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Env Sci, Clark Hall Uva, Ch'ville Va 22903,804-924-0532
10-26-1990, 10:57 PM
To : ELERCAMA@HEITUE5.Bitnet

Dr. Herman J. Woltring
Moderator, Biomch-L

Dear Dr. Woltring,

Your reply to my sign-off request included the following
statement :

While the Mechanics of Tropical Trees is, indeed, a rather
esoteric subject on Biomch-L, it definitely belongs to the
scope of Biomechanics; I seem to recall a related paper in
the Journal of Biomechanics of some years ago.......

I received the following e-mail at about the same time I
received your reply.

From: GBINGHAM@IUBACS.Bitnet
Subject: mechanics of tropical trees

I caught your message on the Biomch-L net.
I am currently engaged in a study of the visual
perception of trees, a study that involves the use
of McMahon's work on scaling branch diameter to
length. I have been in touch with
Rolf Borchert and Brayton Wilson and receive
very kind assistance from them. I have not
seen much in the literature extending McMahon's
original work (1976) and I wonder whether you
are aware of any and in particular, whether you
are involved in relevant work?

Sincerely,
Geoffrey Bingham

Given these encouragement, I have decided
NOT to sign-off from BIOMCH-L.

I have also included (appended) my reply to Geoffrey just
in case others find biomechanics of plants interesting.

Although the majority of BIOMCH-Lers deals
with animal/medical physiology or
with sports medicine and the like,
we may have some data, methods, problems, literature, etc.
in common. Finding out how others solve similar problems
can be very helpful at times.

Thank you very much for your reply and encouragement.

Sincerely,

Faustino A. Daria, Jr.
================================================== ==============
From: "FAUSTINO A. DARIA, JR. (SONNY)"


Subject: VISUAL PERCEPTION OF TREES
BIOMECHANICS OF TREES
To: GBINGHAM@IUBACS.Bitnet


===========================================
I am currently engaged in a study of
the visual perception of trees,
a study that involves the use of
McMahon's work on scaling
branch diameter to length ....

I have not seen much in the literature
extending McMahon's original work (1976) ...
============================================


I am so pleased to know another Homo sapiens find
tree biomechanics/architecture also interesting.

(For some time, I thought there was something
"wrong" with me or my research topic since very
few people seemed to find such topic interesting.
Your e-mail was a great encouragement.)

A. McMAHON, T. A.

I am not aware of any other article by Dr.
McMahon on the same topic; I found his 1983
book very helpful in understanding the principle
of elastic similarity.

McMachon, T. A. and J. T. Bonner. 1983.
On size and life. W. H. Freeman and Co.:
New York. (QH 351 .M34)

There are so mnay interesting statements in said
book that will interest researchers :

A tree without its leaves makes a fairly
satisfactory tuning fork ..... (p. 146)

A tree is a fixed, standing structure, but it
must be mechanically clever enough to spring
back when the wind disturbs it, and must not
buckle under its own weight. (p. 140)

Our colleagues (physiologists / sports medicine
practitioners) will easily recall pictures of
decalcified bones resembling rubber materials.
Such bones allow some bending and twisting but
will 'spring back' when the pressure is removed.

I'm not an orthopaedic researcher but I can imagine
that there have been many studies on remedies to
bone fractures. Instead of temporary immobilization
of the fractured part (to allow the bone to 'heal'),
researches must have considered a number of substances
which could be injected into the fractured bone region
so that the 'bone' will be firm enough under ordinary
circumstances, butelastic enough under extraordinary
circumstances. Researchers would have considered at
least two requirements :

a) SAFETY
The substance should be immunologically 'inert',
i.e., will not trigger an immune response leading
to its rejecion.

b) EFFECTIVITY
The substance should be superior to the normal
or usual healing process ; Such substance should
offer additional advantages: e.g., shorter healing
time, superior strength, possibility of replacement
with natural bone materials later on, and elas-
ticity (bending and twisting within reasonable
limits under extraordinary circumstances.)

So much for bones and elasticity of which I have only
scant information.

Many people find Horn's book (on the adaptive geometry
of trees) very informative. Students who have used the
two programs (CURETREE AND REALTREE) have gained a
deeper understanding of tree geometry (branch order,
branching angle, etc.) I enjoyed using those two
programs based on fractal geometry.

A number of books and articles on fractal geometry
have been published since then which included figures/
pictures of trees, and even forested landscapes
'created' using IFS.

I have considered using fractal geometry in forest
ecosystems modeling, but unfortunately, I am not
equal to the task.

MANY OF OUR FELLOW BIOMCH-L SUBSCRIBERS ARE NOT INTERESTED
IN TREE GEOMETRY BUT MAY BE INTERESTED IN FRACTAL GEOMETRY.

I'D LIKE TO KNOW IF ANY ONE HAS USED FRACTAL GEOMETRY TO
CREATE IMAGES OF SKELETONS OR CONTOURS OF MUSCULAR TISSUES.


B. NORBERG, R.A.

R. A. Norberg has two articles which you might find
interesting :

Norberg, R. Ake. 1988. Self-thinning of
plant populations directed by packing density
and individual growth geometry and relation-
ships between animal population density and
body-mass governed by metabolic rates. in
Eberman, Bo and Lennart Person (eds.) Size-
structured populations: ecology and evolution.
Springer-Verlag: Berlin. (QH 352. S59)

Norberg, R. Ake. 1988. Theory of growth
geometry of plants and self-thinning of plant
populations: geometry, similarity, elastic
similarity, and different growth modes of
plant parts. Am. Natur. 131 : 220 -256.

===========================================
I have been in touch with
Rolf Borchert and Brayton Wilson and
receive very kind assistance from them.
===========================================

Pardon my ignorance, Geoffrey : Kindly provide
me some information about these two gentlemen and
how I could get in touch with them.


************************************************** ****


===========================================

I'd like to share with you some information
about my research interests.

===========================================

Last summer, I tried relating biomechanics of trees to
variables such as

diameter breast height
height

in the hope that, ultimately, I could arrive at
functions relating biomechanics to

growth rate
mortality rate
recruitment/regeneration rate


I spent quite some time studying the buckling line
of big trees of the United States. (see McMahon,
T.A. 1973. Science 179 : 1201 - 1204)

(I also explored the nature of the buckling of
record trees of Virginia.)

There were some problems with this approach :

1. The record tree of a particular species
is not representative of the species.

2. Biomechanical data for a number of species
is not available. (Apparently, availability
of biomechanics data is somehow related to
the commercial value of the tree species.
I could be wrong in my view that the Forest
Products Laboratory (USFS-USDA) seems to
have more biomechanics data on commercially
important trees. This is understandable
from an economic point of view -- generating
biomechanics data is a time-consuming and
expensive activity.)

3. biomechanical properties (e.g., modulus of
elasticity) are related to specific gravity
(relative density) of the wood. The specific
gravity of wood is affected by site charac-
teristics. Within the same species, it varies
with age of the tree. Within the same tree,
different parts have varying specific gravity
values. The value for the upper part of the
bole (stem) is different from that of the lower
part. Likewise, the value of the outer part
(near the bark) is different from that of the
inner part.

Given more time, one could figure out a way of modeling
trees (individual, stand or the whole forest) based on
biomechanical data. Unfortunately, the life of the
forest ecosystems modeler (dealing with problematic
biomechanical data) is finite.

Your suggestion on this matter will be greatly
appreciated.

In your next e-mail, kindly include your address
and phone number.

Yours truly,

FAUSTINO A. DARIA, JR. (SONNY)