Refinements for clinometer measuring techniques   Edward Frank
  Mar 26, 2006 21:19 PST 

Andrew,

If you read Will Blozan's Tree measuring Guidelines of the Eastern
native Tree Society -

http://www.nativetreesociety.org/measure/tree_measuring_guidelines.htm

You will see a nice discussion of errors involved in analog techniques.
There are more discussions about problems discussed on the index page of
the measurements section of the website:

http://www.nativetreesociety.org/measure/index_measure.html

I would in particular look at the page dealing with mismeasured trees:


http://www.nativetreesociety.org/measure/mismeasured_trees.htm

That all said, trees can be measured using a variety of analog
techniques, but with the understanding that if the top is not directly
over the base (in a study of 1800+ trees it was offset an average of 13
feet) will lead to measurement errors in height of 15-25 feet on
average.

One method outlined in basics on the American Forest website is one
using a stick and the principles of similar triangles. This is gone
over in detail on the PA Big Trees website - (I wrote that section so I
think it is correct)

http://www.pabigtrees.com/trees/measurement/measurement_notes.htm

I would read the discussion on the above page on analog measurement
procedures.

With regard to the tape and clinometer method, The PA Bigtrees site
discusses this method also on the same page above. One of the
limitations is the basic method described requires that the viewer be
nearly level with the base of the tree. If he is not more complex math
is required.

The most common method used is to measure height with a clinometer at a
distance of 100 feet. At this distance the tree height can be directly
read from a percentage scale on the clinometer.   The procedure is
repeated for the base of the tree to get the height between eye level
and the base of the tree. If the base of the tree is below eye level,
the two heights are added to get the total tree height. If the eye is
below the base of the tree, the eye to base height is subtracted from
the eye to top of crown height to get actual tree height.

This is fine for many trees, but has some limitations. It can't be used
unless the line of sight to the base of the tree is fairly level. With
increasing angles the actual horizontal distance to the tree becomes
increasingly smaller than the taped distance to the base of the tree.
This can be corrected with some math, but this step is often ignored. A
second and more significant problem is that from a distance of 100 feet,
the tops of many trees can't be seen from the ground. With this
perspective often branches on the front side of the tree are mistaken
for the tree top leading to major busts in the tree height calculations.
One way to avoid this problem is to measure tall trees, or trees with
flatter crowns from a greater distance away. At 150 feet from the tree,
the readings from the scale would be multiplied by 1.5 to calculate
height, from 200 feet the percentage readings on the scale would need to
be multiplied by 2 to calculate tree height. Just because a more hitech
instrument is being used does not mean the readings will necessarily be
more accurate. If the angle to the base is steeper and if the user
doesn't have a laser to measure the eye level distance to the trunk,
this method can still be used but with some modifications and some
trigonometry.

If the angle between the observer and the base of the tree is more than
a few degrees, then it is better to use the degree scale on the
clinometer. This method requires some basic trigonometric calculations
that can be handled by a $10 calculator. Three numbers must be measured
1) taped distance from the eye to the base of the tree, 2) angle up or
down in degrees from the eye to the base of the tree - call this angle
alpha, and 3) angle from the eye to top of the tree - call this angle
beta. The change in height either above or below the eye level to the
base of the tree is sin(alpha) x taped distance. At his point the true
horizontal distance on a level line to the tree must be calculated. The
horizontal distance to the tree is cos(alpha) x taped distance. Write
this number down as it is needed to calculate the total height from a
horizontal line to the top of the tree. The height from eye level to
the top of the tree is tan(beta) x horizontal distance. If the base of
the tree is below eye level, adding these two height measurements
together will give a total tree height. If the base of the tree is
above eye level, subtracting the height to the base of the tree from the
height to the top will give a total tree height.

This method still assumes that the top of the crown is directly over the
base of the tree. Also if the observer is not far enough away from the
tree, it is easy top mistake a forward slanting branch for the true top
of the tree.

Hope this helps.

Ed Frank


Andrew Joslin wrote:
 
Ok, I'm not ready to invest in a laser rangefinder... yet. My technique for
measuring tree height is to use a manual sighting device. The one I'm using
is called a "CrossSight". It's a simple tool typically used by arborists

that allows the user to sight the bottom and top of the tree simultaneously, measure the distance from the sighting position to the base of the trunk and ta-da come up with an"estimated" height as the documentation describes it. Assuming everything is more or less right-on, that the user is standing at the same elevation as the foot of the trunk do you think this tool is useful for ballparking (within 5 ft plus or minus) a height value? ...

Any comments on improving technique for "analog" height measurements? I
will revisit the measuring section on the ENTS web site to see what else I can find. 

Thanks,

Andrew Joslin
Jamaica Plain, MA
RE: Refinements for analog measuring techniques   Andrew Joslin
  Mar 27, 2006 06:16 PST 

Hello Ed.
Thanks for the detailed response, I appreciate the effort you put into it.
I will read the materials suggested and see if I can come up with some
improvement on my technique. It looks like using a laser device is a much
less cumbersome a process and potentially much more accurate, but
expensive. At this point I don't need to have perfectly accurate results
but I would like to get in a reasonably good estimating range (plus or
minus 5')
-Andrew
Analog measuring techniques - Cross triangulation   Edward Frank
  Mar 27, 2006 20:05 PST 

ENTS,

If the top of the tree is not directly over the base of the tree, then could
you locate the point directly under the tree-top and use that point for
measurements? Yes, you can, but it is not easy. As a final round of
discussion, I want to re-examine the idea of cross triangulation to locate
the point on the ground directly below the top of the tree. Will Blozan
provides a nice discussion in his tree measuring guidelines.

To locate the position of the top of the tree you must sight the top of the
tree from two different positions. First walk around the tree at a
disatance and locate the highest point of the crown. It is easier to
triangulate the top of the tree if there are two people. Usie a plumb-bob,
essentially any string with a weight at the bottom. Sight with the string
the top of the tree and the corresponding line on the ground. Run a line -
the tape works well - along the ground along the line of sight under the top
of the tree. From a second position at a approximate angle of 90 degrees
from the first (right angle to the side), sight the top of the tree and the
ground using the plumb-bob. Have the second person walk along the marked
line on the ground until he is in line with the top of the tree as viewed
from this second direction. That point should be the point directly under
the top of the tree. Be sure to mark this point. Walk around the tree with
the assistant standing at this point. If you are actually under the topmost
point of the tree, he will appear to be directly under the top at all
viewing angles.

With the projection of the tree top on the ground marked, find a position
where you can see top of the tree, the bottom of the tree, and the point
below the top of the tree. Follow the procedures described before to
measure the distance the base of the tree is above or below a level line
from your measurement point. To reiterate: Measure the angle in degrees
from your eye level to the base of the tree. Mark this angle in your notes.
Then stretch a tape from your eye level to the base of the tree. You want
to measure the distance to the side of the tree, because you really want the
distance to the center of the tree, not to the front of the tree. The
height of the base of the tree above or below the level line is equal to
sin(angle) x taped distance.   From the same point measure the angle to the
top of the tree. Mark this down. Now you need to measure the horizontal
distance from the measurement position to the projection of the top of the
tree on the ground. If the slope is not great, it may be possible to simply
stretch the tape horizontally between the positions. You don't actually
need to measure the point on the ground, because you are not interested in
the vertical position of the point on the ground, just its horizontal
position. If you can't stretch the tape horizontally, then meaurethe point
as you would the base of the tree above. You can use the point on the
ground, or shoot to your assitants belt buckle, or the top of his head,
just so long as you measure the angle and stretch the tape to the same
target point. The horizontal offset of theis point is cos(angle) x taped
distance. Write these numbers down, so that you can check your calculation
later for confirmation. Now the hieght of the top of the tree above the
horizontal plane is equal to tan(angle to the top) x calculated horizontal
distance to the top's projected position on the ground. The height of the
tree is the sum of the vertical distance above or below the horizontal plae
to the base of the tree, and the height of the top of the tree above the
horizontal plane.

Are the numbers good? They can be. It is difficult to accurately locate
the position of the top on the ground, so this introduces a potential error.
The errors in the clinometer readings are still potentially there. These
potential errors are likely relatively small. The biggest difficulty is the
time it requires to do the cross triangulation. When using a laser
rangefinder to measure trees, the process of cross triangulation is not
needed. You can literally walk through the forest checking out trees as you
move and get a fair approximation of their height. When you find a tall
tree, its height can be calculated in a matter of minutes, as opposed to an
hour or so to do the cross triangulation. Much more forest can be surveyed.
In addition, in rough terraine, or in areas with thick undergrowth or
numerous trees, it may not be physically possible to do a
cross-triangulation to determine the ground position of the tree top. In
some cases the person making the measurement will not be able to see both
the top of the tree and its base from the same position. Measuring relative
to a shared intermediate point is fairly easy to do with the laser
rangefinder and clinometer, but is hideously difficult to do using cross
triangulation methods. And finally, a single person can measure a tree
using a rangefinder and clinometer, and while it is possible it is difficult
for a single person to use the cross-triangulation method.

Ed Frank