In astronomy, geography, and related sciences and contexts, a direction or plane passing by a given point is said to be vertical if it contains the local gravity direction at that point.
Conversely, a direction, plane, or surface is said to be horizontal (or leveled) if it is everywhere perpendicular to the vertical direction.
_q.jpg)
The grade (US) or gradient (UK) (also called slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance (not the distance along the slope) and rise is the vertical distance.
Slopes of existing physical features such as canyons and hillsides, stream and river banks, and beds are often described as grades, but typically the word "grade" is used for human-made surfaces such as roads, landscape grading, roof pitches, railroads, aqueducts, and pedestrian or bicycle routes. The grade may refer to the longitudinal slope or the perpendicular cross slope.
An azimuth (/ˈæzəməθ/ ; from Arabic: اَلسُّمُوت, romanized: as-sumūt, lit. 'the directions') is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system.
Mathematically, the relative position vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane (the horizontal plane); the angle between the projected vector and a reference vector on the reference plane is called the azimuth.
A transform fault or transform boundary, is a fault along a plate boundary where the motion is predominantly horizontal. It ends abruptly where it connects to another plate boundary, either another transform, a spreading ridge, or a subduction zone. A transform fault is a special case of a strike-slip fault that also forms a plate boundary.
Most such faults are found in oceanic crust, where they accommodate the lateral offset between segments of divergent boundaries, forming a zigzag pattern. This results from oblique seafloor spreading where the direction of motion is not perpendicular to the trend of the overall divergent boundary. A smaller number of such faults are found on land, although these are generally better-known, such as the San Andreas Fault and North Anatolian Fault.
In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same A slope is the ratio of the vertical distance (rise) to the horizontal distance (run) between two points, not a direct distance or a direct angle for any choice of points. To explain, a slope is the ratio of the vertical distance (rise) to the horizontal distance (run) between two points, not a direct distance or a direct angleThe line may be physical – as set by a road surveyor, pictorial as in a diagram of a road or roof, or abstract.An application of the mathematical concept is found in the grade or gradient in geography and civil engineering.
The steepness, incline, or grade of a line is the absolute value of its slope: greater absolute value indicates a steeper line. The line trend is defined as follows:
In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress,such as the interface between two homogeneous fluids.An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids, gases cannot form a free surface on their own.Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface.
A liquid in a gravitational field will form a free surface if unconfined from above.Under mechanical equilibrium this free surface must be perpendicular to the forces acting on the liquid; if not there would be a force along the surface, and the liquid would flow in that direction. Thus, on the surface of the Earth, all free surfaces of liquids are horizontal unless disturbed (except near solids dipping into them, where surface tension distorts the surface in a region called the meniscus).
A level is an optical instrument used to establish or verify points in the same horizontal plane in a process known as levelling. It is used in conjunction with a levelling staff to establish the relative height or levels (the vertical separation) of objects or marks. It is widely used in surveying and construction to measure height differences and to transfer, measure, and set heights of known objects or marks.
It is also known as a surveyor's level, builder's level, dumpy level or the historic "Y level". It operates on the principle of establishing a visual level relationship between two or more points, for which an inbuilt optical telescope and a highly accurate bubble level are used to achieve the necessary accuracy. Traditionally the instrument was completely adjusted manually to ensure a level line of sight, but modern automatic versions self-compensate for slight errors in the coarse levelling of the instrument, and are thereby quicker to use.
A spatial gradient is a gradient whose components are spatial derivatives, i.e., rate of change of a given scalar physical quantity with respect to the position coordinates in physical space. Homogeneous regions have spatial gradient vector norm equal to zero.When evaluated over vertical position (altitude or depth), it is called vertical derivative or vertical gradient; the remainder is called horizontal gradient component, the vector projection of the full gradient onto the horizontal plane.
Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track. The term is also applied to measurements used in design, construction and maintenance of track. Track geometry involves standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Standards are usually separately expressed for horizontal and vertical layouts although track geometry is three-dimensional. Modern maintenance regimes increasingly use 3D laser scanning (LiDAR) to capture these geometric parameters and assess structure gauge compliance without physical contact.