Convert Miles per Hour to Meters per Second

Mile - A mile is a unit of length, usually used to measure distance, in a number of different systems. In contemporary English contexts, mile most commonly refers to the statute mile of 5,280 feet (exactly 1,609.344 meters) or the nautical mile of 1,852 meters (about 6,076.1 ft). There are many other historical miles, and similar units in other systems translated as miles in English, varying between one and fifteen kilometers. It is about a third of the old measurement, a League.

The measurement is now used almost exclusively in the United States and the United Kingdom. It has been replaced by the kilometer as a measure of distance elsewhere. It is sometimes retained as a customary unit. There have been several abbreviations for mile (with and without trailing period): mi, ml, m, M. In the United States, the National Institute of Standards and Technology now uses and recommends mi but in everyday usage (at least in the United States and in the United Kingdom) usages such as miles per hour and miles per gallon are almost always abbreviated as mph or mpg (rather than mi/h or mi/gal).

The formula "multiply by 8 and divide by 5" to convert international miles to kilometers gives a conversion of 1.6, which, at less than 1 percent high, makes a useful approximation.

The statute mile was defined by English Act of Parliament (hence the name) in 1592, during the reign of Queen Elizabeth I; it is equal to 1760 yards (5280 feet). For surveying, the statute mile is divided into eight furlongs; each furlong is ten chains; each chain is four rods (also known as poles or perches); and each rod is 25 links. This makes the rod equal to 5.5 yards or 16.5 feet in both Imperial and U.S. usage.

The exact conversion of the mile to SI units depends on which definition of the yard is in use. The different English-speaking countries maintained independent physical standards for the yard that were found to differ by small but measurable amounts, and even to slowly shorten in length. The United States redefined the U.S. yard in 1893, but this meant that U.S. and Imperial units with the same names had very slightly different values. The confusion was resolved in 1959 with the definition of the international yard in terms of the metre by Australia, Canada, New Zealand, South Africa, the United Kingdom, and the United States. The "international mile" of 1760 international yards is exactly 1609.344 metres.

The difference from the previous standards was about 2 ppm, or about a tenth of an inch in each mile, the old U.S. standard being slightly longer and the old Imperial standards slightly shorter than the international mile. The older standards for the yard (and hence the foot and the mile) continue in use for some surveying purposes in the United States and in India.

For most applications, the difference between the two definitions is insignificant - one international foot is exactly 0.999998 of a U.S. survey foot, for a difference of about 3 millimeters per mile - but it affects the definition of the State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles. When international measure was introduced in the English-speaking countries, the basic geodetic datum in North America was the North American Datum of 1927 (NAD27), which had been constructed by triangulation based on the definition of the foot in the Mendenhall Order of 1893, that is 1 foot = 1200/3937 meters: this definition was retained for data derived from NAD27, but renamed the U.S. survey foot to distinguish it from the international foot.

The NAD27 was replaced in the 1980s by the North American Datum of 1983 (NAD83), which is defined in meters. The SPCSs were also updated, but the National Geodetic Survey left the decision of which (if any) definition of the foot to use to the individual states. All SPCSs are defined in meters, but seven states also have SPCSs defined in U.S. survey feet and an eighth state in international feet: the other 42 states use only meter-based SPCSs. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum, which is also used by the Global Positioning System.

State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2 ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). In the U.S., twenty-four states have legislated that surveying measures should be based on the U.S. survey foot, eight have legislated that they be made on the basis of the international foot, and eighteen have not specified the conversion factor from metric units.

Hour - The hour was originally defined in ancient civilizations (including those of Egypt, Sumer, India, and China) as either one twelfth of the time between sunrise and sunset or one twenty-fourth of a full day. In either case the division reflected the widespread use of a duodecimal numbering system. The importance of 12 has been attributed to the number of lunar cycles in a year, and also to the fact that humans have 12 finger bones (phalanges) on one hand (3 on each of 4 fingers). (It is possible to count to 12 with your thumb touching each finger bone in turn.) There is also a widespread tendency to make analogies among sets of data (12 months, 12 zodiacal signs, 12 hours, a dozen).

The Ancient Egyptian civilization is usually credited with establishing the division of the night into 12 parts, although there were many variations over the centuries. Astronomers in the Middle Kingdom (9th and 10th Dynasties) observed a set of 36 decan stars throughout the year. These star tables have been found on the lids of coffins of the period. The heliacal rising of the next decan star marked the start of a new civil week, which was then 10 days. The period from sunset to sunrise was marked by 18 decan stars. Three of these were assigned to each of the two twilight periods, so the period of total darkness was marked by the remaining 12 decan stars, resulting in the 12 divisions of the night. The time between the appearance of each of these decan stars over the horizon during the night would have been about 40 modern minutes. During the New Kingdom, the system was simplified, using a set of 24 stars, 12 of which marked the passage of the night.

Earlier definitions of the hour varied within these parameters: One twelfth of the time from sunrise to sunset. As a consequence, hours on summer days were longer than on winter days, their length varying with latitude and even, to a small extent, with the local weather (since it affects the atmosphere's index of refraction). For this reason, these hours are sometimes called temporal, seasonal, or unequal hours. Romans, Greeks and Jews of the ancient world used this definition; as did the ancient Chinese and Japanese. The Romans and Greeks also divided the night into three or four night watches, but later the night (the time between sunset and sunrise) was also divided into twelve hours. When, in post-classical times, a clock showed these hours, its period had to be changed every morning and evening (for example by changing the length of its pendulum), or it had to keep to the position of the Sun on the ecliptic (see Prague Astronomical Clock). One twenty-fourth of the apparent solar day (between one noon and the next, or between one sunset and the next). As a consequence hours varied a little, as the length of an apparent solar day varies throughout the year. When a clock showed these hours it had to be adjusted a few times in a month. These hours were sometimes referred to as equal or equinoctial hours. One twenty-fourth of the mean solar day. See mean sun for more information on the difference to the apparent solar day. When an accurate clock showed these hours it virtually never had to be adjusted. However, as the Earth's rotation slows down, this definition has been abandoned.

Meter - The metre or meter (from the Greek /'metron/) is a unit of proper length. It is the basic unit of length in the metric system and in the International System of Units (SI), used around the world for general and scientific purposes. Historically, the metre was defined by the French Academy of Sciences as the length between two marks on a platinum-iridium bar, which was designed to represent 1/10,000,000 of the distance from the equator to the north pole through Paris. In 1983, it was redefined by the International Bureau of Weights and Measures (BIPM) as the distance travelled by light in free space in 1/299,792,458 of a second. The symbol for metre is a lower case m. Decimal multiples and submultiples of the metre, such as kilometre (1000 metres) and centimetre (1/100 metre), are indicated by adding SI prefixes to metre.

Meridional definition - In the eighteenth century, there were two favoured approaches to the definition of the standard unit of length. One approach suggested defining the metre as the length of a pendulum with a half-period of one second, a 'seconds pendulum'. The other approach suggested defining the metre as one ten-millionth of the length of the Earth's meridian along a quadrant, that is the distance from the Equator to the North Pole. In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.

In order to establish a universally accepted foundation for the definition of the metre, measurements of this meridian more accurate than those available at that time were imperative. The Bureau des Longitudes commissioned an expedition led by Delambre and Pierre Mechain, lasting from 1792 to 1799, which measured the length of the meridian between Dunkerque and Barcelona. This portion of the meridian, which also passes through Paris, was to serve as the basis for the length of the half meridian, connecting the North Pole with the Equator.

However, in 1793, France adopted as its official unit of length a metre based on provisional results from the expedition as its official unit of length. Although it was later determined that the first prototype metre bar was short by a fifth of a millimetre due to miscalculation of the flattening of the Earth, this length became the standard. The circumference of the Earth through the poles is therefore slightly more than forty million metres.

In the 1870s and in light of modern precision, a series of international conferences were held to devise new metric standards. The Metre Convention (Convention du Metre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sevres, France. This new organisation would preserve the new prototype metre and kilogram standards when constructed, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation created a new prototype bar in 1889 at the first General Conference on Weights and Measures (CGPM: Conference Generale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of ninety percent platinum and ten percent iridium, measured at the melting point of ice.

In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of distance. By 1925, interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new SI system as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889.

Second - The second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock. SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g., the millisecond (one thousandth of a second), the microsecond (one millionth of a second), and the nanosecond (one billionth of a second). Though SI prefixes may also be used to form multiples of the second (such as "kilosecond," or one thousand seconds), such units are rarely used in practice. More commonly encountered, non-SI units of time such as the minute and hour increase by multiples of 60 and 24 (rather than by powers of ten as in SI). The second was also the base unit of time in the centimetre-gram-second, metre-kilogram-second, metre-tonne-second, and foot-pound-second systems of units.

Before mechanical clocks - The Egyptians subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence their hours varied seasonally. The Hellenistic astronomers Hipparchus (c. 150 BC) and Ptolemy (c. AD 150) subdivided the day sexagesimally and also used a mean hour (1/24 day), but did not use distinctly named smaller units of time. Instead they used simple fractions of an hour.

The day was subdivided sexagesimally, that is by 1/60, by 1/60 of that, by 1/60 of that, etc., to at least six places after the sexagesimal point (a precision of less than 2 microseconds) by the Babylonians after 300 BC, but they did not sexagesimally subdivide smaller units of time. For example, six fractional sexagesimal places of a day was used in their specification of the length of the year, although they were unable to measure such a small fraction of a day in real time. As another example, they specified that the mean synodic month was 29;31,50,8,20 days (four fractional sexagesimal positions), which was repeated by Hipparchus and Ptolemy sexagesimally, and is currently the mean synodic month of the Hebrew calendar, though restated as 29 days 12 hours 793 halakim (where 1 hour = 1080 halakim). The Babylonians did not use the hour, but did use a double-hour lasting 120 modern minutes, a time-degree lasting four modern minutes, and a barleycorn lasting 3⅓ modern seconds (the helek of the modern Hebrew calendar).

In 1000, the Persian scholar al-Biruni gave the times of the new moons of specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday. In 1267, the medieval scientist Roger Bacon stated the times of full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates. Although a third for 1/60 of a second remains in some languages, for example Polish (tercja), Turkish (salise), the modern second is subdivided decimally.

Seconds measured by mechanical clocks - The first clock that could show time in seconds was created by Taqi al-Din at the Istanbul observatory of al-Din between 1577-1580. He called it the "observational clock" in his In the Nabik Tree of the Extremity of Thoughts, where he described it as "a mechanical clock with three dials which show the hours, the minutes, and the seconds." He used it as an astronomical clock, particularly for measuring the right ascension of the stars. The first mechanical clock displaying seconds in Europe was constructed in Switzerland at the beginning of the 17th century.

The second first became accurately measurable with the development of pendulum clocks keeping mean time (as opposed to the apparent time displayed by sundials), specifically in 1670 when William Clement added a seconds pendulum to the original pendulum clock of Christian Huygens. The seconds pendulum has a period of two seconds, one second for a swing forward and one second for a swing back, enabling the longcase clock incorporating it to tick seconds. From this time, a second hand that rotated once per minute in a small subdial began to be added to the clock faces of precision clocks.

Modern measurements - In 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particular epoch, because by then it had become recognized that the Earth's rotation on its own axis was not sufficiently uniform as a standard of time. The Earth's motion was described in Newcomb's Tables of the Sun (1895), which provide a formula estimating the motion of the Sun relative to the epoch 1900 based on astronomical observations made between 1750 and 1892. The second thus defined is the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.

This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960. The tropical year in the definition was not measured, but calculated from a formula describing a mean tropical year which decreased linearly over time, hence the curious reference to a specific instantaneous tropical year. This definition of the second was in conformity with the ephemeris time scale adopted by the IAU in 1952, defined as the measure of time that brings the observed positions of the celestial bodies into accord with the Newtonian dynamical theories of their motion (those accepted for use during most of the twentieth century being Newcomb's Tables of the Sun, used from 1900 through 1983, and Brown's Tables of the Moon, used from 1923 through 1983).

With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of the second, rather than the revolution of the Earth around the Sun. Following several years of work, Louis Essen from the National Physical Laboratory (Teddington, England) and William Markowitz from the United States Naval Observatory (USNO) determined the relationship between the hyperfine transition frequency of the cesium atom and the ephemeris second. Using a common-view measurement method based on the received signals from radio station WWV, they determined the orbital motion of the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time as measured by an atomic clock. They found that the second of ephemeris time (ET) had the duration of 9,192,631,770 +- 20 cycles of the chosen cesium frequency. As a result, in 1967 the Thirteenth General Conference on Weights and Measures defined the second of atomic time in the International System of Units as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

This SI second, referred to atomic time, was later verified to be in agreement, within 1 part in 1010, with the second of ephemeris time as determined from lunar observations. During the 1970s it was realized that gravitational time dilation caused the second produced by each atomic clock to differ depending on its altitude. A uniform second was produced by correcting the output of each atomic clock to mean sea level (the rotating geoid), lengthening the second by about 1 x 10-10. This correction was applied at the beginning of 1977 and formalized in 1980. In relativistic terms, the SI second is defined as the proper time on the rotating geoid.

The definition of the second was later refined at the 1997 meeting of the BIPM to include the statement "This definition refers to a cesium atom at rest at a temperature of 0 K." The revised definition would seem to imply that the ideal atomic clock would contain a single cesium atom at rest emitting a single frequency. In practice, however, the definition means that high-precision realizations of the second should compensate for the effects of the ambient temperature (black-body radiation) within which atomic clocks operate, and extrapolate accordingly to the value of the second at a temperature of absolute zero.

Today, the atomic clock operating in the microwave region is challenged by atomic clocks operating in the optical region. To quote Ludlow et al. "In recent years, optical atomic clocks have become increasingly competitive in performance with their microwave counterparts. The overall accuracy of single trapped ion based optical standards closely approaches that of the state-of-the-art cesium fountain standards. Large ensembles of ultracold alkaline earth atoms have provided impressive clock stability for short averaging times, surpassing that of single-ion based systems. So far, interrogation of neutral atom based optical standards has been carried out primarily in free space, unavoidably including atomic motional effects that typically limit the overall system accuracy. An alternative approach is to explore the ultranarrow optical transitions of atoms held in an optical lattice. The atoms are tightly localized so that Doppler and photon-recoil related effects on the transition frequency are eliminated."

The NRC attaches a "relative uncertainty" of 2.5 x 10-11 (limited by day-to-day and device-to-device reproducibility) to their atomic clock based upon the 127I2 molecule, and is advocating use of an Sr88 ion trap instead (relative uncertainty due to linewidth of 2.2 x 10-15). See magneto-optical trap and "Trapped ion optical frequency standards". National Physical Laboratory. Such uncertainties rival that of the NIST F-1 cesium atomic clock in the microwave region, estimated as a few parts in 1016 averaged over a day.