Standing tree volume
Pruned Silver Quandong.
Using measures of Diameter at Breast Height
(DBH) and Total Tree Height (Ht), an estimation of total tree
volume can be made by assuming the tree has a particular form.
For example, if we assume the tree is conical in shape, with
the DBH equivalent to the diameter at the base of the cone,
then the following formula is appropriate:
Tree volume (m3) = Tree Basal Area (m2) x Tree
Height (m) / 3
= (DBH/200)2 x 3.142 x Ht / 3
So, if a tree was 22.7m tall and 42.6cm in DBH,
the total tree volume would be:
Tree volume (m3) = (42.6/200)2 x 3.142 x 22.7
/ 3 = 1.08 m3
As the diameter is actually measured at 1.3
metres above the ground, not at the base, most trees carry
a bit more volume than the cone-form would suggest. This formula
is a conservative estimate of total underbark tree volume.
Measurements of a 10 year old eucalypt
pruned to 6.5m. Assuming the tree has a conical shape this
can be a useful estimate of underbark volume. Source Reid
and Stephen (2001) Farmers Forest.
More detailed formulae are available for particular
species grown in some areas, although rarely for farm grown
trees other than pine.
It is important to be consistent in choice of
method of measuring volume, particularly when comparing growth
on different sites or over time.
If a tree is clearly not conical or if a farmer
is only interested in the volume of the butt log it may be
more appropriate to measure the volume of the lower log only.
Estimating the volume of the parts of a
Assuming a tree is perfectly conical makes it
easy to estimate the volume of different sections of the trunk.
All that is required is an estimate of the tree taper or rate
at which the diameter decreases with height
Taper (T) of a conical tree = Diameter (DBH)/[Height(Ht)
For example: For a conical tree of 42.6cm DBH
and 22.7m tall, the taper (T) is 1.9cm/m.
Using the taper equation, it is possible to
estimate the diameter at different points up the tree. For
example if the same tree was pruned to 6.7 metres and the
stump height was 30cm then it may be assumed to have the following
- Total Tree Height (Ht) = 22.7m
- Diameter Breast Height (DBH) = 42.6cm
- Pruned Height (PHt) = 6.7m
- Stump Height (SHt) = 0.3m
- Estimated total tree Volume (Vol)
Vol = (DBH/200)2 x ( x Ht / 3 = 1.08m3
- Estimated Taper (T)
T = DBH/Ht = 1.9cm/m
- Underbark diameter at stump height (LED)
LED = DBH SHt x T = 42.03cm
- Underbark diameter at pruned height (SED)
SED = DBH PHt x T = 29.9cm
- Crown Log Vol (Cvol)
Cvol = (SED/200)2 x ( x (Ht-PHt) / 3 = 0.37m3
- Stump Vol (Svol)
Svol = Vol - (LED/200)2 x ( x (Ht-SHt) / 3 = 0.04m3
- Pruned Vol (Pvol)
Pvol = Vol Cvol Svol = 1.08-0.37-0.04 = 0.67m3
It is interesting to note that in well-spaced,
pruned trees the taper of the pruned butt log tends to decline
over time resulting in a more cylindrical log at the base
and a more highly tapered upper crown. The graph above shows
some evidence of greater diameter growth in the section just
above the pruned log, even in a ten-year-old pruned tree.
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