How fast could a T-rex run?

22.01.2012
 
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How fast could a T-rex run? And, more importantly, was it fast enough to catch you?

 

Grid computing is helping palaeontologists to understand better how dinosaurs moved around and what roles they played in their ancient world.

 

With its sharp teeth and massive jaws, the T-rex is the stuff of nightmares. It’s not surprising that scientists are convinced the T-rex was a carnivorous predator but huge teeth don’t tell the whole story. Was it like the modern cheetah and catch its prey in short burst-like sprints? Or was the T-rex a sneaky stalk-and-ambush hunter like the jaguar? What was its place in the Cretaceous ecosystem?

Out to get you! But can it?  (Illustration: wikicomnmons / J.M.Luijt)Since we can’t see a real T-rex in action (it disappeared along with the other dinosaurs 65 million years ago), palaeontologists need to look elsewhere to understand its role as a predator. Top running speed offers good clues to solving this mystery – but how do you measure the maximum speed of an extinct animal?

If zebras were to become extinct, the palaeontologists of the future could probably use horses or donkeys as comparisons. People looking at dinosaur behaviour don’t have that luxury because there is nothing alive today quite like a T-rex. The solution is to create a detailed computer simulation of the animal’s skeleton and muscles.

 

Teaching a T-rex how to run

 

Compsognathus was tiny, with a length of just 1 metre, and it not the most scary of the dinosaurs. But it was certainly fast and could probably keep up with a racing greyhound. (Illustration: wikicomnmons / Zach Tirrell)

William Sellers and Phillip Manning, two palaeontologists from the University of Manchester, used a programme called GaitSym to model the top running speeds of five types of bipedal dinosaur – CompsognathusVelociraptorDilophosaurusAllosaurus and T-rex (officially known as Tyrannosaurus rex). They also modelled three living animals – the ostrich, the emu and humans – with relatively well-known top speeds to use as comparison (see table below).

First, they used the information available from known fossils to reconstruct the animal’s locomotive anatomy and to build a 2D musculoskeletal model. The model specifies, for example, where the joints are, where the muscles are, the weight/mass of the trunk, thighs, feet and other parts of the animal alongside the size and properties of its muscles.

Then, they ‘released’ this virtual robot in GaitSym – a simulation environment that respects the real laws of physics (e.g. gravity, inertia) – and told it to run as fast as possible. The key to the model is that the palaeontologists didn’t specify which muscle activation sequence the dinosaurs should use. This is what GaitSym does – the programme experiments with different combinations of muscle activation patterns and searches for an optimum solution. In this case, GaitSym looked for the muscle activation pattern that allowed the animal to cover the most ground in a given amount of time.

Poor solutions – patterns that caused the animal to stagger, stumble or fall – were abandoned while promising patterns were selected for further investigation. Each individual computation is not complex but the problem is that GaitSym needs to go through thousands of muscle activation patterns. This makes the work computationally demanding and impractical to complete using a single computer. Instead, Sellers and Manning accessed the grid computing services provided by the UK’s NW-Grid and used about 170,000 hours of computing time to complete the project in a few months.

 

And the dinosaur speeding record goes to...

 

Sellers and Manning reported in their Proceedings of the Royal Society B paper that all simulations generated high-quality running gaits for the seven tested animals. The computer model also assigned top speeds to living animals that are reasonably close (although slightly slower) than what is measured in real life.

Size comparison of three dinosaurs included in the study and a 1.80m person. Orange: Tyrannosaurus; Blue:Allosaurus; Black (the little blob):Compsognathus

They found that the smallest dinosaur was also the fastest: little Compsognathus was roughly the size of a turkey, but with a top speed of 64 km/h it could keep up with a racing greyhound (see table). The Velociraptor and the Dilophosaurus (both species responsible for more than a few fatalities in the movie Jurassic Park) had top speeds of about 38 km/h, just below what a modern elephant can manage.

The T-rex was the slowest animal in the contest and according to the model can only get up to 29 km/h. This means that Usain Bolt – the world’s fastest man – could probably outrun it with his 9.58s 100 metre record (ca. 37.5 km/h). However, the rest of us should probably take the safest option and wake up from the nightmare.

  Weight (kg) Leg length (m) Stride length (m) Speed (km/h) (modelled) Modern day equivalent* Speed (km/h)
Compsognathus  3  0.18  1.89  64.08 Greyhound (63.5 km/h)  
 
 na
 
 
Velociraptor  20  0.49  3.06  38.88 Elephant (40 km/h)
Dilophosaurus  430  1.35  6.09  37.80 Elephant (40 km/h)
Allosaurus  1400  1.75  5.80  33.84 Brown bear (35 km/h)
Tyrannosaurus(a.k.a. T-rex)  6000  3.09  9.56  28.88 Polar bear (30 km/h)
Emu  27  0.86  5.87  47.88  
 na
 
 50.4
Ostrich  65  1.09  5.69  55.44  61.2
Humans  71  0.99  3.73  28.44  36.0**

*http://www.speedofanimals.com
**Usain Bolt’s 100m record is 9.58s (= 37.5km/h), as of October 2011

 

Sense and sensitivity analysis

 

The GaitSym models show that studying dinosaur locomotion is no longer science fiction. Recent advances in software, processing speeds, the availability of HPC clusters and grid computing made it possible to create very detailed simulations.

There is a lot to learn from these models, but palaeontologists are aware that they are only best-estimate representations with an unknown level of confidence. Simulations cannot provide definitive answers because there is a fair amount of guesswork involved in deciding which values to input into the model. This is a difficult problem to solve. We know roughly what dinosaurs looked like, thanks to skeletons sometimes exquisitely preserved. But muscles rot away and very rarely make it into the fossil record.

Instead of adding precise input values to the model (of questionable accuracy), palaeontologists can perform sensitivity analysis tests, where inputs are tested in a given range to see how they affect the model’s behaviour. Sensitivity analysis doesn’t give a definite answer of A or B, but it gives a good idea about which factors influenced the animals speed the most – which is equally important if the ultimate goal is to understand how dinosaurs lived in their world.

Karl Bates, now at the University of Liverpool, used sensitivity analysis tests to take a closer look at the Sellers & Manning results. For this work, which was part of his PhD at theUniversity of Manchester, he focused on the Allosaurus – a huge carnivore, which lived in the Jurassic, 100 million years before the T-rex – and accessed the grid computing resources provided by the UK’s National Grid Service.

Bates repeated the model runs described above, but instead of inputting precise values, he analysed the ranges of five input parameters: muscle contraction velocity; force per unit area (a proxy for muscle mass); muscle fibre length; body weight and centre of mass. For example, Sellers & Manning considered that the maximum contraction velocity of theAllosaurus’ muscles was 8 per second. But, since we can’t know this for sure, Bates tested the model within the 4-12 per second range and analysed how this change influenced top speed.

Perhaps surprisingly, the first finding was that body-weight related parameters don’t have much influence on top speed. Changing the total body mass of the Allosaurus to values within 1100-2300 kg has minimal impact on top speed, which ranges between 32.4 and 32.7 km/h. The position of the centre of mass also doesn’t seem to have much effect.

What made a real difference are the muscle parameters. Playing with the input values of muscle mass and contraction velocity caused top speed to vary by up to 66% and 42%, respectively.

Thinking of top speed in possible ranges, instead of precise values, is very informative and allows the palaeontologists to interpret their data with a greater degree of confidence.

Even considering the maximum values for all muscle parameters, the Allosaurus model was not able to run very fast. In fact, any speed in excess of about 43 km/h would require extreme adaptations for high speed, including improbable proportions of muscle-to-body weight. The unknowns are still unknown, but models such as this let us know that the Allosaurus and cousin T-rex were certainly not the cheetahs of their time but perhaps more like a jaguar.

 

References

  • W.I. Sellers & P.L. Manning. Estimating dinosaur maximum running speeds using evolutionary robotics. Proceedings of the Royal Society B (full text)
  • K.T. Bates, P.L. Manning, L. Margetts and W.I. Sellers. Sensitivity analysis in evolutionary robotic simulations of bipedal dinosaur running. Journal of Vertebrate Paleontology

This case study was prepared with the help of Karl Bates