On September 7, 2006 the
San Francisco Chronicle reported
that researchers had just discovered a 378 foot (113 meters) tall
tree that is probably the world's tallest living tree. If you think
you can find a tree that can break that record, or just want to
measure that tree in your backyard, try these techniques. These
methods can also give you a good approximation of the heights not
only of trees, but also of telephone poles, buildings, magic
beanstalks—pretty much anything tall.
Shadow Method
[edit]
- Know your exact height in the shoes you will be wearing to
perform this method.
- Stand next to the tree or the object to be measured. For best
results, do this method on a bright, sunny day. If the sky is
overcast, it may be difficult to tell exactly where the shadow’s
tip is
- Measure the length of your shadow. Use a tape measure or
yardstick (meter ruler) to measure your shadow from your feet to
the tip of your shadow. If you don’t have someone to assist you,
you can mark the end of the shadow by tossing a rock onto it while
you’re standing. Or better yet, place the rock anywhere on the
ground, and then position yourself so the tip of your shadow is at
the rock; then measure from where you're standing to the rock.
- Measure the length of the tree’s shadow. Use your measuring
tape to determine the length of the tree’s shadow from the base of
the tree to the tip of the shadow. This works best if the ground
all along the shadow is fairly level; if the tree is on a slope,
for example, your measurement won’t be very accurate. You want to
do this as quickly as possible after measuring your shadow, since
the sun’s position in the sky (and hence the shadow length) is
slowly but constantly changing. If you have an assistant, you can
hold one end of the measuring tape while he or she measures the
tree’s shadow, and then you can immediately measure your
shadow.
- Calculate the tree’s height by using the proportion of your
shadow’s length to your height. Since you know the length of the
tree’s shadow, and you also know that a certain height (your
height) produces a certain shadow length (the length of your
shadow), you can determine the tree’s height with a little math.
Multiply the length of the tree’s shadow by your height, and then
divide the resulting number by the length of your shadow. For
example, if you are 5 feet (1.5 meters) tall, your shadow is 8 feet
(2.4 meters) long, and the tree’s shadow is 100 feet (62.5 meters)
long, the height of the tree is (100 x 5) / 8 = 62.5 feet (30.48 x
1.5 meters) / 2.4 meters. Note that the order of your
multiplication does not matter.
Pencil Method: Requires an
Assistant [edit]
-
A distant view
Stand far enough from the tree so you can view the whole tree—top
to bottom—without moving your head. For the most accurate
measurement, you should stand so that you are on a piece of ground
that is about level with the ground at the tree’s base. Your view
of the tree should be as unobstructed as possible.
- Have a friend stand near the tree.
- Hold a pencil or a small, straight stick (such as a paint stick
or ruler) in one hand and stretch your arm out so that the pencil
is at arm’s length in front of you (between you and the tree).
- Close one eye and adjust the pencil up or down so that you can
sight the very top of the tree at the top of the pencil. This is
easiest if you turn the pencil so that the sharpened point is
pointing straight up. The tip of the pencil should thus just cover
the top of the tree in your line of sight as you look at the tree
“through” the pencil.
- Move your thumb up or down the pencil so that the tip of your
thumbnail is aligned with the tree’s base. While holding the pencil
in position so that the tip is aligned with the tree’s top (as in
step 3), move your thumb to the point on the pencil that covers the
point (again, as you look “through” the pencil with one eye) where
the tree meets the ground.
- Rotate your arm so that the pencil is horizontal (parallel to
the ground). Keep your arm held straight out, and make sure your
thumbnail is still aligned with the tree’s base.
- Have your friend move so that you can sight his or her feet
“through” the point of your pencil. That is, your friend’s feet
should be aligned with the pencil’s tip. He or she may need to move
backward, sideways, or diagonally. Since, depending on the height
of the tree, you may need to be some distance away from your
friend, consider using hand signals (with the hand that is not
holding the pencil) to tell him or her to go farther, come closer,
or move to the left or right.
- Measure the distance between your friend and the tree. Have
your friend remain in the place or mark the spot with a stick or
rock. Then use a measuring tape to measure the straight-line
distance between that spot and the base of the tree. If you don’t
have a measuring tape you can pace out the distance, although this
will not be as accurate. The distance between your friend and the
tree is the height of the tree.
Angle of Elevation Method
[edit]
- Measure the distance to a sighting position. Stand with your
back to the tree and walk out to a point that is approximately
level with the ground at the tree’s base and from which you can
clearly see the tree’s top. Walk in a straight line, and use a
measuring tape to measure your distance from the tree. You need not
stand any set distance from the tree, but this method generally
works best if your distance from the tree is about 1-1.5 times the
height of the tree.
- Measure the angle of elevation to the tree’s top. Sight the top
of the tree and use a clinometer or transit to measure the "angle
of elevation" between the tree and the ground. The angle of
elevation is the angle formed between two lines—the flat plane of
the ground and your sightline, to some elevated point (in this
case, the tree’s top) — with you as the vertex of the angle.
- Find the tangent of the angle of elevation. You can find the
tangent of an angle using a calculator or table of trigonometric
functions. The method for finding the tangent may differ depending
on your calculator, but usually you just push the “TAN” button,
enter the angle, and then press the “equal” button (=). Thus if the
angle of elevation is 60 degrees, you simply push “TAN” and then
enter “60” and then press the equal sign.
- Multiply your distance from the tree (measured in step 1), by
the tangent of the angle of elevation. The resulting number is the
height of the tree minus your height.
- Add your height to the height you calculated in the previous
step. Now you have the height of the tree. You need to add your
height because you measured the angle of elevation from eye level,
not from the ground.
Fixed Angle of Elevation
Method [edit]
- Fold a square piece of paper in half so that it forms a
triangle. The triangle will have one right (90 degree) angle and
two 45 degree angles.
- Hold the triangle near one eye so that the right angle faces
away from you and one side is horizontal (parallel to the ground,
assuming the ground is level).
- Move back from the tree until you can sight the top of the tree
at the top tip of the triangle. Close one eye to sight the tree’s
top. You want to find the point where your line of sight follows
the hypotenuse of the triangle to the very top of the tree.
- Mark this spot and measure the distance from it to the base of
the tree. This distance, plus your height(because you used the
angle of elevation from eye level, not from the ground)is also the
height of the tree. This works because the angle of elevation using
your triangle is 45 degrees, and the tangent of 45 degrees =
1.
- Realize that many times using DBH (diameter at breast height)
is a more useful and much easier way of assessing a tree's size and
age.
- For increased accuracy using the shadow method you can measure
the shadow cast by a yardstick or similar straight stick of known
height instead of a person’s height. Depending on how you are
standing, your height may vary (i.e., if you are slouching or
tilting your head slightly).
- You can improve the accuracy of the pencil method and the angle
of elevation methods by taking several measurements from different
points around the tree.
- Be consistent with your units of measurement (multiply and
divide feet by feet or inches by inches, for example.)
- Clinometers and transits are tools which allow you to measure
the angle between a horizontal plane and the object you are looking
at (the transit, in particular, also is used to measure angles
between vertical planes). You want to measure the angle between the
ground and the tree’s top, but the clinometer or transit will
measure the angle between the horizontal plane at your eye level
(since you look through the instrument), and this is why you need
to add your height to the calculation. Some clinometers and
transits, however, allow you to adjust for your eye height. If you
have already adjusted for your height do not add your height at the
end of the calculation.
- Many trees are not perfectly vertical—they don’t grow straight
up. Using the angle of elevation methods you can adjust for an
angled tree by measuring the distance between you and the point on
the ground that lies directly below the tree’s top, rather than
measuring the distance between you and the base of the tree.
- You can make a simple clinometer very easily using a
protractor. Check out the related wikiHow for instructions.
- This can be a fun activity for 4th to 7th grade kids.
Warnings [edit]
- These methods do not work well if the tree is on sloping
ground.
- While the angle of elevation methods, if used correctly, can
calculate the correct height within 2-3 feet, there is abundant
opportunity for human error, especially if the tree is angled or on
a slope. If precision is absolutely necessary, consult your local
extension service or other such agency for assistance.
Things You'll Need
[edit]
- A friend (optional for three of the methods, but a little help
makes the process easier and more fun)
- A pencil or ruler
- A tape measure or yardstick/ meter ruler
- A clinometer or square piece of paper
