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To compensate for this, the gradient should be a little less steep the sharper the curve is; the necessary grade reduction is assumed to be given by a simple formula such as 0.04 per cent per "degree of curve", the latter being a measure of curve sharpness used in the United States. On a 10-degree curve (radius 573.7 feet) the grade would thus ...
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.
Slope may still be expressed when the horizontal run is not known: the rise can be divided by the hypotenuse (the slope length). This is not the usual way to specify slope; this nonstandard expression follows the sine function rather than the tangent function, so it calls a 45 degree slope a 71 percent grade instead of a 100 percent. But in ...
The world average river reach slope is 2.6 m/km or 0.26%; [2] a slope smaller than 1% and greater than 4% is considered gentle and steep, respectively. [3] Stream gradient may change along the stream course. An average gradient can be defined, known as the relief ratio, which gives the average drop in elevation per unit length of river. [4]
Balsam Mountain Grade, Balsam N.C. Balsam Mountain, home of highest railroad station east of the Rockies; average grade about 4.0%, max 4.5%. 1 of 2 grades on southern railways former Murphy branch that are +4% grade. Balsam Mountain has seen many runaways. It is still in service operated by the Blue Ridge Southern Railroad . 1 in 22 (4.5%)
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]
Drainage gradient (DG) is a term in road design, defined as the combined slope due to road surface cross slope (CS) and longitudinal slope (hilliness). Although the term may not be used, the concept is also used in roof design and landscape architecture. If the drainage gradient is too low, rain and melt water drainage will be insufficient.
where is the superelevation in inches, is the curvature of the track in degrees per 100 feet, and the maximum speed in miles per hour. The maximum value of cant (the height of the outer rail above the inner rail) for a standard gauge railway is approximately 150 mm (6 in).