Dendromorphometry    Robert Leverett
   Apr 07, 2006 06:43 PDT 


   For those on the list who shy away from our discussions of tree
mathematics, you might not want to read this post - then again, you
might, at least for information purposes - especially the newcomers to
the list. Will Blozan, Jess Riddle, John Eichholz, and myself have
finally decided (more or less) to embark upon the perilous journey of
writing a guide book to simple and intermediate tree mathematcis. I'm
sure Ed Frank will be involved. Such an ENTS undertaking without Ed's
participation is unthinkable. I expect a few others to sign on.

   We will probably title the book something like "Dendromorphometry
-the Science of Measuring Trees". Hopefully, some of the big guns on
ENTS will join us, or at least review the work as it proceeds. The big
guns of whom I speak are the stellar PhD scientists on the list, i.e.
Drs. Bob Van Pelt, Lee Frelick, Don Bragg, Tom Diggins, Larry Winship,
Dave Orwig, John Okeefe, Roman Dial, etc. There are other potential big
guns, but we don't often hear from them. So I'm including only those who
post and/or who I know.

   There are many topics that need to be included in the planned book.
Obviously, the ENTS-engineered methods for measuring tree height, crown
spread, and trunk volumes would be included. A full discussion of other
common tree-measuring techniques would also be included with pros and
cons provided for each method. We would discuss which shortcuts work and
which ones don't. An appendix would provide a review of the geometry and
trigonometry that we commonly use to include derivations of some of the
formulas that we use. We would provide a review of the accuracy of the
instruments that we use and how to get the most out of each type. There
would be lots of pictures and diagrams.

    Folks, this is a work that needs to be done. There is so much stuff
out there in the way of measuring and calculating techniques that make
hidden, simplifying assumptions about trees that are just not fulfilled
much of the time. For example, I was looking at the internet, searching
for cross-sectional area determinations and found the following. I omit
the referenced table.

Cross-sectional Areas of Trees
Dr. Kim D. Coder
The University of Georgia

December 1996

Many tree appraisal, measurement, and structural mechanics systems
require cross-sectional areas at some given height or point along a stem
or branch for completing calculations. Table 1 presents these
cross-sectional areas in square feet and square inches across whole-inch
diameters from 1 to 75.
Values were determined by:

Cross-sectional area (square inches) = 0.785 DIAMETER^2
Cross-sectional area (square feet) = (0.785 DIAMETER^2) / 144


 Those who live and breath tree dimensions and formulas, will quickly
recognize that the 0.785 factor comes from the area of a circle formula:

    A = PI * D^2/4   where PI = 3.141593 and PI/4 = 0.785.

   So what's my point? The assumption being made is that the
cross-sectional area of the trunk at the point of interest is that of a
circle. So, all that the user of this method gains is the division
3.141593/4 being reduced to the constant 0.785. The table that
accompanies the formula gives the cross-sectional area for diameters of
1 to 125 inches.

   This simplified formula and accompanying table is an example of one
of the shortcuts I alluded to, but in the age of electronic calculators
and computers, it is hardly needed. What IS needed is a better way to
determine the cross-sectional area of a tree when it isn't circular or
almost circular. Making the assumption of circularity is something we
all do, but there are times when we clearly shouldn't. And our
distinguished president of ENTS, Will Blozan, has risen magnificently to
meet that challenge. Will and associates have engineered a method by
where they climb the tree to the offending trunk section. These pesky
trunk sections, often where fused trunks part company, simply refuse to
act like a self-respecting cylinders and challengingly stick their
tongues out at Will. Honest, folks, I've seen it happen. Will then
encloses the trunk with sticks that form an enclosing a rectangular box.
He then measures distances from the rectangular frame to the trunk. We
then enter his offsets into an Excel spreadsheet and use a series of
trapezoids to calculate the blank space. We arrive at a pretty accurate
cross-sectional area of the trunk at that point.

   Now who, but thoroughly obsessed Ents, would go to so much trouble to
measure the cross-sectional area of a tree trunk? But, alas, we can't
help ourselves. We must do it. It is our calling. So, we'll justify our
obsession by writing a book.

Robert T. Leverett
Cofounder, Eastern Native Tree Society

Dendromorphometry   Robert Leverett
  Apr 10, 2006 

For what it is worth, the attachment provides the step by step process that I used this past weekend to compute diameter at the midpoint of the trunk of the Jake Swamp and Frank Decontie trees. Nothing special about the process. It's straightforward stuff, but I thought it was time to begin formalizing these new procedures that we're using in preparation for "Dendromorphometry".

It seems to me that one of the primary values of our planned book will be the compilation of procedures that can be applied in a series of simple steps for folks who are not comfortable thinking through the mathematics on their own. So, every ENTS method would have its procedure like a military manual with checklists galore. Thoughts, anyone? 


Robert T. Leverett
Cofounder, Eastern Native Tree Society