The koch (Russian: коч , IPA: [ˈkotɕ] ) was a special type of small one- or two- mast wooden sailing ships designed and used in Russia for transpolar voyages in ice conditions of the Arctic seas, popular among the Pomors .
109-455: Because of its additional skin-planking (called kotsa ) and Arctic design of the body and the rudder , it could sail without being damaged in the waters full of ice blocks and ice floes . The koch was the unique ship of this class for several centuries. The development of koch began in the 11th century, when the White Sea shores began to be settled. This type of ship was in wide use during
218-412: A Mediterranean context, side-rudders are more specifically called quarter-rudders as the later term designates more exactly where the rudder was mounted. Stern-mounted rudders are uniformly suspended at the back of the ship in a central position. Although some classify a steering oar as a rudder, others argue that the steering oar used in ancient Egypt and Rome was not a true rudder and define only
327-408: A fluid medium (usually air or water ). On an airplane , the rudder is used primarily to counter adverse yaw and p-factor and is not the primary control used to turn the airplane. A rudder operates by redirecting the fluid past the hull or fuselage , thus imparting a turning or yawing motion to the craft. In basic form, a rudder is a flat plane or sheet of material attached with hinges to
436-437: A manoeuvring thruster in the bow, or be replaced entirely by azimuth thrusters . Boat rudders may be either outboard or inboard. Outboard rudders are hung on the stern or transom. Inboard rudders are hung from a keel or skeg and are thus fully submerged beneath the hull, connected to the steering mechanism by a rudder post that comes up through the hull to deck level, often into a cockpit. Inboard keel hung rudders (which are
545-520: A water clock for telling time. A canonical sundial is one that indicates the canonical hours of liturgical acts. Such sundials were used from the 7th to the 14th centuries by the members of religious communities. The Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani 's Constructio instrumenti ad horologia solaria (c. 1620) discusses how to make
654-537: A broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude . The term sundial can refer to any device that uses the Sun's altitude or azimuth (or both) to show
763-404: A circle on the equatorial plane, and the radius of the circle measures the declination of the sun. The ends of the gnomon bar may be used as the nodus, or some feature along its length. An ancient variant of the equatorial sundial has only a nodus (no style) and the concentric circular hour-lines are arranged to resemble a spider-web. In the horizontal sundial (also called a garden sundial ),
872-419: A continuation of the aft trailing edge of the full keel) are traditionally deemed the most damage resistant rudders for off shore sailing. Better performance with faster handling characteristics can be provided by skeg hung rudders on boats with smaller fin keels. Rudder post and mast placement defines the difference between a ketch and a yawl, as these two-masted vessels are similar. Yawls are defined as having
981-462: A conventional fixed-wing aircraft, but much more slowly than if ailerons are also used in conjunction. Sometimes pilots may intentionally operate the rudder and ailerons in opposite directions in a maneuver called a slip or sideslip. This may be done to overcome crosswinds and keep the fuselage in line with the runway, or to lose altitude by increasing drag, or both. Another technique for yaw control, used on some tailless aircraft and flying wings ,
1090-477: A horizontal and analemmatic dial, mounted together on one plate. In these designs, their times agree only when the plate is aligned properly. Sundials may indicate the local solar time only. To obtain the national clock time, three corrections are required: The principles of sundials are understood most easily from the Sun 's apparent motion. The Earth rotates on its axis, and revolves in an elliptical orbit around
1199-460: A horizontal dial they run anticlockwise (US: counterclockwise) rather than clockwise. Sundials which are designed to be used with their plates horizontal in one hemisphere can be used with their plates vertical at the complementary latitude in the other hemisphere. For example, the illustrated sundial in Perth , Australia , which is at latitude 32° South, would function properly if it were mounted on
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#17327809086311308-500: A line of light may be formed by allowing the Sun's rays through a thin slit or focusing them through a cylindrical lens . A spot of light may be formed by allowing the Sun's rays to pass through a small hole, window, oculus , or by reflecting them from a small circular mirror. A spot of light can be as small as a pinhole in a solargraph or as large as the oculus in the Pantheon. Sundials also may use many types of surfaces to receive
1417-529: A much later "official" time at the western edge of a time-zone, compared to sunrise and sunset times at the eastern edge. If a sundial is located at, say, a longitude 5° west of the reference longitude, then its time will read 20 minutes slow, since the Sun appears to revolve around the Earth at 15° per hour. This is a constant correction throughout the year. For equiangular dials such as equatorial, spherical or Lambert dials, this correction can be made by rotating
1526-408: A perfect sundial. They have been commonly used since the 16th century. In general, sundials indicate the time by casting a shadow or throwing light onto a surface known as a dial face or dial plate . Although usually a flat plane, the dial face may also be the inner or outer surface of a sphere, cylinder, cone, helix, and various other shapes. The time is indicated where a shadow or light falls on
1635-519: A shadow or the edge of a shadow while others use a line or spot of light to indicate the time. The shadow-casting object, known as a gnomon , may be a long thin rod or other object with a sharp tip or a straight edge. Sundials employ many types of gnomon. The gnomon may be fixed or moved according to the season. It may be oriented vertically, horizontally, aligned with the Earth's axis, or oriented in an altogether different direction determined by mathematics. Given that sundials use light to indicate time,
1744-602: A small pin run through the stock of the steering oar, can be traced to the fifth dynasty (2504–2347 BC). Both the tiller and the introduction of an upright steering post abaft reduced the usual number of necessary steering oars to one each side. Single steering oars put on the stern can be found in several tomb models of the time, particularly during the Middle Kingdom when tomb reliefs suggest them commonly employed in Nile navigation. The first literary reference appears in
1853-514: A south-facing vertical wall at latitude 58° (i.e. 90° − 32°) North, which is slightly further north than Perth, Scotland . The surface of the wall in Scotland would be parallel with the horizontal ground in Australia (ignoring the difference of longitude), so the sundial would work identically on both surfaces. Correspondingly, the hour marks, which run counterclockwise on a horizontal sundial in
1962-584: A sternpost-mounted rudder. On their ships "the rudder is controlled by two lines, each attached to a crosspiece mounted on the rudder head perpendicular to the plane of the rudder blade." The earliest evidence comes from the Ahsan al-Taqasim fi Marifat al-Aqalim ('The Best Divisions for the Classification of Regions') written by al-Muqaddasi in 985: Oars mounted on the side of ships evolved into quarter steering oars, which were used from antiquity until
2071-413: A style and a nodus to determine the time and date. The gnomon is usually fixed relative to the dial face, but not always; in some designs such as the analemmatic sundial, the style is moved according to the month. If the style is fixed, the line on the dial plate perpendicularly beneath the style is called the substyle , meaning "below the style". The angle the style makes with the plane of the dial plate
2180-559: A sundial designed for a latitude of 40° can be used at a latitude of 45°, if the sundial plane is tilted upwards by 5°, thus aligning the style with the Earth's rotational axis. Many ornamental sundials are designed to be used at 45 degrees north. Some mass-produced garden sundials fail to correctly calculate the hourlines and so can never be corrected. A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at
2289-410: A sundial must have been designed for the local geographical latitude and its style must be parallel to the Earth's rotational axis; the style must be aligned with true north and its height (its angle with the horizontal) must equal the local latitude. To adjust the style height, the sundial can often be tilted slightly "up" or "down" while maintaining the style's north-south alignment. Some areas of
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#17327809086312398-401: A tiller that fits into the rudder stock that also forms the fixings to the rudder foil. Craft where the length of the tiller could impede movement of the helm can be split with a rubber universal joint and the part adjoined the tiller termed a tiller extension. Tillers can further be extended by means of adjustable telescopic twist locking extension. There is also the barrel type rudder , where
2507-552: Is an oversized oar or board to control the direction of a ship or other watercraft before the invention of the rudder. It is normally attached to the starboard side in larger vessels, though in smaller ones it is rarely if ever, attached. Rowing oars set aside for steering appeared on large Egyptian vessels long before the time of Menes (3100 BC). In the Old Kingdom (2686 BC – 2134 BC) as many as five steering oars are found on each side of passenger boats. The tiller , at first
2616-409: Is at Jaipur , raised 26°55′ above horizontal, reflecting the local latitude. On any given day, the Sun appears to rotate uniformly about this axis, at about 15° per hour, making a full circuit (360°) in 24 hours. A linear gnomon aligned with this axis will cast a sheet of shadow (a half-plane) that, falling opposite to the Sun, likewise rotates about the celestial axis at 15° per hour. The shadow
2725-453: Is called the substyle height, an unusual use of the word height to mean an angle . On many wall dials, the substyle is not the same as the noon line (see below). The angle on the dial plate between the noon line and the substyle is called the substyle distance , an unusual use of the word distance to mean an angle . By tradition, many sundials have a motto . The motto is usually in the form of an epigram : sometimes sombre reflections on
2834-430: Is equal worldwide: it does not depend on the local latitude or longitude of the observer's position. It does, however, change over long periods of time, (centuries or more, ) because of slow variations in the Earth's orbital and rotational motions. Therefore, tables and graphs of the equation of time that were made centuries ago are now significantly incorrect. The reading of an old sundial should be corrected by applying
2943-409: Is made via the relation Near the equinoxes in spring and autumn, the sun moves on a circle that is nearly the same as the equatorial plane; hence, no clear shadow is produced on the equatorial dial at those times of year, a drawback of the design. A nodus is sometimes added to equatorial sundials, which allows the sundial to tell the time of year. On any given day, the shadow of the nodus moves on
3052-433: Is opaque, both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. With translucent dial plates (e.g. glass) the hour angles need only be marked on the sun-facing side, although the hour numberings (if used) need be made on both sides of the dial, owing to the differing hour schema on the sun-facing and sun-backing sides. Another major advantage of this dial
3161-439: Is operated by pedals via mechanical linkages or hydraulics. Generally, a rudder is "part of the steering apparatus of a boat or ship that is fastened outside the hull, " denoting all types of oars, paddles, and rudders. More specifically, the steering gear of ancient vessels can be classified into side-rudders and stern-mounted rudders, depending on their location on the ship. A third term, steering oar , can denote both types. In
3270-444: Is seen by falling on a receiving surface that is usually flat, but which may be spherical, cylindrical, conical or of other shapes. If the shadow falls on a surface that is symmetrical about the celestial axis (as in an armillary sphere, or an equatorial dial), the surface-shadow likewise moves uniformly; the hour-lines on the sundial are equally spaced. However, if the receiving surface is not symmetrical (as in most horizontal sundials),
3379-507: Is symmetrical about that axis; examples include the equatorial dial, the equatorial bow, the armillary sphere, the cylindrical dial and the conical dial. However, other designs are equiangular, such as the Lambert dial, a version of the analemmatic sundial with a moveable style. A sundial at a particular latitude in one hemisphere must be reversed for use at the opposite latitude in the other hemisphere. A vertical direct south sundial in
Koch (boat) - Misplaced Pages Continue
3488-418: Is that equation of time (EoT) and daylight saving time (DST) corrections can be made by simply rotating the dial plate by the appropriate angle each day. This is because the hour angles are equally spaced around the dial. For this reason, an equatorial dial is often a useful choice when the dial is for public display and it is desirable to have it show the true local time to reasonable accuracy. The EoT correction
3597-411: Is the ram type steering gear . It employs four hydraulic rams to rotate the rudder stock (rotation axis), in turn rotating the rudder. On an aircraft, a rudder is the directional control surface along with the rudder-like elevator (usually attached to the horizontal tail structure, if not a slab elevator) and ailerons (attached to the wings) that control pitch and roll, respectively. The rudder
3706-412: Is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and t is the number of hours before or after noon. For example, the angle H V {\displaystyle \ H_{V}\ } of the 3 P.M. hour-line would equal the arctangent of cos L , since tan 45° = 1 . The shadow moves counter-clockwise on
3815-499: Is the angle between a given hour-line and the noon hour-line (which always points towards true north ) on the plane, and t is the number of hours before or after noon. For example, the angle H H {\displaystyle \ H_{H}\ } of the 3 PM hour-line would equal the arctangent of sin L , since tan 45° = 1. When L = 90 ∘ {\displaystyle \ L=90^{\circ }\ } (at
3924-421: Is the intersection of the cone of light rays with the flat surface. This cone and its conic section change with the seasons, as the Sun's declination changes; hence, sundials that follow the motion of such light-spots or shadow-tips often have different hour-lines for different times of the year. This is seen in shepherd's dials, sundial rings, and vertical gnomons such as obelisks. Alternatively, sundials may change
4033-467: Is to add one or more drag-creating surfaces, such as split ailerons, on the outer wing section. Operating one of these surfaces creates drag on the wing, causing the plane to yaw in that direction. These surfaces are often referred to as drag rudders. Rudders are typically controlled with pedals . Sundial A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by
4142-433: Is usually attached to the fin (or vertical stabilizer ), which allows the pilot to control yaw about the vertical axis, i.e., change the horizontal direction in which the nose is pointing. Unlike a ship, both aileron and rudder controls are used together to turn an aircraft, with the ailerons imparting roll and the rudder imparting yaw and also compensating for a phenomenon called adverse yaw . A rudder alone will turn
4251-523: The Middle Ages are known from various travellers to China, such as Ibn Battuta of Tangier , Morocco and Marco Polo of Venice , Italy . The later Chinese encyclopedist Song Yingxing (1587–1666) and the 17th-century European traveler Louis Lecomte wrote of the junk design and its use of the rudder with enthusiasm and admiration. Paul Johnstone and Sean McGrail state that the Chinese invented
4360-480: The North Pole ), the horizontal sundial becomes an equatorial sundial; the style points straight up (vertically), and the horizontal plane is aligned with the equatorial plane; the hour-line formula becomes H H = 15 ∘ × t , {\displaystyle \ H_{H}=15^{\circ }\times t\ ,} as for an equatorial dial. A horizontal sundial at
4469-725: The Northern Hemisphere becomes a vertical direct north sundial in the Southern Hemisphere . To position a horizontal sundial correctly, one has to find true north or south . The same process can be used to do both. The gnomon, set to the correct latitude, has to point to the true south in the Southern Hemisphere as in the Northern Hemisphere it has to point to the true north. The hour numbers also run in opposite directions, so on
Koch (boat) - Misplaced Pages Continue
4578-701: The Old Testament describes a sundial—the "dial of Ahaz" mentioned in Isaiah 38:8 and 2 Kings 20:11 . By 240 BC Eratosthenes had estimated the circumference of the world using an obelisk and a water well and a few centuries later Ptolemy had charted the latitude of cities using the angle of the sun. The people of Kush created sun dials through geometry. The Roman writer Vitruvius lists dials and shadow clocks known at that time in his De architectura . The Tower of Winds constructed in Athens included sundial and
4687-445: The apparent position of the Sun in the sky . In the narrowest sense of the word, it consists of a flat plate (the dial ) and a gnomon , which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts
4796-430: The equation of time . This compensates for the slight eccentricity in the Earth's orbit and the tilt of the Earth's axis that causes up to a 15 minute variation from mean solar time. This is a type of dial furniture seen on more complicated horizontal and vertical dials. Prior to the invention of accurate clocks, in the mid 17th century, sundials were the only timepieces in common use, and were considered to tell
4905-409: The fixed stars , the Sun changes its position on the celestial sphere, being (in the northern hemisphere) at a positive declination in spring and summer, and at a negative declination in autumn and winter, and having exactly zero declination (i.e., being on the celestial equator ) at the equinoxes . The Sun's celestial longitude also varies, changing by one complete revolution per year. The path of
5014-518: The "median, vertical and axial" sternpost-mounted rudder, and that such a kind of rudder preceded the pintle-and-gudgeon rudder found in the West by roughly a millennium. A Chandraketugarh (West Bengal) seal dated between the 1st and 3rd centuries AD depicts a steering mechanism on a ship named ''Indra of the Ocean'' (Jaladhisakra), which indicates that it was a sea-bound vessel. Arab ships also used
5123-497: The "right" time. The equation of time was not used. After the invention of good clocks, sundials were still considered to be correct, and clocks usually incorrect. The equation of time was used in the opposite direction from today, to apply a correction to the time shown by a clock to make it agree with sundial time. Some elaborate " equation clocks ", such as one made by Joseph Williamson in 1720, incorporated mechanisms to do this correction automatically. (Williamson's clock may have been
5232-493: The 1st century AD. In regards to the ancient Phoenician (1550–300 BC) use of the steering oar without a rudder in the Mediterranean , Leo Block (2003) writes: A single sail tends to turn a vessel in an upwind or downwind direction, and rudder action is required to steer a straight course. A steering oar was used at this time because the rudder had not yet been invented. With a single sail, frequent movement of
5341-701: The Chinese stern-mounted rudder ( duò 舵 ) can be seen on a 2-foot (61 cm) pottery model of a junk dating from the 1st century AD, during the Han dynasty (202 BC – 220 AD). It was discovered in Guangzhou in an archaeological excavation carried out by the Guangdong Provincial Museum and Academia Sinica of Taiwan in 1958. Within decades, several other Han dynasty ship models featuring rudders were found in archaeological excavations. The first solid written reference to
5450-408: The Earth's equator , where L = 0 ∘ , {\displaystyle \ L=0^{\circ }\ ,} would require a (raised) horizontal style and would be an example of a polar sundial (see below). The chief advantages of the horizontal sundial are that it is easy to read, and the sunlight lights the face throughout the year. All the hour-lines intersect at
5559-416: The Mediterranean through a long period of constant refinement and improvement so that by Roman times ancient vessels reached extraordinary sizes. The strength of the steering oar lay in its combination of effectiveness, adaptability and simpleness. Roman quarter steering oar mounting systems survived mostly intact through the medieval period. By the first half of the 1st century AD, steering gear mounted on
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#17327809086315668-552: The Russian Arctic shipbuilding and navigation were undermined by the ukase ( decree ) of Tsar Peter the Great . According to the ukase, only novomanerniye ("new-mannered") vessels could be built, that is the civil ships, which could also be used for military purposes. The koch with its special anti-icebound features did not suit this aim. In the 19th century the anti- ice floe protective features of koch were adopted to
5777-399: The Sun is actually on the meridian at official clock time of 3 PM ). This occurs in the far west of Alaska , China , and Spain . For more details and examples, see time zones . Although the Sun appears to rotate uniformly about the Earth, in reality this motion is not perfectly uniform. This is due to the eccentricity of the Earth's orbit (the fact that the Earth's orbit about
5886-426: The Sun is not perfectly circular, but slightly elliptical ) and the tilt (obliquity) of the Earth's rotational axis relative to the plane of its orbit. Therefore, sundial time varies from standard clock time . On four days of the year, the correction is effectively zero. However, on others, it can be as much as a quarter-hour early or late. The amount of correction is described by the equation of time . This correction
5995-426: The Sun on the celestial sphere is called the ecliptic . The ecliptic passes through the twelve constellations of the zodiac in the course of a year. This model of the Sun's motion helps to understand sundials. If the shadow-casting gnomon is aligned with the celestial poles , its shadow will revolve at a constant rate, and this rotation will not change with the seasons. This is the most common design. In such cases,
6104-414: The Sun. An excellent approximation assumes that the Sun revolves around a stationary Earth on the celestial sphere , which rotates every 24 hours about its celestial axis. The celestial axis is the line connecting the celestial poles . Since the celestial axis is aligned with the axis about which the Earth rotates, the angle of the axis with the local horizontal is the local geographical latitude . Unlike
6213-528: The West by a thousand years. In China, miniature models of ships that feature steering oars have been dated to the Warring States period (c. 475–221 BC). Sternpost-mounted rudders started to appear on Chinese ship models starting in the 1st century AD. However, the Chinese continued to use the steering oar long after they invented the rudder, since the steering oar still had practical use for inland rapid-river travel. One of oldest known depictions of
6322-412: The angle or position (or both) of the gnomon relative to the hour lines, as in the analemmatic dial or the Lambert dial. The earliest sundials known from the archaeological record are shadow clocks (1500 BC or BCE ) from ancient Egyptian astronomy and Babylonian astronomy . Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC,
6431-405: The cargo hold amidships. The koch had a flat deck. A typical koch carried one square sail on one mast. A distinctive peculiarity of the koch was the relatively big size of its square rudder fin which compensated for the special extra-slim design of the upper part of the rudder. This type of ship had two 70 pounds (32 kg) main anchors and, very often, light anchors. Naval historians think that
6540-402: The celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5° east to 23° west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time , a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter. Since
6649-405: The craft's stern , tail, or afterend. Often rudders are shaped to minimize hydrodynamic or aerodynamic drag . On simple watercraft , a tiller —essentially, a stick or pole acting as a lever arm—may be attached to the top of the rudder to allow it to be turned by a helmsman . In larger vessels, cables, pushrods , or hydraulics may link rudders to steering wheels. In typical aircraft, the rudder
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#17327809086316758-509: The detailed charts and sailing directions, the stars, and the pilot's marks on the familiar shores. There are two main classifications of koch subtypes. The first, a mixed classification, distinguishes between three subtypes of kochs depending on both their place of origin ( Siberian and Mangazeyan ) and their sea-worthiness ( morskiye , that is "seafaring"). The second classification does not pay any attention to minor shipbuilding differences and divides all kochs into two categories according to
6867-435: The dial face, which is usually inscribed with hour lines. Although usually straight, these hour lines may also be curved, depending on the design of the sundial (see below). In some designs, it is possible to determine the date of the year, or it may be required to know the date to find the correct time. In such cases, there may be multiple sets of hour lines for different months, or there may be mechanisms for setting/calculating
6976-466: The dial surface by an angle equaling the difference in longitude, without changing the gnomon position or orientation. However, this method does not work for other dials, such as a horizontal dial; the correction must be applied by the viewer. However, for political and practical reasons, time-zone boundaries have been skewed. At their most extreme, time zones can cause official noon, including daylight savings, to occur up to three hours early (in which case
7085-655: The end of the Middle Ages in Europe . As the size of ships and the height of the freeboards increased, quarter steering oars became unwieldy and were replaced by the more sturdy rudders with pintle and gudgeon attachment. While steering oars were found in Europe on a wide range of vessels since Roman times, including light war galleys in Mediterranean, the oldest known depiction of a pintle-and-gudgeon rudder can be found on church carvings of Zedelgem and Winchester dating to around 1180. While earlier rudders were mounted on
7194-501: The equatorial bow, offsetting its time measurement. In other cases, the hour lines may be curved, or the equatorial bow may be shaped like a vase, which exploits the changing altitude of the sun over the year to effect the proper offset in time. A heliochronometer is a precision sundial first devised in about 1763 by Philipp Hahn and improved by Abbé Guyoux in about 1827. It corrects apparent solar time to mean solar time or another standard time . Heliochronometers usually indicate
7303-435: The first modern icebreakers , and in fact koch may be regarded as the most ancient form of icebreaker, though wooden and relatively small. The koches were traditionally built shell-first, with overlapping planks, following the once-widespread Northern European clinker shipbuilding tradition . Iron rivets and brackets, as long as shrub branches or tree roots, were used to fasten the planks to each other. Ribs were inserted into
7412-432: The first-ever device to use a differential gear.) Only after about 1800 was uncorrected clock time considered to be "right", and sundial time usually "wrong", so the equation of time became used as it is today. The most commonly observed sundials are those in which the shadow-casting style is fixed in position and aligned with the Earth's rotational axis, being oriented with true north and south, and making an angle with
7521-436: The gnomon's style is aligned with the Earth's axis of rotation. As in the horizontal dial, the line of shadow does not move uniformly on the face; the sundial is not equiangular . If the face of the vertical dial points directly south, the angle of the hour-lines is instead described by the formula where L is the sundial's geographical latitude , H V {\displaystyle \ H_{V}\ }
7630-634: The heyday of Russian polar navigation in the 15th and 16th centuries. There is documentary proof that in those days the private Russian civil fleet in the Arctic seas numbered up to 7,400 small ships in a single year. In the 17th century, kochs were widely used on Siberian rivers during the Russian exploration and conquest of Siberia and the Far East . In 1715, during the Great Northern War ,
7739-575: The horizontal equal to the geographical latitude. This axis is aligned with the celestial poles , which is closely, but not perfectly, aligned with the pole star Polaris . For illustration, the celestial axis points vertically at the true North Pole , whereas it points horizontally on the equator . The world's largest axial gnomon sundial is the mast of the Sundial Bridge at Turtle Bay in Redding, California . A formerly world's largest gnomon
7848-427: The hour angles are not evenly spaced, the equation of time corrections cannot be made via rotating the dial plate about the gnomon axis. These types of dials usually have an equation of time correction tabulation engraved on their pedestals or close by. Horizontal dials are commonly seen in gardens, churchyards and in public areas. In the common vertical dial , the shadow-receiving plane is aligned vertically; as usual,
7957-478: The hour lines must be corrected accordingly. The rays of light that graze the tip of a gnomon, or which pass through a small hole, or reflect from a small mirror, trace out a cone aligned with the celestial poles. The corresponding light-spot or shadow-tip, if it falls onto a flat surface, will trace out a conic section , such as a hyperbola , ellipse or (at the North or South Poles) a circle . This conic section
8066-400: The hour-lines to be calculated for various types of sundial. In some cases, the calculations are simple; in others they are extremely complicated. There is an alternative, simple method of finding the positions of the hour-lines which can be used for many types of sundial, and saves a lot of work in cases where the calculations are complex. This is an empirical procedure in which the position of
8175-468: The hull once the shell of planking was assembled. As these ships were in use as late as early 17th century, this may be by far the last use of the clinker technology on large sea-going vessels. They were flat-bottomed, but there is no reliable information whether the bottom was carvel built , as on the cogs , or clinker built, as on Viking ships (the latter is more likely, as the more recent Pomor boats are entirely clinker-built). The keel length of koch
8284-479: The ice, its rounded bodylines below the water-line would allow for the ship, squeezed by the ice-fields, to be pushed up out of the water and onto the ice with no damage to the body. Besides the anti-icebound equipment, the captains of kochs had the traditional set of navigation instruments, including a sundial and a magnetic compass with floating vetromet ("wind-marker", a wooden 32-point compass rose with 16 major winds). Other tools and means of navigation were
8393-415: The light anchors could have been used for mooring kochs to the edge of the ice fields. Special Arctic design features included the rounded lines of the ship's body below the water line , an additional belt of ice-floe resistant flush skin-planking (made of oak or larch ) along the variable water-line, a false keel for on-ice portage (and for damage prevention from running aground in shallow waters), and
8502-521: The light or shadow. Planes are the most common surface, but partial spheres , cylinders , cones and other shapes have been used for greater accuracy or beauty. Sundials differ in their portability and their need for orientation. The installation of many dials requires knowing the local latitude , the precise vertical direction (e.g., by a level or plumb-bob), and the direction to true north . Portable dials are self-aligning: for example, it may have two dials that operate on different principles, such as
8611-409: The main spheres of their maritime operations: river/sea, and morskiye (seafaring) for long-range sea voyages. The following is added from Fisher. He claims that the koch had a square sail and only one mast. The largest koches were 60 feet long and 20 feet wide(sic), with a draft of 5 or 6 feet and a crew of 6 to 12. They could hold up to 40 people or 45 tonnes of cargo. They were oval when viewed from
8720-405: The minutes to within 1 minute of Universal Time . The Sunquest sundial , designed by Richard L. Schmoyer in the 1950s, uses an analemmic-inspired gnomon to cast a shaft of light onto an equatorial time-scale crescent. Sunquest is adjustable for latitude and longitude, automatically correcting for the equation of time, rendering it "as accurate as most pocket watches". Similarly, in place of
8829-579: The mizzen mast abaft (i.e. "aft of") the rudder post; ketches are defined as having the mizzen mast forward of the rudder post. Small boat rudders that can be steered more or less perpendicular to the hull's longitudinal axis make effective brakes when pushed "hard over." However, terms such as "hard over," "hard to starboard," etc. signify a maximum-rate turn for larger vessels. Transom hung rudders or far aft mounted fin rudders generate greater moment and faster turning than more forward mounted keel hung rudders. Rudders on smaller craft can be operated by means of
8938-406: The month. In addition to the hour lines, the dial face may offer other data—such as the horizon, the equator and the tropics—which are referred to collectively as the dial furniture. The entire object that casts a shadow or light onto the dial face is known as the sundial's gnomon . However, it is usually only an edge of the gnomon (or another linear feature) that casts the shadow used to determine
9047-496: The mouth of the Rhine near Zwammerdam featured a large steering gear mounted on the stern. According to new research, the advanced Nemi ships , the palace barges of emperor Caligula (37-41 AD), may have featured 14 m long rudders. The world's oldest known depiction of a sternpost-mounted rudder can be seen on a pottery model of a Chinese junk dating from the 1st century AD during the Han dynasty , predating their appearance in
9156-423: The passing of time and the brevity of life, but equally often humorous witticisms of the dial maker. One such quip is, I am a sundial, and I make a botch, Of what is done much better by a watch. A dial is said to be equiangular if its hour-lines are straight and spaced equally. Most equiangular sundials have a fixed gnomon style aligned with the Earth's rotational axis, as well as a shadow-receiving surface that
9265-465: The plane that receives the shadow is aligned horizontally, rather than being perpendicular to the style as in the equatorial dial. Hence, the line of shadow does not rotate uniformly on the dial face; rather, the hour lines are spaced according to the rule. Or in other terms: where L is the sundial's geographical latitude (and the angle the gnomon makes with the dial plate), H H {\displaystyle \ H_{H}\ }
9374-428: The point where the gnomon's style crosses the horizontal plane. Since the style is aligned with the Earth's rotational axis, the style points true north and its angle with the horizontal equals the sundial's geographical latitude L . A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base upwards or downwards by an angle equal to the difference in latitude. For example,
9483-435: The present-day equation of time, not one from the period when the dial was made. In some sundials, the equation of time correction is provided as an informational plaque affixed to the sundial, for the observer to calculate. In more sophisticated sundials the equation can be incorporated automatically. For example, some equatorial bow sundials are supplied with a small wheel that sets the time of year; this wheel in turn rotates
9592-446: The same hour lines may be used throughout the year. The hour-lines will be spaced uniformly if the surface receiving the shadow is either perpendicular (as in the equatorial sundial) or circular about the gnomon (as in the armillary sphere ). In other cases, the hour-lines are not spaced evenly, even though the shadow rotates uniformly. If the gnomon is not aligned with the celestial poles, even its shadow will not rotate uniformly, and
9701-402: The shadow of a gnomon the sundial at Miguel Hernández University uses the solar projection of a graph of the equation of time intersecting a time scale to display clock time directly. An analemma may be added to many types of sundials to correct apparent solar time to mean solar time or another standard time . These usually have hour lines shaped like "figure eights" ( analemmas ) according to
9810-402: The shadow of the gnomon of a real sundial is marked at hourly intervals. The equation of time must be taken into account to ensure that the positions of the hour-lines are independent of the time of year when they are marked. An easy way to do this is to set a clock or watch so it shows "sundial time" which is standard time , plus the equation of time on the day in question. The hour-lines on
9919-416: The shaft-like upper part and wide lower part (below water-line) of the rudder. Another Arctic feature was the invariable presence aboard any koch of two or more iceboats and of a windlass with anchor rope. Each iceboat had the cargo capacity of 1.5 to 2.0 metric tons (3,300 to 4,400 lb) and was equipped with long runners (5 to 7 m or 16 to 23 ft) for portage on ice. If a koch became trapped in
10028-494: The ship's screw is enclosed and can be swiveled to steer the vessel. Designers claim that this type of rudder on a smaller vessel will answer the helm faster. Various types of rudders are used in the marine industry, including spade rudders, semi-spade rudders, high-lift rudders, and balanced rudders. Large ships (over 10,000 ton gross tonnage) have requirements on rudder turnover time. To comply with this, high torque rudder controls are employed. One commonly used system
10137-554: The southern hemisphere, also do so on a vertical sundial in the northern hemisphere. (See the first two illustrations at the top of this article.) On horizontal northern-hemisphere sundials, and on vertical southern-hemisphere ones, the hour marks run clockwise. The most common reason for a sundial to differ greatly from clock time is that the sundial has not been oriented correctly or its hour lines have not been drawn correctly. For example, most commercial sundials are designed as horizontal sundials as described above. To be accurate, such
10246-414: The steering oar was required to steer a straight course; this slowed down the vessel because a steering oar (or rudder) course correction acts as a brake. The second sail, located forward, could be trimmed to offset the turning tendency of the mainsail and minimize the need for course corrections by the steering oar, which would have substantially improved sail performance. The steering oar or steering board
10355-522: The stern by the way of rudderposts or tackles, the iron hinges allowed the rudder to be attached to the entire length of the sternpost in a permanent fashion. However, its full potential could only to be realized after the introduction of the vertical sternpost and the full-rigged ship in the 14th century. From the Age of Discovery onwards, European ships with pintle-and-gudgeon rudders sailed successfully on all seven seas. Historian Joseph Needham holds that
10464-637: The stern were also quite common in Roman river and harbour craft as proved from reliefs and archaeological finds ( Zwammerdam , Woerden 7). A tomb plaque of Hadrianic age shows a harbour tug boat in Ostia with a long stern-mounted oar for better leverage. The boat already featured a spritsail , adding to the mobility of the harbour vessel. Further attested Roman uses of stern-mounted steering oars includes barges under tow, transport ships for wine casks, and diverse other ship types. A large river barge found at
10573-471: The stern-mounted rudder used in ancient Han dynasty China as a true rudder. The steering oar can interfere with the handling of the sails (limiting any potential for long ocean-going voyages) while it was fit more for small vessels on narrow, rapid-water transport; the rudder did not disturb the handling of the sails, took less energy to operate by its helmsman , was better fit for larger vessels on ocean-going travel, and first appeared in ancient China during
10682-671: The stern-mounted rudder was transferred from China to Europe and the Islamic world during the Middle Ages. Conventional rudders have been essentially unchanged since Isambard Kingdom Brunel introduced the balanced rudder on the SS Great Britain in 1843 and the steering engine in the SS Great Eastern in 1866. If a vessel requires extra maneuverability at low speeds, the rudder may be supplemented by
10791-399: The sun's apparent rotation about the Earth casts a uniformly rotating sheet of shadow from the gnomon; this produces a uniformly rotating line of shadow on the equatorial plane. Since the Earth rotates 360° in 24 hours, the hour-lines on an equatorial dial are all spaced 15° apart (360/24). The uniformity of their spacing makes this type of sundial easy to construct. If the dial plate material
10900-402: The sundial are marked to show the positions of the shadow of the style when this clock shows whole numbers of hours, and are labelled with these numbers of hours. For example, when the clock reads 5:00, the shadow of the style is marked, and labelled "5" (or "V" in Roman numerals ). If the hour-lines are not all marked in a single day, the clock must be adjusted every day or two to take account of
11009-413: The surface shadow generally moves non-uniformly and the hour-lines are not equally spaced; one exception is the Lambert dial described below. Some types of sundials are designed with a fixed gnomon that is not aligned with the celestial poles like a vertical obelisk. Such sundials are covered below under the section, "Nodus-based sundials". The formulas shown in the paragraphs below allow the positions of
11118-531: The time. Sundials are valued as decorative objects, metaphors , and objects of intrigue and mathematical study. The passing of time can be observed by placing a stick in the sand or a nail in a board and placing markers at the edge of a shadow or outlining a shadow at intervals. It is common for inexpensive, mass-produced decorative sundials to have incorrectly aligned gnomons, shadow lengths, and hour-lines, which cannot be adjusted to tell correct time. There are several different types of sundials. Some sundials use
11227-408: The time; this linear feature is known as the sundial's style . The style is usually aligned parallel to the axis of the celestial sphere, and therefore is aligned with the local geographical meridian. In some sundial designs, only a point-like feature, such as the tip of the style, is used to determine the time and date; this point-like feature is known as the sundial's nodus . Some sundials use both
11336-521: The top or side. The flat or rounded bottom made them maneuverable when dodging ice floes, but probably unstable in a severe storm. The square sail and flat bottom meant that they would not sail well without a following wind. Other boat types used in Siberia include the shitik and the baidarka . Rudder A rudder is a primary control surface used to steer a ship , boat , submarine , hovercraft , airship , or other vehicle that moves through
11445-454: The use of a rudder without a steering oar dates to the 5th century. Chinese rudders are attached to the hull by means of wooden jaws or sockets, while typically larger ones were suspended from above by a rope tackle system so that they could be raised or lowered into the water. Also, many junks incorporated "fenestrated rudders" (rudders with holes in them, supposedly allowing for better control). Detailed descriptions of Chinese junks during
11554-422: The variation of the equation of time. The distinguishing characteristic of the equatorial dial (also called the equinoctial dial ) is the planar surface that receives the shadow, which is exactly perpendicular to the gnomon's style. This plane is called equatorial, because it is parallel to the equator of the Earth and of the celestial sphere. If the gnomon is fixed and aligned with the Earth's rotational axis,
11663-590: The works of the Greek historian Herodotus (484-424 BC), who had spent several months in Egypt : "They make one rudder, and this is thrust through the keel ", probably meaning the crotch at the end of the keel (as depicted in the "Tomb of Menna"). In Iran , oars mounted on the side of ships for steering are documented from the 3rd millennium BCE in artwork, wooden models, and even remnants of actual boats. Roman navigation used sexillie quarter steering oars that went in
11772-483: The world practice daylight saving time , which changes the official time, usually by one hour. This shift must be added to the sundial's time to make it agree with the official time. A standard time zone covers roughly 15° of longitude, so any point within that zone which is not on the reference longitude (generally a multiple of 15°) will experience a difference from standard time that is equal to 4 minutes of time per degree. For illustration, sunsets and sunrises are at
11881-399: Was about 10–25 meters (about 30–70 feet). It had 13 combination ribs, each consisting of several details. The keel was also a combination of several parts. Bulkheads divided the body into several cross-section compartments. Each compartment ( cherdak ) served a specific purpose. There invariably were the fore-part compartment used as the crew's quarters, the stern cabin for the captain , and
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