for a tree with dbh= 45.6cm, height= 27m and total stem volume of 1.78cum, the artificial form factor of the tree is:
Question
For a tree with the following characteristics:
- DBH: 45.6 cm
- Height: 27 m
- Total Stem Volume: 1.78 cum
The artificial form factor of the tree is:
Solution
The form factor of a tree is a dimensionless quantity that describes the shape of its stem. It is defined as the ratio of the actual stem volume to the volume of a cylinder with the same height and diameter at breast height (dbh).
The formula for the form factor (f) is:
f = V / (A * h)
where: V = stem volume A = cross-sectional area at breast height h = height of the tree
Given that the dbh = 45.6 cm, the radius (r) would be dbh/2 = 22.8 cm.
The cross-sectional area (A) can be calculated using the formula for the area of a circle, which is πr². So, A = π * (22.8 cm)² = 1633.5 cm².
However, since the volume is given in cubic meters (cum), we need to convert the area from cm² to m². We know that 1 m² = 10,000 cm², so A = 1633.5 cm² / 10,000 = 0.16335 m².
The height (h) is given as 27 m and the volume (V) is given as 1.78 cum.
Substituting these values into the formula for the form factor, we get:
f = 1.78 cum / (0.16335 m² * 27 m) = 0.403
So, the artificial form factor of the tree is approximately 0.403.
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