Tree Trunk Asymmetry   Edward Frank
  Feb 15, 2006 14:46 PST 


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...

Re: Lowes & Cannon Creeks, GSMNP, TN
  Feb 15, 2006 22:23 PST 

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 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...
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
out-of-round 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

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"

   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 out-of-round 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.


Robert T. Leverett
RE: Out of round - Jess, Will, Lee, others, HELP!   Don Bragg
  Mar 07, 2006 05:11 PST 


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 

Would this be why you're also trying to quantify "round-ness" 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
spring-loaded 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?
RE: Rd 1000 vs Macroscope 25   Robert Leverett
  Mar 09, 2006 08:21 PST 


   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, out-of-round 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 semi-minor and semi-major 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,

       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
semi-major axis of an ellipse)
       b = trunk diameter/2 (taken at right angles to larger diameter
and treated as radius or semi-major axis)   
       c = b/a
       pi = 3.141593.....


       A = pi(ab) = area of ellipse of semi-minor and semi-major 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

   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 semi-major and
semi-minor 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. Out-of-round 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

   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 ???


RE: Rd 1000 vs Macroscope 25   Robert Leverett
  Mar 10, 2006 06:23 PST 


   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.


Don Bertolette wrote:
Very well explained, I actually followed your 'theorems' for the most thoughts then went to growth models, and the reality that the
tree's cross-section, whether it be an ellipse or other geometric
will vary as you go up and down any given tree, in 'direction' and