# Bitterlich Point Sampling Method for Timber Cruising

April 3, 2013 Leave a comment

To estimate the amount of wood that can be harvested from a timber stand, a straightforward method is to divide the timber stand into a number of plots, sample a percentage of the plots then blow up the measurement results accordingly. This method won’t be as accurate as measuring every tree in the stand, but a 10% cruise will usually provide adequate results for a timber stand that is more or less uniformly stocked.

This plot sampling method still requires the forester to measure every merchantable tree within each selected sample plot. To further reduce the amount of sampling time and effort, Mr. Walter Bitterlich devised the point sampling method, which provides a way to select only a few sample trees at each sample point and still arrive at fair estimated results. Many, if not most, foresters now employ the point sampling method, also known as the variable plot method, for timber cruising. However, not everyone understands the rationale behind this ingenious method. In fact, some foresters flat-out discount this sampling method, which makes use of the so-called Basal Area Factor (BAF) and a prism or an angle gauge for selecting the sample trees.

Bitterlich’s method is based on the relationship between the basal area of a tree and the basal area per acre that this tree represents. Here we provide an example to help you see the mathematical relationship between the tree radius, the variable plot radius (limiting distance) and the BAF.

Assume a tree has a circular girth with 12” (1 ft) diameter at breast height.

Then its cross-sectional area at breast height is:

A1 = π * (1/2)^{2} = 0.785398 sq. ft

The area of a circular plot with 33 ft radius is:

A2 = π * (33)^{2} = 3421.192 sq. ft

The ratio A1/A2 = 1/4356

This is the same as (0.5)^{2}/(33)^{2} because the π cancels out in the ratio

We can rewrite the ratio as: A1/A2 = 10/43560

Or, A1/A2 = 10 sq. ft /43560 sq. ft

1 acre = 43560 sq. ft

This means that a tree with 12”diameter in a circular plot with 33’radius represents a basal area of 10 sq. ft per acre.

The factor of 10 is called the Basal Area Factor, or BAF. The 33 ft plot radius is called the limiting distance for a 12” DBH tree representing a BAF of 10.

If you connect the plot center to the two sides of the tree, you will see that any concentric circle within this circular plot will intersect the wedge in an arc (d2) that bears the same relation to its radius (r2) as the 12” tree (d1) to the plot radius (r1). Therefore, a tree with this arc length as the diameter can also represent a basal area of 10 sq. ft per acre. And if you move our 12” tree closer to the plot center, it will be wider than the arc at the point it intersects the wedge.

This means that one could employ an angle gauge for selecting trees in the plot that meet this 10 BAF specification. The forester stands over the sample point and scans the trees all around him or her. Any tree with a stem that completely fills or extends outside the opening of the angle gauge is considered an IN tree, and will be counted.

The total tree count multiplied by the BAF yields the Basal Area per Acre for the point being sampled.

The height and diameter of the selected trees can be measured for log volume computation.

If a timber stand consists of larger trees, then one will make use of a larger BAF, such as BAF = 20, so as to select 5 – 10 representative trees per point. The limiting distance for a 12” DBH tree representing a BAF of 20 is 23.3 ft. A judicious choice of the BAF to use for the timber stand will help minimize the costs and increase efficiency without sacrificing accuracy.

The built-in camera of an iPhone, iPod touch or iPad lends itself well to an angle gauge app for point cruise sample tree selection. The **Cruise Angle iCMT** app provides this functionality. It will automatically display the Tree Tally and the Basal Area Per Acre (BAPA) for the sampling point.

As many foresters already own an iPhone, iPod touch or iPad, it makes economical sense to load a number of apps on their devices to help with their forestry tasks. Besides the Cruise Angle iCMT, there is also the **Stakeout iCMT** app that can help them go from one sampling point to the next.

For iPad users, there is the **iCMTGIS II** for mapping timber stands using GPS and for recording various types of data. There are also the **Farming GPS GIS** app and the soon-to-be released **Forester GPS GIS** app, which will let the users delineate the timber stand, create sampling grid points then record data for each sample point. Forester GPS GIS provides the cruise angle gauge function as well as the stakeout functions.

iPhone users could use the **iGPSGIS II** app to map the timber stand using GPS and to record various types of data.

For a forester, the fewer gadgets one has to take along into the woods, the better. An all-in-one device would be ideal. Smart phones and PDAs are helping to make this a reality.

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