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Tobler's hiking function – walking speed vs. slope angle chart. Tobler's hiking function is an exponential function determining the hiking speed, taking into account the slope angle. [1] [2] [3] It was formulated by Waldo Tobler. This function was estimated from empirical data of Eduard Imhof. [4]
Pace is the reciprocal of speed. It can be calculated here from the following formula: [6] [19] p = p0·(1 + α·m) where: p = pace p0 = pace on flat terrain m = gradient uphill. This formula is true for m≥0 (uphill or flat terrain). [6] [19] It assumes equivalence of distance and climb by applying mentioned earlier α factor. [4] [19]
The vV̇O 2 max of world class middle- and long-distance runners may exceed 24 km/h or 2:30/km pace (15 mph or about 4:00/mile), making this speed slightly comparable to 3000 m race pace. For many athletes, vV̇O 2 max may be slightly slower than 1500 m or mile race pace.
A pace is a unit of length consisting either of one normal walking step (approximately 0.75 metres or 30 inches), or of a double step, returning to the same foot (approximately 1.5 metres or 60 inches). The normal pace length decreases with age and some health conditions. [1]
A metric or distance function is a function d which takes pairs of points or objects to real numbers and satisfies the following rules: The distance between an object and itself is always zero. The distance between distinct objects is always positive. Distance is symmetric: the distance from x to y is always the same as the distance from y to x.
if is in nautical miles, and is in arcminutes (1 ⁄ 60 degree), or; if is in kilometres, and is in gradians. The lengths of the distance units were chosen to make the circumference of the Earth equal 40 000 kilometres, or 21 600 nautical miles. Those are the numbers of the corresponding angle units in one complete turn.
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.
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. This arc is the shortest path ...