Tree
Trunk Asymmetry 
Edward
Frank 
Feb
15, 2006 14:46 PST 
Bob,
You have made a couple of recent posts concerning the asymmetry
of tree
trunks. What kinds of things could be looked at in this
context/? How
asymmetrical are individual trees? Do some species tend to have
more
asymmetrical trunks than others? Does the degree of asymmetry
vary with
age/ What about other factors like stand density? Height to
diamter ratio?
Is the asymmetry oriented in a preferred direction  north/south
or
upslope/downslope? Tree canopies are often asymmetrical. Does
the
asymmetry of the trunk relate to the asymmetry of the crown? Are
the trees
equally assymetircal along their entire height? How does asymmetry
vary
through time (you could measure cookies to determine this one)
There are
lots of potential things to measure...
Ed 
Re:
Lowes & Cannon Creeks, GSMNP, TN 
foresto@npgcable.com 
Feb
15, 2006 22:23 PST 
Ed
One way to look at this issue is to assume that in the East,
barring
broadscale windevents and other climatological extremes, a
forest grows one
tree at a time...as one senesces (from whatever
cause/disturbance), another
one has an opportunity to fill the void, fresh exposed rich
soil, new dose of
sunlight, to the victor seed goes the spoils (space).
Where that seed that grows most successfully falls, determines
its 'space' and
its space determines how the tree fills it. Seed fall may
approximate random
chance, but seed germination/growth success, probably doesn't.
Topography,
aspect affect solar incidence angle (warmth, energy) and tipover
mound
microtopography probably has significant impact on success.
Once the tree roars up into its space, its neighbors constantly
remind it of
its space constraints, as they 'wear' at each other.
Asymmetry should be expected, and the lack of it cause
surprise...
Don

Out
of round  Jess, Will, Lee, others, HELP! 
Robert
Leverett 
Mar
06, 2006 07:55 PST 
Will, Jess, et al:
On Saturday, I started yet another measuring
project  to gather
data on how out of round tree trunks and limbs are at least as
as a
broad average. For the only four measurements I took, on
sections of
what was a round looking red oak that had been cut, I got an
outofround percentage of 7.8%. this was based on two
measurements
taken per cut at right angles to each other.
It occurs to me that we have on this list a
vast reservoir of
experience that could be tapped that would require just a few
measurements, say 25, from study participants. The foresters and
arborists among us have a collective experience looking at cuts
of
trunks and limbs that is awesome to behold. We could build a
simple
spreadsheet of the measurements using something like the
following data
elements:
Species
Trunk or Limb
First diameter
Second diameter
Approximate height of measurements above base
Since most of what we measure will be stumps
or the ends of limb of
trees that have been cut, we won't always be able to determine
how for
above the ground a measurement represents. That's why the
"approximate"
above.
I'm unsure of what we can do with the
information, once gathered, but
I think most of us would like to have a handy dandy factor in
our heads
that sheds light on the average outofround state of trunks and
limbs.
BVP may already have this.
What do you all think? I've never seen any
stats on this. Maybe they
already exist. Inquiring minds want to know.
Bob
Robert T. Leverett

RE:
Out of round  Jess, Will, Lee, others, HELP! 
Don
Bragg 
Mar
07, 2006 05:11 PST 
Bob
You may want to get a copy of the most recent Central Hardwood
Meeting
Proceedings when it is released (this meeting took place last
week in
Knoxville, and I would guess the proceedings will be published
in a few
months). I attended a talk by a forest products guy who was
looking at
the impacts of log ellipiticality on sawlog yield, and found
some pretty
interest results. The authors name was Bond, and his talk title
was:
"The Occurrence of Log Ellipticality in Hardwoods and Its
Impact on
Lumber Value and Volume Recovery". They used both calipers
and digital
photographs analyzed in the lab to look at the ellipticality of
the cut
end of logs in a millyard, but had no way of knowing the exact
site or
stand conditions these trees were growing in. It did get me
thinking
about how elliptical (or simply misshapen) the trees are in our
neck
of the woods, so I would be happy to contribute a sample of tree
measurements (probably from loblolly pine, shortleaf pine,
sweetgum, and
white oak) from south Arkansas, if I knew exactly what was
desired.
Don Bragg

Re:
Rd 1000 vs Macroscope 25 
Don
Bertolette 
Mar
09, 2006 02:22 PST 
Bob
Would this be why you're also trying to quantify
"roundness" or its
absence? From a forester's perspective, estimates are made of
minimum and
maximum "width", most empirically measured with
calipers (a mechanical
'equivalent' of the measurement that your Macroscope 25
makes)...think
springloaded caliper that measures min/max as you 'walk' the
calipers
around the bole...unfortunately, 'walking' the Macrospope 25
around the bole
describes a path 100 plus feet away, in terrain that usually
conspires to
prevent successful passage...
Back to the 'out of roundness' thing...since circumference and
diameter of
out of round trees are by definition averages, would the
solution to
recording their measure involve min/max pairing?
Don

RE:
Rd 1000 vs Macroscope 25 
Robert
Leverett 
Mar
09, 2006 08:21 PST 
Don,
The quantification of "roundness"
began as a move to improve the
accuracy of our trunk and limb volume modeling Will's, Jess's
and my
current obsession. But for me, outofround has gained ground as
a
separate interest, standing on its own.
As a consequence of a discussion we once had,
I posed a question to
myself: how does the cross sectional area of a trunk treated as
an
ellipse relate to the circular cross sectional area derived by
averaging
the semiminor and semimajor axes of the ellipse? Here the
major axis
is taken as the greatest width of the trunk and the minor axis
as the
width of the trunk taken at right angles to the greatest width
(so it
isn't necessarily the minimum width of the trunk). I realize
that
averaging the greatest width with the width taken at right
angles isn't
the same as calculating an average diameter derived from many
diameters,
or at least more than two. But I also recognize that I would
seldom do
the latter. That's a little too much measuring.
But, back to the first problem,
Let
A = cross sectional
area of the trunk as calculated by a formula
based on either the circle or ellipse
a = larger diameter/2
(treated as radius of a circle or
semimajor axis of an ellipse)
b = trunk diameter/2
(taken at right angles to larger diameter
and treated as radius or semimajor axis)
c = b/a
pi = 3.141593.....
Then
A = pi(ab) = area of
ellipse of semiminor and semimajor axes b
and a. This calculation has been our alternative to a circular
cross
sectional area on some of our modelings.
By definition of b and a,
pi(b^2)
<= pi(ab) <= pi(a^2)
Note that pi(b^2) is the circle inscribed in
the ellipse and pi(a^2)
is the circumscribed circle. Diagrams make the above
inequalities
apparent.
Now, if the average cross circular area of the
trunk is calculated as
pi((a+b)/2)^2, the question is how does this latter area relate
to the
elliptical area pi(ab) as the ellipse approaches the circle,
i.e. as b
tends to a? Is the ellipse's area sometimes smaller, sometimes
equal,
and sometimes larger depending on the value of c? Stated as a
mathematical inequality of unknown direction or sense,
pi(ab) ?
pi((a+b)/2)^2 where ? denotes the determination to be
made. Substituting b = ca and simplifying gives
pi(ca^2) ?
pi((a+ca)/2)^2
pi(ca^2) ?
pi(a^2+ 2ca^2+c^2a^2)/4
4pi(ca^2)
? a^2pi(1+2c+c^2)
4c ?
1+2c+c^2
The left side of the last inequality remains
less than the right side
until c = 1, at which point the sides become equal denoting
circularity.
All this shows is that the area of the ellipse of semimajor and
semiminor axes a and b remains smaller than the corresponding
circle of
radius (a+b)/2. I imagine that if I had waded through the
mathematical
discussions of ellipses found in any standard text on analytic
geometry,
I would have found a more elegant proof of the above.
If the cross sectional area of a trunk is
actually elliptical, then
pi(ab) is its area. If not, then what? Having looked at far few
stumps
than foresters and arborists on our list, I don't have a real
sense of
how appropriate the elliptical option is. Taking two diameters
at right
angles to on another and finding that they are not equal does
not prove
the shape is actually elliptical, nor does it prove that an
elliptical
cross sectional area is closer than a circular with an averaged
diameter. Outofround can lead to endless variations on the
circle and
ellipse theme and to other geometrical hybrids. Is it worth the
effort
to gain a half percent in accuracy? The challenge is to find the
an
acceptable methodology to improve our accuracy without
committing
ourselves to a lifetime of measuring one tree. Obsessed Ents
want a
solution.
One final point. The perimeter of an ellipse
can be approximated from
the formula:
P =
pi(3(a+b)[(3a+b)(a+3b)]^(1/2).
As a test of trunk ellipticality (or the
appropriateness of a
particular ellipse as the model of cross sectional area), trunk
widths
could be taken at right angles to one another, halved and run
through
the above formula and the result compared to a measured
perimeter using
a tape measure. If they come close, one could use the ellipse,
if not
then ???
Bob

RE:
Rd 1000 vs Macroscope 25 
Robert
Leverett 
Mar
10, 2006 06:23 PST 
Don,
You've identified the supreme challenge we
face  the changing shape
of the trunk. I hope that we can find a solution that does not
make
modeling each tree a lifetime career.
I've added 6 more measurements to the RD 1000
vs Macroscope 25
comparison. They are very large or small objects at great
distance. The
average difference now stands at 1.22 inches. It would drop back
a
little were I to include smaller trees at close distance.
Bob
Don Bertolette wrote:

Bob
Very well explained, I actually followed your 'theorems'
for the most
part...my thoughts then went to growth models, and the
reality that the
tree's crosssection, whether it be an ellipse or other
geometric
variation,
will vary as you go up and down any given tree, in
'direction' and
dimension...
DonB


