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

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

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 laser-based 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 drop-line measurement. On the Seneca Pine, Dale and I
cross-leveled 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.


Re: Calibration   Howard Stoner
  Nov 10, 2003 07:46 PST 
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

At every click-over 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!


RE: Calibration   Robert Leverett
  Nov 10, 2003 08:28 PST 


   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 cost-cutting leads to quality reduction. Nikons built in
China is a case in point. Shame on Nikon for compromising their good

RE: Calibration
  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

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 
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
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 drop-line 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!
RE: Calibration    NR, Cook Forest Env. Ed.
   Nov 11, 2003 11:12 PST 

I consistently find one of my laser's to be off in your noted range, another is much closer after I had Forestry Suppliers 're-calibrate' 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.

RE: Calibration
   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.
RE: Calibration    Robert Leverett
   Nov 11, 2003 12:36 PST 


   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.

RE: Calibration
   Nov 11, 2003 15:41 PST 


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 

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"...
Re: Calibration
  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.

Juggling the Errors
   Nov 15, 2003 07:20 PST 


    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 over-calculating 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 162-foot 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 sports-minded 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.