**Only in exceptional cases can tree height be measured directly. There are many instruments for measuring heights. They are known as hypsometers, altimeters, or clinometers. In modern times, the smartphone that uses the software based on the augmented reality technology can measure the height of a tree as well, such as one developed by the company ARBOREAL from Sweden. Do you know how these instruments work? **

# How to measure the height of a tree?

## Two principles

Those instruments are based on two principles:

- Geometric principle – the relationship between similar triangles.
- Trigonometric principle – the determination of angles of inclination.

## Geometric principle

Christen, Merritt or JAL altimeter use geometric principle, which is based on the equation: A’C’/AC = A’B’/AB, where AB corresponds to the tree height. Before mentioned instruments that apply this principle use fixed distances of A’B’, A’C’ and AC, where A’B’ and A’C’ are given on the instrument and AC is set by some reference fixed at the tree (see the formula on the main photo).

### Christen altimeter

With the Christen altimeter, the visual image of the tree or part of the tree to be measured must be fit exactly between the upper and lower ends of the scale. The height or length of a tree, a stem, or a stem section is then determined on the basis of a fixed reference length on the stem. Instruments such as Christen altimeter are relatively simple in construction, only one reading is necessary, and the measurement is not affected by the inclination of the terrain.

## Trigonometric principle

By using the trigonometric principle, one measurement is made at the tree tip, another at the stem base. The two angles α_{1 }α_{2 }are read and the distance from of the observer from the tree, *D*, is measured. The tree height is then determined from these three variables according to the formula presented on the main photo.

Examples of instruments using the trigonometric principle are the Abney level, the Haga altimeter, the Blume-Leiss, Matusz (developed by Forest Research Institute in Poland – a figure below) or Suunto clinometer (figure below).

Today more modern instruments for measuring tree height are used, such as Vertex altimeter (photo below), which uses ultrasonic signals to obtain the exact distance from the observer to a tree. The height is calculated trigonometrically through the distance and angle. The Vertex can be used for measuring height, distances, angle, inclination and current temperature.

Very often the Bitterlich Relaskop is used together with Vertex to make sample plots needed to measure the volume of the stand.

## Modern times

The most modern technology uses Augmented Reality (AR) and a company ARBOREAL, led by Johan Ekenstedt, is bringing this technology to forestry. After the application is installed on the smartphone, it is using the sensors and cameras on the phone together with AR-technology to measure the height of a tree. I used Arboreal a few times in the forest, and I have to admit that technology gives great accuracy and it is very intuitive and easy to use. We did some comparisons with Vertex, and Arboreal provided very robust and accurate results.

**Install it on your smartphone and check it out in the forest! Here you have a tutorial on how to use it! **

The Arboreal’s CEO – Johan Ekenstedt – will be present at the **International Forest Business Conference (IFBC)**, held between **December 7-9, 2020** in Poland. Don’t miss this opportunity to listen to his presentation on “*Augmented Reality in the forestry – today and in the future.*”

**Main photo credit: Rafal Chudy**

**Source: Michael Köhl, Steen S. Magnussen, Marco Marchetti. Sampling Methods, Remote Sensing and GIS Multiresource Forest Inventory. Springer, 2006. **