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.
Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve or the volume of a solid . Two different regions may have the same area ; by synecdoche, "area" sometimes is used to refer to the region, as in a "polygonal area".
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three numbers, : the radial distance of the radial liner connecting the point to the fixed point of origin ; the polar angle θ of the radial line r; and the azimuthal angle φ of the radial line r.
The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whether it intersects the relevant body's surface or not.
A tautochrone curve or isochrone curve is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid.
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.
In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.
The Unified Thread Standard (UTS) defines a standard thread form and series—along with allowances, tolerances, and designations—for screw threads commonly used in the United States and Canada. It is the main standard for bolts, nuts, and a wide variety of other threaded fasteners used in these countries. It has the same 60° profile as the ISO metric screw thread, but the characteristic dimensions of each UTS thread were chosen as an inch fraction rather than a millimeter value. The UTS is currently controlled by ASME/ANSI in the United States.
A milliradian is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel. Milliradians are also used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances. When using a scope with both mrad adjustment and a reticle with mrad markings, the shooter can use the reticle as a ruler to count the number of mrads a shot was off-target, which directly translates to the sight adjustment needed to hit the target with a follow-up shot. Optics with mrad markings in the reticle can also be used to make a range estimation of a known size target, or vice versa, to determine a target size if the distance is known, a practice called "milling".
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 typical abbreviation and mathematical variable name for radius is R or r. By extension, the diameter D is defined as twice the radius:
In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk and lines are represented by the chords, straight line segments with ideal endpoints on the boundary sphere.
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 .
In railway engineering, cant deficiency is defined in the context of travel of a rail vehicle at constant speed on a constant-radius curve. Cant itself refers to the superelevation of the curve, that is, the difference between the elevations of the outside and inside rails. Cant deficiency is present when a rail vehicle's speed on the curve is greater than the speed at which the components of wheel to rail force are normal to the plane of the track. In that case, the resultant force exerts on the outside rail more than the inside rail, in which it creates lateral acceleration toward the outside of the curve. In order to reduce cant deficiency, the speed can be reduced or the superelevation can be increased. The amount of cant deficiency is expressed in terms of required superelevation to be added in order to bring the resultant force into balance between the two rails.
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 geometry, a pentagon is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
In forestry, a tree crown measurement is one of the tree measurements taken at 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 is 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.
In shooting sports, a shot grouping, or simply group, is the collective pattern of projectile impacts on a target from multiple consecutive shots taken in one shooting session. The tightness of the grouping is a measure of the precision of a weapon, and a measure of the shooter's consistency and skill. On the other hand, the grouping displacement is a measure of accuracy.
In Einstein's theory of general relativity, the interior Schwarzschild metric is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid and has zero pressure at the surface. This is a static solution, meaning that it does not change over time. It was discovered by Karl Schwarzschild in 1916, who earlier had found the exterior Schwarzschild metric.
Avery, Thomas E., Harold E. Burkhart. Forest Measurements, fifth edition. New York: McGraw-Hill, 2002
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