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Fwd: Re: DINOSAUR digest 2038

Missed one message; here it is (forwarded with permission).  My answer 
is below.

----- Forwarded message from Mike Taylor <mike@tecc.co.uk> -----
From: Mike Taylor <mike@tecc.co.uk>
To: jrhutch@Stanford.EDU
Subject: Re: DINOSAUR digest 2038
Date: Mon, 4 Mar 2002 17:14:27 GMT

> Date: Fri, 01 Mar 2002 10:17:16 -0800
> From: John R Hutchinson <jrhutch@stanford.edu>
> Elastic structures: Think this one over a bit more.  Can a tendon
> experience more force than the muscle attached to it?  We model
> muscle forces.  Muscles are connected to tendons.


Thanks for your kind words about my previous dumb question.  One more
on tendons: surely the point of your paper was not to do with how much
force the leg muscles can _sustain_ before tearing, but how much they
can actively _exert_?  Isn't the idea of the tendons-are-important
brigade, then, the the tendons store rather then exert force, and that
the limit of what they can store is the same as that of what they can

Again I freely admit I don't have the mechanics background to
understand this, but isn't the optimistic see-rex-run model something
lik this: as it takes each step, the foot it's putting down bends,
storing elastic energy in the tendons; then as its centre of mass
moves forward past that point, the foot unfolds and the released
elastic energy helps to propel the body forwards.

Again, thanks for taking the time to address so many of the "yes, but"
points that have been made on the DML.  I've sent this message to you
directly in case it's too stupid for general consumption :-)  But if
you happen to think it's a remotely intelligent question, do feel free
to reply on-list, quoting any parts of my question you like.

Thanks once more,

 _/|_    _______________________________________________________________
/o ) \/  Mike Taylor   <mike@miketaylor.org.uk>   www.miketaylor.org.uk
)_v__/\  Ich spreche nicht Deutsch, ausgenommen diesen Satz.

----- End forwarded message -----

My (John) response:

Not at all dumb questions; the questions on the list in general have 
been very pertinent and creative.  I truly have been having fun.

My answer would be that the elastic structures are important for saving 
energy (restoring "lost" kinetic and potential energy) but are only 
experiencing the same forces as their muscles, and so do not change the 
moments in the model or our results.  Tendons do experience relatively 
higher stresses than their muscles, because stress = force/area, force 
is the same, but tendons are narrower.  Luckily tendons are stronger in 
tension than muscles by many times, and thus they rarely rupture along 
their length (usually at avulsion sites at attachment entheses to bone) 
unless high heat/friction is experienced.  An analysis of tendon 
strength is forthcoming.  Generally, my view is that the muscles will 
fail before the tendons or bones in typical steady-state conditions, 
although there are exceptions to that.

Your question about the consequences of muscle "failure" in my model 
are good ones and others have asked them too.  What would happen if the 
muscle moments were not as high as the GRF moments is hard to predict 
exactly.  The muscles could be strained, the joints could rapidly 
accelerate in the wrong direction, the limb could collapse or stumble, 
or everything could explode, depending on the dynamics which are hard 
to predict.  Bottom line is that it would be bad if somehow a 
tyrannosaur reached that speed (stumbling down a hill?), and the model 
shows that it is unlikely that a large tyrannosaur's muscles could 
achieve it.

My last message to the list got truncated (damn tab key in webmail!) 
but it was almost over anyway.  The last point I wanted to make is 
about speeds.  25mph is pretty fast and like I've said before, my 
models do not conclusively rule it out.  Some people, however, have 
before suggested that a tyrannosaur could walk at 25mph.  I would 
definitely disagree with that. 10mph might be quite possible for 
walking but not 25mph.  At 25 mph (Froude ~5), even though Froude 
numbers are not perfectly precise, I cannot imagine how a tyrannosaur 
could have one foot on the ground at all times, or be moving like an 
inverted pendulum.   25mph or 11 m/s with a stride frequency of 2 Hz (2 
strides/sec... really fast and probably an overestimate) means strides 
of 5.5m; hard for an animal with at most a 3m hip height to achieve, I 
think, without at least a brief aerial phase or spring-mass kinetics 
(i.e., running).

OK, I will reply to messages more sporadically now if at all (must 
focus on work), but it's been a good experience for me talking with you 
nice folks about the paper.