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The 50‰ grade is equivalent to 50 m/km or 5%. There are several ways to express slope: as an angle of inclination to the horizontal. (This is the angle α opposite the "rise" side of a triangle with a right angle between vertical rise and horizontal run.)
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Greek: the ridge height is 1 ⁄ 9 to 1 ⁄ 7 the span (an angle of 12.5° to 16°); Roman: the ridge height is 2 ⁄ 9 to 1 ⁄ 3 the span (an angle of 24° to 34°); Common: the rafter length is 3 ⁄ 4 the span (about 48°); Gothic: the rafters equal the span (60°); and; Elizabethan: the rafters are longer than the span (more than 60°). [7]
As "percent" it is used to describe the grade or slope, the steepness of a road or railway, formula for which is 100 × rise / run which could also be expressed as the tangent of the angle of inclination times 100. This is the ratio of distances a vehicle would advance vertically and horizontally, respectively, when going up- or ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown.. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them.
Sag vertical curves are curves which, when viewed from the side, are concave upwards. This includes vertical curves at valley bottoms, but it also includes locations where an uphill grade becomes steeper, or a downhill grade becomes less steep. The most important design criterion for these curves is headlight sight distance. [2]
Finding the geodesic between two points on the Earth, the so-called inverse geodetic problem, was the focus of many mathematicians and geodesists over the course of the 18th and 19th centuries with major contributions by Clairaut, [5] Legendre, [6] Bessel, [7] and Helmert English translation of Astron. Nachr. 4, 241–254 (1825). Errata. [8]