Leaning
Trees 
Will
Blozan 
Nov
24, 2004 08:32 PST 
Tom,
As would be expected with virtually every eastern site with
tuliptree in
good growing conditions, tulips will invariably be the dominant
species
(with regard to height), and I have no doubt a 150' tree lives
in there
somewhere. If the site was hemlock dominated, hemlock might
actually come
close to matching the max height for the site.
BTW, have you used the "law of cosines" (correct
term?) to see if the
supposed 160' hemlock was leaning, and then calculated the error
from a
conventional baseline measurement to see if it was the source of
the 160
number? This test almost always accounts for the source of error
(conventionally assuming the tree to be straight or the top
directly over
the base). It is also a great way to check if the
"top" you measured was
reasonably displaced off the base, and if in fact you measured
the same tree
in dense stands. I have used this exercise to illustrate sources
of errors
(+ and ) in my tree measuring workshops.
Just take your hypotenuse and covert it to horizontal distance (cos)
and
compare it to the hd for the base (same formula). To check for
conventional
error, multiply the base baseline by the tangent of the top
angle. This
number will be the erroneous height using conventional forestry
methods.
For example, here is a Norway spruce at the Biltmore Estate,
which I knew
was leaning:
ENTS method:
Top 189' @ SINE 36 degrees= 111.1'
Base 165' @ SINE 5.9 degrees= 17'
Total height is 128.1'
Cosine baseline calculations:
Top baseline 189' @ COS 36 degrees= 152.9'
Base baseline 165' @ COS 5.9 degrees= 164.1'
Thus, the tree has a lean (top displacement) in one direction of
164.1'152.9'= 11.2'.
If the tree was measured using the base's (uncorrected for
slope) baseline
for the top, the error would make the tree 119.9 feet above eye,
not 11.09',
an error of 7.2% (just for the top). This tree would also be
listed as the
tallest Norway spruce in North America! (But we ENTS know
better!)
Perhaps our ENTS database gurus could calculate the average
error generated
from actual trees we have measured, and come up with an average
error for
each species we measure, at least for the tops we measured. It
would be all
the more profound in the sense that we would have the ACTUAL top
measured,
and not just an estimation as is the basis for conventional
TANGENT or %
methods. I think this would be an excellent illustration of
error source in
general and by species. This would be so easy since the data are
already
collected as the calculations use the same numbers we gather for
the SINE+
SINE ENTS method.
Hope this makes sense!
Will 
