Outside 6 How Tall Is Your Tree?

Missouri Trees, the Missouri Department of Conservation guide to trees, gives height ranges for the different trees. The Department has a list of champion trees with their heights. There must be a way to measure how tall a tree is.

A short tree is easy to measure. Use a tape measure held at the bottom and read the inches at the top of the tree.

A tall tree is not so easy. It might be possible to climb the tree carrying a rope or long measuring tape with you. Those top branches might not be sturdy enough to hold you. Maybe, like me, you are not a very good tree climber.

There must be a better way to measure the height of a tree.

In fact, there are two methods.

tree

Method 1 will not work for my tree so I picked out the tall straight tree by a pasture.

Method 1

The first method only works for a tree out in the open so its shadow is easy to see. If your tree is like that, you will need a rod three or four feet tall, a way to pound the rod into the ground and a measuring tape or stick.

My tree is in the middle of lots of other trees so I couldn’t use this method. Instead I chose a tree by a pasture to show how this method works.

Watch your tree’s shadow. When is it long and easy to see? This is the time you to measure your tree.

rod in pasture

The rod was 41.5 inches with a shadow of 34 inches.

Go out early on a sunny day. Pound the rod into the ground so the sun shines on it to make a shadow. Measure how tall the rod is.

When the right time arrives, quickly measure the length of the rod’s shadow. Then measure the length of your tree’s shadow. Write all your measurements down. Change all of them into inches.

tree shadow

The tree’s shadow reached 799 inches into the pasture.

My measurements were 41.5 inches height of the rod, 34 inches length of its shadow and 799 inches the length of the tree’s shadow.

Calculating the height of your tree:

This calculation is simple algebra. Don’t give up if you don’t know any algebra. This is easy to learn.

First you need to know this axiom: What you do on one side of an equation (a math sentence) must be done on the other side so they stay equal.

Stop and think. Write the equation 3 = 3. I hope you agree that three does equal three.

Now, if you multiply one of those threes by two and want the equation to stay true, you must multiply the other side by two as well. This is written as: 3 x 2 = 3 x 2 or 6 = 6.

Second you will do a simple proportion. You know the height of the rod, the length of the rod’s shadow and the length of your tree’s shadow. You want to know your tree’s height so this is not known. Pick a letter to take its place for now.

The math proportion can be said as:

The height of my rod is to the length of its shadow as the height of the tree is to the length of its shadow.

In numbers these are written as two fractions with an equal sign between them. For the tree I used this would be: 41.5”/34” = x / 799”

Now comes the part the axiom tells us about. Multiply both fractions by the length of the tree’s shadow. For me that is 799”. My equation now looks like: (799”)(41.5”/34”) = (799”)x/799”.

Since a number over itself is another way to write one, the two lengths of the tree shadow become one and the letter is alone.

Do the calculation with the numbers. For the tree I used the answer is 975” or 81 ft tall.

Method 2

This method needs a special tool that is easy to make. You need a protractor, a straw, a piece of string, a paperclip and some tape. A large protractor is easier to read the angles on.

Fold the string over the flat part of the protractor in the middle. Tape the string to the protractor. Tie the paperclip on the other end of the string. Tip the protractor to make sure the string moves easily over the angles on the protractor.

homemade clinometer

You can make a clinometer with a protractor, straw, string and paper clips.

Tape the straw across the flat part of the protractor. Don’t tape over the string, just in front of and behind the string.

This tool is called a clinometer. It’s like the sextant used by surveyors and sailors. It is used to measure angles.

Take your clinometer, a yard stick and your journal out to your spot. A friend is helpful doing the measuring.

Standing a little ways away from your tree, look through the straw to the top of your tree. Put a finger on the string to keep it on the protractor angle when you put the clinometer down. What is the angle?

clinometer

The clinometer shows an angle of 55 degrees to the top of my tree.

This method works the best if the angle is between 40 and 70. If your angle is less than 40, try to move a little closer to your tree. If your angle is more than 70, try to move farther away.

Once you have your angle, write it down.

You held the clinometer at your eye level. How far is that above the ground? If you have a friend helping you, have your friend stand by your tree and put a hand on the trunk. Use the clinometer to find out when the angle is 90 degrees. Your friend may have to raise or lower the hand to get it right.

Measure how high the hand is. Write this down.

Now measure how far you stood from your tree to get your angle.

The angle to my tree was 55 degrees. The clinometer height was 61 inches. The distance to my tree was 172.5 inches.

my tree

My tree is surrounded by other trees so i must use Method 2.

Calculating the Height of Your Tree

This method uses a little trigonometry. It isn’t hard.

First make sure all your measurements are in inches.

You will need to find the tangent of your angle. Perhaps you have a calculator that will tell you. Otherwise you must look in a trigonometry table. I used a table.

Multiply the tangent of the angle times the distance to your tree. Then add the height to your friend’s hand.

The tangent of 55 degrees is 0.7002. I multiplied 172.5” x 0.7002 to get 120.8 inches. I added the 61 inches for a total of 181.8 inches or 15 ft.

How tall is your tree?