How to Draw Tall Tree

There are many reasons to measure the height of a tree. You may need to know what it could hit if it falls, how high up the fruit is, or may simply want to establish bragging rights. Whatever the reason, measuring the height of a tree is not difficult. Below are four methods that work in most situations. All methods require that you are fairly level with base of the tree.

45° Triangle Method – Easy

This method requires a square piece of paper or card and a way to measure distance from the tree.

Measuring the height of a tree using a 45 degree angle.

1. Fold the paper/card square in half to make a 45° right angle triangle.
2. Hold the triangle up to your eye and look along the longest side at the top of the tree.
3. Move backwards/forwards until your eye lines up with the top of the tree and the two shorter sides run parallel with the ground and tree trunk.
4. Measure the distance from where you stand in step 3 to the base of the tree. The distance is equal to the height of the tree from the height of your eye (see diagram above for clarification).
5. Add the measured distance/height to your eye height. Remember you calculated the tree height from your eye level and so you need to add your height for total tree height.

A limitation is when the tree has a spreading canopy, you might be unable to see the top with a 45 degree angle. In that case you would need to use the 'full version' of this technique, the trigonometry method.

Trigonometry Method – Medium

This is the 'full version' of the 45° triangle method above. With an angle of 45°, the math is easy and height equals distance. When you use an angle other than 45° (when you are forced to stand closer or further away) the math is a little more involved. For this method you will need clinometer and a way to measure your distance from the base of the tree.

Measuring the height of a tree using trigonometry.

1. Measure the angle between the top of the tree and the ground from your eye. Ideally do this using a clinometer. Stand up straight on level ground. You need to be far enough back that you can easily see the top of tree. Put the clinometer to your eye and line it up with the top of the tree while holding the lever (lets the indicator swing freely). Release the lever to trap the indicator and then read off the indicated angle. If you don't have a clinometer you can just mark the angle on a peice of card and measure using a protractor.
2. Now that you have the angle, measure the distance between the tree and where you were standing in step one. Do this with a measuring tape or wheel for a more accurate result.
3. Use the Tangent rule to calculate height of the tree (above eye level).
   tan(angle) = opposite/adjacent
   Where opposite is the height of the tree and adjacent is the distance between you and the tree. This is rearranged to:
   opposite = tan(angle) x adjacent
   or more simply
   height = tan(angle) x distance
4. Add the height of your eyes to the calculated height of the tree. This gives you the total height of the tree. Remember you measured from your eye height and so you have to include how high your eyes are. See the diagram above for clarification.

For example, if I stood 20 m from a tree and the angle between the tree's top and horizontal from my eye was 30 degrees, I would calculate the height as follows:

height = tan(angle) x distance
height = tan(30) x 20
height = 11.55 m

I am 1.75 m tall at my eyes and so

total height = 11.55 m + 1.75 m
total height = 13.3 m

Pencil Method – Easy

An easy method that can be done on the fly. I find this especially useful when I want a quick method for seeing if anything is within the fall zone of a tree. Note the danger zone when felling trees is generally considered to be a radius of two times the height of the tree.

1. Hold a pencil up in your outstretched arm. You can also use a small, straight stick for this method.
2. Stand far enough back that the tree height fits within the length of the pencil.
3. Hold the base of the pencil in line with the base of the tree and mark the top of the tree on the pencil (you can just use your thumb on the other hand).
4. Turn the pencil sideways as though the tree had fallen over. Remember (or have somebody mark) where the 'top of tree' mark (or thumb) is in relation to the tree along the ground. The distance from this point on the ground to the base of the tree is roughly equal to the tree's height.

Smartphone Method – Very Easy

Technology to the rescue! Apps have changed the way we do so many things and it looks like estimating tree height is no exception. There are a few apps that will do the job and the ones I have tried seem to be fairly accurate. Until I have more experience with these apps I won't recommend any particular one. I also won't suggest they are an adequate replacement for more time tested methods, but perhaps they soon will be? Height measuring apps are certainly worth looking into though.

Final Thoughts

Sometimes we need to calculate the height of a tree and the above four methods will get the job done. Each method has its limitations but they can usually be worked around. Please let me know if you have another method worth adding!

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Source: https://practicalprimate.com/measure-tree-height/

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