People: John Hutchinson
Newer studies relating back to the original Nature paper
- 9. Pontzer, H., Allen, V., Hutchinson, J.R. 2009. Biomechanics of running indicates endothermy in bipedal dinosaurs. PLoS One 4(11): e7783. doi:10.1371/journal.pone.0007783 (link with open access)
- A fusion of the methods of Pontzer (linking morphology and mechanics to metabolic cost) and Hutchinson et al. (estimating muscle mass requirements from morphology and posture), which infers that endothermic-level metabolism was ancestral to all dinosaurs and retained even by large taxa like Tyrannosaurus. This follows logically from our earlier finding that dinosaurs needed to have large active volumes of leg muscle even to walk; active leg muscle is metabolically costly which must be fueled by an active metabolism.
- 8. Gatesy, S.M, Baeker, M., Hutchinson, J.R. 2009. Constraint-based exclusion of limb poses for reconstructing theropod dinosaur locomotion. Journal of Vertebrate Paleontology 29:535-544. [pdf]
- A new method building on the Hutchinson and Garcia (2002) and Hutchinson (2004a,b) models, which allows us to survey a very wide range of limb poses and identify which were less/more likely to have been used by different theropod dinosaurs. We find solutions that may have allowed Tyrannosaurus to run slowly (peak limb forces around 1.6-1.8 body weights or so), but still not very quickly.
- 7. Hutchinson, J.R. and Allen, V. 2008. The evolutionary continuum of limb function from early theropods to birds. Naturwissenschaften 96:423-448. [pdf]
- Another review, but focusing on post-2000 studies of theropod dinosaur pectoral and pelvic limb function and evolution. This includes review of Tyrannosaur locomotion studies by Sellers and Manning, Paul and others.
- 6. Hutchinson, J.R., C.E. Miller, G. Fritsch, T. Hildebrandt. 2008. The anatomical foundation for multidisciplinary studies of animal limb function: examples from dinosaur and elephant limb imaging studies. pp. 23-38 in H. Endo and R. Frey (eds.), Anatomical Imaging Techniques: Towards a New Morphology. Berlin: Springer-Verlag. [pdf]
- An essay on the importance of anatomy, including a new 3D biomechanical model of the muscle moment arms in the hindlimb of the dinosaur Velociraptor mongoliensis and comparison with Tyrannosaurus (see Hutchinson et al. 2005; paper #3 below).
- 5.Hutchinson, J.R., V. Ng-Thow-Hing, F.C. Anderson. 2007. A 3D interactive method for estimating body segmental parameters in animals: application to the turning and running performance of Tyrannosaurus rex. Journal of Theoretical Biology 246:660-680. [pdf]
- Here we constructed 30 models of the whole body of Tyrannosaurus rex to estimate its mass, center of mass, and inertial tensor values. We varied the shape of the body and its internal cavities in a detailed sensitivity analysis, and found good validation for the method using an ostrich. We then used our results in two biomechanical calculations, showing that it would take some 1-2 seconds to turn 45 degrees on one leg, and that it still could not run very fast even with some changed parameter values. Mass was ~6000-8500kg, the center of mass was 0.45-0.75m in front of and ~0.3m below the hips, and inertias in yaw and pitch were immense.
- 4. Hutchinson, J.R. 2006. The evolution of archosaur locomotion. Comptes Rendus Palevol 5:519-530. [pdf]
- This is a general review of the changes of limb anatomy and function from basal reptiles through archosaurian reptiles (incl. birds) but also illustrated using simple biomechanical models how, if we knew the joint angle of an animal's limb reasonably well, we should be able to bound its overall limb posture fairly tightly (~20deg range) as the limb joints are interdependent; only some combinations of joint angles are viable..
- 3. Hutchinson, J.R., F.C. Anderson, S. Blemker, S.L. Delp. 2005. Analysis of hindlimb muscle moment arms in Tyrannosaurus rex using a three-dimensional musculoskeletal computer model: implications for stance, gait, and speed. Paleobiology 31:676–701. [pdf]
- We developed a highly detailed anatomical model of all the major hindlimb muscles in T. rex, which allows us to estimate what its moment arms (leverage) of different muscle groups was, and how these depended on posture. We found that more upright (straight-legged) poses had greater moment arms for supporting body weight, and hence T. rex might have used more extended (but not fully columnar) limbs. We also found that my earlier analyses generally used overestimates of the moment arms of antigravity muscles, which biased our results toward favoring faster running speeds, and hence actually strengthened our conclusions that it was not a fast runner.
- 2. Hutchinson, J.R. 2004a. Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa. Journal of Morphology 262:421-440. [pdf]
1. Hutchinson, J.R. 2004b. Biomechanical modeling and sensitivity analysis of bipedal running ability. II. Extinct taxa. Journal of Morphology 262:441-461. [pdf]
- These two linked studies are especially important as many input and output parameters from the original 2002 Nature study were improved here. I strongly validated the modeling approach with multiple extant animals (birds, mammals, and reptiles), finding that ankle muscle mass seemed to typically be most limiting for speed. My estimates of muscle masses needed for Tyrannosaurus rex to run quickly were smaller (~20-35% body mass per leg) but still too high to allow very fast running, which I estimated as over 11m/s (25mph). Further validation for the approach was provided by showing that smaller dinosaurs could indeed run quickly (as known from footprints), and relative (and perhaps absolute) running performance dropped with size (above ~1000kg).
COMMENT: John R. Hutchinson, Mechanical Engineering (650) 736-0804; firstname.lastname@example.org
(Now at the Structure & Motion Lab, RVC; email@example.com)
RELEVANT URLs are listed on the links tab.
Tyrannosaurus rex probably could not run fast, scientists say
King of the Cretaceous, Tyrannosaurus rex stood on two powerful hind limbs and terrorized potential prey with its elephantine size and lethal jaws. The dinosaur was big and bad. But was it fast?
That's long been a topic of scientific debate, with some paleontologists arguing T. rex ran at a zippy top speed of 45 miles per hour and others suggesting a more moderate 25 miles per hour. Both estimates seemed fast to John Hutchinson of Stanford, who as a graduate student at the University of California-Berkeley set out with help from postdoctoral researcher Mariano Garcia, now of Borg-Warner Automotive, to test them using principles of biomechanics.
The researchers created a computer model to calculate how much leg muscle a land animal would need to support running fast. In the Feb. 28 2002 issue of the journal Nature, they report that T. rex probably could not run quickly. In fact, hindered by its size, it may not have been able to run at all. Though not enough is known to give an exact speed limit for T. rex, a range of 10 to 25 miles per hour is possible, according to the authors.
"When you get down to the science of how animals move, relatively speaking, big things really don't move fast," says Hutchinson, a National Science Foundation postdoctoral research fellow. At Stanford since September, he studies the evolution of anatomy and locomotion. When small animals move quickly - rabbits jump, monkeys climb, birds fly, cheetahs sprint - they endure high physical forces for their body weights. Such forces are biomechanically impossible for large animals. Aquatic animals, such as whales, are less limited than land animals, such as elephants, because water buoys them.
Skeletal muscle is built similarly in all vertebrate animals. The force that it can exert depends on its cross-sectional area - that is, two factors: muscle length and muscle width. But an animal's weight, or body mass, depends on three factors: length, width and height. The math behind that physical reality results in limitations.
"That's why as animals get really enormous, eventually to support their weight, their muscles have to be bigger and bigger and bigger," Hutchinson says. "But as they get bigger, they add more mass. So you run up against a problem as animals grow larger in that they need to be adding more muscle cross-sectional area to support their own weight, but the mere fact of adding that muscle adds weight. Eventually, something's got to give."
Says Hutchinson: "No one's really ever tried to look at, or barely thought about, how much muscle a huge animal like a T. rex would need in order to run quickly. A lot of discussion has been over the bones - were they strong enough? - or other lines of evidence. But the main question to me is, could the muscles generate enough force to support the body during running?"
Finding an answer was tricky, as the researchers were studying something they couldn't observe directly. "We're looking at extinct animals, which we know very little about, and we're trying to understand their locomotion, which we have almost no evidence of directly," says Hutchinson. While fossils provide evidence of small dinosaurs moving fast, none indicates that big dinosaurs could do the same.
Models of the extant and the extinct
Garcia and Hutchinson created a computer program to analyze animal motion. Their model has a firm foundation in anatomy but emphasizes biomechanics. By varying different biomechanical parameters - posture, center of mass, leg weight and total weight - the researchers can quickly quantify the physical forces exerted during movement and the amount of muscle needed to support various postures and speeds. They can create two-dimensional stick figures to show how animals move and study conditions at each moving joint.
To gain expertise in biomechanics,Hutchinson as a graduate student worked with Associate Professor Scott Delp, co-chair of Stanford's Biomechanical Engineering Division. Delp's computer model of human movement accurately predicts how moving a tendon during surgery will affect a patient's gait, for example. But Delp's model is also a great tool for studying any animal with muscles and joints, says Hutchinson, who currently uses such 3-D models. Researchers around the world have used it to study biomechanics in cockroaches, frogs, monkeys and more.
A key part of Hutchinson's calculations involve knowing the torque, or twisting force, that muscles need to apply about the joints, says Garcia, who wrote the programs that do these calculations. As a graduate student in the lab of Cornell's Andy Ruina and as a postdoctoral researcher in the lab of Berkeley's Bob Full, Garcia had created similar programs to model the biomechanics of walking robots and multi-legged creatures.
"It has been known for a long time that as things get bigger, they don't move as fast relative to their size, and in fact as they get really, really big, they can't run at all," Garcia says. "But until now, no one that I know of has tried to predict the cutoffs, which is what we are doing."
According to Professor Kevin Padian of Berkeley, a curator in the University of California-Berkeley Museum of Paleontology, Hutchinson and Garcia's paper is "setting a standard for how this kind of work will have to be done in the future. It's the first study to use this kind of computer analysis and to build in sensitivity. What that means is John can check each value and see if a difference in each value can make a difference to the overall model - and that's a big thing to do when projecting models."
Hutchinson and Garcia tested the accuracy of their model with data from living animals that are distant cousins of T. rex - alligators and birds - as well as from humans.
Asking the model to calculate how much muscle each of these animals would need to run quickly, the researchers got values that made sense, Hutchinson says. "Chickens and humans have almost twice as much leg muscle as they need for bipedal running, whereas an alligator has only half the muscle mass it needs to run. Thus, humans can chase chickens around the barnyard, whereas alligators don't run around on their hind legs."
Then the researchers turned to dinosaurs. Using dinosaur data from Hutchinson's doctoral dissertation, they tried the model on two small dinosaurs and a big adult Tyrannosaur. It turned out that the smaller dinosaurs needed much less muscle mass to run than did the adult T. rex.
To run 45 miles per hour, the adult T. rex in a crouched posture would need almost 43 percent of its weight in each leg as supportive muscles, the model showed. "It might have needed 86 percent of its body weight to be leg muscles," says Hutchinson. "That is ridiculous, because it would leave very little room for anything else in the body - a skeleton, other muscles, et cetera!"
Even a T. rex in a nearly straight-legged stance - biomechanically the best - still needed 13 percent of its weight as supportive muscle in each leg. That's an extreme amount compared to living animals: Good runners typically have 5 to 10 percent of their body weight as supportive muscle in each leg, and bad runners have less than 5 percent.
"Our model shows that these really fast speeds of 50 miles an hour and probably down to even 25 miles an hour just don't hold up when you really scrutinize them and look at the physics," Hutchinson says. "It doesn't make a lot of sense that these animals could go that fast. There's really no good evidence that they could."
This doesn't mean T. rex was too slow to prey on large herbivores such as horn-faced Triceratops or duck-billedEdmontosaurus. All were elephant-sized, and all were likely poor runners. Remains indicate T. rex ate those animals, but whether it killed or scavenged them is still a mystery.
The Great Race: T. rex vs. Col. Sanders' Dream
To further illustrate that size limits speed, Garcia and Hutchinson used their model to scale up a chicken to the size of a T. rex - 13,228 pounds (6,000 kilograms) - to see if it would be able to run.
"We know from a lot of fossil evidence that birds actually are the descendants of dinosaurs, so we thought, we should look at one of the descendants of dinosaurs to see how it moves today," reasons Hutchinson. "A chicken is a two-legged animal. We know how they move. We can study them in the laboratory or in the barnyard or anywhere. We can go out and buy a recently dead chicken and dissect it to understand its anatomy. So a chicken was a logical choice for many reasons in terms of limb design, evolution and anatomy."
According to the model, could a giant chicken run? "Very clearly no, no matter what," Hutchinson says.
To run, a normal-sized chicken needs about 5 percent of its body mass in each leg to be muscle, Hutchinson says. It has almost 10 percent of its body mass in each leg as muscle, however, so it's "overbuilt" for running. The model showed that a giant cicken would need about 99 percent of its body mass in each leg as muscle to run quickly. "That's far more than is possible," Hutchinson says. "A giant chicken could not even walk."
That explains why elephants and hippos don't move like gazelles. Hutchinson recalls a high school physics teacher using a similar example to explain why Godzilla and King Kong are physical impossibilities: "That really struck home to me. That was probably the first moment where I thought in [terms of] biomechanics and applied it to big things like dinosaurs."
What the paper DOES say
- Bottom Line:
- Tyrannosaurus could not run quickly, if at all.
- Underlying Principle:
- Large animals have more restricted locomotor performance, such as lower maximum forward velocity (speed).
These so-called "scaling principles" have been well established in the literature. For earlier related research, see papers by A.V. Hill, R. McNeil Alexander, and Andrew Biewener (examples provided in the Naturereferences).
- Word-For-Word Abstract:
- The fastest gait and speed of the largest theropod (carnivorous) dinosaurs, such as Tyrannosaurus, is controversial. Some studies contend that Tyrannosaurus was limited to walking, or at best a "conservative" (11 m/s) top speed, whereas others argue for at least 20 m/s running speeds. We demonstrate a method to gauge running ability by estimating the minimum mass of extensor (supportive) muscle needed for fast running. The model's predictions are validated for a living alligator and chicken. Applying the method to small dinosaurs corroborates other studies by showing that they could have been competent runners. However, models show that in order to run quickly, an adult Tyrannosaurus would have needed an unreasonably large mass of extensor muscle, even with generous assumptions. Therefore, it is doubtful that Tyrannosaurus and other huge dinosaurs (~6000 kg) were capable runners or could reach high speeds.
- Simplified Abstract:
- How fast could large dinosaurs run? Could they run at all? This issue has been controversial in dinosaur research, especially with regard to Tyrannosaurus rex. Some believe that Tyrannosaurus could not run, or at best was limited to a top speed of 11 m/s (40 km/hr, 25 miles/hr), while others argue for speeds of 20 m/s (72 km/hr, 45 miles/hr) or more. Using simple equations from physics and biology, we demonstrate a method to gauge running ability by estimating the minimum amount of leg muscle needed for fast two-legged running. The calculations are based on size, weight, posture, and other parameters. For living animals, we can compare the predicted minimum amount to the actual amount. If the animal does not have enough muscle, then it cannot run bipedally. If the animal has much more muscle than it needs, chances are it is a good runner. The method correctly predicts that an alligator cannot run on two legs, whereas a chicken is a good runner. For extinct animals, we compare the predicted minimum amount of leg muscle needed to what we know about the animal's body. Applying the method to smaller dinosaurs agrees with fossil findings which suggest that they could have been competent runners. For T. rex, our best guess is that in order to be a good runner, it required 80% of its weight to be in its leg muscles, which is next to impossible given what we know about its size and shape. So it is doubtful that T. rex or other large dinosaurs were good runners.
What the paper DOES NOT say
- We DO NOT specify exactly how fast Tyrannosaurus could have moved, or that it definitely could not run.
- Why? These are very difficult problems to solve for living animals, let alone extinct ones. We specify a very rough upper-end estimate of walking speed (about 5 meters per second; 11 mph or 18 kph), but faster or slower speeds are not impossible. We argue that faster speeds of 20 m/s (45 mph or 72 kph) would be biomechanically unfeasible, and even the more "conservative" speed estimates of 11 m/s (25 mph or 40 kph) are questionable. Thus the maximum speed of Tyrannosaurus might be in the range of 5-11 m/s, or perhaps slower. Honestly, it is too hard to say for sure; currently there are too many unknowns.
- Our research has NO bearing on the possible metabolic physiology of Tyrannosaurus or other extinct dinosaurs.
- Why? Our model and equations do not require information on metabolic physiology or energetics. The parameters we use are relatively independent of whether the animal modeled is "warm/cold-blooded" (endo/ectothermic). If we are correct that Tyrannosaurus was not a fast runner, that does not mean that it was cold-blooded or sluggish, nor does it mean that it was warm-blooded or agile. We merely show that it is unreasonable to reconstruct Tyrannosaurus (and other larger dinosaurs) as very fast runners. Consequently, the metabolism of Tyrannosaurus had no need to fuel fast running.
- We DO NOT argue that Tyrannosaurus was only a scavenger, or only a predator.
- Why? This dichotomy is false; living carnivores generally scavenge and hunt opportunistically. Our study only shows that large dinosaurs probably were too large to run quickly. This hypothesis should hold for all large dinosaurs, including potential prey items of Tyrannosaurus such as Edmontosaurus (large duckbill) and Triceratops (horned dinosaur). Conversely, smaller dinosaurs should have been relatively fleeter. The argument that if Tyrannosaurus could not run quickly, it could not have been a predator because it could not have caught potential prey, is nonsensical because the aforementioned potential prey were likely just as inept at running as Tyrannosaurus was. In fact, these potential prey might have been even slower than Tyrannosaurus.
- Our model IS NOT an extremely complex three-dimensional simulation or animation.
- Why? All the information we needed could be obtained from a simple model; In fact, more complex models make more assumptions and can be misleading. We used a quasi-static (stationary at an instant in time, but accelerating) 2-D computer model (in Matlab) to estimate the internal and external moments (torques; or rotational forces) acting about the limb joints at the midpoint of stance phase (ground contact) during fast bipedal running. This quasi-static approach is valid for snapshots of the motion where the limb velocities are small. These estimates of the joint moments were used in an equation that incorporates anatomical data from muscles to calculate how much muscle mass would be needed to balance those moments. This muscle mass, expressed as a percentage of body mass, was either insufficient or sufficient for running.
- Our research DOES NOT explain why large dinosaurs such as Tyrannosaurus went extinct.
- Why? There is simply no evidence for any connection.
Corrections And Errata
Corrections to PDF preprints and published text
Table 1, Alligator information: L row numbers should read as follows:
0.092 - 0.037 0.019
Table 1, Gallus information: L row numbers should read as follows:
0.085 0.051 0.032 0.026
Table 1, Gallus information: m_i row numbers should read as follows (correction published in Nature 417:349):
1.1 0.079 2.0 1.5
Page 1020, second column, 3rd full paragraph: "dashed curve" should read "solid curve."
Corrections to supplementary information
Table A corrections:
CM position of small tyrannosaur thigh should be 0.163m, not 0.160; metatarsus should be 0.185m; not 0.163.
Toe joint angle for Alligator should be 10 degrees, not 110.
Joint angles for Gallus should be 50 and 65 for the hip and toe, not 55 and 95.
The giant chicken scaling example used slightly different joint angles [10/55/90/120/75] than the Gallus model [15/50/90/120/65]; hence T was about 21x higher (99%), rather than 13x higher (62%) with identical joint angles, as the scaling of T predicts.
Trex_3 hip joint angle should be 80 degrees, not 180 degrees.
Comment on the use of italics and proper spelling of dinosaur names
The official wording is "Tyrannosaurus rex" (italicized with capital "T" and lower case "r"). After that name is used once, the abbreviation "T. rex" (not Trex, T-rex, or T-Rex) may be used. This is the formal way to use all genus and species names in biology. Alternatively, just the genus name Tyrannosaurus can be used, without the rex.
Comments on other dinosaurs
Theropod ("thair-oh-pod"; not therapod or theripod) dinosaurs are the bipedal carnivores including Tyrannosaurus, Velociraptor, Allosaurus, and similar forms. Smaller, non-flying theropods were ancestral to birds. Herbivorous dinosaurs such as the ornithiscians Triceratops and Edmontosaurus, and the huge sauropods Diplodocus and Brachiosaurus, were not theropods but were dinosaurs.
Popular Depictions Of Dinosaur Running: Did "Jurassic Park" Get It Wrong?
Our research refutes the popular conception that large dinosaurs were fast runners. Fast-running dinosaurs are not the brainchild of the "Jurassic Park" films; reconstructions of moving dinosaurs in the late 1800s often showed them as lively, fast animals. The trend in the early to mid-1900s was for artists to reconstruct large dinosaurs as sluggish leviathans, and this is the version that many people were familiar with until recently. Since Dr. John Ostrom and Robert Bakker's revival of "hot-blooded dinosaurs" in the 1960s-1970s, it has become more fashionable to depict dinosaurs, large and small, as being at least as active and athletic as mammals, if not more so. Often this practice includes depicting all of them as fast runners, which we infer might be the case for smaller dinosaurs but we argue is unreasonable for the larger ones.
Sequences of large dinosaurs in the "Jurassic Park" films provide an eloquent example of our point. The famous sequence in the first film with a Tyrannosaurus chasing the vehicle filled with tasty human morsels seems fast, doesn't it? If you watch closely, the vehicle is shifted into second, third, then fourth gears, implying a speed of 40 or more miles per hour. The actors are screaming, the music is dramatic, the Tyrannosaurus is roaring, and the editing cuts quickly between cameras. Take a closer look at the Tyrannosaurus motion, though, and you spot some incongruities. It always has one foot on the ground, and the cadence of its footfalls is rather slow, less than two steps (one stride) per second. To be moving over 40 mph with such slow strides, the Tyrannosaurus would have to have been taking ridiculously long steps. A casual survey of the movie shows this is not the case. The conclusion (first pointed out by scientist Stephen Gatesy of Brown University, and acknowledged to us by the moviemakers), is that the scene (Tyrannosaurus and all) was only moving at around 10-15 mph! Our eyes are easily fooled by movie magic into thinking that the Tyrannosaurus was faster. Why didn't the filmmakers just have the Tyrannosaurus moving 40+ mph? Those basic biomechanical principles of size and locomotion just wouldn't allow it to "look right" to our eyes. The scene would strain credulity, and our research shows why.
We're not demanding a return to the "sluggish leviathan" reconstructions of the early 20th century. Our study simply shows that the same long-understood biomechanical principles of size and locomotion that apply to living land animals also applied to extinct ones such as dinosaurs. Paleontologists and artists need to incorporate these principles more consistently in their conceptions of past life. Researchers often have cited the "cursorial" (locomotion-related) adaptations of large dinosaurs including Tyrannosaurus as evidence of their athletic prowess. These features, such as long legs, large muscle attachments, and hingelike joints, are surely important for efficient locomotion but they are not necessary and sufficient to predict locomotor performance, such as maximum speed. Size, mechanics, behavior, physiology, and nervous system control also play crucial roles in determining how fast animals can move. The fact that many of these parameters are not preserved in fossils does not remove their importance. We feel that paleontologists have focused too much attention on the cursorial features of dinosaurs simply because they are the only features preserved. In the process, the underlying principles of locomotion have been forgotten. Furthemore, the actual significance of cursorial features for locomotor performance remains poorly understood. Giraffes and flamingoes have long, slender legs but they are not the fastest land animals. We do not know exactly why, but those features that fossils do not preserve are surely parts of the explanation.
Paleontologists were not necessarily being foolish when they reconstructed large dinosaurs as fast animals; they just did not use the newer, more realistic modeling tools and approaches that we used in our study. Biomechanics is becoming a more popular and properly-applied tool in paleobiological research. This is an important trend, because previous approaches often used a non-quantitative, somewhat intuitive or subjective methodology that did not consider the fundamental physics and biology underlying the movement of animals. We hope that our research compels others to use similar mathematical approaches to studying extinct life. Our research might also be used as an example by educators to teach students math, physics, biology, and scientific philosophy and methodology.
Questions And Answers
(last update on February 27, 2002)
Can you summarise what you did and what your findings are?
JRH: Biomechanical theory predicts that the locomotion of larger land animals becomes more restricted as they get bigger. They move relatively more slowly and keep their legs straighter, for example.
We were interested in whether an enormous biped such as Tyrannosaurus could run quickly, if at all. Some paleontologists have argued vehemently that a Tyrannosaurus could run at least 20 meters per second, or 70 kph! Even some more "conservative" paleontologists thought that 11 m/s (40 kph) was a reasonable top speed for Tyrannosaurus. All of these estimates seemed rather fast to us, so we set out to test them using biomechanics.
We designed a quasi-motionless but realistic 2D computer model that lets us estimate how much the leg muscles of a running biped would have to weigh in order to support the animal during fast running. We used dissections of an alligator and a chicken as well as published data on a human to build models of these living animals, posing them in a bipedal running stance. The estimates of muscle mass that the model output were interesting: chickens and humans have almost twice as much leg muscle as they need for running, whereas an alligator has only half the muscle mass it needs to run on two legs. Thus humans can chase chickens around the barnyard, whereas alligators don't run around on their hind legs.
Based on my doctoral dissertation work on the anatomy of extinct dinosaurs, we then built models of two smaller dinosaurs and a big adult Tyrannosaurus. We varied all of the parameters that we did not know exactly (such as masses and standing pose) to see how much those unknown parameters changed the results of the model. It turned out that the smaller dinosaurs needed much less muscle mass to run than the adult Tyrannosaurus.
Even though we entered very reasonable assumptions for the adult T. rex, the model showed that it needed almost 50% of its weight in EACH LEG as supportive muscles in order to run fast. Thus for two legs, it might have needed 100% of its body weight to be leg muscles. That is ridiculous, because it would leave no room for a skeleton, other muscles, etc.! Even if we posed the model in a fairly straight-legged stance, it still needed at least 13% of its weight as supportive muscle in each leg. This is extreme compared to living animals which generally have less than 10% of their weight as supportive muscle in each leg, usually 1-5%.
Thus we concluded that it is very unlikely that Tyrannosaurus was a fast runner. In fact, it may not have been able to run at all. The 70 kph estimates that paleontologists have suggested are unreasonable, and even the 40 kph estimates would require a huge amount of muscle. On theoretical grounds, a walking Tyrannosaurus might have been able to move about 5 m/s, or 18 kph, and this would require much less exertion.
As a further illustration of the biomechanical principles in our research, we scaled our chicken model up to the size and weight of the T. rex. So we modeled a 6000-kilogram chicken to see if it could run. Not surprisingly, a giant chicken would need about 99% of its weight in the muscles of each leg in order to run. That is impossible; a giant chicken could not even walk. Although this example might seem silly, it shows how large land animals inevitably are limited by their sheer size, and can't do the same activities that smaller animals can. I remember my high-school physics teacher using a similar example to explain why Godzilla and King Kong are physical impossibilities.
Bottom line: Tyrannosaurus could not run quickly, if at all.
Can you speculate on the broad implications of the research - how might it affect what we understand about the topic currently?
- Larger dinosaurs in general moved more slowly than their smaller relatives.
- When birds evolved from small dinosaurs, their small size not only allowed them to fly but kept them good runners.
- We refute the idea that Tyrannosaurus was too slow to prey on large contemporaries such asTriceratops (the three-horned face) and Edmontosaurus (the duckbill). All of them were likely poor runners.
- In a broader sense, our study reinforces the long-held theory that giant land animals cannot use the same sorts of extreme activities that their smaller relatives can. They don't run as fast, jump around as easily, or fly. This relates to why elephants, hippos, and other large mammals don't move like gazelles, for example. We simply show that this general biomechanical principle that applies to living animals also applied to extinct ones, and paleontologists should embrace this principle. Aquatic animals such as whales are less limited by the influence of gravity because they have water to buoy them; aerial animals such as birds and bats are much more restricted.
- We show how useful and important sensitivity analysis (changing unknown parameters to see how they affect the results, if at all) is for all paleontologists. With this simple approach, commonly used by engineers and computer scientists, it is possible to analyze the many unknowns involved in studies of extinct life while still answering interesting questions.
- Our mathematical approach can and will be applied to similar problems in paleontology, such as: Could pterosaurs run bipedally? Could Triceratops trot or gallop? Could sauropods stand or walk bipedally? Which early tetrapod vertebrates could walk around on land? And so on.
You say that your model is accelerating but not moving - can you explain?
MG & JRH: At the mid-stance of running, the center of mass of a running biped has theoretically zero vertical velocity (an analogy would be that a ball thrown up in the air has zero vertical velocity at the instant it turns around and starts falling back to the earth, even though it is accelerating the whole time). The individual limb velocities are also small. But the leg is pushing the body upwards, and so the body is accelerating as it is about to spring off the ground. This situation allows us to approximate mid-stance as a "snapshot" that is standing still at an instant in time. The advantage is that certain kinds of forces disappear when the limbs are not moving, and the calculation is greatly simplified. It still involves some assumptions, but they are fairly standard ones. This approximate model is called "quasi-static".
Where do humans fit as far as predicted vs. actual mass?
JRH: As shown in our Supplementary Information, the 71 kg human we modeled needed 4.9% of his/her body mass in each leg's extensor muscles to sprint at 9 m/s. In reality, we have about 9.5% of our body mass in leg extensor muscles, so like the chicken, we are "overbuilt" by a factor of about two.
What about the recent paper (Nature, 31 Jan 2002, 415: 494-495, "Dinosaur locomotion from a new trackway" by Day et al.) on fossilized footprints from a large theropod? If that animal is running 29 kph (about 8 m/s) isn't that a problem for your model?
JRH: There are several issues to consider here:
- The animal that made the tracks was certainly not a tyrannosaurid or anything closely related to it. The tracks are about 163 million years old; Tyrannosaurus existed only 65 million years ago. Thus these tracks do not reveal much about the locomotion of tyrannosaurids in particular.
- There were large theropods and there were LARGE theropods. An adult Tyrannosaurus was perhaps 3-5 times as massive as the trackmaker. Thus the trackmaker is not among the largest theropod dinosaurs, which our model focuses on. It is important to keep this size difference in perspective and not dichotomize the issue into simply "small" versus "large" theropods.
- The estimated speed of the trackmaker is about 8 m/s, which is slower than the fastest known theropod running tracks (11 m/s from smaller animals) and is nowhere near the extreme estimates of running speed of 20 m/s. It's not that fast. The fastest human sprinters (e.g. Maurice Green, 100m dash world record-holder) can run 10.2 m/s, for comparison. However, 8 m/s does fall within the range (5-11 m/s) of the speeds that our paper considered at the lower and upper ends of plausible speeds for Tyrannosaurus.
- Speed estimation from trackways is imprecise. A 50% margin of error is not impossible.
- It is questionable, although still possible, that the tracks show an animal switching from a walking to a running gait. What is unambiguous to us from the data in that paper is that the trackmaker was walking, then sped up, then slowed down quickly. Whether that change in speed was actually a change of gait is not so clear. It depends on the definition of running that is applied, and what assumptions are used to apply it. The significance of the change of step widths and angles in the tracks is not understood, and does not necessarily indicate a gait change.
What biomechanical parameters did you consider to create a model that could accurately predict locomotion abilities of animals, extinct and extant?
MG: When you say the word "model" people think of a 3-D animation of a big dinosaur - it's really not like that. Its basically just a simple calculation based on a stick figure drawing of a dinosaur. In fact, a junior engineering student has learned enough to do these kinds of calculations, although they may not know it. I just happened to use a computer to do the calculations because we wanted to be able to sweep through lots of different inputs to seee how they affected the output. The inputs you need to specify are the posture (joint locations), the mass of the leg parts, the location of the center of mass of the body, and the total mass.
Is this the first time a computer model has been applied to an extinct animal? Are there any other "firsts" involved in this work?
MG: Well, like I said above, this really isn't a computer model in the sense that most people understand those words. I don't know enough about the dinosaur literature to say if we are the first to do stick-figure calculations, but I doubt it. I would say, however, that may be the first people to put it all together and try to quantify running ability based on the results of the model.
Another way to say this is that it has been known for a long time that as things get bigger, they don't move as fast relative to their size, and in fact as they get really really big they can't run at all. But until now, no one that I know of has tried to predict the cutoffs, which is what we are doing.
Of course, you have to keep in mind that my background is in mechanics and I don't know the dinosaur literature too well. I just enjoy applying the tools I have to these kinds of problems.
Two related points I would like to make:
- What John and I are doing seems to mirror a trend in the sciences where engineers collaborate with biologists (broadly defined) in order to bring some engineering tools to bear on problems where they traditionally were not used. I enjoy doing this kind of thing and think it is a good paradigm for research.
- People tend to be overly impressed by "computer models". The fact is that the more complicated the model, the more assumptions that are built in which may or may not be true. Fancy computer models can be useful but they can also be tricky to interpret. Einstein is often quoted as having said something to the effect that models must be as simple as possible but no simpler. That is the idea behind the modeling in this paper and also the modeling that I did for my thesis work at Cornell (in Andy Ruina's lab).
What would you say to people who are skeptical of computer models?
MG: Well, first of all I think it's good to be skeptical of computer models. Part of the problem is that there are many flavors of computer models, and its not always clear what you mean when you say those words. Some people mean using computers to analyze dynamics. Some people mean animations. Some people mean just doing spreadsheet calculations. Some people mean simulations. Within the realm of simulations, you can have all kinds of different control strategies and levels of sophistication which might give you different results. There is no universal definition of a ``computer model''.
Our model is basically a series of engineering calculations to look at the joint torques (or muscle forces) needed to hold up the animal, given a certain posture and other anatomical parameters. It is simple and, for the most part, unambiguous. All computer models involve some degree of simplification, but the simplifications we use here are very standard and reasonable among biomechanists because they capture the bulk of the physics that governs walking and running animals. Whether you like computer models or not, everything large enough and slow enough is bound to follow the laws of classical mechanics.
Is it fair to say that your research paints a picture of the time of dinosaurs as a time of large, slow, lumbering beasts -- something akin to "Jurassic Park" in slow motion?
JRH: To a degree. Our research doesn't show that the larger animals had to be totally sluggish and restricted only to slow walking, but it does rule out that they could run at extremely high speeds, as some paleontologists have argued persistently. The speeds of 11-20 m/s (25-45mph) suggested by some paleontologists would require an outrageously large amount of limb muscle. Slower speeds around 10 mph, or maybe even more, are not unreasonable.
See the "Jurassic Park" page for more on the speed of the T. rex in the film.
According to your research, large dinosaurs such as T. rex are intrinsically slow. Why? Is it essentially because they are big creatures on small legs that are not physically capable of supporting the rapid movement of a great mass? For example, are large dinosaurs not able to run fast for the same reasons a person carrying an 80 pound backpack has difficulty running?
JRH: Yes, the problem is that large animals need a larger fraction of their body mass as leg muscles in order to do the same things that smaller animals can do, but there is a limit to how large that fraction can be. An animal cannot be made 100% out of leg muscle, of course. In fact, muscle (of any kind) normally is about 1/2 of an animal's mass, and supportive leg muscle is usually only 5-20% of an animal's mass. For example, humans have about 20% of their body mass as supportive leg muscles; they need about 1/2 of that in order to run quickly (10-15mph).
You do have a hard time running faster if you carry an 80lb backpack for very similar reasons. Your muscles cannot exert high enough forces to withstand that sort of exertion, so you either slow down or fall down. Same problem for Tyrannosaurus, and presumably other large dinosaurs.
MG: One fundamental issue (long-established) is that muscle stress is proportional to force divided by cross-sectional area. Force is proportional to volume. So muscle stress involves a volume-to-area ratio that gets higher as things get bigger, and there is a material limit on how much stress muscle tissue can take.
Your rough estimate for the top speed of T. rex is 25 miles per hour. Isn't that actually fairly fast? In other words, the average running speed of a human is just 10 miles per hour, correct? If so, isn't it correct to say that a slow, lumbering T. rex could still probably catch up with a human in flight?
JRH: A good point. Speeds need to be kept in perspective. The 25mph estimate is what we think is the upper end of possibility, and even that is dubious. Theoretically, at 10mph a Tyrannosaurus would need to switch from a walk to a run; we think at least that much is possible. Thus the top speed might have been between 10-25mph. There are too many unknowns to narrow it down further.
Maurice Green, the world record holder in the 100m dash, ran about 10.2 m/s (almost 25mph). An average human like me can do about 10mph, yes. So there is a lot of variability in humans, at least, when we train singlemindedly. But an average human would need to run in order to outpace even a fast-walking tyrannosaur, if our models are accurate.
MG: There is also the issue of so-called "nondimensionalization" of speed. A hypohetical 1-foot tall person would have a step length that is 6 times smaller than a 6-foot tall person. At the same absolute speed, the short person would probably be running if the tall person was walking. There is a speed formula called the Froude number which takes the size factor into account. "Running" and "walking" have various biomechanical definitions but they are not dependent on absolute speed; one definition is based on the value of the Froude number. When we say that Tyrannosaurus could not run fast, that is like saying that it could not reach high Froude numbers. But because of scaling reasons, even when walking it moved fast by human standards.
You say there are too many unknowns to really determine how fast T. rex could have moved. What are some of these unknowns? Will these unknowns ever be known or are they characteristics not preserved in the fossil record?
JRH: Yes, the unknown parameters are a big problem in modeling these extinct animals. It is hard enough to predict how fast a living animal can move! The unknowns include how fast the muscles could contract, how stiff the limbs were, how quickly the leg could be swung through the air, and how long the tendons and muscle fibers were in relation to one another, for example. All of these are unpreserved in fossils, and highly variable in living animals. More realistic dynamic models such as ones I am developing at Stanford could be used to assess the importance of these unknowns better, but we chose to leave them out and tackle a simpler question to start with. It is doubtful that any of these unknowns will ever be revealed by the fossil record. The one thing I'm hoping for is preservation of some more details of muscle anatomy (for any dinosaur), such as exactly where the muscles attach. We can figure out most of them from scarred regions on bones, but fossilized muscles would tell us a lot with more confidence.
Is it possible that T. rex had massive legs but it has been overlooked in our interpretations of the skeleton out of a desire for an elegant (aesthetically pleasing) dinosaur design?
JRH: Massive to a degree, perhaps, but not to the degree that 45mph running would become feasible. It is ironic that the same people who advocate 25-45mph running speeds for Tyrannosaurus often draw it as having skinny legs! To put leg size into perspective, our "best guess" model required 43% of body mass per leg to be extensor muscle; 86% total. If only 50% of the body, maybe 60% in an extreme case, was any kind of muscle, then there still wouldn't have been enough muscle available to reach that 86% total. So having massive legs within any realm of possibility would not help. I imagine that Tyrannosaurus did have fairly large leg muscles, perhaps 10% of body mass per leg. But that's not enough to run 45mph, for sure.
You say that your model/equation has nothing to do with T. rex's metabolism. Why might some researchers believe metabolism to be an important factor in determining dinosaur speed?
JRH: It would be important for endurance; how long a Tyrannosaurus could sustain an elevated activity level. That much we know nothing about. Other parameters that influence maximum speed, as I noted above, are correlated with metabolic strategy, but are not needed in our model.
According to your statement, is it fair to say that T. rex may have had high metabolism, but if T. rex did have high metabolism it was fueling something other than speed?
JRH: Yes. Or it may have had a lower metabolic rate. Metabolism and running speed are not so tightly linked; many ectothermic (coldblooded) lizards can run about as fast as similar-sized mammals, for short bursts.
Why does the popular theory of "hot-blooded" dinosaurs of the 1960s and 1970s lead some researchers to equate hot bloodedness with fast mobility?
JRH: I think that correlation is a popular idea in many people's minds. The discovery of animals such asDeinonychus (a relative of Velociraptor) showed that some dinosaurs had smaller body size and a very sleek, fierce and athletic-looking profile. With the idea that birds evolved from dinosaurs also came the idea that dinosaurs might have been endothermic (hotblooded) like their bird descendants. And because birds are pretty fast and active, dinosaurs started to be reconstructed that way. Another trend was to depict dinosaurs as "as good as, or superior to" mammals. In strong contrast to previous ideas, dinosaurs were shown as doing things just as well or better than mammals, and that including running. Triceratops was shown galloping like a rhino, and sauropods reared up to graze on trees like elephants, and Tyrannosaurus was almost as fast as a cheetah. It came naturally, I think.
Do the producers/writers of "Jurassic Park" agree with your theory that T. rex was probably not a fast runner?
JRH: I don't know any of the head honchos personally, so I am not sure. But from my conversations with animators at Industrial Light and Magic, I've learned that they do agree with this idea. They tried animatingTyrannosaurus at 50mph or so, and it "just didn't look right" to them, so they had to pull movie tricks. This was very interesting to me, how movies and science did arrive at similar conclusions independently. They didn't do biomechanics; they just went with their gut feeling.
Simply put, how does your model work?
JRH: We start with a 2D representation of the body and limb segments (trunk, thigh, shank, foot, etc.) of an animal standing on one leg. Each segment has a mass located at a certain point along its length (the center of mass). The joints are posed in a certain configuration, like a crouched or columnar pose. We then solve for the moments (torques, or rotational forces) that these masses would incur about each joint in the limb in that pose. During fast running, those forces are about 2.5 times normal forces, so we included that multiplier.
Next step, we calculate how much muscle mass (as a % of body mass) would be needed to exert the same moments about each leg joint. We total the amount of muscle for all 4 major limb joints and that is our final value: the amount of extensor muscle mass that would have to be actively contracting in order to maintain that one pose during fast running. We tried many different poses and parameter values to see how much the unknown parameters in the model affected our results.
Even more simply put, the model shows us how large the rotational forces on the leg joints would have been, and then we can estimate how much muscle that would have taken to balance.
What lesson do you think school children should take from this research?
JRH: Physics shows us why large animals cannot do the same things that their smaller kin can. Big animals are relatively less athletic than their smaller relatives.
Another lesson would be, although we don't know much directly about extinct animals, we can still test interesting hypotheses with a little math, biology, physics, and computers.
OK, so if T. rex cannot run, can't it at least walk fast?
JRH: We do not argue that Tyrannosaurus could not run at all, merely that it was a poor runner at best, and certainly could not run at high speeds such as the 45mph (20m/s) estimate paleontologists have often cited. Even 25 mph (11 m/s) seems to have been a little too fast, judging from our models. Running at relatively slow speeds might have been possible. On theoretical grounds, we predict that Tyrannosaurus would have to shift from a walk to a run at about 10 mph (5 m/s), so perhaps the top speed of Tyrannosaurus is between 10-25mph. However, we do note that even a fast-walking tyrannosaur would have needed large leg muscles that were being pushed to their limits in order to move 10mph.
Does the argument over whether dinosaurs are cold-blooded or warm-blooded have an impact on your model?
JRH: No, luckily for the parameters our model needed to include, metabolic strategy did not matter. The force that muscles can exert per unit cross-sectional area is relatively independent of metabolic rate or activity in vertebrate animals. And that's the main parameter we needed.
How does an elephant fit into your equation of muscle mass vs speed?
JRH: We haven't yet modeled an elephant yet, or other four-legged animals; just bipedal running. That being said, my guess for an elephant is that the muscle mass required for them to trot or gallop quickly would be enormous and far beyond their capacity to achieve. I have been studying the movement of living elephants a lot recently (with collaborators) and hope to solve this problem.
Were you surprised by the results? Were they what you expected?
JRH: We were a little worried at the start of the project that there would be too many unknown data for us to answer the question rigorously. We were pleased that we were able to accomodate these unknowns in the model and find that many of them did not matter much for the question. The exciting part was that the limb orientation, or posture, that we posed the model in made a lot of difference. Tyrannosaurus needed a lot more muscle mass to run quickly if it used a crouched pose than if it used a more columnar pose. But in either case, we felt we could rule out 45mph running; it required too much muscle mass.
Is there anyone else doing this type of research? Has anyone shown some level of contradictory results?
JRH: Yes, Don Henderson at the Univ of Calgary in Canada has done similar work and had similar results. No one else has used biomechanics to convincingly show that fast speeds were possible, in my opinion. Either their math was wrong, or they didn't consider the unknowns appropriately, or they didn't even consider the physics of locomotion. Seemingly contradictory arguments have been posed based on tyrannosaur leg anatomy (long bones similar to living fast runners), but anatomy alone does not sufficiently predict running speed.
Haven't there been some new discoveries pertaining to this recently?
JRH: The paper published by Day et al. in Nature a few weeks ago showed an animal about 1/3 to 1/5 the size of Tyrannosaurus speeding up, then slowing down. It might have been running, but not very fast. They estimated a speed of about 8 m/s (29kph), which is in the middle of the speed range that our model estimates was perhaps possible. Some people have said that there are other tracks that show big animals moving even faster, but I've never seen them published and will wait for the results. The speed estimates from tracks are notoriously imprecise and often off by a factor of 2.
What happens to the model results if you assume that gravity was not as strong at the time of the dinosaurs?
MG: The muscles need to counteract the force of gravity, so the amount of necessary muscle mass would go down proportionally, according to the model. However, I don't know of any evidence for this and I don't think it's a scientifically-accepted possibility. Even if it was, I am guessing that the changes are miniscule, on the order of a couple of percentage points, not enough to make a real difference.
What about if dinosaurs hopped around? Would that improve their speed?
MG and JRH: The forces generated on one leg during two-legged hopping are generally at least as high, if not higher than, the forces generated on one leg during running. So the results would be the same or worse for hopping as compared to running. Additionally, although many hundreds of dinosaur trackways (fossilized footprints) have been discovered, there is no evidence of hopping.
What is the value of gravity used in the model? Might a lower gravitational force change the results?
MG and JRH: The twisting forces (moments) at the joints are linearly proportional to the segment weights, partially determined by the gravitational constant. We put the standard 9.81 m/s^2 in for gravity, because there is no evidence that gravity was appreciably different during the age of the dinosaurs. It was only 65 million years ago, which is brief for geological/astronomical time. Even if there might have been a difference, it is unlikely that the difference would have been enough to change the conclusions.
A follow-up question is sometimes whether the meteor that hit the Yucatan peninsula 65 mya might have increased gravity to modern levels from much lower levels. I am pretty sure that more than a few straggler dinosaurs would have been wiped out if that were true; think of the disastrous consequences of an impact massive enough to do that. Also, the estimated size of the bolide (based on crater size, etc.) is roughly the size of Manhattan, which would require one heck of a dense meteorite to change gravity much.
Could T. rex have behaved like a duck and swam a lot, thus changing the muscle force needed?
MG and JRH: We are generally very hesitant to make broad ecological generalizations about dinosaur ecology, given that we have precious little scientific evidence to work from and probably much ecological complexity (given how hard it is to work these things out with living animals).
Whether T. rex lived in water or on land, the conclusion stands that it could not run fast on land. However, based on tracks and studies of tooth wear, among other things, it seems unlikely that T. rex was aquatic.