Tree taper

Definition

Taper is the degree to which a tree's stem or bole decreases in diameter as a function of height above ground. Trees with a high degree of taper are said to have poor form, while those with low taper have good form. The form of a tree is sometimes quantified by the Girard form class, which is the ratio, expressed as a percentage, of the butt-log scaling diameter to diameter at breast height.^[1]

Taper is often represented by mathematical functions fitted to empirical data, called taper equations. One such function, attributed to Ormerod,^[2] is

$d(h)^2 = {D^2} \left({H-h \over H-h_b}\right)^{1.6}$

where:

$d(h)$ = stem diameter at height h,

$D$ = tree diameter at breast height,

$H$ = tree total height,

$h$ height of interest (h ≤ H), and

$h_b$ = breast height.

Once developed, taper equations can be used to predict the diameter at a given height, or the height for a given diameter.

Footnotes

^ Mesavage, C., and J.W. Girard. 1946. Tables for estimating board foot volume of timber. Department of Agriculture, Forest Service, Washington, DC. 94 pp.
^ Ormerod, D.W., 1973. A simple bole model. Forestry Chronicle. 49:136-138.