Stem Form in Forestry: A Detailed Overview

Stem form refers to the shape and tapering characteristics of a tree stem or log. The rate of taper describes how the diameter of a tree’s stem decreases from the base upwards, which is influenced by factors like species, age, site conditions, and crop density. Additionally, taper varies in different parts of the tree, with the basal portion resembling the frustum of a cone or frustum of Neiloid, the middle portion taking the form of a frustum of Paraboloid, and the top portion shaped like a cone.

Metzger’s Theory on Stem Form

Metzger’s theory on stem form suggests that the tree stem should be considered a cantilever beam of uniform size against the bending force exerted by wind. Key points of Metzger’s theory are:

Wind Pressure and Stem Reinforcement

• • Wind pressure acts on the crown and increases in force as it is transmitted down the length of the tree’s stem.
  • The base of the tree experiences the greatest pressure, leading to the possibility of snapping. To counteract this, the tree naturally reinforces itself towards the base.
  • Tapering Increases in isolated areas where wind force is most pronounced.
  • Tapering Decreases in areas with the highest density of trees, due to reduced wind pressure.

Human Influence on Tapering

• • While tapering is a natural process, human interference can influence its extent. In conditions of high competition (e.g., dense stands), tapering tends to decrease, as trees compete for space and resources.

Methods of Studying Stem Form

Stem form can be analyzed through various methods:

• Comparison of Standard Form Ratios These ratios help determine the relative proportions of the tree and its parts.
• Form Ratios Classification Classification of trees based on their form ratios to categorize different stem shapes.
• Compilation of Taper Tables These tables provide data about the diameters of trees at fixed points from base to tip, enabling volume estimation.

Form Factor (F)

The form factor is a ratio used to estimate the volume of a tree or its parts relative to a cylinder with the same length and cross-sectional area as the tree.

• Formula:
  F = V/Sh ​ Where:

• F = Form factor
• V = Volume of the tree
• S = Basal area at breast height (dbh)
• h = Height of the tree

Types of Form Factors

• Artificial Form Factor: Known as breast height form factor. The basal area or diameter is measured at dbh, and the volume refers to the whole tree, both above and below the point of measurement.
• Absolute Form Factor: Basal area is measured at any convenient height, and volume refers only to the part above this measurement point.
• Normal Form Factor: Basal area or diameter is measured at a constant proportion of the tree’s total height (e.g., 1/10th, 1/20th), and volume refers to the whole tree above ground level.

Uses of Form Factor

• Estimating the volume of a standing tree.
• Studying the law of growth in trees.

Form Height (Fh)

• Form height is the product of the form factor and the total height of the tree. Fh=V/S ​
• It helps determine the total height of the tree based on its form factor and basal area.

Form Quotient (F.Q.)

The form quotient is the ratio of the mid-diameter (or mid-girth) of a tree to the diameter at breast height (dbh). It indicates how much a tree tapers as it grows.

• Formula: F.Q.=Mid diameter / dbh

Types of Form Quotients

• Normal Form Quotient: The ratio of the mid-diameter or mid-girth of a tree to its diameter or girth at breast height (dbh).
• Absolute Form Quotient: The ratio of the diameter or girth of the stem at half its height above dbh to the diameter at breast height (dbh).

Uses of Form Quotient

• Form quotient is one of the independent variables in volume tables that can help predict the volume of a tree stem.
• It helps classify trees into form classes for better forest management and inventory.

Form Class and Form Point Ratio

Form Class:

• Defined as a range of form quotients, categorizing trees based on their taper characteristics. For example, trees with form quotients between 0.5 and 0.55 belong to one form class, and trees with form quotients between 0.55 and 0.6 belong to another.

Form Point Ratio:

• The form point is the estimated point in the crown where wind pressure is most concentrated. The form point ratio is the relationship between the height of the form point and the total height of the tree.
• This ratio helps determine both the form quotient and form class of a tree.

Taper Tables

Taper tables provide diameters at fixed points along the stem of a tree. These tables are useful for estimating the volume of a tree at different heights.

Types of Taper Tables

• Ordinary Taper Tables: Provide the taper directly for the diameter at breast height (dbh), without considering the specific form of the tree.
• Form Class Tables: Provide diameters at fixed points along the stem for different form classes.

Taper Equations

Taper equations represent the expected diameter at any given height hhh as a function of the tree’s height HHH, dbh, and other regression coefficients. These equations are generalized for different species and form classes.

• Example Equation:
  D = dbh √ (bo + b1 (h/H)+ b2 (h2/H2)
  • Where,
  • d = stem diameter at any given height h above ground,
  • H = total tree height
  • bo, b1 and b2 = regression coefficient

Hojer’s Formula:
d/dbh = C log c+l c
Where, d is the diameter at any point on the stem. C and c are constants for each form class, l is the distance from the top of the tree to the point at which d is measured, expressed in percentage.

Behre`s formula d/dbh = l/a+b1
Where, a and b are constants for each class, such that a +b =1 and d an l have the same meaning as given for Hojer`s formula. This formula is more consistent.