Natural Frequency Method: estimating the preferred walking speed of Tyrannosaurus rex based on tail natural frequency

Abstract

Locomotor energetics are an important determinant of an animal's ecological niche. It is commonly assumed that animals minimize locomotor energy expenditure by selecting gait kinematics tuned to the natural frequencies of relevant body parts. We demonstrate that this allows estimation of the preferred step frequency and walking speed of Tyrannosaurus rex , using an approach we introduce as the Natural Frequency Method. Although the tail of bipedal dinosaurs was actively involved in walking, it was suspended passively by the caudal interspinous ligaments. These allowed for elastic energy storage, thereby reducing the metabolic cost of transport. In order for elastic energy storage to be high, step and natural frequencies would have to be matched. Using a 3D morphological reconstruction and a spring-suspended biomechanical model, we determined the tail natural frequency of T. rex (0.66 s −1 , range 0.41–0.84), and the corresponding walking speed (1.28 m s −1 , range 0.80–1.64), which we argue to be a good indicator of preferred walking speed (PWS). The walking speeds found here are lower than earlier estimations for large theropods, but agree quite closely with PWS of a diverse group of extant animals. The results are most sensitive to uncertainties regarding ligament moment arms, vertebral kinematics and ligament composition. However, our model formulation and method for estimation of walking speed are unaffected by assumptions regarding muscularity, and therefore offer an independent line of evidence within the field of dinosaur locomotion.

Muscle-controlled physics simulations of the emu (a large running bird) resolve grounded running paradox

“…Future simulation work on extinct taxa would be required to untangle the effects of COM location, leg posture, and body mass reduction on the evolutionary history of birds. Soft-tissue information is often lacking in biomechanical analyses of extinct taxa ( 48 , 67 , 72 ), but our simulations are encouraging in that respect: despite numerous simplifications regarding the contractile and other soft-tissue anatomy, our simulations are able to capture salient features of emu gait dynamics (Figures 4 and 5). Our results suggest that although muscular uncertainties can impact the transition speeds and maximal performance, many spatiotemporal variables (such as stride lengths) are relatively unaffected and remain similar to experimental data.…”

“…Birds are direct descendants of (non-avian) theropod dinosaurs, who relied heavily on their massive tails to power locomotion ( 65–67 ). Birds lost this massive tail – and resulting cranial shift in COM likely contributed to more crouched postures being required to stand in equilibrium ( 40 ).…”

Editorial: Technological Frontiers in Dinosaur Science Mark a New Age of Opportunity for Early Career Researchers

“…In fact, young researchers are taking the lead in research with new scientific approaches (e.g. Falkingham et al, 2018;Lefebvre et al, 2020;Manafzadeh and Gatesy, 2020;Bailleul et al, 2021;Nieto et al, 2021;Serrano-Martínez et al, 2021;Van Bijlert et al, 2021;Ma et al, 2022;Wiemann et al, 2022). Young scientists are the key to bringing new perspectives into science and pushing technological and methodological developments.…”

Updating studies of past life and ancient ecologies using defossilized organismal proxies

“…1) Researchers can conduct sensitivity analyses during the experimental design process. Sensitivity analysis entails systematically changing parameters to determine effects on results (Tseng et al, 2011;Bijlert et al, 2021;Bishop et al, 2021) and demonstrate methodological constraints. Such tests are often used to validate VDOP studies and to tune parameters over many iterations.…”