As promised, here is the third and final article on ways of measuring in woodcraft that are a not based on lasers, tapes or any gadgets. In this article we'll be using the maths teacher's best friend - the triangle - and looking at how its special properties can be useful in the woods.
An Old "Indian" Trick
The first use of the triangle is an old, possibly native American, trick for measuring the height of trees and other objects. I still remember being taught this on a trip to a nature reserve when I was ten. The idea is simple. You start with your back to the tree and walk away from it. Occasionally you bend over and look back at the tree through your legs. Once you have got so you can just see the top of the tree then you turn around and count your paces back to the tree. The number of paces away you are is equal to the height of the tree. Of course, this is prone to errors depending on how flexible you are and any lean of the tree but can be surprisingly consistent between people. It works as your field of vision when bending over forms a special 45-90-45 triangle and means that the distance from the tree is mathematically equal to its height.
The Magic Stick
A similar principle can be used for lengths as well as heights. The first step is to get a stick. The next part is the clever bit - the stick needs to be cut or broken to the same length as your arm, from knuckle to shoulder. When you hold your arm parallel to the ground you once again form this magic 45-90-45 triangle when you hold the stick straight up. This is true because you are holding the stick up at 90 degrees and the stick and your arm are the same length. Measurements can be made in the same way as the Indian trick but can be made in different planes too.
Measuring a River
There is a method that can be used to measure river widths that uses the magic little triangle too. It is well diagrammed here and essentially makes you create a large triangle and then a scale model of it. By measuring the scale version on dry land you are then able to multiply up to the real size of the river.
Shadows in Scale
What is a shadow? Simply one side of a triangle formed by the sun with the suns rays and the object making the other two sides. This enables us to use shadows as a measure for tall objects (largely trees). First off you need to find a stick and then using the techniques discussed in part one work out its length. This stick is then placed into the ground. A second stick is then cut to the same length as the shadow of the original stick. The number of times this second stick will fit into the length of the trees shadow can be used to tell us the height. For example, if it fits in 26 times and our first stick was 1m tall then we know our tree is 26 times taller and hence 26m tall.
The laws of trigonometry are used by professional foresters as they use a special tool called a clinometer which measures angles enabling heights to be deduced. Indeed, the clinometer is not particularly different from the sextant and I hope to have a play with one of those in a future post.
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