Measurement Notes
The various big tree website list a variety of methods
for measuring trees. Some are good methods, some are seriously
flawed, and some are contradictory. The best overview of how
to measure trees is provided in the document "The Tree measuring
Guidelines of the Eastern Native Tree Society", by Will Blozan and
can be found at the Eastern Native Tree Society website:
tree_measuring_guidelines.htm
For tree height measurements and girth measurements the same
starting point on the ground is used. They are both measured
relative to where the tree first sprouted. If on a slope that
point is where the pith or center of the tree intersects the ground
surface - from mid-slope on the ground surface. On level ground be
sure to measure from the actual base of the tree rather than from the
debris pile that often mounds atop the root surface - look for the low
point in the notches between the exposed roots.
Tree Height
Tree Height is the most difficult of the three parameters to measure
accurately. The two biggest sources of error are misidentifying what
is the actual top of the tree, and the fact that the tree top may not be
directly over the base of the tree. An analysis of 1800 tree
measurements by Bob Leverett found that the average offset of the top of
the tree in the direction of measurement for the entire dataset was 8.2
feet (representing and actual offset of around 13 feet). What does
that mean in practical terms? If you were measuring a 1o0 foot
tall tree at an angle of 45 degrees, a 1:1 slope, then this offset alone
would lead to an error of 11.6 feet.
The Eastern Native Tree Society measurement technique involves the use of a laser
rangefinder to directly measure the distance to the top of the tree and
to the bottom of the tree. With these numbers and a little trigonometry
the actual vertical height from the top of the tree to a
horizontal plane and the actual vertical height from the base of the
tree to the same horizontal plane can be calculated. It doesn't
matter if the top of the tree is directly over the base of the
tree. In addition the crown of the tree can be explored to find
what is the actual top of the tree and not a high looking branch on the
front of the tree. Tree heights can be measured with
these techniques to within a few inches. However the downside of
using these methods is the cost of the instruments needed to do the
measurements.
For most people wanting to measure a tree the interest is more
casual. An accurate measurement is wanted, but without the expense
of several hundred dollars of instruments. To
get accurate measurements some care must be taken. First try
to view the tree from several different angles to see where the actual
top of the tree is located. Use that point for the
measurements. This will eliminate the greatest potential for
error. The second step you can take is to see if the top of
the tree is offset from the base of the tree. If you can determine
the point directly below the top of the tree use that distance when when
making your distance measurements. The stick method requires only a straight stick or yardstick and a tape to
measure the distance along the ground to the base of the tree.
First, measure the distance from your eye to the joint of your thumb
and index finger (arm is stretched out). Next, hold the stick
straight up and down at arm's length in front of you and make sure
the portion above your hand is the same as what you measured from
your eye to your hand. Step backwards until the tree's base
appears to rest on the top of your fist, while the top of the stick
appears to touch the top of the tree. At this exact point, the
height of the tree is equal to the distance from the base of the
tree to you. Place a stake in the ground and measure (in feet)
from the trunk of the tree to the stake to find the height!
The stick method works because of the trigonometric principle of
similar triangles. The hand-stick-eye triangle is proportional in
size to the base of the tree-the height of the tree-distance to the tree
triangle. In the illustration above of the stick method, the
measurer's arm is shown being held straight out in front of them, with
the distance from the users eye equal to the height of the stick above
the hand. Using this pattern the distance to the tree is the
same as the height of the tree - no math is involved. However it
is not always easy or possible to get a good shot on level ground to
measure the tree height and if as you hold the yardstick and move your
hand up and down the distance from your hand to your eye
changes.
The same procedure can be used with a few measurements and some basic
multiplication. So long as the yardstick is held straight up
and down, the various measurements are still proportional. The
ratio of (the height of the stick above your hand to the distance from
your hand to your eye) is the same as ratio of (the height of the tree
is to your distance from the tree.) Therefore if you measure the
height of the stick above your hand (in inches), the distance from your
hand to your eye (in inches), and the distance from your position to the
base of the tree (in feet) you can calculate the height of the
tree. This can be written as a simple formula:
(length of stick x distance to the
tree)/(distance to eye) = Tree Height
Using this simple formula the height of the tree can be calculated no
matter what angle you are holding your arm, and no matter what the
length of the yardstick that extends above your hand. This has a
big advantage if you are measuring a tree on uneven ground or if you can
only measure the tree from a single angle. One problem that also
often occurs is that to actually see the top of the tree, the measurer
must be farther away from the tree than possible using a yardstick
length of 23-25 inches (average arm to eye length). Using the
simple formula above a smaller length of yardstick can be used allowing
the measurer to actually see the top of the tree. This is an
excellent low-tech method to measure tree height.
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. This basic
methodology 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
hi-tech 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 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
sine(alpha) x taped distance. At this point the true horizontal distance
on a level line to the tree must be calculated. The horizontal distance
to the tree is cosine(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
tangent(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 to mistake a forward slanting branch for the true top of the tree.
Cross-triangulation: 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.
Let's re-examine the idea of cross triangulation to locate the point on
the ground directly below the top of the tree.
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 distance
and locate the highest point of the crown. It is easier to triangulate the
top of the tree if there are two people. Use 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 measure the point as you would the base of
the tree above. You can use the point on the ground, or shoot to your assistants
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 this
point is cos (angle) x taped distance. Write these numbers down, so that you
can check your calculation later for confirmation. Now the height 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 plane 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 the ENTS
methodology for measuring trees with a laser rangefinder and clinometer, 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 terrain, 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.
CBH
Circumference at breast height - Also known as CBH, this
measurement is made in inches at a point on the tree trunk, 4 1/2
feet above the ground. If the tree is growing on a slope, the 4
1/2 feet is determined at mid slope. This is the point halfway
between the high and low points where the trunk meets the soil. If
the tree is multi-stemmed, meaning it has more than one pith at ground
level, then largest leader or trunk is measured at a height of 4 1/2
feet. If fused multiple trunks extend above the 4 1/2 foot height,
then the girth should be measured above the height of the fusion.
For a single stemmed tree that branches below 4 1/2 feet, the girth should
be
measured at the narrowest point below the lower most significant fork of
the tree
noting the height of the measurement. If the tree has abnormal
swelling, burl,
or other abnormality, the measurement is to be taken at the
narrowest point
below 4 1/2 feet, and the height of measurement is to be noted.
Use reasonable
sense when measuring these types of trees as occasionally a measurement
just
above the 4 1/2 foot height might be more appropriate.
In all cases the girth is taken perpendicular to the axis of the trunk,
not
parallel to the soil. Measured girth is the best approximation of size,
since it
is a real number, without the built in assumptions of circularity used
to
calculate a diameter. Even girth has its limitations, as a sinewy or
contorted
trunk will have of hollows and ridges that are not accounted for in the
measurements. Diameters calculated from such trees will be overstated
Crown Spread
The last two measurements needed are for average crown spread.
This is a horizontal measurement, from leaf tip to leaf tip, of the
shortest spread, and the longest spread of the tree through the main
mass of the tree canopy. Adding the two numbers together, and then
dividing by two will give you the average crown spread.
The Pennsylvania Big Tree program collects both average crown spread
information for use in the American Forests Big Tree Program and maximum
crown spread for the Pennsylvania big tree list.
Measuring crown spread is difficult on trees where the branches are
high off the ground. If two people are present, each should walk
to where the tips of the farthest branch tips are directly overhead,
then measure the distance between the two points at ground level.
It is often hard to estimate when a branch tip is directly
overhead. If you have a clinometer use it to determine 90
degrees. Otherwise use your best estimate. Someone viewing
the tree and you from the side may be able to help align your position
to better locate the branch tip.
Good Luck with your tree measurements, and we hope to see your
submissions to the Pennsylvania Big Tree Program.
Stick Method and Crown Spread
diagrams courtesy of Ohio Big Tree Program