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Posts tagged ‘mensuration’

Forest mensuration on a smartphone

April 20, 2012

Gabriel Hemery


Forest mensuration (measuring trees and forests) has come of age. I have written a few posts about forest mensuration and also how to use a smartphone to measure tree height – see links below. I recently came across some really impressive apps for use by foresters and woodland owners to measure trees and areas, and to calculate stand basal area, using an iPhone smartphone.

The Relascope (Spiegelrelaskop), invented by Austrian forester Walter Bitterlich (1908-2008), is a specialist and expensive instrument used by foresters to estimating tree height, distance to tree (although this is complicated), and the basal area of a stand (the sum of the cross-sectional area of trees, taken as a dbh and calculated inside the bark). Although a superb instrument and highly accurate in trained hands, the Spiegelrelaskop is not likely to be used by many private woodland owners as it is unaffordable to many (£1500/$2400). Other relascope types are available, see How to use a wedge prism relascope to measure basal area, but the development of powerful forest mensuration tools for smartphones, which most people carry today, is very welcome.

The apps that I’ve been trying are available free from the Apple app store, developed by Taakkumn Watakushi from Fukushima  in Japan. I have no hesitation in recommending these two apps as I’m not aware of anything else like these that are available for foresters.  He also provides a compass surveying app (iCompass Surveying) that enables areas to be measured but I have not tested it.

iHypsometer-developer's website

iHypsometer - click to read more on the developer's website

The iHypsometer is a free (in the ‘Lite’ version) tool for estimating tree height. It works on the same principles of trigonometry that I explained in How to measure tree height using a smartphone but it copes with sloping ground (i.e. when the base of tree is not level with your feet) and it completes all the tricky maths for you. It requires that you have a ‘friend’, whose height you should measure, and who should stand next to the tree, although I find that a stick cut to a suitable height works just as well. Angle measurement works in the same way as I described in How to measure tree height using a smartphone except that it uses the short side of the phone. The only feature that I would like the developer to improve is to use the longer side of the phone for sighting along, as I have found in other apps that this provides much greater accuracy. Visit the iTunes app store to download iHypsometer

iBitterlich-developer's website

iBitterlich - click to read more on the developer's website

The iBitterlich is a free app for calculating forest stand basal area. It uses the view from the camera on an iTouch (latest model)/iPhone 3G and up/iPad, on which it overlays buttons where the number of trees of different categories of dbh can be counted simply by pressing them. In the screenshot (below) I was looking at the second tree that I had counted as a ‘+3’, and I had already counted 4x ‘+2’ and 11x ‘+1’ trees in my sweep, that at this point was almost complete at 320 degrees.

iBitterlich iphone app screenshot

iBitterlich iphone app screenshot. This tree is a '+3'. Basal area and Stand volume are displayed at the top.

After finishing a 360 degree sweep of the forest stand and counting all the trees, the average tree height is entered in another field, and form factor can be adjusted. The stand volume m3/ha and basal m3/ha are then displayed at the top of the screen. Visit the iTunes app store to download iBitterlich

Have you tried these apps in the forest and did they work for you? Are you aware of similar apps from other developers? Is there a similar set of apps for the Android platform? Do let me and readers know by sharing your views via a comment.

Gabriel Hemery

Other posts about forest mensuration

Basal Areas for common walnut

December 27, 2011

Gabriel Hemery

common walnut basal areas

There are no published Yield Class tables for common walnut Juglans regia – at least that I am aware of. A search on the European Forest Yield Tables Database reveals that data are only available for black walnut Juglans nigra in Hungary.

I wrote previously about research that I undertook exploring the crown sizes of major hardwood species – Estimating tree crown size. This work provides the next best available data on managing a stand of common walnut, in the form of basal areas for common walnut ref.

The table below shows the stem diameter (dbh), crown diameter (cd), crown/stem ratio (cd/dbh), number of trees per hectare (Nha) and acre (Nac), and Basal Areas (G) in m2 per hectare. These data were collected from trees grown in open conditions, and calculated for stand densities with zero crown overlap.




N trees per ha

N trees per acre

Basal Area m2 per ha















































































common walnut basal areas

Common walnut Juglans regia basal areas with dbh.

A growth rate of 1cm per year in stem diameter can be presumed, permitting this graph and data to be used in estimating suitable basal areas at different stand ages. If real dbh data is available, then the accurate growth rates will provide accurate basal area increase projections for a given site.

Gabriel Hemery


Hemery, G.E., Savill, P. & Pryor, S.N. (2005). Applications of the crown diameter – stem diameter relationship for different species of broadleaved trees. Forest Ecology and Management 215, 285-294. View abstract

How to use a wedge prism relascope to measure basal area

December 5, 2011

Gabriel Hemery

how to use a wedge prism relascope

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 breast height (at 1.3m above ground level), and is normally described per as the tree stem area per hectare (m2 ha-1). 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

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

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

Estimating tree crown size

May 23, 2011

Gabriel Hemery

I co-authored an academic paper in 2005 that summarised research undertaken to explore the relationship between a tree’s stem diameter and its crown (or canopy) diameter 1.  Out of my 60 or so publications, it has been one of the most popular among forest scientists (e.g. Google Scholar citations).

It was fascinating to discover that statistically there was a very good relationship (scientists would refer to a correlation from a regression analysis) between stem diameter and crown diameter.  We decided to explore this further by calculating the ratio between the two, we called it the z ratio (= crown diameter ÷ stem diameter).  We then plotted this z ratio against stem size.  You can see the result on the graph below for nine common European broadleaved trees.

Tree crown and stem diameter ratio graph

Crown diameter: stem diameter relationship for nine broadleaved tree species. The z ratio (y axis) is crown diameter divided by stem diameter; the dbh (x axis) is stem diameter at breast height (measured at 1.3m). Click to enlarge graph

The graph highlights some very interesting growth patterns and difference between different species:

  • Common walnut (Juglans regia) has the largest crown diameter at any given stage in its stem size.  When a walnut stem is 15 cm in diameter its crown can be estimated to be 5m wide.  Foresters can use that knowledge to design walnut plantations: e.g. if they plant their walnut trees 5m apart, their crowns will not compete until their stem diameter is 15 cm (which will take about 15 years from planting in the UK).
  • Sweet chestnut (Castanea sativa), like walnut, has a very large crown while it is young (with a small stem size).  Unlike walnut however, as its stem size increases, the ratio with its crown diameter decreases rapidly to the point after 35cm in diameter, when it has the smallest crown diameter for any of the nine tree species assessed.
  • Sycamore (Acer pseudoplatanus) has the most consistent crown to stem ratio while it grows.

basal area per hectare (G, m2 ha-1)The data can be used to plan tree spacings and to calculate basal area.  For example: for walnut with a stem diameter of 0.60m, its crown diameter is 13.27m, and its z ratio is 22.12.   Using the equation (left) for estimating basal area per hectare (G, m2 ha-1) tells us that there would be 57 trees per hectare with a basal area of 16.1 m2 ha-1.

These findings can be used beyond tree spacings and calculating basal area; they can also be used to help in:

  • planning thinning regimes (how many trees to remove in a growing plantation and when)
  • planning stand density (how many trees to retain in a forest stand at any given size)
  • assisting in managing mixed conifer-broadleaved stands
  • estimating branchwood  and woodfuel volumes
  • maintaining free-growth silvicultural systems, and
  • in urban tree planning by arboriculturists and landscape gardeners (e.g. designing and managing tree avenues).

Gabriel Hemery


1 Hemery, G.E., Savill, P. & Pryor, S.N. (2005).  Applications of the crown diameter – stem diameter relationship for different species of broadleaved trees. Forest Ecology and Management 215, 285-294. View abstract

How to calculate tree height using a smartphone

May 15, 2011

Gabriel Hemery

Foresters use a clinometer to calculate the height of a tree.  These can be quite expensive to buy so you’re not likely to invest in one unless you need to measure trees frequently. However, don’t despair as it is quite possible to achieve good results with a smartphone; with the advantage that you nearly always have one with you.  This is a method I’ve developed that I hope others will find useful.


Install a spirit level app

iPhone and Google Android phones (sorry, I have no working knowledge of Blackberrys) allow apps to be downloaded.  There are a number of apps available that use the smartphone’s accelerometer to provide a virtual spirit level.  Some of these include a tilt meter or level meter and it’s this kind that you will need to be able to measure an angle of elevation.

For the example below I use an iPhone and the Carpenter app from iHandy.  The full version costs under $2 and I’ve found that it works very well.  Even better the Level app, which you need for this method, is currently free as a stand-alone app.

Calibrate – the level … and yourself

  1. Zero your virtual spirit level
    If you’ve installed a good spirit level app it should allow you to calibrate your smartphone to reasonable accuracy.  On a shelf that you’ve checked to be perfectly level with a real spirit level, place your smartphone on its side , then ‘zero’ it (calibrate it to read ‘0’).
  2. Calibrate your pacing
    You will need to be able measure the distance that you are standing away from a tree.  You can of course carry a long tape measure with you when you think you’ll need one but I find it very helpful to know my pacing with reasonable accuracy.  For example I know that 21 of my strides equal 20m.
  3. Measure the height above ground of your eye
    Simply measure the distance from the ground under your feet to one of your eyes.

The data and the maths

The data required

You will need to know three things:

  1. The angle of elevation to the top of the tree from the horizontal
    As shown below the horizontal will be equivalent to a line between your eye and someone of the same height standing next to the tree.
  2. The distance from where you stand to the base of the tree
  3. The height of your eye above the ground
how to calculate tree height

The three measurements needed to calculate the height of a tree

The maths

Don’t be put off if you’re not confident about the maths as, although it may seem daunting, it’s actually quite simple.  You will use trigonometry but your smartphone’s calculator will do all the hard calculations for you.

The equation you will use is:

Tan angle of elevation   x  distance to tree


+ height of eye above ground

Step by step guide (with working example)

1.   Stand away from the tree

Stand away from the tree so that you can see its top.  The method works best if your angle of elevation is about 45o .  In other words that your distance from the tree is equivalent roughly to the height of the tree (you’ll get better at estimating this, the more trees you measure).

2.  Pace (or measure) the distance away from the tree

If you are working with someone else they can help you measure the distance from where you’re standing to the tree.  If you’re on your own, drop something where you’re standing to mark the position so that you can return once you’ve paced or measured the distance to the tree.

I was 21m away from my tree.  Write this distance down or memorise it.

3.  Measure the angle of elevation

measuring the angle of elevation with a smartphone

measuring the angle of elevation with a smartphone = 43.7 degrees

Standing at your spot (step 2) open the virtual spirit level app on your smartphone and select the angle measure.  Bring the smartphone to your eye and sight along its edge, as if you’re looking down a gunsight, aiming at the very top of the tree.  You will need to hold the phone so that your fingers are not in the way (see photo).

With the app I use there is a ‘hold’ button that freezes it when you are satisfied that you are ready to record the angle.

My angle of elevation was 43.7o.  Write this angle down or memorise it.

4.  Calculate tree height

Open the calculator on your smartphone.  You will need to access the scientific calculator.  For iPhones and HTCs you can do this by tilting your phone onto its side (landscape), where you will find the function for Tangent or Tan.

enter angle of elevation

enter the angle of elevation (43.7)

tan of angle

press tan (= 0.9556)

x distance to tree

multiply this by the distance to the tree (x 21m)

add height to eye

add height to eye (+ 1.73m)


press equals (result = 21.79m tall)

So my tree was 21.798m tall. Given that there is lots of room for error I would recommend that you round the result to the nearest whole number = 22m tall. It doesn’t matter whether you use metres or feet as long as you use consistently the same units throughout (i.e. don’t switch between m and cm, or between feet and inches).

Increasing accuracy

The method I describe above works well on level ground.  However, if you want to increase accuracy especially if the ground is not level, you can improve it quite simply.  Instead of using the height of your eye above ground, you substitute it with (Tan angle to the base of the tree x distance to tree).  So the full equation would be:

(Tan ∠ to tree top x distance to tree) + (Tan ∠ to tree base x distance to tree)

Other applications

You can use this method to calculate the height of other features on trees, such as the height of the lowest branch, a major fork, a bird nest or bat roost, or of course for any tall object such as a bridge or building.

Gabriel Hemery

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