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α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, 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 ...
The user may choose to replace the inclination angle by its complement, the elevation angle (or altitude angle), measured upward between the reference plane and the radial line—i.e., from the reference plane upward (towards to the positive z-axis) to the radial line. The depression angle is the negative of the elevation angle.
dh = elevation difference, dx = distance, S = slope, θ = angle of slope (inclination). The velocity on the flat terrain is 5 km / h, the maximum speed of 6 km / h is achieved roughly at -2.86°. [5] On flat terrain this formula works out to 5 km/h. For off-path travel, this value should be multiplied by 3/5, for horseback by 5/4. [1]
Dip is the inclination of a given feature, and is measured from the steepest angle of descent of a tilted bed or feature relative to a horizontal plane. [5] [6] True dip is always perpendicular to the strike. It is written as a number (between 0° and 90°) indicating the angle in degrees below horizontal.
This can be expressed in the distance traveled horizontally for a rise of one unit, or in terms of an angle of inclination or a percentage difference in elevation for a given distance of the track. The allowable gradients may be based on the ruling gradient which is the maximum gradient over which a tonnage train can be hauled with one locomotive.
It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. [1] [2] At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans. [3]
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
The inclination of measured slopes was therefore expressed as the number of horizontal palms and digits relative to each royal cubit rise. The seked is proportional to the reciprocal of our modern measure of slope or gradient, and to the cotangent of the angle of elevation. [ 2 ]