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l = slope length 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 ...
Stream gradient (or stream slope) is the grade (or slope) of a stream.It is measured by the ratio of drop in elevation and horizontal distance. [1] It is a dimensionless quantity, usually expressed in units of meters per kilometer (m/km) or feet per mile (ft/mi); it may also be expressed in percent (%).
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]
In principle, it is the projection of the gradient onto the horizontal slope. In practice using a raster digital elevation model, it is approximated using one of the same partial derivative approximation methods developed for slope. [12] Then the aspect is calculated as: [15]
Webpage with program to calculate Distance & Bearing; Calculate distance and bearing between two Latitude/Longitude points and much more; See the end point on a map when you specify a start point, a bearing and a distance. More understandable definitions from an online classroom
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.
That is, 7.92 units of distance are equivalent to 1 unit of climb. For convenience an 8 to 1 rule can be used. So, for example, if a route is 20 kilometres (12 mi) with 1600 metres of climb (as is the case on leg 1 of the Bob Graham Round , Keswick to Threlkeld), the equivalent flat distance of this route is 20+(1.6×8)=32.8 kilometres (20.4 mi).
Examples of this include the backwater behind an in-stream structure (e.g. dam, sluice gate, weir, etc.), when there is a constriction in the channel, and when there is a minor change in channel slope. Rapidly varied flow occurs when the change in flow depth per change in flow distance is significant.