing the range of uncertainty but many of the previous caveats still apply. Our previous work on sensitivity analysis (

The finding that

The results presented demonstrate that the range of speeds predicted by earlier biomechanical models for

The authors would like to thank NERC, the Leverhulme Trust, BBSRC, EPSRC and PRACE for their ongoing support developing GaitSym; the staff at the high performance computer centres where the simulations were carried out (Archer, Hartree and N8); and the staff at the Black Hills Institute for allowing us to scan BHI 3033.

The authors declare there are no competing interests.

The following information was supplied regarding data availability:

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