within fossilized bone. Speed Scientists have produced a wide range of possible maximum running speeds for Tyrannosaurus: mostly around , but as low as and as high as , though it running this speed is very unlikely. Tyrannosaurus was a bulky and heavy carnivore so it is unlikely to run very fast at all compared to other theropods like Carnotaurus or Giganotosaurus. Researchers have relied on various estimating techniques because, while there are many tracks of large theropods walking, none showed evidence of running. A 2002 report used a mathematical model (validated by applying it to three living animals: alligators, chickens, and humans; and eight more species, including emus and ostriches) to gauge the leg muscle mass needed for fast running (over ). Scientists who think that Tyrannosaurus was able to run point out that hollow bones and other features that would have lightened its body may have kept adult weight to a mere or so, or that other animals like ostriches and horses with long, flexible legs are able to achieve high speeds through slower but longer strides. Proposed top speeds exceeded for Tyrannosaurus, but were deemed infeasible because they would require exceptional leg muscles of approximately 40–86% of total body mass. Even moderately fast speeds would have required large leg muscles. If the muscle mass was less, only for walking or jogging would have been possible. Holtz noted that tyrannosaurids and some closely related groups had significantly longer distal hindlimb components (shin plus foot plus toes) relative to the femur length than most other theropods, and that tyrannosaurids and their close relatives had a tightly interlocked metatarsus (foot bones). The third metatarsal was squeezed between the second and fourth metatarsals to form a single unit called an arctometatarsus. This ankle feature may have helped the animal to run more efficiently. Together, these leg features allowed Tyrannosaurus to transmit locomotory forces from the foot to the lower leg more effectively than in earlier theropods. Additionally, a 2020 study indicates that Tyrannosaurus and other tyrannosaurids were exceptionally efficient walkers. Studies by Dececchi et al., compared the leg proportions, body mass, and the gaits of more than 70 species of theropod dinosaurs including Tyrannosaurus and its relatives. The research team then applied a variety of methods to estimate each dinosaur's top speed when running as well as how much energy each dinosaur expended while moving at more relaxed speeds such as