Tree 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]
Girard form class is a form quotient calculated as the ratio of diameter inside bark at the top of the first 16 foot log to the diameter outside bark at breast height (DBH). Girard form class is the primary expression of tree form in the United States.
Diameter at breast height, or DBH, is a standard method of expressing the diameter of the trunk or bole of a standing tree. DBH is one of the most common dendrometric measurements.
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
where:
= stem diameter at height h,
= tree diameter at breast height,
= tree total height,
height of interest (h ≤ H), and
= 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.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
Related Research Articles
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f (x) at a point x = c on the curve if the line passes through the point (c, f ) on the curve and has slope f'(c) where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.
A right triangle or right-angled triangle is a triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry.
In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has the same property of symmetry.
In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree. For example, a quadratic function in three variables x, y, and z contains exclusively terms x2, y2, z2, xy, xz, yz, x, y, z, and a constant:
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset.
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach.
In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables that satisfy canonical Poisson bracket relations. The set of possible canonical transformations is always very rich. For instance, it is often possible to choose the Hamiltonian itself
as one of the new canonical momentum coordinates.
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves, and algebraic plane curves.
Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.
The Van Deemter equation in chromatography relates the variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a separation. These properties include pathways within the column, diffusion, and mass transfer kinetics between stationary and mobile phases. In liquid chromatography, the mobile phase velocity is taken as the exit velocity, that is, the ratio of the flow rate in ml/second to the cross-sectional area of the ‘column-exit flow path.’ For a packed column, the cross-sectional area of the column exit flow path is usually taken as 0.6 times the cross-sectional area of the column. Alternatively, the linear velocity can be taken as the ratio of the column length to the dead time. If the mobile phase is a gas, then the pressure correction must be applied. The variance per unit length of the column is taken as the ratio of the column length to the column efficiency in theoretical plates. The Van Deemter equation is a hyperbolic function that predicts that there is an optimum velocity at which there will be the minimum variance per unit column length and, thence, a maximum efficiency. The Van Deemter equation was the result of the first application of rate theory to the chromatography elution process.
Basal area is the area of a given section of land that is occupied by the cross-section of tree trunks and stems at the base. The term is used in forest management and forest ecology.
A diameter tape (D-tape) is a measuring tape used to estimate the diameter of a cylinder object, typically the stem of a tree or pipe. A diameter tape has either metric or imperial measurements reduced by the value of π. This means the tape measures the diameter of the object. It is assumed that the cylinder object is a perfect circle. The diameter tape provides an approximation of diameter; most commonly used in dendrometry.
A Volume table is a chart to aid in the estimation of standing timber volume. These tables are based on volume equations and use correlations between certain aspects of a tree to estimate the volume to a degree of certainty. The diameter at breast height (DBH) and the merchantable height are used to determine the total volume. Difficulties occur when estimating the form class of the tree in question. The Mesavage and Girard form classes used to classify the trees to decide which volume table should be used. These volume tables are also based on different log rules such a Scribner, Doyle, and International ¼” scale. In order to be effective, the proper form class must be selected as well as accurate DBH and height measurements.
Forest inventory is the systematic collection of data and forest information for assessment or analysis. An estimate of the value and possible uses of timber is an important part of the broader information required to sustain ecosystems. When taking forest inventory the following are important things to measure and note: species, diameter at breast height (DBH), height, site quality, age, and defects. From the data collected one can calculate the number of trees per acre, the basal area, the volume of trees in an area, and the value of the timber. Inventories can be done for other reasons than just calculating the value. A forest can be cruised to visually assess timber and determine potential fire hazards and the risk of fire. The results of this type of inventory can be used in preventive actions and also awareness. Wildlife surveys can be undertaken in conjunction with timber inventory to determine the number and type of wildlife within a forest.
The aim of the statistical forest inventory is to provide comprehensive information about the state and dynamics of forests for strategic and management planning. Merely looking at the forest for assessment is called taxation.
In algebra, a septic equation is an equation of the form
Tree volume is one of many parameters that are measured to document the size of individual trees. Tree volume measurements serve a variety of purposes, some economic, some scientific, and some for sporting competitions. Measurements may include just the volume of the trunk, or the volume of the trunk and the branches depending on the detail needed and the sophistication of the measurement methodology.
