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Estimating Height of Trees

In the Garden > Others

If you have ever tried to guess the height of a tree, you'll know that it is difficult. Well, there is a simple method to estimate the height of a tree, which doesn't require any guess work or tree climbing. The method is based on the theory of proportions and works like this: the height of the tree divided by the length of its shadow is equal to the height of a stake divided by the length of its shadow (see diagram). If all but one of the measurements is known (for example the height of the tree), the unknown quantity can be worked out using a simple mathematical formula.

What you need
You will need:
* a tomato stake (any height, it doesn't matter);
* a hammer (to hammer in the stake);
* a tape measure;
* a pen and paper; and
* a calculator (unless you are good at mental arithmetic).

Measurements
All measurements should be in the same quantity for example metres:
Step 1: Measure the length of the shadow of the tree whose height you wish to estimate. Measure from the base of the tree to the tip of the shadow. Make a note of the length. In our example it was 20 metres. Hint: If the shadow is longer than your measuring tape simply use a coin to mark the length of the tape and then continue to measure from the coin.
Step 2: Hammer in a stake nearby and measure the height of the stake from top to ground. Make a note of the measurement. In our example, the height of the stake was 1.68m.
Step 3: Measure the length of the stake's shadow. Note: The two shadows must be measured at about the same time as the length varies with the position of the sun. Make a note of the measurement. In our example it was 2.88m.

Calculation To estimate the tree's height, multiply the length of the tree's shadow by the height of the stake and divide this calculation by the length of the stake's shadow. This is best described using the following equation:

(Length of the tree's shadow x Height of the stake) / (Length of the stake's shadow)

In our example this would be:
20m x 1.68m
2.88m
Answer: the height of our sample tree is 11.6 metres (or approximately 38').

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