Tree taper

Tree taper is the degree to which a tree's stem or bole decreases in diameter as a function of height above ground. Within Forestry and for the purposes of timber production, trees with a high degree of taper are said to have poor form, while those with low taper have good form. The opposite is the case for open-grown amenity trees. 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

Tree taper equation

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

where:

${\displaystyle d(h)}$ = stem diameter at height h,

${\displaystyle D}$ = tree diameter at breast height,

${\displaystyle H}$ = tree total height,

${\displaystyle h}$ height of interest (h ≤ H), and

${\displaystyle h_{b}}$ = breast height.

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