Stand basal area
Farmers measuring stand basal area using
the Australian Master TreeGrower Tape.
Stand Basal Area (SBA) is simply the crosssectional
area of all the trees at breast height per hectare of forest
or plantation (m2/ha). Stand Basal Area can be used to estimate
stand volume and is a useful measure of the degree of competition
in the stand.
Measuring Stand Basal Area
The basal area of a stand or plot can be determined
in different ways:
 The sum of individual tree basal areas.
 The optical method of assessing basal area.
 The spacing factor method.
1. Sum of individual tree basal areas
The most accurate method of assessing the basal
area of a stand of trees is to measure all tree diameters
in a plot, calculate the individual tree basal areas and then
add them up. Computer spreadsheets are ideal for this.
Basal Area of a tree (m2) = (DBH/200)2
x 3.142
Stand Basal Area (m2/ha) = (Sum of the
basal area of each tree in the plot)
(Area of the plot (ha))
A quicker method is to calculate the basal area
using the average tree diameter. Because larger trees contribute
more to the basal area than small trees, this technique may
underestimate the true basal area of a stand by about 10%,
depending upon how varied the tree size is on the plot:
Stand Basal Area (m2/ha) = (Basal area of the
average tree diameter) x (Stocking (tree/ha))
2. Optical methods of assessing Basal Area
Basal Area per hectare can be estimated using
an optical method. A gauge of known width is held at a set
distance from the eye. The observer then turns around on a
set point observing each tree (at breast height) counting
the number of trees that appear wider than the width of the
gauge. If a tree appears wider than the gauge, it is considered
as 'in' and counted as 1. If a tree appears to be exactly
the same width as the gauge it is counted as 1/2. Trees that
appear smaller than the width of the gauge are ignored. The
total count is multiplied by the "factor" of the
gauge to give the basal area per hectare.
Example:
Using a 2 factor gauge, the operator counts 11 trees that
appear wider than the gauge and 3 that appear to be the same
width:.
The Basal Area (m2/ha) = Factor x Count
= 2 x (11 + (3 x 0.5))
= 25 m2/ha
Measuring Stand BA using an optical gauge.
If the tree appears wider than the tree stem at breast height,
the tree is counted as "in" or "1". If
the tree is the same width as the gauge, it is counted as
"1/2". Any tree smaller than the width of the gauge
is ignored. Count x Gauge Factor = Stand Basal Area (m2/ha).
This method was developed by foresters in Europe
in the 1930s and was introduced to Australia in 1952. In some
cases foresters use a glass prism that subtends the angle,
although the gauge method is just as legitimate and much cheaper.
The mathematics behind the technique is not complicated but
it is not important to understand it in order to use the technique
anyway. See Additional Information.
All that is needed to make up an optical basal
area gauge is something of known width that can be held at
a set distance from the eye. The table below gives the specifications
for gauges of different factors and shows the distance a gauge
of a particular width should be held from the eye. Distances
of less than 40cm are impractical due to the difficulty of
simultaneously focusing the eye on both the gauge and the
tree in the distance. Distances of more than 60cm are difficult
to reach.

Factor
1 
Factor
2 
Factor
3 
Factor
4 
Gauge Width (cm) 
Calculation:
50xWidth 
50xWidth/SQRT(2) 
50xWidth/SQRT(3) 
50xWidth/SQRT(4) 
1.0 
50 
35.4 
28.9 
25.0 
1.4 
70 
49.5 
40.4 
35.0 
1.6 
80 
56.6 
46.2 
40.0 
1.8 
90 
63.6 
52.0 
45.0 
2.0 
100 
70.7 
57.7 
50.0 
Testing doubtful trees.
If a high degree of accuracy is required it is necessary to
test doubtful trees:
A tree is "in" if its DBH is greater
than:
 the distance from the operator/50.0 for
a 1factor gauge,
 the distance from the operator/35.4 for a 2factor gauge,
 the distance from the operator/25.0 for a 4factor gauge.
Precautions
 Each tree must be viewed at breast height
(1.3m).
 It is important to turn on a single point
keeping an eye over the same point on the ground.
 Leaning trees should be viewed at right
angles to the stem.
 The distance from the eye to the gauge is
important, although if the user holds the tape 1cm away
from the correct position then the error will be less than
about 5%.
 The greater the number of "1/2"
trees the less reliable the result. For accurate measurements
the diameter and distance to these trees must be measured
to confirm their status.
 Care must be taken to view trees hidden
behind other stems or undergrowth. If necessary the user
can move sideways provided the distance to the tree is not
altered. The user should then return to the original point
before turning to view the next tree.
 A total count of about 10 trees is recommended.
If the count is lower than 5 or greater than 15, a different
factor gauge should be used.
Basal areas in plantations and native forests
normally vary from about 10 to more than 60 m2/ha and therefore
gauges with factors of 2 and 4 should be sufficient in most
cases. The more sample points used and care by the operator
to ensure that the correct method is implemented, will increase
the accuracy of the results.
3. Spacing Factor Method of Estimating Basal
Area
In planning silvicultural regimes, it is useful
to have a feel for how basal area varies with the average
spacing between trees. The spacing factor is simply the average
distance between the trees (in cms not metres) divided by
the average stem diameter (cms), and is a useful way of estimating
basal area in uniform plantations. For example, if the trees
are spaced at an average of 5m (500cm) and the mean diameter
is 20cm, the spacing factor is 500/20 = 25. The figure below
shows the relationship between the spacing factor and basal
area.
This technique assumes all trees are of equal
size and is helpful to predict the basal area at maturity
for a given final stocking and tree size. To thin a plantation
to a certain basal area, simply thin to an average spacing
equal to the diameter of the retained trees, multiplied by
the appropriate spacing
factor. The higher the spacing factor the lower the competition
or basal area.
Some useful numbers to remember are:
If the spacing factor = 12.5, basal area is
approximately 50m2/ha
If the spacing factor = 15, basal area is approximately
35m2/ha
If the spacing factor = 20, basal area is approximately
20m2/ha
If the spacing factor = 30, basal area is approximately
10m2/ha
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