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that paper of ours



Hi folks,
        I am exhausted from a long week of media frenzy and only get the daily digest version of this list, so please be patient with my slow replies.  I want to reply to everyone's comments, because this is a great forum to talk about issues like this.  I wish more researchers would talk about their published papers on this list, because it is the perfect opportunity to exchange ideas with people who know lots of stuff.  And it's a fun topic!

Please:  Read the paper and the news and views.  Also read the supplementary information, it is critical.  Then check out the website at: http://tam.cornell.edu/students/garcia/.trex_www/naturepaper.html

Reporters have all had access to this site, which was prepared with the goal of minimizing misinterpretation of our research.  So if you see a report and wonder what we really said, check this webpage.  Careful reporters took a look, and it shows in their work.

The same should apply to listmembers, I hope.


Here goes:
==================================

From: "Thomas R. Holtz, Jr." <tholtz@geol.umd.edu>
To: "dinosaur" <dinosaur@usc.edu>
Subject: New Nature paper on Tyrannosaur Locomotion
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Yes, Tim Williams found me out...

In this week's Nature:
JOHN R. HUTCHINSON and MARIANO GARCIA (2002).  _Tyrannosaurus_ was not a
fast runner.  Nature 415: 1018 - 1021

and the News & Views:
ANDREW A. BIEWENER (2002). Walking with tyrannosaurs.  Nature 415: 972-973.

In brief, Hutchinson & Garcia model various hindlimb paramaters (limb
lengths, segment weights, muscle fibre lengths, and more) from various
specimens (MOR 555, a _T. rex_; a small tyrannosaur from the Field Museum; a
_Coelophysis_; a modern alligator; a modern chicken).  They attempted to
calculate (for various body positions) the value T, the percent of the body
mass represented by leg muscles per leg required to allow the animal to run.
"Running" in this case was set at Froude number (Fr) = 2.5, based on
observations of modern animals and on biomechanical theory.


A correction:  We made a distinction between "fast running" (45 mph, Froude 16) and running (theoretically, with lots of slop, Froude 1 or more).
The magnitude of the ground reaction force at mid-stance was 2.5 times body weight (is 2.5-4 times body weight during fast running regardless of size, etc.); the Froude # was not 2.5.


(The Froude number is a dimensionless descriptor of speed.  For their model
they calculate Fr  = (velocity)^2/(hip height x g).  An ostrich running at
12 m/s is doing Fr = 16; in biomechanical theory, Fr = 1 represents the
walk/run transition).

Most of their estimates for the adult _T. rex_ found values of T which were
unreasonably high (each leg's muscle mass being 30-50% of the organism!) for
nearly all the different postures for the Big Guy they tried.  The other
specimens they looked at had lower values: T = 20 for the young leggy
tyrannosaur, down to T =  4.7 or so for the chicken.

The basic conclusion: big _T. rex_ specimens did not have sufficient muscle
mass to be able to produce a fast run.  However, they point at that at a
fast walk (presumably close to but not exceeding Fr = 1), MOR 555 would
still be moving at 5 m/s (that is, 11 mph).

A side note: other big theropods and big non-theropod dinosaurs would be
suffering from the same set backs (and arguably worse with broad stumpy
feet), so this does not invalidate _T. rex_ as a _Triceratops_ or
_Anatotitan_ chaser.

Checking this against the recent Day et al. (2002) Middle Jurassic trackway,
their critter (estimated to be 1.93 m tall and moving at an estimated
maximum speed of 8 m/s) seems to be moving at a Froude number of 3.8.  This
is faster than the walk-run transition (theoretically at Fr = 1).  Now an
1.93 m hip height theropod is big: comparable to _Dryptosaurus_ or a smidge
under the UUVP 6000 specimen of _Allosaurus_: Greg Paul estimates that
latter specimen at 1.32 tonnes.  So *if* the size and speed estimates of the
MJ theropod are correct, then one tonne theropods could run, at least
slowly.

Perhaps.  Do note that the speed estimate equations are based on lots of different biomechanical equations (read up on work by Alexander, Jayes, and others since 1976) and data from a wide assortment of living animals.  Bakker's NPR blurb seemed to say that they are simple equations.  They are not.  They are based on a lot of underlying theory and assumptions.  Speed estimates are often off by a factor of 2.


Very, very interesting stuff.  It will be even more interesting to see this
model tested against other, smaller theropods and other dinosaurs.  I would
be interested in seeing how other young tyrannosaurs and ornithomimosaurs
fare in this model.


We model a quite small tyrannosaur (FMNH PR 2211 I think), which should be the same as an ornithomimosaur I'd expect; about twice as good at running as an adult Tyrannosaurus.

We also model a human, which (like a chicken) has about 2x the muscle mass needed for fast running.

The model is a first step in a long series of modeling and experimental studies that I'm undertaking.  I am not ashamed to admit that details about the model might be shown to be wrong by myself or others in the future.  That's science.  An important point of the study is that we need to start using more sophisticated biomechanics in paleontology.  There is a lot more that can be done.  People have been using Alexander's simple models for >25 yrs now; it's time to move on and do something new.  Like other people in the field such as Gatesy, Carrano, Blob, Henderson, etc., I am trying to develop new techniques that yield new insights, rather than drone on and on about the same old data and methods.


                Thomas R. Holtz, Jr.
                Vertebrate Paleontologist
Department of Geology           Director, Earth, Life & Time Program
University of Maryland          College Park Scholars
                College Park, MD  20742
http://www.geol.umd.edu/~tholtz/tholtz.htm
http://www.geol.umd.edu/~jmerck/eltsite
Phone:  301-405-4084    Email:  tholtz@geol.umd.edu
Fax (Geol):  301-314-9661       Fax (CPS-ELT): 301-405-0796

[snip]

Date: Wed, 27 Feb 2002 23:54:47 +0100
From: "David Marjanovic" <david.marjanovic@gmx.at>
To: "The Dinosaur Mailing List" <dinosaur@usc.edu>
Subject: Re: New Nature paper on Tyrannosaur Locomotion
Message-ID: <004001c1bfe1$c2585440$b4432fd5@chello.at>
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> In brief, Hutchinson & Garcia model various hindlimb paramaters (limb
> lengths, segment weights, muscle fibre lengths, and more) from various
> specimens (MOR 555, a _T. rex_; a small tyrannosaur from the Field Museum;
a
> _Coelophysis_; a modern alligator; a modern chicken).  They attempted to
> calculate (for various body positions) [...]

What about various weight estimates? They used 6 t... did they also try 4 t,
for example? What about, say, the elastic effects of tendons and cartilage?

This is a subtle point that is easily missed on reading the paper, but we factor out body mass from the equation, so it doesn't matter much really.  That is confusing, I know, because mass does matter in the end.  It will be explained in more detail in a later paper.

Soft tissue elasticity is implictly part of the muscle force/area in the model.  Cartilage elasticity has not been shown to matter much at all for these sort of problems in living animals.  It can safely be ignored.


BTW, 5 and 8 m/s are 18 and 28.8 km/h, respectively.

Yes.



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Date: Wed, 27 Feb 2002 19:32:26 -0600
From: "Steve  Brusatte" <dinoland@lycos.com>
To: dinosaur@usc.edu
Subject: Re: New Nature paper on Tyrannosaur Locomotion

>The basic conclusion: big _T. rex_ specimens did not have sufficient muscle
>mass to be able to produce a fast run. 

Currie seemed very interested at the Burpee Museum this weekend in the possibility that young members of a _Tyrannosaurus_ "herd" may have done the majority of the hunting.  Speculation, of course, but he points to the _Albertosaurus_ bone beds in Alberta as evidence that tyrannosaurids may have been gregarious.  He extrapolated these data to speculate that perhaps the more agile youngsters may have done the hunting for the older, slower adults.



The model of the juvenile tyrannosaur that we did is consistent with Currie's idea; they likely had a broader range of locomotor performance.



Date: Wed, 27 Feb 2002 18:57:43 -0700 (MST)
From: Richard W Travsky <rtravsky@uwyo.edu>
To: dinosaur@usc.edu
Subject: Re: New Nature paper on Tyrannosaur Locomotion
Message-ID: <Pine.GSO.4.10.10202271852300.25662-100000@asuwlink.uwyo.edu>
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On Wed, 27 Feb 2002, Thomas R. Holtz, Jr. wrote:
> Yes, Tim Williams found me out...
>
> In this week's Nature:
> JOHN R. HUTCHINSON and MARIANO GARCIA (2002).  _Tyrannosaurus_ was not a
> fast runner.  Nature 415: 1018 - 1021
>
> and the News & Views:
> ANDREW A. BIEWENER (2002). Walking with tyrannosaurs.  Nature 415: 972-973.
> [...]

ABC News did a feature on this tonight (Wednesday the 27th).

Their web site has a page on this, including a picture of the chicken
comparision from Hutchinson's computer simulation.


Minor note, the 3D model shown is part of the newer, more realistic work I'm doing at Stanford. The model in the Nature paper is as simple as it needed to be, which was 2D.


 http://abcnews.go.com/sections/wnt/DailyNews/t_rex_020227.html

A link for the  video of this segment is also on this page.

Date: Wed, 27 Feb 2002 18:26:09 -0800
From: "Michael de Sosa" <ofsosa@uclink4.berkeley.edu>
To: "Dinosaur Mailing List" <dinosaur@usc.edu>
Subject: RE: New Nature paper on Tyrannosaur Locomotion
Message-ID: <ILEGKCHIMGAMCPJCMCNKCEGJCHAA.ofsosa@uclink4.berkeley.edu>
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John was on NPR's All Things Considered radio show this evening talking
about the research. The counter-argument was given by... wait for it... you
can probably guess... Bob Bakker! No, really!

Mike D.


As is the tiresome case when dealing with luddites and numerophobes, Bakker brought up the Ye Olde "Bumblebees can't fly" Myth.  This is a misleading approach that is often used to confuse people about modeling.  In 30 seconds I found these 3 pages that discuss what science really said about the bumblebee:
http://www.maa.org/mathland/mathland_3_31.html
http://www.sciam.com/2001/0601issue/0601dickinson.html
http://www.news.cornell.edu/releases/March00/APS_Wang.hrs.html

Yes, science can be wrong, but that does not mean that science is always wrong...


Date: Wed, 27 Feb 2002 21:03:05 -0600
From: "Toby White" <mwhite@houston.rr.com>
To: <dinosaur@usc.edu>
Subject: RE: New Nature paper on Tyrannosaur Locomotion
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An article on this is on the front page of the web version of the NY
Times (article at
http://www.nytimes.com/2002/02/27/science/27CND-DINO.html.

I've always been a fan of slow theropods, but this seems almost too
slow.  One reason for a slower speed would be the amount of damage
caused by a fall -- a huge risk for a high mass animal, even if the
probability of a fall were small.  However, Tyrannosaurus was a biped.
It had to have enough agility to balance, and to correct its balance if
the ground shifted.  Unless Tyrannosaurus was confined to plains, it
also had to have *some* ability to go up and down hills. That should
require more than a minimal amount of dexterity for a digitigrade biped.

A *really* slow theropod is almost harder to understand than a rocket
raptor.  Then again, maybe grade and terrain really were important to
dinosaur behavior.  [Wild speculation begins here] For example,
hadrosaurs with hoof-like feet on unequal front and hind legs look funny
on a plain.  On the other hand (or foot) they'd probably be quite nimble
climbing a slope, particularly outracing a slow biped who was having
trouble keeping its balance.

  --Toby White

The Vertebrate Notes at http://home.houston.rr.com/vnotes/index.html
and http://www.dinodata.net
[moving soon!]


I have no disagreement here,  except to note that speeds are all relative.   Is 5 or 11 m/s all that slow, really?  I think not!   But it's not fast compared to 20 m/s (45mph).  Our point in the paper was that 11 m/s does not make biomechanical sense, and we have our doubts about even 11 m/s.

Again, the mantra: We Might Be Wrong (every scientist should be comfortable saying this sentence).  But we have accomodated all of the data and assumptions that we felt we needed to, and came up with our answer.  Science will keep moving on.



Date: Wed, 27 Feb 2002 19:15:31 -0800
From: "Tracy L. Ford" <dino.hunter@cox.net>
To: "Dinonet \(E-mail\)" <dinosaur@usc.edu>
Subject: RE: New Tyrannosaurus paper
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I wonder about this, and if they really looked at the skeletons?

Umm, yes... I spent the last 7 years studying every sauropsid specimen I could find, living or dead, from the US to Argentina, China, etc.  I've seen practically every tyrannosaur skeleton that exists and spent a lot of time with it.  Intensive anatomical work is the foundation of this research; check out my recent papers in ZJLS, Paleobiology, and upcoming J Morph etc.  I am not just some engineering guy; I am trained as a biologist and work hands-on with specimens, Recent and Mesozoic, on a daily basis.



Fact, Tyrannosaurs rex's ilia are tightly oppressed, almost to a point where
the sacral neural spines are crushed, more than any other theropod; meaning
large muscles. Giganotosaurus doesn't have this. The cnemial crest on the
tibia is HUGE. If the animal didn't move fast why have such a huge cnemial
crest?

We accomodated all of these anatomical features in the model.  The "huge" cnemial crest is merely proportional to the animal's size.  It helps create a large knee extensor moment, but our models show that it was not enough for 20m/s.


 A chicken is not a T. rex. A chicken's body is totally different. The femur
articulation is totally different. The femoral head is nearly at a right
angle to the tibia in a chicken while in a theropods is nearly vertical,
I've said this before and should be some where in the archives. Birds and
dinosaurs walk differently, and differently with their muscles. Did the
authors just ASSUME birds and theropods walked the same? You can't assume
they did because the skeletal structure is different. Greg Paul and Per
Christian have an article in the theropod Gaia volume on the leg movement in
Tyrannosaurus. Was this article mentioned?

Yes, the articles were mentioned.  Read the paper.  And I am more aware than most researchers about the similarities and differences between chickens and tyrannosaurs.  That was all considered in the paper, and is actually one of the points of the paper.  And I have published long arguments about that point in several papers.  It is a foundation of my work that tyrannosaurs were different from living animals.  So we used a model in order to understand them better.


I'll have to wait till next week when I get the article. I doubt the paper
is all that accurate in depicting the behavior of Tyrannosaurus rex.


We think we did a good job, but anyone is free to disagree with us if they have evidence that is relevant.


Tracy L. Ford
P. O. Box 1171
Poway Ca  92074

Date: Wed, 27 Feb 2002 20:12:59 -0700 (MST)
From: Richard W Travsky <rtravsky@uwyo.edu>
To: dinosaur@usc.edu
Subject: RE: New Nature paper on Tyrannosaur Locomotion
Message-ID: <Pine.GSO.4.10.10202272012250.17648-100000@asuwlink.uwyo.edu>
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Ok, so what about other large carnivores?


We have only modeled a few larger things so far., It's part of the plan for later work, but the clear conclusion is that they had similar limits on their locomotion, for similar reasons.


Date: Wed, 27 Feb 2002 22:28:20 -0500
From: "Jordan Mallon" <j_mallon@hotmail.com>
To: dinosaur@usc.edu, vrtpaleo@usc.edu
Subject: Big Theropod Running
Message-ID: <F3li5MRaBC3T9cVHK2F0001ac14@hotmail.com>
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G'day all,

I was wondering...
With all these papers coming to light on the subject of big theropod speed these days (Farlow's analysis comes to mind, along with those of Blanco and Mazzetta, R. McNeil Alexander, and Hutchinson and Garcia's most recent), which of these are considered to be most accurate?  I understand that different approaches have been taken in each case, but are any one of these studies considered to be better or more valid than the others?
Just curious.

Jordan Mallon

http://www.geocities.com/paleoportfolio/

BTW: there's a great supplement to Hutchinson and Garcia's latest paper in Nature here: http://tam.cornell.edu/students/garcia/.trex_www/naturepaper.html

_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp.

Thanks.  Blanco and Mazzetta's paper lacks enough data to evaluate their work in any way, so I'm waiting to see data.  Farlow's, Alexander's etc. modeling is wonderfully complementary to our paper.  To my mind, the available biomechanical evidence is in agreement.




Date: Wed, 27 Feb 2002 22:13:36 -0600
From: "Toby White" <mwhite@houston.rr.com>
To: <dino.hunter@cox.net>, "'Dinonet \(E-mail\)'" <dinosaur@usc.edu>
Subject: RE: New Tyrannosaurus paper
Message-ID: <000001c1c00e$4bb65440$9b191942@houston.rr.com>
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Tracy:

Hutchison has gone into the differences in locomotion between birds and
more basal theropods in huge detail in previous papers.  A few are cited
below.  I don't pretend to understand all of it, but its fairly safe to
assume that this is not a mistake he'd make. 

>From the newspaper accounts, it also doesn't look like the detailed
mechanics have much to do with the result here. Its just a matter of the
energetics of moving a body of that size over the ground.  How the
pieces fit together won't have much effect on the muscle mass needed to
do the job.


The mechanics have everything to do with the result; that's biomechanics.  Or if you mean the anatomy, that's in there too.  What was necessary to include was included.  What was irrelevant was excluded.  Later models will become more realistic.  We chose to start simple and move from there.


That said, you may have a point about the ilia.  If (big if) I remember
Hutchison's papers well enough, that would mean a big caudofemoralis.
Having much of the muscle mass for the legs actually reside along the
hip and base of the tail might allow the dinosaur to cheat a bit on any
assumption that the leg muscles must be in the leg.



We considered the caudofemoralis in all of our models; it is crucial.



The cnemial crest may be more problematic.  I dunno exactly what the
crest was used for in non-avian dinosaurs, but one might suspect that it
is related to an ability to swing the lower leg through a wide arc
*without* moving the femur so much. That's the way it gets used in, for
example, loons.  Now a real bipedal sprinter might not need that
mechanism. Its got time in the air to move the tibia, and it's pumping
the femur up and down for all it's worth in order to get speed at the
expense of efficiency.  The more likely conclusion might be that the
tyrannosaur was either adapted for long-distance efficiency or to make
the most of stride length in a fast walk.


The cnemial crest provides a larger moment arm (compared to lacking a cnemial crest) for the knee extensors ("quadriceps").  Large moment arms are good for producing large moments about joints, but not so good for producing high joint velocities.




Date: Thu, 28 Feb 2002 00:20:24 EST
From: MariusRomanus@aol.com
To: dinosaur@usc.edu
Subject: Re: New Nature paper on Tyrannosaur Locomotion
Message-ID: <47.18f0b558.29af1818@aol.com>
MIME-Version: 1.0
Content-Type: multipart/alternative; boundary="part1_47.18f0b558.29af1818_boundary"

Ok..... This is really interesting.... BUT... we are doing the math based on the wrong assumptions again. Here, we are saying that theropods ran like birds and mammals. They ran like neither. They ran like theropods. Why is this fact usually shoved under the carpet and the couch moved over it?


It is not.  We say nothing of the sort in the paper.  I don't know why I keep hearing comments like this.  People are deeply misunderstanding what we do in the paper.  Please read it carefully.


 Never mind that we are talking about a combination of crocodilian hips coupled with an avian lower leg that no longer exists in modern animals, but you have a huge ilium that gives great leverage. You have the crocodilian pull of the tail.... The get up and go bit..... This pulls it off its mark and gets it going. The caudofemoralis... it's huge in tyrannosaurs. It's tiny in birds. Bird locomotion is thus all in the knees. And mammals? Mammals have both the knee as well as the lumbar. The â??arch-range of motion' of the femur is increased by the lumbar region as it acts as a sort of spring. The shoulder region in mammals also acts as their spring. This â??arch-range of motion' is rare in bird femurs most of the time in the first place, and never seen aided by a moving lumbar region because their dorsal vertabrae are fused. We all know this. In birds, their spring is in the cnemial tendons. Only when the pectoral region grows larger to help power the flight muscles do we see the increased lower limbs in birds and this is most likely because of weight. With all the weight forwards the body in birds, they needed to move the gut back to displace some weight. This spreading of both the distal symphysis of the ischia and pubis, as well as flare in the ilium in a lateral manner of birds, put the femur at a disadvantage mechanically. So, the only way birds could make up for this was to select for moving the motion of the femur that was once a prime mover of the rear limb to the knee. They did this by elongating the tibia as well as the metatarsal elements. In this way it helped also to balance the animal as well by being able to keep its feet further forward when standing... I'm going offf on a tangent....... Someone smack me...

Smack.  None of these criticisms matter much for the paper.  It is not so complicated that these things would matter, but it is complicated enough that their general importance is captured in the mathematics.


So anyway, non-avian theropods use the entire leg...... They use their femur to make up for the difference. Their caudofemoralis. Leg length.... Foot prints.... Everything shows this. Yes, the study definitely showed that they walked fast.... Tyrannosaurs were speed walkers... Works for me... BUT... they still could also take off from the ground as well... They still had a "ballistic phase". It's all the knee cartilage and tendon spring.  In birds, its the cnemial tendons. In theropods, you have the cnemial tendons and lots of cartilage as well. And by the way, crocodilians are slow??? I guess the footage of "galloping" crocodiles must be more of that Lucasfilm movie magic....


Again, we know this.  Read the paper.  Knee cartilage?  I don't know of a study that shows that it is a major part of elastic energy storage.

We are very aware of galloping crocs.  However, what we modeled, as you'll see if you read the paper, is bipedal running in an alligator.  They do not do that, to my knowledge, and our model shows part of the explanation:  wimpy leg muscles.


Face it... Bumble bees would not have been able to fly if we had not seen them do so. That made the people go back over and over to get their math right so they didn't have to say "I did the math and they can't do it."

Again, just because science can be wrong doesn't mean that it is wrong when you don't like the results.  Hypotheses are tested and either fail or prevail.  We're comfortable with either outcome, as long as science is done.


It's like a friend of mine says... How about the vaulted palate in birds? In most animals, we would have thought anything without a secondary palate was an ectotherm. But, birds do not have in most cases anything like a secondary palate. So, if we had only theropods, a lack of the secondary palate would have been proof positive that they were cold blooded. It would have been wrong, yet proof positive.

Things work like this..... As I see it, if we do not have an example these days to go by, and we cannot make it work with clever math, then, it ain't so...... You know, even when we still cannot figure out how in the hell whales can dive so deep...... And we are only now starting to maybe figure how tuna swim so fast. All the math says they cannot swim as fast as they do.... If they were extinct, that case would have been closed. To make this even funnier, here we are comparing theropods to animals that look nothing like them and drawing conclusions for them based on the math we use on these animals that look nothing like them. Ok...... Sure..... Yeah.... crocs that are alive today look so much like theropods.... Yup... that is soooooo true.  ::rolling eyes:: And chickens...... closer to theropods, but still greatly changed. I mean face it.... Chickens are built for chicken sized lives.... Not theropods..... as in mega theropods. Chicken femurs articulate with the tibia different then tyrannosaur femurs.... Chicken femurs move in the vertical. Theropod femurs more more in the horizontal. The locomotion is completely different in the two animals. Tyrannosaurus are very close in build to ornithomimids. I mean, they look the same but have more robust bones. Maybe those are the animals we should be comparing tyrannosaurs too???? Paul's 1988 book comes to mind.

This is all missing the point of the research.  Anatomy matters a lot, but so does physics.  The best we can do is try to evaluate their importance using scientific methods.


After reading the paper, (I'll send it to anyone who doesn't want to wait for their issue to arrive at the house) as far as I can tell, this study left out the elasticity of cartilage and tendons. I look at it this way... A friend pointed out to me that whales could not swim without their skin. If it did not bounce back, all their energy would be lost at a huge rate. The skin is very tight.. made up of a web stock of connective tissue. When the whale makes a tail stroke, its power is not lost. It bounces back and is saved. This is one way that an animal that huge with the metabolic make-up of the average cow can swim so damn fast. Birds use their tendons and cartilage like whales use their skin. It's like a pogo stick effect. They tighten the tendons and sort of bounce. It's more of a falling forwards and just holding themselves from falling over. Bounce.... bounce...... bounce.... If this is not put into calculations correctly, you are completely lost. You loose all your energy at a very fast rate, and ya blame it on the lack of muscles. :-) Poor math is always there to help people prove that an animal cannot do what it does 24 hours a day.


I don't have time to mull over rhetorical arguments like this.  If a revised model shows that any factors that we did or did not consider in the model  falsify our results, then fine.  That's science.  But for now, we feel that the models adequately capture the mechanics of locomotion.  We study animal biomechanics extensively, and biomechanists who know the animals and the mechanics tend to agree with our results.  We may all be wrong, but at least we made our arguments explicit and testable.  I see no hypothesis testing in your comments above; just smokescreens.


My conclusion:

Fr  = (velocity)^2/(hip height x g)..... As far as I am concerned, the formula is really no good for theropods. It is again, based on mammals with their lumbar region moving and birds with motion mostly from the knee. Theropods need to be measured as living animals to see if they actually fit the formula. I mean, most of the mammals as well as birds that run go from the knee down. Theropods do not in any way fit this. They are femur and knee. And what about measuring how the caudofemoralis fits in, as well as how the femur works without the flaring of the ilia? And what about how the muscles of the pubic bone fit in as well? In birds, they are separated distally, and are thus no good for moving the femur at all. But in theropods like the rex? Talk about having a nuclear generator. All of these things have to be added in. Tail muscles.... Iliac muscles... Pubic muscles... All going to the femur. Then in comes the flexed knee. The monsterous cnemial crest on the tibia. The flexible ankle. Then comes in the bouncy tendons as well as cartilage.


Show that the formula is wrong in a paper, and it would be an interesting contribution.  Part of what we do in the paper is treat theropods as living animals; we do not force them into a strict bird, crocodile, or other model.


Looks like I'm going to have to break out the Ouija board and ask Capt. Howdy for the location of a _Tyrannosaurus rex_ trackway that will show it's stride and maybe even its speed.  In my humble opinion, that's the best we can hope for.

Kris


I agree.  Trackways will always be an important source of data that should be compared to other independent lines of evidence to see what hypotheses hold up best.





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John R Hutchinson
NSF Postdoctoral Research Fellow
Stanford University
Durand 209, BME
Stanford, CA 94305-4038
(650) 736-0804 lab
(415) 871-6437 cell
(650) 725-1587 fax
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