In topography, the line of greatest slope is a curve following the steepest slope. In mountain biking and skiing, the line of greatest slope is sometimes called the fall line. [1]
In topography, the line of greatest slope is a curve following the steepest slope. In mountain biking and skiing, the line of greatest slope is sometimes called the fall line. [1]
Mathematically, the line (or path) of greatest slope from a point is determined by the gradient of height, taken as a potential field with respect to an acceleration from the force of gravity. Lines of greatest slope are analogous to lines of force acting to accelerate an object downward at that point.[ citation needed ] These lines are orthogonal to contour lines. Discounting inertial forces and terrain roughness, a ball rolling down a slope, or water flowing down, will accelerate in the direction of greatest slope.[ citation needed ]
In mountain biking the line of greatest slope defines the fall line, which is the path a trail will follow to descend a hill or mountain with the shortest path, [1] and will also cause the rider to gain the most velocity (assuming brakes are not used, and other factors such as rolling resistance are equal).
In mountain climbing, the line of greatest slope defines the fall line, which is the path a climber will take to gain the most elevation with the shortest possible path.
The line of greatest slope has practical significance in map reading. On the terrain it is often far more discernible, even intuitively obvious, rather than accurately picking out the consistent height level on what is likely the undulating uneven ground along the ground represented on the contour line. But knowing that a greatest slope vector is orthogonal to the contour line, one can readily deduce the direction of the contour lines from the line of greatest slope. The extent and overall direction of the contour line to a map scale can only be found on the topographic map.
By noting the corresponding compass vector, walking along the contour one can line up a hand held compass aligning the expected direction, and eye-balling the line of contour's estimated level, move up or down along the bearing faster— to closely locate a desired point (planned point) along the hillside.[ clarification needed ] Pragmatically, this can be 'good enough' for rough project landscaping, such as timber clear cutting the work site of a structure like a bridge abutment or connecting ramps. The approximation can then be refined by transit and other surveyor tools to construct on target.
A trail, also known as a path or track, is an unpaved lane or a small paved road not intended for usage by motorized vehicles, usually passing through a natural area. In the United Kingdom and the Republic of Ireland, a path or footpath is the preferred term for a pedestrian or hiking trail. The term is also applied in North America to accompanying routes along rivers, and sometimes to highways. In the US, the term was historically used for a route into or through wild territory used by explorers and migrants. In the United States, "trace" is a synonym for trail, as in Natchez Trace.
In elementary geometry, two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂. Perpendicular intersections can happen between two lines, between a line and a plane, and between two planes.
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps.
In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north.
In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.
In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero, but which is not a local extremum of the function. An example of a saddle point is when there is a critical point with a relative minimum along one axial direction and at a relative maximum along the crossing axis. However, a saddle point need not be in this form. For example, the function has a critical point at that is a saddle point since it is neither a relative maximum nor relative minimum, but it does not have a relative maximum or relative minimum in the -direction.
A contour line of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value.
A geologic map or geological map is a special-purpose map made to show various geological features. Rock units or geologic strata are shown by color or symbols. Bedding planes and structural features such as faults, folds, are shown with strike and dip or trend and plunge symbols which give three-dimensional orientations features.
In topography, prominence measures the height of a mountain or hill's summit relative to the lowest contour line encircling it but containing no higher summit within it. It is a measure of the independence of a summit. The key col ("saddle") around the peak is a unique point on this contour line and the parent peak is some higher mountain, selected according to various criteria.
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation.
The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface . The term elevation is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an aircraft in flight or a spacecraft in orbit, and depth is used for points below the surface.
A topographic profile or topographic cut or elevation profile is a representation of the relief of the terrain that is obtained by cutting transversely the lines of a topographic map. Each contour line can be defined as a closed line joining relief points at equal height above sea level. It is usually drawn on the same horizontal scale as the map, but the use of an exaggerated vertical scale is advisable to underline the elements of the relief. This can vary according to the slope and amplitude of the terrestrial relief, but is usually three to five times the horizontal scale.
Diver navigation, termed "underwater navigation" by scuba divers, is a set of techniques—including observing natural features, the use of a compass, and surface observations—that divers use to navigate underwater. Free-divers do not spend enough time underwater for navigation to be important, and surface supplied divers are limited in the distance they can travel by the length of their umbilicals and are usually directed from the surface control point. On those occasions when they need to navigate they can use the same methods used by scuba divers.
Terrain cartography or relief mapping is the depiction of the shape of the surface of the Earth on a map, using one or more of several techniques that have been developed. Terrain or relief is an essential aspect of physical geography, and as such its portrayal presents a central problem in cartographic design, and more recently geographic information systems and geovisualization.
A fall line refers to the line down a mountain or hill which is most directly downhill; that is, the direction a ball or other body would accelerate if it were free to move on the slope under gravity. Mathematically the fall line, the line of greatest slope, is the negative of the gradient and perpendicular to the contour lines.
A stereoplotter uses stereo photographs to determine elevations. It has been the primary method to plot contour lines on topographic maps since the 1930s. Although the specific devices have advanced technologically, they are all based on the apparent change in position of a feature in the two stereo photographs.
Hachures are an older mode of representing relief. They show orientation of slope, and by their thickness and overall density they provide a general sense of steepness. Being non-numeric, they are less useful to a scientific survey than contours, but can successfully communicate quite specific shapes of terrain. They are a form of shading, although different from the one used in shaded maps.
An orienteering map is a map specially prepared for use in orienteering events. It is a large-scale topographic map with extra markings to help the participant navigate through the course.
Mountain bike orienteering is an orienteering endurance racing sport on a mountain bike where navigation is done along trails and tracks. Compared with foot orienteering, competitors usually are not permitted to leave the trail and track network. Navigation tactics are similar to ski-orienteering, where the major focus is route choice while navigating. The main difference compared to ski-orienteering is that navigation is done at a higher pace, because the bike can reach higher speeds. As the biker reaches higher speeds, map reading becomes more challenging.
This glossary of geography terms is a list of definitions of terms and concepts used in geography and related fields, including Earth science, oceanography, cartography, and human geography, as well as those describing spatial dimension, topographical features, natural resources, and the collection, analysis, and visualization of geographic data. It is split across two articles: