How to Outrun a Dinosaur

How to Outrun a Dinosaur

Just in case you want to know:

If, through some scientific malfunction, you found yourself transported 70 million years into the past, you might be safer from certain hungry reptiles than you think.

IF A MOUSE fell down a 1,000-foot mine shaft, the renowned evolutionary biologist JBS Haldane once proposed, the mouse would rise, shake the dust off itself, and scurry away. Maybe even right back up to do it again.

If a rat fell from the same height, however, it would die.

A human would break, Haldane writes, and a horse would splash.

Haldane does not provide a colorful verb in his 1926 essay On Being the Right Size for what would occur if a 9-ton Tyrannosaurus rex fell into that mine. But the giant predator would scream down the shaft at 172 mph, hit the ground with 120 tons of force and … shatter? Dismember? Detonate? Erupt?

Regardless, the purpose of Haldane’s gruesome thought experiment is to demonstrate the dramatically different relationship large animals have with gravity compared to smaller ones. This relationship, and the differing fates of the mouse and rat, are explained by the “square-cube” law, which is the simple idea that as an object expands, its volume cubes while its surface area merely squares. Because an animal’s surface area provides the brakes when falling, and its mass determines the force of its impact, the falls of various species can be either thrilling, tragic, or messy, depending on seemingly small differences in their size. It may be a simple concept—but because the law involves such rapid growth, it’s exceedingly difficult to intuit its occasionally dramatic effects. That’s particularly true with regards to the largest land animals to have ever walked the earth, and particularly important if you had to outrun them.

For example, if you traveled back to the dinosaur age, or it traveled to you in some kind of scientific disaster, you might find yourself running from a duplex-sized reptile. But don’t panic. You have the disproportionate effects of size on your side. The T. rex’s eruptive demise at the bottom of the mine shaft illustrates the most important factor to consider when facing the giant saurian’s pursuit. In the run for your life, its awe-inspiring, terrifying, stupefying size would be, in fact, your greatest advantage.

A FULL-GROWNTyrannosaurus rex was absurdly huge and absurdly powerful. It had rows of teeth it could push through Triceratops bone, could toss human-sized chunks of meat 16 feet into the air with its jaws, was as tall as a giraffe, and, at nine tons, was as heavy as an elephant. And yet if you see one, you should be only mildly concerned. Tyrannosaurus rex had proportionally more muscles devoted to its movement than nearly any animal that’s ever lived, Eric Snively, a biologist at Oklahoma State who studies the biomechanics of dinosaurs tells me. And yet you could likely escape it, because a Tyrannosaur couldn’t run.

I asked John R. Hutchinson, lead author of a paper in Nature titled “Tyrannosaurus Was Not a Fast Runner,” what a Tyrannosaurus’ performance in a race would look like. “A short-distance jog is about the best we’d expect,” he said. “And not with a fast start, either.”

Illustration showing top running speed of a dinosaur that is 40ft long with a top speed of 13mph

The incredibly powerful, long-legged Tyrannosaurus was slow for the same mathematical reason its demise in the mine shaft was so eruptive. Like surface area, bone strength only squares in strength as volume cubes. The result is that as an animal increases in size, it requires proportionally more muscle and leg bone to stand, move, and run. Beyond a certain size, the latter becomes physically impossible. For all its muscular bulk, the Tyrannosaurus rex’s leg bones would have shattered under anything more than the stress of a brisk jog. Judging by its mass, muscle, and bones, Snively doesn’t believe an adult Tyrannosaurus rex could have moved faster than 12 or 13 miles per hour. (Though 12 miles per hour approaches the top speed of a typical human, depending on conditioning—it equates to a 20-second 100 meter dash or a 5-minute mile—the T. rex’s slow acceleration and inspiring teeth would give the average runner a reasonable chance of outsprinting or outmaneuvering the lumbering predator.)1

1 Admittedly, there is some concerning speculation that T. rex hunted in packs, which would complicate your escape. Thankfully, the best current evidence suggests that, though they may have killed in packs like crocodiles, they did not coordinate their pursuits like wolves.

Of course, the Tyrannosaurus rex would hardly be your only concern. Numerous meat-eating dinosaurs of various sizes might take an interest in snacking on you, and whether you could outrun them again depends on their weight.

Three years ago the biologist Myriam Hirt, who studies animal movement at the German Centre for Biodiversity Research, asked a seemingly simple question: Why is it that the biggest, most powerful animals—the whales, elephants, and rhinoceroses—are not the fastest, while the smallest—the mice, minnows, and millipedes—are some of the slowest? Is the implication that there is an optimum size for speed?

The answer, Hirt found, is yes. If you were designing an animal for speed, that animal should weigh approximately 200 pounds. A bit heavier for a swimmer, and a bit lighter for a flyer.

Hirt found a precise parabolic relationship between size and speed that not only suggests you need to fear the midsize dinosaurs most but also that you shouldn’t fear the largest at all. The reason, she tells me, is a result of the interplay between power, acceleration, and the metabolism that fuels both.

An animal’s top speed, Hirt found, is the meeting point of two factors. The first is an animal’s total muscle power, which scales proportionally to its mass. But the second is its ability to accelerate that mass, which does not scale. Acceleration is reliant on the anaerobic muscle power or stored ATP energy in the muscle fibers. These so-called fast-twitch muscles produce the rapid, powerful contractions needed for acceleration, but they quickly deplete. And their capacity is determined by metabolism.

For reasons that aren’t totally understood, an animal’s energy production (metabolism) decreases proportional to its mass (more precisely, it decreases to the power of 0.75). If we had the metabolism proportional to that of a mouse, we’d have to eat around 25 pounds of food per day. Instead, we eat only around four. Larger animals are thus stronger and more efficient but produce proportionally less energy to accelerate and overcome their inertia.

By creating a simple formula that represents this balance, Hirt predicted the speeds of animals based upon nothing but their weight. When she placed it on a graph alongside the measured speeds of modern animals, the result looked something like this:

chart showing running speed vs. weight of animals

Most intriguingly (at least for our purposes), Hirt’s discovery enabled her to predict the speeds of the largest dinosaurs. When she plugged dinosaur weights onto her formula, this is what she found:

chart showing running speed vs. weight of dinosaurs and other animals

Thanks to the limits of metabolism and mass, we can eliminate every dinosaur over roughly 6,000 pounds as a predatory threat. There is likely no animal of that size or larger, neither today nor at any point in history, that a young, well-conditioned human couldn’t outrun.

Unfortunately, there are numerous predatory threats that weigh substantially less. Hirt’s discovery reveals a speed limit on the largest dinosaurs, but beneath that limit an animal’s size is not the only determinate for its speed. Clearly, two species of roughly the same weight—such as, say, the human and the cheetah—can run at dramatically different speeds depending on their body design. Before you lace up your running shoes, you need to know the precise speed of your foe. You need to know if you can outrun the dinosaur in the distance or whether you’re betting your life on a race against a reptilian roadrunner.

But how does one determine the precise speed of an extinct species based upon nothing but bones and a few fossilized footprints?

Fortunately, in a study published in May in PLOS One, a group of scientists led by the paleontologist Alexander Dececchi managed to estimate the speeds of 71 different dinosaurs by combining Hirt’s data with an equation developed by a British zoologist named Robert Alexander. (In 1976, Alexander made the remarkable observation that every animal from ferrets to rhinos runs with a dynamically similar gait, which is an engineering term used when motions can be made the same simply by changing their scale—like swinging pendulums of different sizes. Just as you can solve for the swinging frequency of a pendulum if you know its length and angle, Alexander’s discovery enabled scientists to estimate a dinosaur’s running speed based on nothing but its hip height and stride length.)

Unfortunately, it’s no more than a rough formula with the possibility of serious error, Hutchinson tells me. For example, Dececchi’s calculations suggest that the carnivorous Albertosaurus ran 22 mph. That would give you some possibility of escape. But there’s a chance it runs more like a cheetah. In which case …­ ¯\_(ツ)_/¯

Nevertheless, Alexander’s and Hirt’s findings have provided intriguing insights into dinosaur behavior, athleticism, and evolution. By comparing a Tyrannosaurus’ stride length, weight, and running speed, Dececchi’s study revealed that the Tyrannosaurus did not evolve its long legs to increase its velocity. Its speed, they found, was already capped by its ability to accelerate. Instead, the Tyrannosaurus evolved its leggy stature to improve its walking efficiency and endurance. Their results suggest that if you traveled through time to the dinosaur age, the T. rex couldn’t outsprint you, but it might stalk you like a late-Cretaceous Jason Voorhees. (Though Snively tells me it probably wouldn’t, simply because a full grown Tyrannosaurus rex hunted much larger prey, like the Edmontosaurus or Triceratops.)

Dececchi’s estimates make it clear, however, that other carnivorous threats would be more difficult to elude. There are too many medium-size, fast, and dangerous carnivores to make a complete compendium. However, we can use a few species as examples. If the dinosaur you see has similar body dimensions to one listed below, expect a similar athletic performance.

Dromaeosauridae (aka raptors) | Mildly concerning.2
Illustration showing top running speed of a dinosaur that is 23ft long with a top speed of 1520mph
Albertosaurus | Concerning.
Illustration showing top running speed of a dinosaur that is 30ft long with a top speed of 22mph
Deltadromeus | Very concerning.
Illustration showing top running speed of a dinosaur that is 23ft long with a top speed of 30mph

2I have measured my top speed at a dead sprint (about 15 mph) and input what my level of concern would be for the corresponding dinosaurs using the formula I discuss below. I would suggest you do the same, but as a rough guide to human speed a gold medal contender in the 100-meter dash can run 27 mph, a good high school sprinter might run 22, an average person like myself could hope to reach 15 given proper motivation, and a brisk jog is around 7.

Unless you’re in contention for a gold medal or are, at the very least, a fast amateur sprinter, all of these dinosaurs athletically outclass you. Yet all is not lost if one should attack. Studies of the chases between cheetah and impalas, and lions and zebras, prove a prey animal like you has a few significant advantages.

Alan Wilson, a professor at the Royal Veterinary College at the University of London who studies locomotor biomechanics, attached accelerometers to these predators and their prey to calculate their exact speed, agility, and tactics in a chase—and came away with encouraging results. His measurements suggest the cheetah is capable of running at least 53 miles per hour, while its prey the impala tops out at a mere 40. Likewise the lion can reach 46 miles per hour, while the zebra runs only 31. But despite their significant speed deficit, both the impala and the zebra successfully escape their pursuers in two out of every three pursuits. And even though the lion is faster than the impala, its capture rate is low enough that it won’t even attempt to chase one in an open field. Wilson’s findings suggest a pursuing dinosaur cannot catch you unless it’s significantly faster.

 But that’s only if you know how to run. If you merely flee at top speed from these reptiles, you will exit the Mesozoic era as a coprolite. Instead, to successfully escape a more athletic pursuer, you have to run smart. You have to use tactics. And above all, you must be unpredictable.
When Wilson’s accelerometer measured the speeds of impalas fleeing from cheetahs, he found that, while they are capable of a blistering 40 miles per hour, in a race for their life they almost never ran faster than 31. The explanation for this surprising result, his study concludes, is that at top speed an animal sacrifices maneuverability. Their turning angles widen at higher speeds, and thus their trajectory is far more predictable. To successfully escape a pursuing cheetah, or in this case a dinosaur, you must ensure that your pursuer cannot predict your course. That necessitates the sharp, sudden turns that you can only perform at reduced speeds.

When Wilson plugged in the athletic parameters of predator and prey into a computer model and ran simulations, he found two simple tactics those being chased must employ. First, when the dinosaur begins chasing you, change course frequently but do not decelerate. The predator’s high rate of closing speed will cause late reactions and result in inefficient routes. Second, when the predator draws within two or three strides, rapidly decelerate, turn sharply, and accelerate. Time this maneuver correctly and your pursuer’s faster speed will result in a wider turn and a loss of a stride or two off the pace. When it catches up, do it again.

Your goal is the same as the impala’s: To buy time. You will have the endurance advantage. Recent studies like Dececchi’s suggest some dinosaur species may have possessed remarkable endurance for their size—but your springy hips, stretchy Achilles tendons, and efficient cooling systems make you one of the greatest endurance runners nature has ever created. The longer the race, the greater your chances.

At some unfortunate point however, the athletic disparity breaches a certain threshold, and no amount of correctly timed turns will be enough. That will likely be the case should you find yourself against what Snively tells me would be your most dangerous purser—the same Tyrannosaurus rex we’ve discussed, but with one significant difference. It’s not the biggest, full-grown T. rexes you should fear, says Snively. It’s the juveniles.

A 14 year-old Tyrannosaurus rex. | Terrifying.
Illustration showing top running speed of a dinosaur that is 20ft long with a top speed of 33mph

Unlike most animals, a T. rex is not at its fastest as an adult. Instead, it reaches its peak speed in its youth before being slowed by its immense bulk. At 14 it is relatively lithe at 2,000 pounds, has an estimated speed of 33 miles per hour, and already has jaws strong enough to tear through your bones. The young T. rex is more likely to attack as well, because unlike an adult, which hunted 7,000-pound duckbill dinosaurs and five-ton Triceratops, a teenage Tyrannosaurus probably ate animals of your size.

Unless you’re an Olympic sprinter—in which case you may stand an impala-like chance—you may have to resort to other means of escape. You may need the luck of a small cave to squeeze into or a thick bramble in which you can dive headlong. Or you can make your own luck by running the Tyrannosaurus into a trap. Try laying a blanket of brush over a watering hole, a pit lined with stakes or, if you’d prefer an eruptive result, over a very deep mine shaft.




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