New
measurement method 
Robert
Leverett 
Jan
11, 2007 06:51 PST 
ENTS,
As I mentioned in a prior email,
at the April 2007 ENTS rendezvous
at Cook Forest, I will be giving an update presentation on our
ENTS
measurement methods to include new measurement techniques. As an
example
of what will be included, what follows is a new formula for
measuring
tree height above eye level using nothing but a clinometer and
tape
measure. The advantage of the method is that it avoids the
pitfall of
the top being measured not being directly over the base.
However, there
is an assumption that absolutely must be met. The measurer is on
a patch
of level ground that allows forward and/or backward movement.
The method
works as follows.
From a vantage point, either the angle
to the crown point or the
slope percent is determined (left scale angle, right scale slope
percent
on the Suunto clinometer with those scales). The measurer then
moves
directly forward or backward a known distance to a second point
where
the crown point is still visible. The crown point, measurer's
original
position, and measurer's new position all fall in the same line.
The
measurer's eye level remains unchanged. The measurer takes the
angle or
slope percentage of the crown point from the new position. The
measurer
takes the distance between the two points of measurement. This
is a
level distance.
So we end up with three measurements:
two angles or two slope
percentages from the eye to the crown point and the linear
distance
between the two points of measurement. If the assumptions are
fulfilled,
the following formula calculates the height of the crown point
above eye
level.
Let:
D = level distance between the two
measurement points
A = angle of
eye to crown point from nearer location
B = angle of eye to crown point from
more distant location
H = height of crown point above eye
level
Then:
H = [(D)tan(A)tan(B)] /
[tan(A)  tan(B)]
The algebraic derivation of the above
formula along with others will
be handed out at the Cook Forest rendezvous.
Note that the reading of the right
scale of the Suunto clinometer
with a percent scale is just the tangent of the angle expressed
as a
percent. The measurer need only move the decimal place two
positions to
the left to get the tangent. Consequently, no trigonometry
tables need
to be accessed. The calculations can be done by the simplest
calculators.
The dangers of carelessly applying this
technique are the same as
the simple baseline to trunk and slope angle to crown. If the
measurer
is indeed on level ground then adding height to eye level gives
the full
height of the crown point above the tree's base. However, if
that is not
the case, then the procedure for shooting the crown can be
applied to
shooting the base. I suspect that many wouldbe measurers will
find the
procedure to already be too calculation intensive, but it avoids
the
pitfall of assuming the crown point is directly over the base 
the most
common source of tree height calculation errors.
Note that no assumption has to be made
as to how distant the trunk
is. There is no baseline from measurer to trunk. So this method
can be
applied where getting to the base of the trunk is difficult such
as when
there is an intervening stream. Of course, the base of the trunk
has to
be visible.
A caution is immediately in order
for the users of the percent
slope scale of a clinometer. It cannot be read to a sufficient
number of
decimal places to replace actually calculating the tangent of
the angle.
However, the process, as described above, still provides a
better height
approximation than ignoring the horizontal offset of the
crownpoint
from the tree's base. As is frequently pointed out, measurers
armed with
only clinometer and tape measurer usually apply the vertical
telephone
pole in the level parking lot model that is the basis for the
heightmeasuring instructions accompanying clinometers and
hypsometers.
The fundamental lesson to be
learned in the application of all
these measurement techniques is that the measurer MUST
understand the
assumptions made behind the model and verify that those
assumptions are
fulfilled. Ignorance is not bliss. Our ENTS workshops will
increasingly
focus on different models, the assumptions behind the models,
and the
magnitude of the errors introduced when assumptions are not
fulfilled.
This new method in no way replaces the
much preferred sine topsine
bottom method, but should be useful as an interim method for
folks who
possess a clinometer and tape measure and who are saving their
pennies
for a laser rangefinder.
Bob
Robert T. Leverett
Cofounder, Eastern Native Tree Society

Re:
New measurement method 
Jess
Riddle 
Jan
11, 2007 19:57 PST 
Bob,
Seeing a new strategy for measuring trees proposed is exciting.
When I saw how you had the triangles set up, I had to try and
derive
the formula myself. What I came up with produces the same
results as
the formula you provided, but is much messier to use. In
checking the
formulas, it appears to me that the distances involved with
applying
this technique are realistic for practical application. Shifting
15
or 20' will provide a reasonably large angle difference to work
with
for a 100' tall tree.
The one part of your explanation that I didn't follow regarded
calculating the tangents instead of reading them directly off
the
clinometer. How does using a calculator to find the tangents
increase
the resolution of the clinometer? If you calculate the tangents
from
the angle in degrees read off the clinometer, aren't you just
'rounding' to some irrational number that you obtained after
rounding
the degrees?
This technique's ability to preclude projecting heights to an
illusionary top (produced by the high point not being over the
base),
and doing so without complicated calculations, give it great
potentially. Certainly, the requirement for level ground will
restrict the use, but many state big tree programs could still
improve
a significant proportion of their data if they used this method
instead of the standard tangent method where applicable.
Jess

Back
to Jess 
Robert
Leverett 
Jan
15, 2007 05:46 PST 
Jess,
You are absolutely correct. Good thinking. I
thought about the
rounding error situation after I submitted the email. Having
all those
extra digits from a tangent table based on an approximate clinometer
reading is of no real value to accuracy. Two heads are
definitely better
than one, especially if one of the heads is yours.
I had intuitively settled on 20 feet as the
baseline between the two
angles, but had not done any calculations to investigate
sensitivity. I
have a process in the mill for dealing with the situation where
the
baseline between the two measurement points is not level. The
math is
messy and I doubt that anyone would want to adopt it, but I'll
submit it
nonetheless.
Bob

Dendromorphometry
extended 
Robert
Leverett 
Jan
19, 2007 05:23 PST 
ENTS,
Not all ENTSdeveloped formulas are destined
for high use in the
field, but nonetheless form part of our "fleshing out"
of the new
discipline of dendromorphometry.
I recently gave a formula for calculating the
height of a crownpoint
above eye level that requires only a clinometer and tape
measure. The
assumptions that must be fulfilled for the formula to be used
are: two
clinomter angle measurements are made of the same crownpoint
from
locations that are on the same level. The crownpoint, eye
position of
the first measurement point, and eye position of the second
measurement
point all lie in the same vertical plane.
If:
a1 = clinometer angle to crownpoint from
nearer measurement point
a2 = clinometer angle to crownpoint from more
distant measurement
point
D = level distance between two measurement
points (eye position to
eye position)
H = height of crownpoint above eye level
then:
H = [(D)tan(a1)tan(a2)]/[tan(a1)  tan(a2)]
Since, the right scale of a clinometer with a
degrees and percent
slope scale is just the tangent of the angle x 100, one can use
the
above formula without trigonometry tables. That makes it
attractive to
people who want to avoid trigonometry. Jess Riddle independently
tested
the formula and stated that a baseline of 15 or 20 feet should
be
sufficient to get sufficient angle differentiation to allow the
formula
to do its work.
The toughest condition to be met is the
requirement that both eye
positions be at the same level. In mountainous terrain, this
condition
often cannot be met will keeping the two eye positions and the
crownpoint all in the same vertical plane. One might be able to
move
laterally at the same level, but that would violate a key
requirement
that the three points lie in the same vertical plane.
Suppose that the second observation point is
not at the same level as
the first. Can we still solve the problem? Suppose the second,
more
distant eye position is at a higher elevation. In this case more
triangles that must be constructed to model the situation and
the
calculations become more involved, as can be seen below.
If:
a1 = clinometer angle to crownpoint from
nearer measurement point
a2 = clinometer angle from eyelevel at second
measurement point down
to eye level at first measurement point (note that a2 here is
not the
same as a2 in the first formula)
a3 = clinometer angle to crownpoint from more
distant measurement
point (at the hiher elevation)
d5 = straightline distance from the eye at
first measuremet point to
second the eye at the second measurement point. The line d5 is
sloped.
Remember that the crownpoint, first eye
position, and second eye
position all lie in the same vertical plane. If the assumptions
are met,
then the height of the crownpoint above the first eye position
is:
h = [tan(a1){d5cos(a2)tan(a3) + d5sin(a2)}] /
[tan(a1)  tan(a3)]
This toad strangler of a formula is not likely
to take the measuring
world by storm, but it can be used by those who want as many
tools in
their toolkit as they can get.
Both formulas with accompanying diagrams will
be thoroughly explained
at the April ENTS event at Cook Forest.
Bob
Robert T. Leverett
Cofounder, Eastern Native Tree Society

Refinements
on tangentbased calculations 
Robert
Leverett 
Jan
29, 2007 05:26 PST 
ENTS,
What follows below is a more complete
treatment than was previously
given for measuring the height of a crownpoint above eye level
using a
clinometer and a baseline between two measurement points that
are
aligned with the crownpoint. The procedure and formulas that
are
presented below are not meant as substitutes for sinebased
measuring,
but the tangentbased procedure can fill the accuracy gap that
ordinarily accompanies the typical use of a clinometer.
First a quick review. If the measurer is
able to see top of the tree
and the top is directly over the base, then a baseline from eye
to trunk
and the slope % to the crown top is all one needs to compute
height
above eye level. A similar procedure can be used for height
below eye
level. The slope percent converted to the equivalent decimal
value times
the level baseline distance from eye to trunk gives the height
of the
tree above eye level. This is the standard clinometerbaseline
procedure
for instruments that have a percent slope scale. The two scales
for a
clinometer that make the most sense are degrees and percent
slope. Of
the two, degrees is the most important.
But what if the crownpoint is not
directly over the base? What can
be done to get an accurate height measurement if one does not
know where
a plumb line from the crownpoint to the ground would fall? Some
timber
specialists develop a good eye and can make educated guesses,
but that
is risky, especially for broadcrowned hardwoods. There is the
crownpoint crosstriangulation method as described in our
guidelines,
but that process is difficult to implement without two long
tapes, an
assistant, and continuous visibility of the crownpoint being
measured
as one moves from one location to another. However, there is
another
procedure that one can apply that uses just the clinometer and
tape.
The measurer positions himself/herself at a
spot where the target is
visible and shoots the angle to the target (or percent slope).
The
measurer then moves back to a second vantage point and takes a
second
reading with the clinometer. The height of the crown spot above
the eye
position at the first vantage points is calculated by using any
of the
three formulas below.
DEFINTIONS:
d5 = straight line distance between positions of the eye at
first and
second vantage points. This is the baseline. Note that it does
not go
from measurer to the trunk, which is the traditional baseline.
a1 = angle to crown spot an closer vantage point
a2 = angle to crown spot at farther vantage point
a3 = angle between eye positions at the two vantage points
(You may nned a pole to keep track of the locations.)
FORMULAS FOR THE THREE SITUATIONS:
(1). Baseline between two vantage points is level
h = [(d5){tan(a1)tan(a2)}] / [tan(a1)  tan(a2)]
(2). Baseline is not level, more distant point at higher
elevation
h = [(d5)tan(a1){sin(a2)+cos(a2)tan(a3)}] / [tan(a1)tan(a3)]
(3). Baseline is not level, more distant point at lower
elevation
h = [(d5)tan(a1){sin(a2)cos(a2)tan(a3)}] / [tan(a3)tan(a1)]
I used a combination of brackets,
braces, and parentheses to make
the formulas clearer.
It's apparent that cases (2) and (3)
lead to awkward calculations. I
doubt many people will want to use these formulas. However, case
(1) is
more straightforward, and again, please note that the distance
from the
measurer's position to the tree does not have to be determined.
This may
come as a surprise. Also note that the crownpoint, eye position
#1, and
eye position #2 all must lie in the same vertical plane. Also,
please
bear in mind that the tangent of angles a1, a2, and a3 can be
determined
directly from the right scale of a Suunto clinometer with a
degrees and
percent slope scale. You simply divide the percent slope read
from the
right scale by 100 to get the tangent of the angle. Slope,
defined as
the rise divided by the run IS the tangent of the angle. The
challenge
in applying this technique is find a place to get a level
baseline. This
new procedure is especially useful when the measurer cannot get
to the
trunk of the tree (across water, surrounded by briars, poison
ivy,
etc.).
DISCUSSION ABOUT THE PROCEDURE:
I highly doubt that the above procedure
is going to take the
measuring world by storm. Those who have a laser rangefinder,
clinometer, and scientific calculator can apply the much
superior sine
topsine bottom method. Those who don’t need high accuracy,
but do need
great efficiency in the forest, will likely not employ a
technique that
is calculationintensive. Those who nourish delusions about tree
form
aren’t reachable. However, there is a third group of intrepid
souls who
want to measure the best way, but are operating on a razor thin
budget.
They are saving their pennies for the needed equipment, but in
the
interim, they want to be out in the forest measuring trees. The
above
procedure could be of help.
Bob
Robert T. Leverett
Cofounder, Eastern Native Tree Society

