As a relative bearing

This is a system of denoting impromptu relative bearing widely used in practical navigation to give the position of an observed object readily and comprehensibly. "Relative" means that it does not state or imply any compass directions whatsoever. The vessel can be pointed in any direction. The clock numbers are relative to the direction in which the vessel points. The angular distance between adjacent clock numbers is 30 degrees, a round unit that simplifies mathematical juggling. A quick clock number can be shouted by a lookout, whereas after a calculation and comparison of compass points, which might be unknown anyway, it might be too late for the vessel to avoid danger.

As an example of a standard use, the clock position of every approaching vessel is monitored. If the clock number for the observed vessel does not change, it is on a collision course for the observer vessel, as vessels that pass by must change relative bearing. In warfare the clock system is especially useful in drawing attention to enemy locations.

The clock system is easily converted into a 360 degree system for more precise denotation. One bearing, or point, is termed an azimuth.^[2] The convention is that of analytic geometry: the y-axis at zero degrees is the longitudinal axis of the vehicle. Angles grow larger in the clockwise direction. Thus, directly to port is at 270 degrees. Negative angles are not used. In navigational contexts, the bearing must be stated as 3 digits: 010 (not so in other contexts).^[3] These circles are not to be confused with latitude and longitude, or with any sort of compass reading, which are not relative to the vehicle, but to the magnetic and spin axes of the Earth.

As a true bearing

For maritime and aviation applications, the clock bearing is almost always a relative bearing; i.e., the angle stated or implied is angular distance from the longitudinal axis of the vessel or imaginary vessel to the bearing. However, if the 12:00 position is associated with a true bearing, then the observed position is also.

For example, clock position on a 12-hour analog watch can be used to find the approximate bearing of true north or south on a day clear enough for the sun to cast a shadow. The technique takes a line of sight (LOS) on the visible sun, or on the direction pointed to by a shadow stick, through the hour hand of the watch. It exploits the one true bearing of the sun in its course across the sky: the LOS from the observer to the zenith of its course. There the sun is seen mid-way between sunrise and sunset. A vertical plane including sun and observer is perpendicular to the plane of the sun's course. Its intersection with the surface of the earth is a meridian, a line passing through a geographical pole. If the sun is in the southern half of the sky, the zenith bearing points true south; if northern, north. The time at that moment is 12:00 P.M., solar time. The clock position to the observer is 12.

If the watch is set to uncorrected solar time, both hands point to the sun. In a 12-hour watch, the sun and the hour hand both advance, but not at the same rate; the sun covers 15 degrees per hour, and watch 30. To keep the hour hand on the sun, 12:00 must recede from the zenith at the same rate the hour hand advances. Thus when the observer takes an arbitrary LOS, the zenith LOS – true north or south – is to be found at half the angle between 12 and the LOS. On a 24-hour watch, the sun and the hour hand advance at the same rate. There is no need to half the angle.

The zenith LOS is only an approximation due to changes in the time kept by the watch. That time is based on mean solar time rather than observed solar time. Also, time changes with longitude, and the institution of daylight saving time. The time generally available for watch settings in the observer's region is called civil time. It can be corrected to solar time, but LOS on a watch is generally too imprecise to make the trouble worth the effort.^[4]

From aviation

In World War II aircraft pilots needed a quick method of communicating the relative position of threats, for which the clock system was ideal. The gunners of a bomber, or the other aircraft in the squadron, had to be kept informed for purposes of immediate response. However, in aviation, a clock position refers to a horizontal direction. The pilots needed a vertical dimension, so they supplemented the clock position with the word high or low to describe the vertical direction; e.g., 6 o'clock high means behind and above the horizon, while 12 o'clock low means ahead and below the horizon.^[5]

The horizon line was only visible in clear weather in daylight, and was only useful as a reference line in straight and level flight, when it appeared on the nose of the aircraft. The vocabulary therefore was only of use during daylight patrols or missions. The reference line and reference clock positions did not exist during combat aerobatics, at night, or during cloudy weather, when other means had to be found for locating the combatants, such as radar.

For airplanes in rapid maneuvers, air traffic controllers will issue the eight cardinal compass points instead.^[6]

From community planning

In 1916, J.B. Plato devised a clock system to identify farms around reference points in rural areas. A clock face was imagined centered on a rural community with 12:00 pointing true north. The circle was divided into concentric numbered bands at each mile of radius. The bands were divided into 12 segments at each position of the clock numbered after the clock hour. Within a segment, every building was assigned a letter. For instance, Alton 3-0 L meant house L in segment 3 of the central circle of 1 mile radius at Alton, where 3 was at 3:00.^[7]

From medicine

Medical pathology uses the clock system to describe the location of breast tumors. A clock face is considered imposed over each breast, left and right, centered on the alveolar region, with the positions shown around it. Tumors are located at one or more subsites, or clock positions, identified by one or more clock numbers. In addition the numbers are arranged in quadrants: Upper Outer Quadrant (UOQ), Lower Inner Quadrant (LIQ), and so on. Codes are assigned to the quadrants, the alveolar region, and the whole breast.^[8]

From golf

Golf players use the clock system to study the course of the ball in putting situations. For holes that are on a slope, the hole is imagined to be the center of a clock face with 12:00 at the high point and 6:00 at the low point. The ball will only run true when hit from the high or low points; otherwise, its course will break, or bend on the slope. Some golfers practice clock drill – hitting the ball from all the positions of the clock – to learn how it breaks.^[9]

From microscopy

An article in the Journal of Applied Microscopy for 1898 recommends the use of a polar coordinate system in the form of a clockface for recording the positions of microscopic objects on a slide. The face is conceived centered on the circle visible under the lens. The pole is the center. Angle is given as a clock number, and distance as a decimal percentage of the radius through the object. For example, “3,9” means 3:00 o'clock at 9 tenths of the radius.^[10]

The Mesopotamian system

The Babylonian time system is documented by thousands of Mesopotamian cuneiform tablets. The Babylonians inherited the better part of their system from the Sumerians, whose culture they absorbed. Tablets of different periods reveal the development of a sexagesimal numbering system from decimal and duodecimal systems, which reveals itself in the construction of unique symbols for numerals 1-59 from natural finger decimals (ten fingers, ten symbols). Why they developed this system is a matter for academic debate, but there are multiple advantages, including division by several factors, offering several possible subdivisions, one of which is by 12's.^[14] Classical civilization adopted and adapted the Mesopotamian time system, and modern civilization adapted it still further. The modern system retains much of the sexagesimalism of the Sumerians, but typically not with the same detail.^[15]

Time today and generally in ancient Mesopotamia is given mainly in three digits. Today's state the hours, minutes, and seconds. In a strict sexagesimal system these three would be expressed in a single, three-digit sexagesimal number: h,m,s with values on each of the three letters of 0-59; that is, hours up to 60, minutes up to 60, and seconds up to 60. Because integer numbers are expressed as sums, in this case

h times 60² + m times 60 + s

for the number of seconds, h, m, and s can be broken out and treated as separate numbers. Each number, however, implies the other two; e.g., a minute implies 60 seconds. m and s are straightforward, but h is different. There are no explicit 60 hours; the number instead is 24, and yet they are part of an implied sexagesimal system. 60 minutes is implied by one of the 24 hours, not one of the 60. The system is not strictly sexagesimal but is based on the sexagesimal.

A full Babylonian time determination also had three digits.^[16] Zeros were blank spaces, causing some difficulty of discerning them from character separators. For reasons that are not clear, the Mesopotamians adopted a standard of 12 hours per day for their first-order digit. Their day, however, was designed for measurement on their most ancient and widely used timepiece, the sundial, which showed only daylight hours. Daylight was the time between sunrise and sunset, each of those being defined as the appearance or disappearance of the top rim of the sun on the horizon. Daylight hours problematically were seasonal; that is, due to the variation of the length of the day with time of year, hour length was variable also. The Mesopotamians had discovered, however, that if the darkness was divided into 12 hours also, and each run of 12 was matched number for number: 1st to 1st, 2nd to 2nd, etc., the sum of each match was constant.^[17]

The 12-hour, seasonal day was one of many metrological arrangements that had developed during the 3rd millennium BC. It was in use in the Ur III period, at the end of the 3rd millennium.^[18] The vocabulary of time was not yet set. For example, the 60-hour day existed as the time-shekel, 1/60 of a working day, presumably so named from the labor cost of one hexagesimal hour. This was a time of strong kings and continuing administrations that took responsibility for weights and standards. Englund distinguishes two main types of system: the cultic, in which the events of the seasonal calendar assume religious significance, and are perpetuated for religious reasons, and a second, new type, the state, defined by an administration that needed to standardize its time units.

The state system came to predominate in the subsequent Old Babylonian period. The state administrators had perceived that the sun advances at a uniform rate no matter what the season. One sun cycle is always the same. Moreover, it matches the cycle of rotation of the stars around the pole star, the real reason being that the Earth rotates at a constant angular velocity. If hours were to represent divisions of the uniform rotation, they must also be uniform, and not be variable. There were two days of the year when all 24 hours were of the same length: the two equinoxes. The standard double hour (beru), of equinoctial length, representing two modern hours, of which there were 12 in the standard day (umu), was not conceived as being one of day and one of night, but as being just two consecutive equal-length hours. One standard day thus went on to become two consecutive equal 12-hour clockfaces in modern clock time. 30 standard days were a standard month, and 12 of those a standard year of 360 days. Some juggling of month lengths to make the 12 months fit the year was still required.

Within a day, single hours were unreliable. They came in all sizes. The double hour, however, originally the sum of a daylight hour and the corresponding night hour, was always the same. The statists therefore chose to use double units in definition. The 12-hour daytime had been divided into three seasonal watches. These were matched to three seasonal night watches, 1st to 1st, 2nd to 2nd, etc. One double watch (8 hours) was four double hours. One single watch (four hours) was two double hours.

To produce a second-order digit of a Babylonian time, the statists changed from solar to stellar time. The stars moved in visible circles at a fixed rate, which could be measured by the constant escape of water from a water clock. The single standard watch of 4 hours (two double hours) was divided into 60 time-degrees (ush). One double hour had 30, and one complete stellar day, 360 (12 times 30).^[19] This assignment was the creation of the 360-degree circle, as the degree went from being a time division to an angular distance of rotation. Time-degrees were all the same (one is about 4 minutes of modern time). The second-order digit counted the degrees that had gone by in the hour, notwithstanding the fact that its number of degrees were seasonal.

The third and last order digit divided the time-degree into 60 parts (the gar), which appears to be sexagesimal. In modern time it is 4 seconds. There are not 60 time-degrees in an hour, nor 60 hours in a day. The Babylonian time was thus three different numbers, only one of which was sexagesimal. Only its general features are modern: the 12-hour day followed by a 12-hour night, the 60-division 3rd-order digit, and the 360-degree circle.