Doug Riddle's "angle" on measuring big trees
Doug Riddle firstname.lastname@example.org
Here is my $0.02 for measuring tree
heights from another "angle". There are 2 trigonometric rules that govern
what is done in measuring the height of trees. 1. For a triangle, if you
know 2 angles and 1 length you can calculate the other angle and other
2 lengths. 2. For a triangle, if you know 2 lengths or "legs" of the triangle
and the angle between the legs you can calculate the other length and other
2 angles. When you measure the height of a tree you are creating a "right"
triangle. That is a triangle with one angle fixed at 90 degrees. So part
of your work is done for you. Assuming a flat area of ground and a single
visible crown: Using the clinometer and laser you can measure the angle
to the highest crown of the tree and you can read the distance with the
laser from you to that point at the crown of the tree. This gives you an
angle and a length. The second angle is the 90 degree angle formed by an
imaginary line from the tree's visible top to the horizontal ground. So
you have the necessary information to know the height of the tree. The
tree's height = laser distance x sine of the angle read with the clinometer.+
your height from eye level to ground. The sine of angles from 0 to 90 degrees
is found either in a trigonometric table or by using a calculator with
trig functions. You simply read the trig value of the angle and multiple
times the laser distance.
Bob Leverett mentioned the fact that
the clinometer gives you 2 numbers on the wheel insider the instrument.
The number on the left, when you look inside the clinometer, is the angle
value that you want to record. The number on the right is a percent value.
The percent can be used to calculate the height of the tree based on another
equation which I won't digress to explain. The value of using the laser
is that you read the height from the point you see as the top of the tree
to ground. This avoids the problem of measuring the angle to a high point
on the tree and then pulling a tape from your reference point to the base
of the tree and assuming that the high point is directly above the trunk
of the tree. Whether the high point of the tree is over the trunk or not
, the laser and clinometer gives you a true vertical distance for height.
The above example is the basic equation.
There are endless variations. There are situations where you are not standing
level with the base of the tree. Elementary trig equations can be used
to solve these differences and give you an accurate height. Don't worry
about the variations, just know that in time you will be able to handle
all the variables.
Some priorities to keep in mind for
now: A. Get far enough back to see the top of the tree. I try to be far
enough back that the angle is less than 45 degrees. That is not a requirement,
nor is it always possible; but if the angle is less than 45 degrees I seem
to have a good view of the crown of the tree. B. Don't worry how far back
you go, the laser will still give you a reading. The only time you will
not get a laser reading is if you are less than the minimum distance. For
the Bushnell 400 it requires a minimum distance of 25 yards. C. Walk around
the tree looking for a window in the canopy to see clearly the top of the
tree. The laser is sometimes fussy about having a clear view and you can
get false short readings from intervening twigs and limbs. D. Use triangulation,
(ie measure the height of the tree from more than one side), to find the
highest point of the tree. A spreading crown obscures the top of many trees.
Some benefits: A. If you want a quick
reading you can stand beneath the tree and use the laser for a vertical
height. It will give you a "ball park" value to let you know if you want
to take the time for a more accurate reading. Remember to add to your reading
in this case your height from eye level to ground. B. If you are on one
side of Cedar Cr. and the tree is on the opposite side you can still measure
its height with the laser and clinometer. C. Similarly if the tree is a
cypress in the middle of a body of water, you can use the laser for height
and clinometer for angle and know the height above water of the tree. Of
course you will not know that portion of the tree's height that is below
water. D. If you are in a canoe you can still measure the height of the