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Having a nice trip



Here are my responses to Mr. Roger Stephenson's critique of my recent
paper on tripping tyrannosaurs in Journal of Vertebrate Paleontology.  To
facilitate discussion of our positions, I will reproduce his comments
and then give my responses.

> Let me begin by giving Dr. James Farlowand his associates, Matt
> B. Smith and John M. Robinson due credit for undertaking such a
> study as outlined in the paper we are talking about. (Body mass,
> bone "strength indicator," and cursorial potential of Tyrannosaurus
> rex, Journal of Vertebrate Paleontology 15(4):713-725). Obviously
> much work and thought went into this project. I now formally thank
> Dr. Farlow for caring enough to send this non-pro a copy of this
> paper which allows me present my thoughts from a slightly less
> ignorant position.

Many thanks for the kind words.

> There are some points I wish to address, as follows;
> 
> 1. Hard surface falls are not proven to speed deceleration, and the
> reverse is likely. Motocycle crash comparisons are valid because the
> increased speed decreases the "crush" effect stated in the
> paper. The validity of my statement is supported by physics. The
> speed of racing motorcyclist, sometimes in excess of 150MPH(200
> Lbs. X 150MPH), more than offsets the lowered hieght from which they
> fall. Potential energy is increased geometricly with speed, however
> the contact force is spread over time and distance. A bullet, fired
> from a exactly level rifle has the exact same falling speed as one
> dropped by hand at a given height. The variable, forward speed, has
> no effect on fall rate, until one reaches near escape velocity. At
> that point what goes up does not have to come down. This is why a
> stone skips when thrown across a water surface and sinks immediately
> when dropped straight down. Hard surfaces are desirable when
> impacting at speed.

As best I can tell, the comparison of the crash-and-burn cyclist with the
tripping tyrannosaur is not very appropriate.  Mr. Stephenson says that
the faster speed of the cyclist more than compensates for the greater
height of the dinosaur.  But those are not the only pertinent variables.
What does the damage in a fall is the sudden absorption of kinetic energy
by the faller.  Kinetic energy is equal to 1/2 * mass * velocity**2.
If we do the calculation for the entire body of our cyclist and of our
tyrannosaur, we get the following:

cyclist:  (1/2) * (mass) * velocity**2 = (1/2) * 91 kg * (67 m/s)**2
          = 204,000 kg m**2/s**2

tyrannosaur: (1/2) * 6000 kg * (20 m/s)**2 = 1,200,000 kg m**2/s**2

Thus the horizontal component of impact force is about 6 times that of the
cyclist, due to the considerably greater mass of the dinosaur than of the
human.  
     What is more important in predicting the impact behavior of the two
bodies, however, is the relative magnitude of the vertical and horizontal
components of impact force.  As described in our paper, the vertical
component of impact force of a falling tyrannosaur will greatly exceed the
horizontal component.  The reverse will be true for the crashing cyclist.
Consequently the cyclist is considerably more likely to mimic a skipping
stone than the falling dinosaur is. 

> 2. The specimen studied specifically, MOR 555, is the gracile morph,
> and strength indicators may not be accurate for the more robust
> morph.  Variables unaccounted for, or at least not mentioned,
> include bone strength and body mass placement. By this I mean weight
> and size differences in neck and tail structure. These difference
> could allow the robust form to react and balance differently than
> the gracile form. The gracile form may have also been quicker to
> react to the possiblity of a fall.

This could very well be true, but I don't think it relevant to our argument.
The gracile form might well have been better able to react to a fall than 
the robust form could.  Our calculations are for the gracile morph.  
However, I suspect that, if anything, the consequences of a fall would be 
worse for the robust form than for the gracile form.  

> 3. On page #722 the paper states, "We did not do a seperate
> calculation for the head of the rhinoceros, because we had no basis
> for estimating its mass". Either this is a misprint or there is
> something wrong. If an estimation of mass cannot be made for an
> extant creature, how can one even begin to estimate the mass of an
> extinct one?

Nope, not a misprint.  You're reading too much into our statement.  We
didn't do the calculation for a rhino head because we didn't have a model
of a rhino head--or a dead rhino's head--to play around with.  This doesn't
mean that such a thing could not be done.

> 4. Head size does not equal strength or weight. I would be willing
> to bet a fair sum of American dollars that the head of a rhino is
> much heavier, cubic inch for cubic inch, than the flexible and
> air-filled head of T-rex.  The flexibility factor alone precludes a
> comparison of the rhino and the Tyrannosaurus rex. The skull of
> T-rex, with that flexibility built-in, would seem to be a great
> impact absorption tool, whether from falls or from hunting lunges.

Maybe--yo no se.  It would be an interesting thing to model.  Be aware, though,
that there is some dispute as to how much give there was in the skull of
Tyrannosaurus.  Ralph Molnar doubts that it was as kinetic as the skulls of
smaller theropods, for example.  I suppose that one could sculpt models of
the skulls of the two animals, build in the joints, and see how much the
two heads would differ in response to an impact.  I would not be surprised
if the Tyrannosaurus head is more flexible than the rhino's, but is this
enough to counteract the differences in absolute mass, and the height 
difference over which the two heads would fall?  I'd bet not, but hey, I
could be wrong.  It'd be fun to try to model this, but I have too many other
things on my research plate right now to do it.

> 5. Falling from a greater hieght, while adding to the impact forces,
> also allows for corrections as time before the event is also
> increased. In the event a T-rex. were to be aware of the imbalance
> prior to the "point of no return" surely it would have enough
> reaction speed to alter its angle of attack. Headlong plunges toward
> the dirt, without correction, doesn't fit any predatory creature. I
> submit that bipedal predatory dinosaurs were generally quicker than
> quadrapedal mamals, on the basis that the dinosaurs reptillian
> nature was instilled in evolutionary selection.  Elephants herding
> and near freedom from predation, and rhinos too in the later, don't
> require the same swiftness as needed by dinosaurs in either the
> young or old.

Well, maybe.  It's hard for me to say.  Pretty damn hard to test any of the
hypotheses contained in the preceding paragraph.

> 6. No mention is made in the paper in regards to neck strength in
> T-rex.  and without this data the statement that the body would
> overtake the head and break the neck is suspect. Would it not be
> possible for the T-rex. to stiffen its neck, shift its head to the
> side, or take whatever means needed to protect itself? What animal
> doesn't?

Again, maybe.  Our argument is based on the behavior of different parts of
the body in response to a fall, based on their mass, momentum, etc.  Sure,
maybe the beast could turn its head to the side--hence our use of the word
"might" in the relevant statement on p. 723 of our paper.

> 7. Without soft tissue data, and complete data at that, the overall
> mass of any creature must be questioned. Estimations and geusswork
> lead to guesstimations, and that leads to errors. Lung capacity,
> stomach and gut size, and other soft tissues could varry wildly from
> what we think we know now. These variables have to be considered
> before any assumptions are put forward as fact.

Whoa, dude!  We didn't do any such thing!  Look at our paper again, and
note all the weaselly uses of words like "might," "could," and "suggest."
What we did is to construct some mathematical models, based on what we
thought were reasonable assumptions and estimates of or about the relevant
parameters, and describe the implications of the models for the cursorial
potential of Tyrannosaurus.  We think that our model is robust, and that
its results will hold for any reasonable alternative assumptions about the
parameters we use.  If somebody thinks we're wrong, though, then it is
incumbent upon them to propose and defend an alternative model, or to do
an experiment, or present observations, that clearly falsify our hypotheses.
In our paper we explicitly identified one kind of observation that would shoot
us down.  So if anybody wants to take shots at us, fire away!

> I know I have placed a black cloud on the paper by these men, and
> after having said all of this I could be entirely wrong. Logic,
> however, leads me the believe that T-rex could not only run swiftly
> but if it fell most likely survive.

     If this is your opinion, then you need to develop a better model than
ours to support your case.  And don't forget to indicate how your conclusions
could be proved wrong!

> Further study could prove me all wet, as wet as a carp.  Please do
> not take offense for this longwinded expression of doubt. When we
> stop questioning each other our overall knowledge of the world we
> live in will decline.

No offense is taken.  In fact, I would hold up Mr. Stephenson's message as
a model of how to disagree with somebody in a reasonable, respectful fashion.
He states his disagreements clearly, without a lot of overblown rhetoric
about the putative shortcomings of the persons with whom he disagrees.
I hope that my replies to his comments are in the same vein.
     Beyond that, I hope that I have revealed the silver lining in the black
cloud that Mr. Stephenson has cast upon our study.