# Mensuration

## Mensuration: working out lengths, areas and volumes

Woodland managers need to take a range of different measurements from trees including the height and diameter. They use these measurements to help them calculate the volume of saleable timber they have in their woodland.

**Height**

Forest and woodland managers are normally interested in two different types of tree height: the total height and the timber height.

The total height of a standing tree – is the vertical distance from its base to the uppermost or highest point or tip. Care is needed to make sure the true top of the tree is visible. In a woodland environment, this can be difficult if the crowns interlace.

- The timber height – the vertical distance from the base of the tree to the point on the main stem where the diameter is a minimum of 7cm.

A diameter of 7cm is the minimum size for a trunk to be useful for conventionally saleable timber. Exactly where that point is on the tree is easier to determine in theory than in practice. Issues such as side branches and establishing exact ground level when a tree is growing on a slope can make this tricky.

Tree height is usually measured using a clinometer or ‘angle gauge’ or by using a device called a hypsometer.

**Using a hypsometer**

Using a hypsometer is quite simple.

Sight the base of the tree and take a reading which, if you are on level ground, should be zero. Next, sight the top of the tree (or the timber height) and take a second reading.

The height of the tree can then be calculated by subtracting the first reading from the second reading. On sloping ground, if the base of the tree is below you, add the two readings together instead.

The clinometer and the hypsometer use the principles of trigonometry to measure angles and distances.

However, to get a good idea of a tree height without the aid of special equipment you can use the following manual method with the help of a friend.

**A simple manual method**

Ask a classmate to stand at the base of the tree you wish to measure. Hold your ruler in front of you (a) with your arm out straight and back away from the tree slowly until the tree and the ruler appear to be the same size. (You may need to close one eye to get it just right).

Next, keeping your arm straight, turn your ruler sideways so that it runs level with the ground. Keep the bottom of the ruler next to the tree trunk and ask your classmate to walk to the point on the ground where the top of the ruler is. Finally, using a measuring tape or wheel, measure the distance along the ground between your classmate and the tree and this will give you the tree height.

**Measuring diameter**

Measuring trunk diameter for forestry purposes is always done at breast height; conventionally the diameter at breast height (or DBH) is 1.3m above ground level. Slight adjustments are needed for trees growing on a slope, or for those that lean, fork low down or have misshapen trunks.

The diameter measurement can be taken using calipers which will provide a direct measure of diameter. A caliper measurement is best taken twice: take two measures of diameter at right angles to one another and use the average.

Alternatively, a non-stretch tape can be used to measure the circumference which is then converted to diameter using the following calculation: diameter = circumference ÷ π, where π (Pi) is a constant (3.14).

So, to find the tree diameter you simply divide your circumference by 3.14.

It is possible to purchase special girthing tapes to do the mathematics for you. These are number-marked to take π into consideration, so you can measure the tree circumference and read off the diameter in centimetres directly from the tape.

**Calculating volume**

Once the tree height and diameter are measured, woodland managers can begin to calculate specific merchantable volumes depending upon how the wood is to be used.

If you think of a tree as a cylinder-shaped object then the volume would normally be calculated by simply using π multiplied by the square of the radius: volume = π r^{2}.

If you think of a tree as a cylinder-shaped object, then the volume would normally be calculated by simply using the following calculation: height x π x r^{2}.

However, forest managers use a range of complex formulae to calculate volume which also takes into account tree species, shape and form.

In addition, it would be impractical to measure every tree in a woodland so forest managers sample random plots, taking height and diameter measures and counting the number of trees of each species. From this information, they can establish species composition, size distribution, basal area and timber volumes.