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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. [1][4] It is included in the last sentence of his report from a trip. [1][8] Today it is formulated in many ways. Naismith's 1 h / 3 mi + 1 h / 2000 ft can be replaced by:
A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of territorial waters. [2] [3] [4] Historically, it was defined as the meridian arc length corresponding to one minute ( 1 / 60 of a degree) of latitude at the equator, so that Earth's polar circumference is very near to 21,600 nautical miles (that is 60 minutes × 360 degrees).
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
kilometre (km) or kilometer is a metric unit used, outside the US, to measure the length of a journey; the international statute mile (mi) is used in the US; 1 mi = 1.609344 km. nautical mile is rarely used to derive units of transportation quantity.
Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
The knot (/ nɒt /) is a unit of speed equal to one nautical mile per hour, exactly 1.852 km/h (approximately 1.151 mph or 0.514 m/s). [1][2] The ISO standard symbol for the knot is kn. [3] The same symbol is preferred by the Institute of Electrical and Electronics Engineers (IEEE), while kt is also common, especially in aviation, where it is ...
The informal term "metric mile" is used in some countries, in sports such as track and field athletics and speed skating, to denote a distance of 1,500 metres (0.932 miles). The 1500 meters is the premier middle distance running event in Olympic sports. In United States high-school competition, the term is sometimes used for a race of 1,600 ...
Noting that sin ( π 2 − φ) = cos (φ), the haversine formula immediately follows. To derive the law of haversines, one starts with the spherical law of cosines: As mentioned above, this formula is an ill-conditioned way of solving for c when c is small. Instead, we substitute the identity that cos (θ) = 1 − 2 hav (θ), and also ...