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This is a bit of a primer intended to correct some of the misinformation that
has circulated on this subject. 

On science and evidence - 

First, some comments on what is and is not valid in science. Say you open a
book and it says that elephants can move at 25 mph, and can chase down
humans. If the author has not documented the evidence him or her self, and
does not cite a well documented study, then this is the equivalent of hearsay
evidence. It is not allowed in court, nor is it accepted in science. Remember
that even if the person is highly respected, hearsay evidence is still not
accepted in either venue. At most it is a piece of potential evidence worth
further investigation. Now assume that an author has seen what appeared to
him to be a case of an elephant moving at 25 mph, or outpacing a human, but
had no reliable measurements (track timed, radar gun, lateral view motion
picture - speedometer data is generally suspect). This is eyewitness
testimony. It's better than hearsay, but mind researchers have recently been
emphasizing how very unreliable eyewitness testimony really is. The human
brain is a messy and easily fooled perceiving and recording machine, it is
not a scientific instrument. Eyewitness is essentially equivalent to
anecdotal, and does not meet scientific rigor. 

Ergo, citing a list of anecdotal statements from books etc does not show that
elephants can move fast. If someone can show they can do so, here's how to
document it. Write up a paper with the evidence. Send it around to some of
the researchers who work in the field. See what they say. If the reaction is
positive, get the paper published. For example, N. Sharp happened to reliably
time cheetahs back in 1965, but did not realize the data was important until
he was encouraged by McNeill Alexander to publish his data in J. Zool. Lond.
this year. Now we know the cats can run 65 mph, something I was previously
skeptical about. 

On gaits - 

In this list it has been claimed that elephants can pace, that the amble is a
version of a pace, and that the pace and the trot are not functionally
equivalent. None of this is true. In quadrupedal tetrapods, gaits come in
three basic levels. Basic references are Muybridge 1957(printing) Animals in
Motion, and Gumbaryan 1974 How Mammals Run. If you think otherwise than
described below, then please first check the figures etc in these works. 

Walk & amble - These are the slow nonrunning gaits, in which at least one
foot is always in contact with the ground. The amble is nothing more than a
faster version of a walk. In mammals, in both the walk and amble legs on one
side are both in the air for part of the same time. This is NOT a pace,
because the hindfoot contacts the ground well before the forefoot. In giants,
maximum possible speed is about 12 mph. The amble was probably the fastest
gait of elephantine sauropods and stegosaurs. 

Trot & pace - These are the symmetrical medium speed running gaits with a
suspended phase. They are essentially the same thing, so identical that if
the animal is seen only in lateral silhouette they are indistinguishable. As
Muybridge said in the pace "the legs of the animal are used in lateral pairs,
instead of, as in the trot, diagonal pairs". Because in both cases, two legs
work is nearly exact parallel - either the opposite corners of the same side
- these are very simple gaits. The trot is very common, the pace is only
resorted to when the legs are so long - as in giraffes and camels - that
those on the same side may hit one another during a trot. Because ceratopsids
had such short trunks it is possible that they paced, but a trot is at least
equally possible. Trotting may have been the prefered gait of iguanodonts and
hadrosaurs if they were not bipedal. Trotting was probably the fastest gait
of ankylosaurs. 

Gallop - This is basically the quadrupedal version of bounding, it is very
variable in form. In juvenile crocodilians it is a simple bounding run that
looks like a silly squirrel in armor plate dragging a fat tail behind, in
bigger mammals it is a complex, asymmetrical affair. If prosauropods galloped
they may have done so like crocs, ceratopsians more like mammals. 

On energetics - 

It has been claimed that the relationship between energy consumption and
speed is complex in most animals. Not so. Here is how to calculate how much
energy a given land animal will use to walk or run. This equation is the
standard based on data from Fedak & Seeherman 1979, Taylor et al 1982,
Schmidt-Nielsen 1984, Hill & Wyse 1989, etc., etc. 

kilocalories used to move 1 km = 2.5 times body mass in kg to the 0.7 power. 
(The slope is a little lower in some studies, I use the regressions that
include reptiles.) 

Have used this equation so often can cite it in my sleep. This applies to
virtually anything, a lizard, a chicken, a cat, a human, an elephant. Even
snakes! Does not apply to kangaroos. For caribou and gnu divide by about
half, because these migrators have evolved unusually efficient legs - how is

The formula is so simple because the cost of locomotion is independent of
speed - why this is so, and why the cost of locomotion is so similar in so
many animals, is one of the most important questions in bioenergetics. Say
you have a 1 tonne animal. It costs it about 315 kcal (equals 0.315 dietary
calories) for it to move a kilometer regardless of whether it walks, ambles,
trots, paces or gallops at a speed of 1 or 50 km/h. If the animal walks at 1
km/h, it burns 5.25 kcal/min. If it gallops at 35 km/h, then it burns 35
times as much in that minute. Actually, it is to the benefit of an animal to
move as fast as possible because it burns less of its basal metabolic rate
while moving a given distance, but the effect is moderate because the cost of
moving at even moderate speeds is so many times larger than the resting MR. 

Those physcial fitness experts who know their stuff will tell you that you
burn the same number of calories whether you walk, jog or run a mile. The
advantage of running is that you cover three times the distance and burn
three times as many calories in the same amount of time as walking, and you
work your heart many times harder. 

On who knows what - 

Some of those who contribute to this list may wish to remember that some of
us have been investigating and publishing on animal locomotion for a long
time. Moi, for example, has been at it for two decades. I recall reviewing
Alexander's seminal book on Dynamics of Dinosaurs for the New York Times and
Historical Biology. Just completed a major study on ceratopsian locomotion
(in which I shall publish my data on elephant speed) with a Danish
researcher. Have submitted another study on locomotion in giant theropods.
Why, I've used the above equation to prove that polar dinosaurs could not
have migrated away from winters in a number of papers, and to disprove
assertions that ectothermic dinosaurs could migrate further than endothermic
ones (now that was a REALLY silly notion). Was the first person to show the
link between foot immobility and the inability to run back in
DinosPast&Present VII. Also the first to show that limb posture and possibly
speed was independent of size in ornithomimids and tyrannosaurs, a hypothesis
included by T. MacMahon in his 1984 book. 

Science is like a rough contact sport. Its fun, but you get knocked about,
and to win you have to know you're business. We all get our bruises and
sometimes we lose. So play the game with the big boys at your own risk.