# Elms Environmental Education Center

## How to Use a Clinometer

A clinometer is used to measure angles. This is the method used by foresters to measure the height of a tree. The clinometer only works for measuring height when the observer is standing exactly one "chain" length away from the tree (66’ or 100 links). A “chain” is a unit of measure unique to forestry and dates back to the use of chains to drag felled trees out of the forest.

1. To use the clinometer, pinch the brass ring between your thumb and forefinger and look through the black eye piece using only one eye. If possible, the other eye should be looking at the tree. In the eyepiece you will see a black line and a scale. The right side of the scale is the height reading, the left is % slope. You want to read the right side of the scale.

a. Tilt your head until the black line is on the base of the tree and read and remember the number where the black line crosses the right hand side of the scale. (It will be a negative number because zero equals the height of your eye and you will inevitably be looking down at the base of the tree.) This is the distance from the height of your eye to the base of the tree.

b. Repeat the process above except this time place the black line where you think the top of the tree is located. Read and remember the number where the black line crosses the right side of the scale. This is the distance from the top of the tree to the height of your eye. (It will be a positive number because you will be looking above the height of your eye. Unless, of course, the height of the tree is level or below eye level.) Note: When using the clinometer one must often “guesstimate” where the highest point of the tree is located.

c. Simply add these two numbers together to get the overall height of the tree. (When adding the negative number from the first reading, forget what you learned in math class. In this case the number is negative only because it is below the height of your eye.)

Remember, the easiest way to measure 66', so you are standing in the right place when you use the clinometer, is to know your pace. Your pace is simply how far you have walked when your right or left foot strikes the ground . For example, start walking with your right foot, then your left then your right again. STOP! Measure this distance. You will have to do this many times and walk the same way every time so that, with practice, you can accurately duplicate the same distance. Knowing this, you can now measure distances in the field without the need for a tape measure. (Note; as you grow and your legs get longer your "pace" will change.)

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The math involved uses trigonometry, which you will encounter in high school. Fortunately, the instrument does all the calculations for you. Foresters are LAZY! (not really) But they are also SMART! (A much better combination than lazy and stupid, and not nearly as good as hard-working and smart!)

Math Explanation: Note that the theory behind the clinometer utilizes trigonometry, which you will encounter in high school. Trigonometry is frequently used for indirect measurements like measuring the height of an object.

i. First note that we are working with two right triangles (one formed by the height of the eye to the top of the tree and the other formed by the height of the eye to the base of the tree. See the red lines in the diagram above) and we know only three things about each:

1. The base of the triangle is equal to 66’ (one chain)

2. One of the three angles is 90°

3. The clinometer is measuring another one of the angles.

ii. From this we can quickly determine the third interior angle of the triangle, though it is not particularly useful to know for our purposes. All three interior angles of a triangle must equal 180°. Use this formula: x = 180 - (c+90), where “c” is the angle measured by the clinometer.

iii. What we want to know is the length of the side opposite the angle measured by the clinometer (the height of the triangle) and all we know is the length of the base and all three interior angles. The trigonomic ratio called “tangent”, abbreviated “tan”, will allow us to calculate the height of the triangle. (The tangent of an angle is a ratio of the length of the side opposite the reference angle, to the length of the side adjacent to the reference angle. In other words, tangent of an angle = opposite side ÷ adjacent side) Use the following formula:

h

Tan(c) = ---- or h = 66 x tan(c)

66

where h=height of triangle and c=the angle measured by the clinometer.

iv. Whew! So to measure the height of the tree we must use the clinometer to perform this calculation for both right triangles. By assuming the base of the triangle (eye level) is 66’ and knowing the angle measured when you tilt your head, the clinometer simply has a calibrated scale of results that moves as you move your head – or as you change the angle you are measuring. For a dynamic interpretation of the relationships between the sides and angles of a right triangle see: http://catcode.com/trig/trig04.html.