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I am curious why GSP's paper below was refused publication. It appears to me
to be a significant counter to some probably erroneous material in H  & G!
Ray McAllister
(954) 426-0808

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.
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
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
the dinosaur than observed in the bird. The failure to correctly model even
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
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,
trunks that needed minimal musculature, tails that were distally shorter
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
big bellied elephants which cannot run not because of their size, but
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
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
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
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
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
of leg extensor mass presented in Table 1, which includes their widely
publicized 86% leg extensor value for an adult Tyrannosaurus. These
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,
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
(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
results in increased leg muscle mass has yet to be demonstrated by
measurements, especially of animals of similar size and locomotary
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
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
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
(fore plus hind) muscles yet measured are tinamous at 56% (Hartman 61).
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
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
established that the mass specific power needed to support a body and move
at a given speed falls dramatically with increasing size without exception
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.
increase in energy efficiency with increasing size is driven not be
decreasing leg flexion, but by factors more inherent to large sizes
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
 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
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
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
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
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
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,
kg of muscle would need to generate a mere 16 W), which forces one to ask
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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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