Formulas
Limiting Distance = DBH x PRF
PRF = , metric:
Borderline tree is a term used in forestry.
It is a concept that comes from variable radius plots, or point sampling. It happens when a tree cannot be easily determined as in or out when using a prism or angle gauge. Borderline trees occur only when the distance from the sampling point to the center of the tree is equal to the DBH times plot radius factor (PRF). The PRF is determined based on the type of prism or angle gauge being used. Basal Area Factor (BAF) 5, 10, and 20 angle gauges result in PRFs of 3.89, 2.75, and 1.94 (feet inch−1) respectively. The metric equivalents of these PRFs are 0.467, 0.33, and 0.233 (m cm−1).
When a tree is borderline, a series of measurements and calculations must be made to determine if the tree is in or out. The horizontal distance from the sampling point to the center of the tree must be measured along with the DBH of the tree. The DBH should then be multiplied by the PRF, which will give a limiting distance. If the measured distance is less than or equal to this limiting distance, the tree is counted as in. If it is greater than the limiting distance, it is out.
BAF: ft2/acre, (metric: m2/ha)
PRF: ft/inch, (metric: m/cm)
Limiting Distance = DBH x PRF
PRF = , metric:
A tree that appears borderline using a BAF 10 instrument was measured as 12.4 inches (310 mm) DBH.
The horizontal distance from the sampling point to the center of the tree is 34 feet (10 m).
DBH x PRF = Limiting Distance
12.4in. x 2.75ft./in. = 34.1ft.
34.1 feet (limiting distance) is greater than 34 feet (measured distance), tree is in.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system.
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
The horizon or skyline is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. The true horizon is actually a theoretical line, which can only be observed when it lies on the sea surface. At many locations, this line is obscured by land, trees, buildings, mountains, etc., and the resulting intersection of earth and sky is called the visible horizon. When looking at a sea from a shore, the part of the sea closest to the horizon is called the offing.
Earth radius is the distance from the center of Earth to a point on its surface. Its value ranges from 6,378 km (3,963 mi) at the equator to 6,357 km (3,950 mi) at a pole. A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics, denoted in astronomy by the symbol R⊕. In other contexts, it is denoted or sometimes .
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches the three sides. The center of the incircle is a triangle center called the triangle's incenter.
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle.
A helix, plural helixes or helices, is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word helix comes from the Greek word ἕλιξ, "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is called a helicoid.
In differential geometry, the Gaussian curvature or Gauss curvatureΚ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point:
In optics, the Airy disk and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, optics, and astronomy.
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel. The plural of radius can be either radii or the conventional English plural radiuses. The typical abbreviation and mathematical variable name for radius is r. By extension, the diameter d is defined as twice the radius:
In cartography, a Tissot's indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.
Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial slices are flat. There is no coordinate singularity at the Schwarzschild radius. The outgoing ones are simply the time reverse of ingoing coordinates.
Basal area is the cross-sectional area of trees at breast height. It is a common way to describe stand density. In forest management, basal area usually refers to merchantable timber and is given on a per hectare or per acre basis. If you cut down all the merchantable trees on an acre at 4 ½ feet off the ground and measured the square inches on the top of each stump (πr*r), added them all together and divided by square feet, that would be the basal area on that acre. In forest ecology, basal area is used as a relatively easily-measured surrogate of total forest biomass and structural complexity, and change in basal area over time is an important indicator of forest recovery during succession .
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.
An angle gauge is a tool used by foresters to determine which trees to measure when using a variable radius plot design in forest inventory. Using this tool a forester can quickly measure the trees that are in or out of the plot. An angle gauge is similar to a wedge prism though it must be held a fixed distance from the eye to work properly. Unlike the wedge prism, which is held over the plot center, the surveyor's eye is kept over plot-center when using an angle gauge.
The wedge prism is a prism with a shallow angle between its input and output surfaces. This angle is usually 3 degrees or less. Refraction at the surfaces causes the prism to deflect light by a fixed angle. When viewing a scene through such a prism, objects will appear to be offset by an amount that varies with their distance from the prism.
In forestry, quadratic mean diameter or QMD is a measure of central tendency which is considered more appropriate than arithmetic mean for characterizing the group of trees which have been measured. For n trees, QMD is calculated using the quadratic mean formula:
In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all circular arcs contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.
A part of tree measurement is measurement of the crown of a tree, which consists of the mass of foliage and branches growing outward from the trunk of the tree. The average crown spread is the average horizontal width of the crown, taken from dripline to dripline as one moves around the crown. The dripline being the outer boundary to the area located directly under the outer circumference of the tree branches. When the tree canopy gets wet, any excess water is shed to the ground along this dripline. Some listings will also list the maximum crown spread which represents the greatest width from dripline to dripline across the crown. Other crown measurements that are commonly taken include limb length, crown volume, and foliage density. Canopy mapping surveys the position and size of all of the limbs down to a certain size in the crown of the tree and is commonly used when measuring the overall wood volume of a tree.
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.
Avery, Thomas E., Harold E. Burkhart. Forest Measurements, fifth edition. New York: McGraw-Hill, 2002
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