Calibration 
john@bcn.net 
Nov
06, 2003 19:01 PST 
Hi All,
In regards to calibrating clinometers, first consider two
distinct
sources of error. First, there is reading and leveling error,
caused by
inaccuracies in determining the reading of the crosshair and of
not
pointing exactly at the target. For this, probably do a series
(20?) of
readings taken of a fixed point from a fixed point, hand held
and all,
then determine the standard deviation of the readings by the
usual
statistical formulas. Or, just see what the range of error is in
the
set.
Next, there is instrument or systematic error. For measuring
this, I
offer a method my brother (a surveyor) suggested. It is called a
"peg
test". You set up two surveyor poles or other objects
separated by say
100'. Set up a station midway between these objects. Preferably,
the
clinometer will be stabilized, either hold it against a wall or
fasten
it to a tripod. (The Suunto clinometers have a tripod mount
point on
the side.) Read and mark the point on each post that corresponds
to 0
degrees. A helper is useful here. These points should be at the
same
elevation regardless of error, since the distance is equal
(principle of
similar triangles). Then go right next to one of the posts, and
align 0
degrees with the mark there. There will be basically no error
there,
because the distance is minimal. Then sight and mark the point
at 0
degrees on the other post. The difference between the two marks
on that
post is the systematic error. (Plus or minus the random error
from
above.)
The length of the systematic error will be proportional to the
distance
to your target. In this example, you have determined the size of
error
in 100'. This can also be converted to a degree error. Since the
systematic error in degrees is always the same, you should
adjust all
your measurements by that amount. The reading and leveling error
is
random, and reduces the accuracy of the measurement. You do not
adjust
for the random error, just accept it and report it.
As for calibrating the rangefinder, I agree in principle with
the post
suggesting readings at varying clickover points, but would add,
if you
have time, to do a number of readings at each distance, to
determine the
variability (standard deviation, etc.) of the results.
Basically, you
want to account for both systematic and random errors, as above.
I hope that helps further the accuracy of our measurements.
John Eichholz
Charlemont, Massachusetts
neophyte tree measurer and ent seedling

Re:
Calibration 
Colby
Rucker 
Nov
06, 2003 20:51 PST 
Howard and all,
When I started using laserbased measurements, I spent a fair
amount of time
thinking up methods that were new to me, trying to increase the
accuracy of
my findings. I stretched tapes across the front yard,
determining where
laser readings intersected actual distance, and where they
didn't. I shot
to various colors of construction paper, and got different
distance
readings. I shot to material of various surface contours, and
got different
readings. I also got different readings on different days.
I finally decided that I had only paid $199 for the rangefinder,
and it was
not realistic to expect absolute accuracy. If it was supposed to
be
accurate to a yard, and it was consistent to several inches,
that wasn't
bad. Calibrating for all sorts of possible deviations would be a
nuisance
and might add as many (or more) errors than it corrected. I knew
the
equipment was reasonably close, but conditions (including body
movement)
were so changeable that I might as well accept things as they
were.
That said, there were lots of other things I could do to
increase accuracy.
These included carefully backing to clickover, eliminating
multiple
triangles, making careful basal adjustments, minimizing
distances, and
recording all measurement elements to 1/2 inch.
As a result, I pretty much went to the pole method, and also
using the pole
and clinometer as a level to adjust basal measurements to 1/2
inch accuracy.
I practiced recording clinometer angles to 1/10 of a degree,
which is a
judgment call, since the scale's only marked in full degrees.
I don't abuse my equipment, and check it occasionally. When I
remeasure
certain trees, I get very compatible measurements. This
indicates
consistency as far as individual trees are concerned. Dale used
the pole
method on the Longfellow Pine and got an extremely accurate
finding,
compatible with the dropline measurement. On the Seneca Pine,
Dale and I
crossleveled the central basal contour on both sides of the
tree to
establish a basal starting point for Will's dropline. Otherwise,
even a
steel tape doesn't mean anything.
So, there are lots of things that can and should be done to
increase
accuracy. At present, I don't think trying to calibrate an
inexpensive
piece of equipment beyond its inherent tolerance is one of them.
Colby

Re:
Calibration 
Howard
Stoner 
Nov
10, 2003 07:46 PST 
Colby,
Thanks for the insights. Thanks also to John, your input is
informative
and I appreciate
that, however, I am with Colby on trying to get more out of
instrument
than it is designed
for.
At every clickover point from 20 yds to 100 yds. my range
finder is
long by 1.5 to 3.5 feet.
For example: 20 yds = 58.5', 50 yds =147.2', 60 yds=176.9',
80'=237.5, etc.
Is my range finder the only one that is consistently this far
off and
always on the long side?
Though it is true that these numbers will change some with
different
objects and conditions,
it seems to me they achieve a more accurate result than
multiplying my
reading by 3.
Convince me otherwise and I will throw out my calibration table.
Is there such a thing as calibrating an inexpensive piece of
equipment
"to" its inherent
tolerance? It seems to me it is worth an hour of my time every
few
months to try!
Howard

RE:
Calibration 
Robert
Leverett 
Nov
10, 2003 08:28 PST 
Howard:
You should keep your calibration table,
because it is needed for your
particular instrument. I was lucky enough to get a laser (the
800 meter
one) that is extremely accurate. However, I have to watch
carefully when
I use either the 500 or the 400.
The testing and research that each of us does
adds measurably to our
collective understanding of our individual instruments, brand
reliability, etc. There comes a point of trying to calibrate the
"uncalibrateable", but that decision needs to be made
for each
instrument. Constant attention to the accuracy of our
instruments is
part of the price we pay to be Ents.
My experience with production models is
that they get increasingly
unreliable as costcutting leads to quality reduction. Nikons
built in
China is a case in point. Shame on Nikon for compromising their
good
name.
Bob

RE:
Calibration 
john@bcn.net 
Nov
10, 2003 22:51 PST 
Bob, Howard, Lee, all,
(Summary: Theoretical means are used to show plausible error
rates of
+/3 feet for typical measurements, with 3 out of 4 falling
within +/
1.5 feet)
I've been doing a little work on theoretical rates of error.
Hold on
now, its not that bad. I think I can prove mathematically that
the
error in tree height that results from each degree of clinometer
error
is approximately between 1.75% and 1.9% of the horizontal
distance to
the trunk.
To show this, let DT be the true distance to the tip and let DB
be the
true distance to the point directly below the tip. Let @ be the
true
angle to the tip, and let e be the measurement error of the
angle. Let
H be the true height of the tip above horizontal, and let H' be
the
height calculated from the true distance to the tip times the
sine of
the measured angle. Then H  H' is the height error due to angle
error.
It is true that H = DT*sin(@). We have decided that H' =
DT*sin(@+e).
It is also true that DT = DB*1/cos(@). So we can then be sure
that:
H  H' = DB*(1/cos(@))*(Sin(@)Sin(@+e)).
Why bother with all this?
Because the factor: (1/cos(@))*(Sin(@)sin(@+e)) is nearly a
constant!
Its range is a smooth progression from 1.74% at 0 degrees to
1.9% at 80
degrees. Because of this, we can safely say that an upper bound
of
clinometer error is 2% of baseline per degree of error no matter
what
the angle.
I think I'm always within +/0.4 degrees with my Suunto. This
translates
to +/0.8 feet per segment on a 100 foot baseline, or +/1.6
feet
overall.
This clinometer error is pointing and leveling error, but the
same logic
applies to systematic error.
Rangefinder error contribution to height error is proportional
to the
sine of the tip or base angle. It varies more by angle, from
very little
at 0 degrees to 1:0.5 at 30 degrees to 1:0.86 at 60 degrees. If
the
rangefinder is off by a constant 1.5 feet across its range (like
Howard's  also 1/2 the clickover interval on mine), then we
can expect
an error in height of from 0 feet to 0.75 feet to 1.29 feet per
reading
due to rangefinder error, and it doesn't matter how far away!
Since the bottom angle is usually smaller than the top angle, we
can
average this off to about 1.5 feet of error for every 1.5 feet
of
rangefinder error on the typical tree having angles of 60
degrees up and
10 degrees down.
This rangefinder error is systematic error, but the same ratios
apply to
pointing error.
It seems clear to me that getting rangefinder error at 1.5' and
clinometer error of 0.4 degrees at 100' baseline have comparable
effects
on height accuracy, and that without statistical methods, we
shouldn't
be getting closer than +/3 feet at these rates. Since we are
getting
better, more consistent results than that, our equipment
accuracy is
probably somewhat better than I have put forth here! (Actually,
random
results would be +/1.5 feet 3 times out of 4.)
If you got this far, thanks for putting up with my ramblings!
John Eichholz

Re:
Calibration 
Howard
Stoner 
Nov
11, 2003 05:41 PST 
John,
Thanks for the calculations. Of course being a so called "mathematician"
I am excited
about your calculations and formulas and will be
"scrutinizing" your
work carefully
to make sure there are no errors in your error calculation.
(Just
kidding!)
I don't know statistics well but it seems there should be a
principle of
central
tendency, law of averages or something like it. Meaning: no
matter what
the error,
so long as it is distributed evenly on both sides of the true
distance,
the average
of an increasing number of measurements will eventually approach
the
true value.
How does one know that you are getting that even distribution
other than
field testing?
I think we all agree that Will's dropline measurements are the
most
accurate we will get.
On two occasions I have been within .8 ft on one and .2 ft of
his
measurement on the second.
This is certainly a small sample to be drawing major conclusions
but at
least it is a start.
Is it possible that my calibration chart gives me that even
distribution?
It seems to me that it might!
Howard

RE:
Calibration 
NR,
Cook Forest Env. Ed. 
Nov
11, 2003 11:12 PST 
Howard,
I consistently find one of my laser's to be off in your noted
range, another is much closer after I had Forestry Suppliers
'recalibrate' it . They sent me one that was way over specs, at
least in my humble opinion. The unit was brand new and was
supposed to be within +/ 1 yard of actual distance. Trials at
every click over point in 100 yards yielded an error off true by
+1.5 yards. I've only had 3 lasers over the years, and I've had
to run trials on them periodically to note any major changes in
their readings. All of these lasers have always overstated the
length to some degree during trials. I still use a
"calibration" factor determined from each laser that
brings me closer to the actual distance to target. It has helped
me to be more consistent in the long run, especially in terms of
comparing to Will's tape dropped trees at Cook Forest.
Maybe this calibration method won't work for everyone, but I've
found that when using ENTS methods with a properly calibrated
laser rangefinder I am consistently within +/ 1ft of Will
Blozan's taped dropped Seneca and Longfellow Pines. I'm not sure
if calibrating lasers will work with everyone else when we start
to examine other possibilities of error in terms of humans and
equipment. Maybe my calibration works out just right to offset
other possible errors. Anyway you look at it though, I think
that if we can get to within +/ 1ft of the trees height consistently, we must be doing something right.
Dale

RE:
Calibration 
john@bcn.net 
Nov
11, 2003 12:24 PST 
Hi Bob, Howard,
I am glad for all the peer review you can give. Peer review is
our best
asset and so important as theories are being formed. There is a
lot
going on out in the field and we are pushing these instruments
to their
limits (in a good way). Forgive me (and please share your work)
if this
has been gone over before. I am looking to establish how much
error in
height results from a given inaccuracy in measurement. This
seems to be
doable on paper using these formulas. In practice, good
technique might
be inspired by an understanding of the mechanics of the
situation. For
instance I am inclined to believe that setting up at clickover
for the
upper (largest) angle sightline would minimize total error,
because
rangefinder error on the horizontal has so little effect and by
staying
put, we can reduce clinometer (pointing) error caused by moving
around.
I am impressed, though that this group questions and discusses
both
theory and social policy at their intersection, as with the GPS
issue. I
had been watching with interest for only a short while, and yet
I feel
welcomed in my participation. Thank you very much.
JE

RE:
Calibration 
Robert
Leverett 
Nov
11, 2003 12:36 PST 
John:
A point worth noting about theoretical
maximums versus actual errors.
Sometimes the errors encountered from the laser and clinometer
are
partially offsetting, i.e. clinometer error going in one
direction and
laser in the other. This can certainly occur when you get the
clinometer
needle sticking. In addition Paul Jost found that the accuracy
limits of
the lasers was about +/ 0.75 feet despite the units of
changeover of a
yard/meter used. So at the changeover of laser readings, we're
probably
within +/ 1.0 feet of actual distance.
To get truly accurate measurements,
statistics is definitely
involved. At the simple end, Lee and I believe that it takes
about 10
readings to be confident of an accuracy to less than +/1 foot.
I'll have a simple spreadsheet for
everyone tonight showing the
laser error problem in a tabular layout.
Bob

RE:
Calibration 
john@bcn.net 
Nov
11, 2003 15:41 PST 
Don,
Well, as long as the error "e" is "real"
angle minus measured angle, it
is both accuracy and precision. If we are talking about the
clustering
and variability of results around an average, then that
component is
precision, and the difference between that average and the
"true" (if we
could ever know that) is accuracy. But I believe my error covers
both.
(And is impossible to really know.) I'm really only saying if
you put a
wrong number in for angle, off by 1 degree from the
"real" angle, and
the "real" baseline is known, that your height
measurement from the
result will be off by no more than 2% of the baseline. Anything
else
thrown into the mix and all bets are off. But it does give you a
reason
to be precise to a certain level and an awareness of how your
instrument
capabilities may be influencing the result.
Again, the results I am seeing on this list and in the field are
surprisingly repeatable, and confirmed to be accurate using
physical
measurements. I think my analysis applies more to confirming the
quality of our tools and methods than to justifying a claim to
accuracy
of the results.
That is what is so valuable about everybody's experimental
approach.
By comparing different methods and seeking replicable precision
with
verifiable accuracy we have met the real test of science.
John Eichholz

Re:
Calibration 
Don
Bertolette 
Nov
11, 2003 17:13 PST 
John
Thanks for the clear explanation! I've always considered simple
clear
explanations a measure of the depth of the understanding.
Regarding "the error "e" is "real"
angle minus measured angle", if the angle
is measured like a transit, with the angle measured at the exact
point of
'pivot', this would be in my mind a measured angle (with great
potential for
accuracy). Again in my mind, the real angle that we commonly use
in the
field (using a clinometer or similar angle measuring device) is
truncated,
as we reposition our head/eye for tree base and tree top
measures...the
'pivot' point is actually somewhere (maybe as much as a half of
a foot)
behind the eye...that was my idea of error "e"...
Don

Re:
Calibration 
dbhg@comcast.net 
Nov
11, 2003 17:28 PST 
Don,
John, Howard, et al.:
Don, On occasion, I use simple reflectors,
mostly paper. So maybe it is time to move up to the next level.
As promised from an earlier post today, the
attached spreadsheet provides an easy way to show the maximum
error with the laser rangefinder as a function of laser distance
error along the hypotenuse line and the angle to the point being
measured. For a fixed/maximum laser distance error, the error in
the height is a function of the angle. Of course, the
spreadsheet calculations cannot tell us the best location to
seek. That is driven by crown and base visibility. However, for
tall white pines in Mohawk, if you are close enough that your
angle to the point you are measuring is over 60 degrees, there's
an excellent chance you're not seeing the top. I try to reduce
the angle to 55 degrees or less. If I can find a vantage point
on a hill, I can usually get the angle down to between 35 and 50
degrees. So I can expect up to a 1 foot error from the chart. A
0.2 degree error with the clinometer is not unusual. So I can
quickly account for a +/ 2 foot error range. Repeat
measurements with different instruments can bring that down to
about a foot.
I've got other spreadsheets that show the
maximum range for various combinations of laser and clinometer
error. I'll spruce it up and send it in a day or two.
Bob 
Juggling
the Errors 
dbhg@comcast.net 
Nov
15, 2003 07:20 PST 
ENTS:
The current flurry of activity to
identify the major sources of measurement error and reduce them
set me to thinking about the Jake Swamp tree and what different
assumptions about the sources and magnitudes of error would
produce as a range of possible heights. My current measured
height of 163.5 feet seems a bit high to me. I would guess that
a taped height would be 163.1 or 163.2 feet at the most. But
with a lot of individual measurements going higher than that, it
is tempting to justify a particular figure as conservative.
However, if I begin by assuming the worst case scenario for my
equipment, what do I get. Well, I suppose my laser can be off by
1.5 yards on both top and bottom of the tree and my clinometer
by 0.4 degrees on both top and bottom and all these errors could
be in the direction of overcalculating the height. Should that
be the case, then the height of Jake would be only 157.3 feet.
However, if all the errors were off in the direction of
shortchanging the tree, Jake would be a whopping 169.8 feet tall
 a preposterous number. The Jake Swamp pine was taped by
Michael Davie and myself in Oct 2001 to 160.9 feet in height. So
the 157.3 and the 169.8 are impossible figures.
The odds are that if the clinometer reads
high, it reads high at both the upper and lower angles. In
addition, my 800M laser is extremely accurate. It has been
tested and retested. Plus/minus 1 foot of error is about the
most it can ever be expected to be off in good lighting with
repeat measurements. Assuming the clinometer reads high by 0.4
degrees and the laser reads long by 1 foot, Jake would be 160.2
feet tall  still too short. Various combinations of more
probable errors produce two clusters: a cluster of results
around 162foot mean and another cluster around the mean of 164
feet. The center of gravity for the two clusters is 163 feet.
I'd better dollars to donuts that Jake is 163.1 feet tall. Just
feel it in my bones.
What does all this add up to? Well, one must
treat each tree as a case study, thinking about it as the tree
actually exists, not as a stick figure. One must think about
one's instruments and the limits of the accuracy of each. One
must think about where the big mistakes occur versus the small
ones. One then focuses on controlling the major sources of
error. Colby thinks a lot about this and has done a superb job.
BTW, one does all this because one has a genuine interest in the
subject and one's interest does come by way of one's profession
that may obscure rather than clarify the right approach. We
DON'T look at trees with a latent timber interest, developing
our methods and priorities around what is practical for meeting
timber objectives. We approach our craft no differently than
does a runner seeking to shave fractions of a second off an
already stellar performance. The runner's determination is
completely accepted and understood by a sportsminded public.
As we search for relationships of practical
value, we learn more about the processes we must master. We
cannot allow ourselves to become complacent in developing
shortcut measurement techniques. This isn't about achieving high
volumes, least we miss the boat a country mile on individual
cases. We're about the cases.
Bob 
