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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.
I–VI)–is used to grade the "overall" risk and difficulty of mountain routes (with the gradient of the snow/ice fields) (e.g. the 1938 Heckmair Route on the Eiger is graded: ED2 (IFAS), VI− (UIAA), A0 (A-grade), WI4 (WI-grade), 60° slope). The related "commitment grade" systems include the notable American National Climbing Classification ...
The gradient can also be used to measure how a scalar field changes in other directions, rather than just the direction of greatest change, by taking a dot product. Suppose that the steepest slope on a hill is 40%. A road going directly uphill has slope 40%, but a road going around the hill at an angle will have a shallower slope.
Compensation for curvature: the gradient is slightly eased on sharpest curves so that the tractive effort to pull the train is uniform. Horseshoe curves; Spirals; Zig zags; A descending momentum gradient on the approach to a hill allows a train to increase speed before a climb. [1]
Hill climbing attempts to maximize (or minimize) a target function (), where is a vector of continuous and/or discrete values. At each iteration, hill climbing will adjust a single element in and determine whether the change improves the value of ().
A horseshoe curve is a means to lengthen an ascending or descending grade and thereby reduce the maximum gradient. Grade or gradient is defined as the rise divided by the run (length) or distance, so in principle such curves add to length for the same altitude gain, just as would a climbing spiral around one or more peaks, or a climbing traverse (cutting) wrapping around an end of a ridge.
GOP Rep. Mike Lawler (NY-17), a possible challenger to Hochul for governor, hailed it as “a huge win for New York families, commuters, and small businesses ruthlessly targeted by this unjust tax
Pace [6] in minutes per kilometre or mile vs. slope angle resulting from Naismith's rule [7] for basal speeds of 5 and 4 km / h. [n 1]The original Naismith's rule from 1892 says that one should allow one hour per three miles on the map and an additional hour per 2000 feet of ascent.