The relascope is a forester’s tool used for forest mensuration, or tree and forest stand measurements. The Spiegel relascope is the bee’s knees of forest inventory tools; allowing the user to estimate tree heights, stem diameters at different heights, and Basal Areas. It comes at a high price though as it’s a complex surveying tool (expect to pay £1500/€1750/$2400), so it is only used typically by professionals who measure a lot of trees. There are cheaper ways of measuring trees, such as a diameter tape for stem diameter or a clinometer for tree height (or even use a smartphone to estimate tree height). To assess Basal Area there is a different type of relascope available; the wedge prism relascope. This post aims to provide a simple explanation of how to use a wedge prism but first some background information.

What is basal area?

Basal Area (BA) is the cross-sectional area of a tree at dbh (stem diameter at breast height – measured at 1.3m), and is normally described per hectare of land area (G m² ha^-1). The Basal Area provides an indication of the productivity of the land, and the growth rate of the trees when one or basal area estimates are compared.

How to measure basal area of a stand the hard way

To estimate the Basal Area of a single tree, measure the tree’s diameter at breast height (dbh) and convert to BA with the following formula:

BA = 0.00007854 x dbh²     dbh is in cm.

The result will be in m².

You can them estimate the Basal Area of a forest stand by adding together the basal areas (as calculated above) of all of the single trees in the area, and then by dividing this figure by the area of land (in m²) in which the trees were measured (e.g. /10,000 if in one hectare). As you can imagine, estimating Basal Area for a forest stand with this method is hard work; this is where a wedge prism relascope comes into its own.

Using a wedge prism relascope

A wedge prism can be used to estimate quickly the Basal Area per hectare, and one costs only 2% the price of a Spiegel relascope! It is a simple wedge-shaped prism of glass or see-through plastic, typically 5 x 2 cm. It distorts the light and shifts the position of a tree stem when looked at through the prism. Different factors of prism relascopes are available, with common Basal Area Factors being 5, 8, or 10.

How to use a wedge prism relascope

I created this diagram to explain simply how a wedge prism relascope is used in the forest. The technique with the relascope is to stand at one point among the trees and to complete a 360 degree sweep around, counting all the trees that are ‘in’. Those that are ‘borderline’ should be counted every other time, and those that are ‘out’ discounted. To estimate the Basal Area simply multiply the number of counted trees by the Basal Area Factor (e.g. 5, 8 or 10).

Using a wedge prism relascope. Count (left), borderline (centre), and Don't count (right). Click to enlarge.

You should conduct as many sweeps around the stand of trees as you can, as this will provide a more accurate estimate when averaged over the stand.

Gabriel Hemery