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Speed Potential in Tyrannosaurs (long)

Hutchinson and Garcia?s paper on speed potential in tyrannosaurs in Nature 
garnered widespread attention and considerable approval. This summer I and 
others (Christiansen, and Blanco & Mazetta) sent three separate replies to 
Nature, all were rejected. The replies of leading researchers into speed 
potential of giant avepods(see Paul 2002) which expose critical flaws in 
H&G?s study will therefore not receive proper attention in the near future. I 
am working with others to produce an extensive study into the locomotion of 
giant avepods, which will take substantial time to appear. My Nature reply 
with some alterations is below, followed by further discussion (which is 
largely limited to factors pertinent to the H&G study, this is not a 
comprehensive analysis of all aspects of the issue). I and Guy Leahy will 
also present a poster on the subject at the SVP meeting.


Estimates of leg extensor mass by H&G limit Tyrannosaurus to a slow pace 
whose metabolic expense was ?considerable, but numerous problems cast doubt 
on their analysis. The zones in their Fig. 3 imply that running potential 
decreases as leg extensors become a larger percentage of body mass when the 
opposite is true (the correct question is what is the maximum portion of 
total mass that can be dedicated to leg extensors), and the ?uncertain 
running ability? zone starts at just 10% when the total leg extensor/total 
mass ratio in chickens and ostriches is far higher (H&G, Alexander 79) (Fig. 
1). From only one small modern biped they extrapolated to far larger sizes 
without living intermediates. Their estimate of the leg extensors needed for 
a juvenile tyrannosaur to run fast (42%) places it high in their zone of 
uncertain running ability, and is over twice that actually present in similar 
sized ostriches (<20%, less than a third of an ostrich consists of leg 
muscles). It is all the more peculiar that their method predicts increasing 
extensor mass as limb flexion increases, yet restored knee flexion is less in 
the dinosaur than observed in the bird. The failure to correctly model even a 
small tyrannosaur falsifies their results, and their extreme projections for 
a running Tyrannosaurus must be considered at least as excessive. 
    Anatomical comparisons of living and extinct animals remains important to 
restoring the speed potential and related parameters of the latter. 2 tonne 
rhinos can gallop even though they are bulky herbivores with short, lightly 
muscled limbs. Tyrannosaurs of similar mass were at least as fast because 
they were long legged predators whose small bellies, air filled bodies, rigid 
trunks that needed minimal musculature, tails that were distally shorter than 
in other large theropods, and reduced arms allowed a high portion of total 
mass, a bird-like quarter to a third, to be concentrated in leg muscles 
anchored on their thick tail bases, very large pelves and prominent cnemial 
crests. No other animals of their size have been as adapted for speed. These 
points further contradict the implication of H&G?s analysis that rhino sized 
tyrannosaurs would have needed well over half of their mass dedicated to leg 
extensors in order to run fast. Tyrannosaurus had the same basic running 
adaptations as its lesser relatives (Paul 88, 00), and was also uniquely 
speed adapted for its size, so it should had much higher speed potential than 
big bellied elephants which cannot run not because of their size, but because 
they have relatively small leg muscles, inflexible ankles and abbreviated 
feet (Paul 00, Anderson et al. 79, Robertson-Bullock 62, Paul & Christiansen 
00). If it were not possible for elephant sized animals to be faster than 
elephants because of limb loading constraints, then elephants would have 
oversized, metabolically expensive limb muscles. That the opposite is true 
contradicts both the view that elephants are close to biomechanical speed and 
size limits, and the extremely steep decline in locomotary performance in 
their size range projected by H&G; views also contradicted by the ability of 
sauropods to grow an order of magnitude larger than elephants. The running 
potential of elephants sized animals is supported by the long flexible feet 
and very large areas for leg muscle attachment present in the largest 
ceratopsids (Christiansen & Paul 00, Paul & Christiansen 01).
    That some extinct tetrapods had much larger muscle attachments and 
running adaptations not seen in elephants indicates that they were faster 
than the latter, the question is by how much; the top speed of elephant sized 
theropods has been estimated to be 14 m s-1 (Christiansen 00, Blanco & 
Mazzetta 01). If a method of restoring the locomotion of extinct forms is to 
be considered reliable it must demonstrate the ability to realistically model 
key, interrelated aspects of the problem including leg extensor mass, limb 
posture and form, and cost of locomotion in a broad range of tetrapods, as 
well as super sauropods. Only then can it be used to estimate running 
performance in giant, flexed limbed dinosaurs.   

Additional Comments

Leg extensor mass

The extremity of the error of the high leg extensor mass estimated by H&G for 
a juvenile tyrannosaur (which is not discussed in the text of their paper) 
cannot be overemphasized. This is part of their ?best guess? set of estimates 
of leg extensor mass presented in Table 1, which includes their widely 
publicized 86% leg extensor value for an adult Tyrannosaurus. These estimates 
used my restoration of tyrannosaur leg flexion, as shown in their Fig 1. The 
degree of flexion is less than observed in ostriches (Paul 1988, Gatsey & 
Biewener 1991; the low knee flexion restored by Abourachio & Renous 2000 
appears to be due to an overly short tibia length estimate). That ratite 
sized tyrannosaurs would have had leg extensors twice as large as birds even 
if they had similarly or less flexed joints is essentially impossible. The 
only way to reduce the leg extensor ratio is by decreasing leg flexion, which 
leaves unanswered why tyrannosaurs would have needed such straight legs to 
have leg extensors as small as those of big birds with strongly flexed legs, 
and is not feasible since tyrannosaurs could not straighten the knee more 
than I have restored for reasons I have repeatedly detailed in the literature 
(Paul 87, 88, 00, 00; to date no detailed refutation of the anatomical 
evidence for strongly flexed knees in tyrannosaurs of all sizes has been 
    In any case, as noted in the reply, the belief that increased leg flexion 
results in increased leg muscle mass has yet to be demonstrated by 
measurements, especially of animals of similar size and locomotary potential. 
Straight legged juvenile elephants may have smaller leg muscles than horses 
of the same mass, but the latter are much faster. The increased cost of 
locomotion observed when humans deliberately move with overly flexed knees is 
meaningless since significant alteration in limb function away from the 
optimal evolved condition usually decreases energy efficiency.
    In research of this type a basic principle is to first produce results 
for relatively noncontroversial examples that are reasonable, and then 
extrapolate to the controversial subjects. When the juvenile tyrannosaur with 
moderately flexed legs was estimated to have such enormous leg muscles the 
method should have been adjusted until reasonable results were obtained.   

Speed zones and extensor mass

The leg extensor/body mass ratio issue is actually an either/or problem in 
which the question is what is the maximum portion of total mass that can be 
dedicated to leg extensors in order to maximize running potential. The 
terrestrial tetrapods with the highest portion of body mass dedicated to limb 
(fore plus hind) muscles yet measured are tinamous at 56% (Hartman 61). Since 
limb extensors make up about 70% of limb muscles, in principle about 40% of 
total mass can be leg extensors in tetrapods with nonlocomotary body mass 
reducing adaptations including rigid, lightly muscled trunks, and that lack 
large digestive tracts. Animals that have well developed trunk muscles or 
large digestive tracts probably cannot place such a high percentage of their 
body mass on the legs. It is also questionable whether bipeds can carry such 
a large portion of total mass on just one set of legs, the highest observed 
portion of body mass dedicated to leg extensors in bipedal tetrapods is about 
half the above value.  

Tyrannosaurus moved with surprisingly little effort

H&G?s high estimates of leg extensor mass in giant tyrannosaurs has subtle 
but critical secondary implications that contradict their results. It is well 
established that the mass specific power needed to support a body and move it 
at a given speed falls dramatically with increasing size without exception in 
land animals, to the point that the observed cost of locomotion for an 
elephant sized creature is 1/20 that of a mouse and 1/300 that of an ant. The 
increase in energy efficiency with increasing size is driven not be 
decreasing leg flexion, but by factors more inherent to large sizes including 
lower stride frequencies, shorter muscle stretch and action factors due to 
less extreme limb excursion arcs, and shortening of relative muscle fiber 
length associated with increasing reliance on energy storing spring action 
tendons that also provide a degree of support with a corresponding reduction 
in muscle activity (Dimery et al. 86, Heglund & Cavagna 87, Taylor 94). 
    If there is one thing we can be certain of, it is that adult Tyrannosaurus
 moved with the same, low level of mass specific power output observed in 
elephants. Yet H&G calculated ?that even a walking tyrannosaur required 
activation of a large fraction of its extensor muscle volume, at considerable 
metabolic expense?. In other words, they suggest  that big tyrannosaurs 
should have had an unusually high cost of locomotion - a low energy 
efficiency not observed in any land animal - because even to just walk the 
giant biped needed oversized leg muscles that required a large amount of 
energy to operate. H&G?s overestimation of the cost of locomotion in adult 
Tyrannosaurus  limited to a slow pace is additional evidence that they 
overestimated the required mass of its leg muscles. The overestimate appears 
to be due to failure to account for the increasing role of tendons and muscle 
fiber shortening in large runners. 

High speeds at large size 

The hypothesis that speed must decline with great size is intuitive, but is 
dubious on multiple grounds. Because, as the reply notes, both power 
available from muscles and power needed to move at a given speed scale to 
similar powers, muscle mass should remain a constant percent of body mass in 
animals capable of achieving the same top speed according to all theories of 
animal scaling (geometric similarity (isometry), elastic similarity and 
static stress similarity). Animals of increasing size would need to increase 
limb muscle mass as a percentage of total mass only if the muscles needed to 
do increasing work relative to the 2/3s power in order to support the total 
mass and propel it at a given absolute speed. If so then the relative cost of 
locomotion would not decline with increasing size in the observed manner. To 
look at it another way, if relative muscle mass increases as a percentage of 
total mass as size increases in animals of otherwise similar form, but power 
needed to support a body and propel it at a given speed scales to the 2/3s 
power, then the increasingly enormous muscles would have increasingly less 
work/kg to do to a degree far greater than is actually observed in land 

Strange scaling 

    The leg extensor/total body mass ratio of H&G?s geometrically similar 
chicken initially scales close to 1 as per the predictions of scaling models. 
But starting at about 100 kg the curve of the ratio increasingly diverges 
from 1 in a peculiar manner that is not linear even on a log-log plot, and 
matches no theoretical or observed scaling rule. The extensor/body mass ratio 
calculated by H&G is 4 times higher than expected at 1000 kg, and 20 fold at 
6000 kg. If giant animals did scale leg muscle mass in this manner then the 
enormous muscles would do amazingly little work per unit mass (if an adult 
Tyrannosaurus with 85% of its body mass as limb muscles ran at 20 m s-1, each 
kg of muscle would need to generate a mere 16 W), which forces one to ask why 
the muscles would be so huge in the first place. Conversely, if muscles did 
scale in the manner calculated by H&G, then the cost of locomotion should 
scale to a curve well above 2/3s in animals over 100 kg. Such odd scalings 
and extreme results cast great doubt upon H&G?s methods and conclusions. It 
is further perplexing that H&G?s scaling of extensor/body mass ratios for 
tyrannosaurs, although also significantly higher than 1 at ~1.23, is much 
less extreme than seen for their isometric chicken. Although the nonisometry 
of the tyrannosaurs is in part responsible for this difference, the extremity 
of the different scaling patterns as well as the consistency of tyrannosaur 
form cast additional doubt upon their methods and results. These strange 
patterns suggest that H&Gs computer calculations invented scaling curves that 
do not exist in nature. 

Real scaling, and the myth of big muscles in giants

    If increasing size forces dramatic increases in the relative mass of 
supporting muscles then elephants and especially galloping rhinos should have 
oversized limb muscles, and correspondingly high costs of locomotion. But 
giant rhinos and elephants are so energy efficient when walking or running 
because their limb muscles are not enlarged.
    This is a fascinating issue. Although some think that leg muscles must 
become an increasingly large percentage of total mass as size increases, this 
has never been verified, and what  data has been published suggests 
otherwise. Alexander et al. (79, 81) did not observe an increase in relative 
leg muscle mass in either birds or mammals. In house cats, greyhounds and 
macaques, leg muscles make up 15-20% of total mass (Grand 77). 
Robertson-Bullock (62) cut up a few elephants and weighed the parts. His data 
indicates that the leg muscles make up a mere 5-9% of total mass, with the 
lowest values from the biggest specimens! (As an artist I?ve long pointed out 
that there is not much in the way of muscles on elephant-type legs, nice to 
see data). If so, then rather than having legs muscles as relatively large or 
larger than cats, dogs and monkeys, elephant?s are two to four times smaller 
in this regard. Elephant leg muscles are so extremely small because they are 
so slow. There is no good data for rhinos, but they have very short legs 
dwarfed by their massive heads, necks and fermenting vat bellies so there leg 
muscle percentage is probably in the 10% range or less. Far from there being 
a dramatic increase in leg muscles as size goes up, if anything they decline 
in relative size. Unfortunately leg muscle mass in a series of animals of 
similar design and top speed has not been done, ceratomorphs (tapirs to 
rhinos) would be ideal. Looking at side view photos I can see no sign that 
leg muscles are relatively smaller in small tapirs that can gallop no faster 
than giant rhinos, instead the latter have much shorter legs to hang muscles 
on. Its up to those who think otherwise to produce data showing that relative 
leg muscle mass increases in animals of similar top speed as size increases. 
Good luck.
    It has been claimed that bipeds need a much larger percentage of their 
body mass to be dedicated to leg muscles than quadrupeds of the same size 
(Roberts et al. 98). Now, although it makes sense that bipeds would need more 
HINDleg muscles than quadrupeds, the notion that animals with only two legs 
would need a greater % of their total mass to be leg muscles is peculiar. 
According to Hartman (61) the leg muscles of running birds make up the same 
percentage of total mass seen in quadrupedal mammals (Grand 77). Ostriches 
have relatively larger leg muscles, but they may be the fastest animals in 
the world except for cheetahs and maybe thoroughbreds (too bad there is no 
data for other ratites). So leg muscles in bipeds are similar in size to 
those of quadrupeds. There is no reason to think this changes with size.   
    As size goes up the relative thickness of the legs tends to increase in 
order to support the increasingly massive body. But the relative length of 
the legs tends to decrease. So leg muscle/total mass ratio remains constant. 
The result of real scaling patterns is that top absolute speed can remain 
constant as size increases if muscle mass remains a constant percentage of 
total mass in animals of similar form. In fact, because it is relatively 
harder to move at a given speed as size decreases it is small animals that 
cannot attain high absolute speeds, while giants have the potential to move 
fast at low cost. With total leg muscle mass making up between a quarter and 
a third of body mass, the approximate average watts/kg of leg muscle needed 
to run at 14 m s-1 is an unattainable 400 in the chicken, which is why fowl 
cannot run so fast. 200 W/kg, which is achievable in aerobically capable 
muscles, powers ostriches at the same speed. Just 40 W/kg of leg muscles 
would power Tyrannosaurus at 14 m s-1. (Genetically selected and trained dogs 
and horses win races at 15-19 m s-1, similarly specialized Olympic sprinters 
reach 10 m s-1.)


According to H&G, Tyrannosaurus, the most speed adapted tetrapod in its size 
class, was not much faster than elephants, among the least speed adapted of 
tetrapods. Think about it. 

Wrap up

H&G overestimated by 100% the leg extensor mass of fast running juvenile 
tyrannosaurs with legs less flexed than those of big birds, overestimated the 
cost of locomotion in a walking adult Tyrannosaurus, did not take into 
account the dramatic decrease in the power needed to move at a given speed as 
size increases, did not take into full account the increasing importance of 
tendons and muscle fiber shortening in large runners, failed to use a 
sufficiently large sample of living bipeds (especially ostrich), failed to 
document that muscle mass increases in animals of similar form and top speed 
as size increases, and failed to take into account or account for the extreme 
speed adaptations of tyrannosaurs of all sizes. The results of their study 
cannot therefore be considered reliable. 
    Although computer simulations are useful, they often fail to incorporate 
the complexities of the real world to the degree needed to produce reliable 
results. It is necessary for researchers to gather far more basic data on 
living animals, including the masses and other aspects of locomotary muscles, 
tendons etc. Such data will allow us to make fundamental conclusions about 
the locomotion of extinct forms without computer simulations. Indeed, we 
already know enough to conclude that giant tyrannosaurs were very fast. 
    We know that giant rhinos can achieve fast full gallops with modest leg 
muscles on short legs. There is no good reason to doubt that similar sized 
tyrannosaurs could run faster because they were much better adapted for 
speed, and must have had larger limb muscles for the reasons detailed in the 
reply (one fifth to a quarter or more of total mass). That the anatomical 
adaptations of the most gigantic tyrannosaurs were essentially identical to 
those of small tyrannosaurs, and were different only in those respects 
necessary to maintain constant absolute speed, shows that Tyrannosaurus was 
as swift as it?s smaller brethren.  

(Thanks to Per Christiansen, Ernesto Blanco and Guy Leahy for their comments 
and assistance.)

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