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The navigator plots their 9 a.m. position, indicated by the triangle, and, using their course and speed, estimates their own position at 9:30 and 10 a.m.
In navigation, dead reckoning is the process of calculating the current position of a moving object by using a previously determined position, or fix, and incorporating estimates of speed, heading (or direction or course), and elapsed time. The corresponding term in biology, to describe the processes by which animals update their estimates of position or heading, is path integration.
Advances in navigational aids that give accurate information on position, in particular satellite navigation using the Global Positioning System, have made simple dead reckoning by humans obsolete for most purposes. However, inertial navigation systems, which provide very accurate directional information, use dead reckoning and are very widely applied.
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Contrary to myth, the term "dead reckoning" was not originally used to abbreviate "deduced reckoning", nor is it a misspelling of the term "ded reckoning". The use of "ded" or "deduced reckoning" is not known to have appeared earlier than , much later in history than "dead reckoning", which appeared as early as in the Oxford English Dictionary. The original intention of "dead" in the term is generally assumed to mean using a stationary object that is "dead in the water" as a basis for calculations. Additionally, at the time the first appearance of "dead reckoning", "ded" was considered a common spelling of "dead". This potentially led to later confusion of the origin of the term.[1]
By analogy with their navigational use, the words dead reckoning are also used to mean the process of estimating the value of any variable quantity by using an earlier value and adding whatever changes have occurred in the meantime. Often, this usage implies that the changes are not known accurately. The earlier value and the changes may be measured or calculated quantities.[citation needed]
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Drift is an error that can arise in dead reckoning when speed of a medium is not accounted for. A is the last known position (fix), B is the position calculated by dead reckoning, and C is the true position after the time interval. The vector from A to B is the expected path for plane based on the initial heading (HDG) and true airspeed (TAS). The vector from B to C is the wind velocity (W/V), and the third vector is the actual track (TR) and ground speed (GS). The drift angle is marked in red.While dead reckoning can give the best available information on the present position with little math or analysis, it is subject to significant errors of approximation. For precise positional information, both speed and direction must be accurately known at all times during travel. Most notably, dead reckoning does not account for directional drift during travel through a fluid medium. These errors tend to compound themselves over greater distances, making dead reckoning a difficult method of navigation for longer journeys.
For example, if displacement is measured by the number of rotations of a wheel, any discrepancy between the actual and assumed traveled distance per rotation, due perhaps to slippage or surface irregularities, will be a source of error. As each estimate of position is relative to the previous one, errors are cumulative, or compounding, over time.
The accuracy of dead reckoning can be increased significantly by using other, more reliable methods to get a new fix part way through the journey. For example, if one was navigating on land in poor visibility, then dead reckoning could be used to get close enough to the known position of a landmark to be able to see it, before walking to the landmark itself&#;giving a precisely known starting point&#;and then setting off again.
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Localizing a static sensor node is not a difficult task because attaching a Global Positioning System (GPS) device suffices the need of localization. But a mobile sensor node, which continuously changes its geographical location with time is difficult to localize. Mostly mobile sensor nodes within some particular domain for data collection can be used, i.e, sensor node attached to an animal within a grazing field or attached to a soldier on a battlefield. Within these scenarios a GPS device for each sensor node cannot be afforded. Some of the reasons for this include cost, size and battery drainage of constrained sensor nodes. To overcome this problem a limited number of reference nodes (with GPS) within a field is employed. These nodes continuously broadcast their locations and other nodes in proximity receive these locations and calculate their position using some mathematical technique like trilateration. For localization, at least three known reference locations are necessary to localize. Several localization algorithms based on Sequential Monte Carlo (SMC) method have been proposed in literature.[2][3] Sometimes a node at some places receives only two known locations and hence it becomes impossible to localize. To overcome this problem, dead reckoning technique is used. With this technique a sensor node uses its previous calculated location for localization at later time intervals.[4] For example, at time instant 1 if node A calculates its position as loca_1 with the help of three known reference locations; then at time instant 2 it uses loca_1 along with two other reference locations received from other two reference nodes. This not only localizes a node in less time but also localizes in positions where it is difficult to get three reference locations.[5]
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In studies of animal navigation, dead reckoning is more commonly (though not exclusively) known as path integration. Animals use it to estimate their current location based on their movements from their last known location. Animals such as ants, rodents, and geese have been shown to track their locations continuously relative to a starting point and to return to it, an important skill for foragers with a fixed home.[6][7]
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Dead reckoning navigation tools in coastal navigationIn marine navigation a "dead" reckoning plot generally does not take into account the effect of currents or wind. Aboard ship a dead reckoning plot is considered important in evaluating position information and planning the movement of the vessel.[8]
Dead reckoning begins with a known position, or fix, which is then advanced, mathematically or directly on the chart, by means of recorded heading, speed, and time. Speed can be determined by many methods. Before modern instrumentation, it was determined aboard ship using a chip log. More modern methods include pit log referencing engine speed (e.g. in rpm) against a table of total displacement (for ships) or referencing one's indicated airspeed fed by the pressure from a pitot tube. This measurement is converted to an equivalent airspeed based upon known atmospheric conditions and measured errors in the indicated airspeed system. A naval vessel uses a device called a pit sword (rodmeter), which uses two sensors on a metal rod to measure the electromagnetic variance caused by the ship moving through water. This change is then converted to ship's speed. Distance is determined by multiplying the speed and the time. This initial position can then be adjusted resulting in an estimated position by taking into account the current (known as set and drift in marine navigation). If there is no positional information available, a new dead reckoning plot may start from an estimated position. In this case subsequent dead reckoning positions will have taken into account estimated set and drift.
Dead reckoning positions are calculated at predetermined intervals, and are maintained between fixes. The duration of the interval varies. Factors including one's speed made good and the nature of heading and other course changes, and the navigator's judgment determine when dead reckoning positions are calculated.
Before the 18th-century development of the marine chronometer by John Harrison and the lunar distance method, dead reckoning was the primary method of determining longitude available to mariners such as Christopher Columbus and John Cabot on their trans-Atlantic voyages. Tools such as the traverse board were developed to enable even illiterate crew members to collect the data needed for dead reckoning. Polynesian navigation, however, uses different wayfinding techniques.
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British P10 Magnetic Compass with dead reckoning navigation toolsOn 14 June, , John Alcock and Arthur Brown took off from Lester's Field in St. John's, Newfoundland in a Vickers Vimy. They navigated across the Atlantic Ocean by dead reckoning and landed in County Galway, Ireland at 8:40 a.m. on 15 June completing the first non-stop transatlantic flight.
On 21 May Charles Lindbergh landed in Paris, France after a successful non-stop flight from the United States in the single-engined Spirit of St. Louis. As the aircraft was equipped with very basic instruments, Lindbergh used dead reckoning to navigate.
Dead reckoning in the air is similar to dead reckoning on the sea, but slightly more complicated. The density of the air the aircraft moves through affects its performance as well as winds, weight, and power settings.
The basic formula for DR is Distance = Speed x Time. An aircraft flying at 250 knots airspeed for 2 hours has flown 500 nautical miles through the air. The wind triangle is used to calculate the effects of wind on heading and airspeed to obtain a magnetic heading to steer and the speed over the ground (groundspeed). Printed tables, formulae, or an E6B flight computer are used to calculate the effects of air density on aircraft rate of climb, rate of fuel burn, and airspeed.[9]
A course line is drawn on the aeronautical chart along with estimated positions at fixed intervals (say every half hour). Visual observations of ground features are used to obtain fixes. By comparing the fix and the estimated position corrections are made to the aircraft's heading and groundspeed.
Dead reckoning is on the curriculum for VFR (visual flight rules &#; or basic level) pilots worldwide.[10] It is taught regardless of whether the aircraft has navigation aids such as GPS, ADF and VOR and is an ICAO Requirement. Many flying training schools will prevent a student from using electronic aids until they have mastered dead reckoning.
Inertial navigation systems (INSes), which are nearly universal on more advanced aircraft, use dead reckoning internally. The INS provides reliable navigation capability under virtually any conditions, without the need for external navigation references, although it is still prone to slight errors.
Automotive[
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Dead reckoning is today implemented in some high-end automotive navigation systems in order to overcome the limitations of GPS/GNSS technology alone. Satellite microwave signals are unavailable in parking garages and tunnels, and often severely degraded in urban canyons and near trees due to blocked lines of sight to the satellites or multipath propagation. In a dead-reckoning navigation system, the car is equipped with sensors that know the wheel circumference and record wheel rotations and steering direction. These sensors are often already present in cars for other purposes (anti-lock braking system, electronic stability control) and can be read by the navigation system from the controller-area network bus. The navigation system then uses a Kalman filter to integrate the always-available sensor data with the accurate but occasionally unavailable position information from the satellite data into a combined position fix.
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Dead reckoning is utilized in some robotic applications.[11] It is usually used to reduce the need for sensing technology, such as ultrasonic sensors, GPS, or placement of some linear and rotary encoders, in an autonomous robot, thus greatly reducing cost and complexity at the expense of performance and repeatability. The proper utilization of dead reckoning in this sense would be to supply a known percentage of electrical power or hydraulic pressure to the robot's drive motors over a given amount of time from a general starting point. Dead reckoning is not totally accurate, which can lead to errors in distance estimates ranging from a few millimeters (in CNC machining) to kilometers (in UAVs), based upon the duration of the run, the speed of the robot, the length of the run, and several other factors.[citation needed]
Pedestrian dead reckoning[
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With the increased sensor offering in smartphones, built-in accelerometers can be used as a pedometer and built-in magnetometer as a compass heading provider. Pedestrian dead reckoning (PDR) can be used to supplement other navigation methods in a similar way to automotive navigation, or to extend navigation into areas where other navigation systems are unavailable.[12]
In a simple implementation, the user holds their in front of them and each step causes position to move forward a fixed distance in the direction measured by the compass. Accuracy is limited by the sensor precision, magnetic disturbances inside structures, and unknown variables such as carrying position and stride length. Another challenge is differentiating walking from running, and recognizing movements like bicycling, climbing stairs, or riding an elevator.
Before -based systems existed, many custom PDR systems existed. While a pedometer can only be used to measure linear distance traveled, PDR systems have an embedded magnetometer for heading measurement. Custom PDR systems can take many forms including special boots, belts, and watches, where the variability of carrying position has been minimized to better utilize magnetometer heading. True dead reckoning is fairly complicated, as it is not only important to minimize basic drift, but also to handle different carrying scenarios and movements, as well as hardware differences across models.[13]
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The south-pointing chariot was an ancient Chinese device consisting of a two-wheeled horse-drawn vehicle which carried a pointer that was intended always to aim to the south, no matter how the chariot turned. The chariot pre-dated the navigational use of the magnetic compass, and could not detect the direction that was south. Instead it used a kind of directional dead reckoning: at the start of a journey, the pointer was aimed southward by hand, using local knowledge or astronomical observations e.g. of the Pole Star. Then, as it traveled, a mechanism possibly containing differential gears used the different rotational speeds of the two wheels to turn the pointer relative to the body of the chariot by the angle of turns made (subject to available mechanical accuracy), keeping the pointer aiming in its original direction, to the south. Errors, as always with dead reckoning, would accumulate as distance traveled increased.
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Networked games and simulation tools routinely use dead reckoning to predict where an actor should be right now, using its last known kinematic state (position, velocity, acceleration, orientation, and angular velocity).[14] This is primarily needed because it is impractical to send network updates at the rate that most games run, 60 Hz. The basic solution starts by projecting into the future using linear physics:[15]
P t = P 0 + V 0 T + 1 2 A 0 T 2 {\displaystyle P_{t}=P_{0}+V_{0}T+{\frac {1}{2}}A_{0}T^{2}}
This formula is used to move the object until a new update is received over the network. At that point, the problem is that there are now two kinematic states: the currently estimated position and the just received, actual position. Resolving these two states in a believable way can be quite complex. One approach is to create a curve (e.g. cubic Bézier splines, centripetal Catmull&#;Rom splines, and Hermite curves)[16] between the two states while still projecting into the future. Another technique is to use projective velocity blending, which is the blending of two projections (last known and current) where the current projection uses a blending between the last known and current velocity over a set time.[14]
V b = V 0 + ( V ´ 0 &#; V 0 ) T ^ {\displaystyle V_{b}=V_{0}+\left({\acute {V}}_{0}-V_{0}\right){\hat {T}}}
P t = P 0 + V b T t + 1 2 A ´ 0 T t 2 {\displaystyle P_{t}=P_{0}+V_{b}T_{t}+{\frac {1}{2}}{\acute {A}}_{0}T_{t}^{2}}
P ´ t = P ´ 0 + V ´ 0 T t + 1 2 A ´ 0 T t 2 {\displaystyle {\acute {P}}_{t}={\acute {P}}_{0}+{\acute {V}}_{0}T_{t}+{\frac {1}{2}}{\acute {A}}_{0}T_{t}^{2}}
P o s = P t + ( P ´ t &#; P t ) T ^ {\displaystyle Pos=P_{t}+\left({\acute {P}}_{t}-P_{t}\right){\hat {T}}}
The first equation calculates a blended velocity V b {\displaystyle V_{b}} given the client-side velocity at the time of the last server update V 0 {\displaystyle V_{0}} and the last known server-side velocity V ´ 0 {\displaystyle {\acute {V}}_{0}} . This essentially blends from the client-side velocity towards the server-side velocity for a smooth transition. Note that T ^ {\displaystyle {\hat {T}}} should go from zero (at the time of the server update) to one (at the time at which the next update should be arriving). A late server update is unproblematic as long as T ^ {\displaystyle {\hat {T}}} remains at one.
Next, two positions are calculated: firstly, the blended velocity V b {\displaystyle V_{b}} and the last known server-side acceleration A ´ 0 {\displaystyle {\acute {A}}_{0}} are used to calculate P t {\displaystyle P_{t}} . This is a position which is projected from the client-side start position P 0 {\displaystyle P_{0}} based on T t {\displaystyle T_{t}} , the time which has passed since the last server update. Secondly, the same equation is used with the last known server-side parameters to calculate the position projected from the last known server-side position P ´ 0 {\displaystyle {\acute {P}}_{0}} and velocity V ´ 0 {\displaystyle {\acute {V}}_{0}} , resulting in P ´ t {\displaystyle {\acute {P}}_{t}} .
Finally, the new position to display on the client P o s {\displaystyle Pos} is the result of interpolating from the projected position based on client information P t {\displaystyle P_{t}} towards the projected position based on the last known server information P ´ t {\displaystyle {\acute {P}}_{t}} . The resulting movement smoothly resolves the discrepancy between client-side and server-side information, even if this server-side information arrives infrequently or inconsistently. It is also free of oscillations which spline-based interpolation may suffer from.
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In computer science, dead-reckoning refers to navigating an array data structure using indexes. Since every array element has the same size, it is possible to directly access one array element by knowing any position in the array.[17]
Given the following array:
A B C D Eknowing the memory address where the array starts, it is easy to compute the memory address of D:
address D = address start of array + ( size array element &#; arrayIndex D ) {\displaystyle {\text{address}}_{\text{D}}={\text{address}}_{\text{start of array}}+({\text{size}}_{\text{array element}}*{\text{arrayIndex}}_{\text{D}})}
Likewise, knowing D's memory address, it is easy to compute the memory address of B:
address B = address D &#; ( size array element &#; ( arrayIndex D &#; arrayIndex B ) ) {\displaystyle {\text{address}}_{\text{B}}={\text{address}}_{\text{D}}-({\text{size}}_{\text{array element}}*({\text{arrayIndex}}_{\text{D}}-{\text{arrayIndex}}_{\text{B}}))}
This property is particularly important for performance when used in conjunction with arrays of structures because data can be directly accessed, without going through a pointer dereference.
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Want more information on marine navigation equipment? Feel free to contact us.
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Marine navigation is the art and science of steering a ship from a starting point (sailing) to a destination, efficiently and responsibly. It is an art because of the skill that the navigator must have to avoid the dangers of navigation, and it is a science because it is based on physical, mathematical, oceanographic, cartographic, astronomical, and other knowledge.
Marine navigation can be surface or submarine.
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Navigation (from the Latin word navigatio) is the act of sailing or voyaging. Nautical (from Latin nautĭca, and this from Greek ναυτική [τέχνη] nautik&#; [téjne] "[art of] sailing" and from ναύτης nautes "sailor") is that pertaining to navigation and the science and art of sailing. Naval (from the Latin adjective navalis) is that relating to ships and navigation, or particularly to the navy.[1]
In Ancient Rome, the navicularii conducted long-distance trade by sea.
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Coastal navigation was practiced since the most ancient times.[2] The biblical account of the great flood, where the Noah's Ark appears, is based both on myths and on the navigational practice of the Mesopotamian civilizations, who from the Sumerians onwards navigated their two rivers (Tigris and Euphrates) and the Persian Gulf. The ancient Egyptians did not limit themselves to inland navigation of the Nile either, and used the Mediterranean sea routes existing since the Neolithic &#; through which cultural phenomena such as megalithism or the metallurgy would have spread for millennia. The Cretans even established a true thalassocracy (government of the seas, attributed to King Minos) until the Mycenaean period (2nd millennium BC), when the events mythologized in the Homeric poems[Note 1] ought to be placed.
flotilla or "procession of boats".Fresco from the Western House of Akrotiri , calledor "procession of boats".
The Hittites, led by King Šuppiluliuma II faced the Cyprus in the first historically recorded naval battle (ca. BC); at the same time, all the civilizations of the Eastern Mediterranean suffered from the incursions of the denominated "Sea Peoples".
The Phoenicians &#; whom the Greeks considered their masters in navigation and who are also cited in the Bible &#;[Note 2][3] would have been the first Mediterranean civilization to sail the high seas by sculling and sailing, guided by the sun during the day and by the North Star at night. It is recorded that, crossing the Strait of Gibraltar &#; the "Rock of Gibraltar", the so-called "Pillars of Hercules" in the Greek myths &#; they sailed across the Atlantic Ocean reaching the south to some point on the west coast of Africa and the north to the British Isles (or even beyond, to the place that the texts call Thule), but it is unclear if they circumnavigated Africa or crossed the Atlantic reaching America, something most likely achieved by the Norsemen in the 10th century.
Boat depicted on Egyptian pottery from the Predynastic period (Naqada II, mid-4th millennium BC). Boat building depicted in reliefs from the Mastaba of Ti at Saqqara, dynasty V, mid-3rd millennium BC. Model of an Egyptian ship and crew. Type of Phoenician ships called hippos (name given by the Greeks, because of its mascaron shaped like a horse's head) carrying wood, depicted in an Assyrian relief from Sargon's palace at Khorsabad. King Luli of Sidon flees from his city, attacked by Sargon II, in a type of Phoenician warship called dieris (bireme, with two rows of rowers). Assyrian relief from the palace of Sennacherib, ca. 700-692 BC. One of the Phoenician vessels of Mazarrón, 7th century BC. Dionysus Cup, by Exekias, 6th Century Scene from the Odyssey (Ulysses' companions manage to free their ship from the Sirens' trap, while their leader listens to their song tied to the mast). 5th century. Roman ship represented in a fresco of the 2nd or 3rd century in the port city of Ostia. The inscriptions reflect the name of the ship (Isis Giminiana), the name of the captain or magister (Farnaces, at the helm) and the name of the owner (Arascanius, in charge of the cargo).[
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Roman sarcophagus from the 3rd century. It is the oldest representation of a spritsail. Byzantine ships in Classe (the port of Ravenna), depicted in a mosaic of Basilica of Sant'Apollinare Nuovo, 6th century. Norman ship represented in the Bayeux tapestry, 11th century. Viking ships depicted in a 12th-century manuscript. Nautical combat with Greek fire depicted in a 12th-century Byzantine manuscript (Madrid Skylitzes). Replica of a Spanish-Muslim ship from the 10th to 14th century. Galley or dromon in a Byzantine fresco from the 13th century. The design of the flags is similar to the Senyera of the Crown of Aragon, and the design of the ship can be compared to the traditional mitjana ship. The earliest known representation of a compass, used aboard ship, depicted in an illustration dated .Remains of a 1st-century Gallo-Roman ship archaeologically named
Roman ship depicted on a coin.
Relief of a 2nd-century sarcophagus representing a "gauloi", a trading ship.
Model depicting a naval confrontation between a Roman ship and Omani ships in the Indian Ocean, 2nd century.
In the Indian and Pacific oceans, the oceanic navigations made it possible to populate all the archipelagoes (Polynesian navigation). However, the possibility of reaching South America is still a matter of debate &#; the settlement of the Americas through the Bering Strait would not have required navigation, or in any case, coastal navigation would have sufficed &#; as well as other possible pre-Columbian transoceanic contacts. In the first quarter of the 15th century, the Chinese expeditions led by Zheng He reached the African coasts of the Indian Ocean. It has been proposed that they might have reached the South Atlantic and even America and Europe, but this proposal has not been accepted beyond mere speculation.
Mediterranean navigation, which the Romans had come to control (undisputed Mare Nostrum since their victories over the Carthaginians in the Punic Wars [264-146 BC], the Egyptians during the Battle of Actium [31 BC], and pirates), was once again a contested environment in the Middle Ages, from the moment the Vandals managed to attack the Italian coasts from the sea. In the 6th century, the Byzantines managed to regain control, and in the 7th century it was the Arabs who ended up dividing the Mediterranean area,[5] which even the Vikings and Normans were able to access. Since the time of the Crusades, Venetian,[6] Genoese[7] and Crown of Aragon[8] navigators also had a strong presence. Knowledge of the compass, transmitted to the Europeans by the Arabs (who in turn had obtained it from the Chinese), together with other improvements in astronomical techniques (astrolabe, Jacob's staff, sextant, cartographic techniques (portulan and shipbuilding (caravel, nau, galleon), made the Age of Discovery &#; initially led by the Portuguese and Castilians &#; possible, especially after Henry the Navigator impulsed the school of Sagres. In , the first voyage of Christopher Columbus took place. In , Bartolomeu Dias rounded the Cape of Good Hope, which opened the route to the Indian Ocean &#; Vasco de Gama reached Calicut (India) in . Between and , the Magellan-Elcano expedition circumnavigated the world &#; measuring the geographical longitude with the method of its scientific organizer, Rui Faleiro. Until the 6th century, the Spanish-Portuguese hegemony in navigation was patent in fields such as geography and cosmography. Both English and French pilots learned to navigate from the texts of Pedro de Medina, Martín Fernández de Enciso and Martín Cortés, among others.[9][10] The conjunction of "cannons and sails" has been argued to have given European states the advantage to prevail over the rest,[11] launching the modern "world system".[12]
Permanent navigation routes of the Spanish (in white) and Portuguese (in blue) fleets since the 16th century. The Spanish treasure fleet crossed the Atlantic, the Manila Galleon the Pacific; the India armada circumnavigated Africa.
Navigation of Henry Hudson in search of the Northeast Passage , &#;.
, flagship of the Swedish navy, sunk on her maiden voyage, .
Dutch ships of the VOC ) in Batavia (today Jakarta ), .
Since the 18th century, England exercised maritime hegemony, a fact that was confirmed in the early 19th century with the Battle of Trafalgar (). Among the main English expeditions of the time were Captain Cook's (-), also the second expedition of the Beagle (-) &#; which was of great importance for the later development of Charles Darwin's theory of evolution. Already fully in the age of steam navigation, techniques and vessels continued to be perfected in transoceanic sailing (clipper), that did not become obsolete for commercial navigation until the 20th century &#; especially after the opening of the Panama Canal. Even then, the unbridled optimism that characterized the naval design of the time suffered a severe blow with the sinking of the Titanic ().
Contemporary shipping has massively ceased to perform one of its traditional functions and has been replaced by aviation, such as passenger transport, although with two important exceptions: leisure travel (tourism by cruise ships) and irregular traffic of people (irregular immigration). Since the Second Industrial Revolution, the main volume of freight transport has been hydrocarbons (oil tankers and gas tankers). Other raw materials are also transported in bulk on cargo ships, but from onward, a large part of goods of all kinds were adapted to standardized containers that speed up loading and unloading, allowing a combination with land transport (hub). Highly technological navigation has reduced crews and increased the size of ships. For example, in deep-sea fishing, which locates its prey with sophisticated means and lasts indefinitely in time &#; freezer ships or factory ships &#; which in some circumstances has made them vulnerable to new forms of piracy.
Hellespont Alhambra, a TI-class supertanker that is considered among the largest ships in the world in dimensions, displacement and cargo capacity., a TI-class supertanker that is considered among the largest ships in the world in dimensions, displacement and cargo capacity.
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These are the methods used in maritime navigation to solve the three problems of the navigator:
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Navigation and location of the ship by positioning techniques based on the observation of bearings and distances to notable points on the coast (lighthouses, capes, buoys, etc.) by visual means (pelorus), observation of horizontal angles (sextant) or electronic methods (bearings from radar to racons, transponders, etc.)
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Navigation and location of the ship by analytical means, after considering the following elements: initial location, bearing(s) &#; whether absolute bearings, surface bearings, or relative bearings. Also velocity as well as the external factors that have influenced the course either partially or entirely, such as the wind (leeway) and/or the current (bearing of the current and hourly current intensity). The point obtained from the calculations is called the "Dead reckoning location", with its corresponding latitude and longitude. This point is also known as Fantasy point.
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Rhumb line navigation path: β = constantNavigation that follows a rhumb line &#; that is, all meridians are cut at the same angle. On a nautical chart following the Mercator projection, a loxodromic is represented by a straight line.
This type of navigation is useful for not too long distances, as it allows the course to remain steady,[16] but it does not offer the shortest distance.
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Navigation that follows the shortest distance between two points, i.e., that which follows a great circle. Such routes yield the shortest distance between two points on the globe.[16] To calculate the bearing and distance between two points it is necessary to solve a spherical triangle whose vertices are the origin, the destination, and the pole.[17]
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Navigation and location of the ship by geopositioning techniques based on the observation of the stars and other celestial bodies. The variables measured to find the location are: the observed angular height of the stars above the horizon, measured with the sextant (formerly with the astrolabe or other instrument), and the time, measured with the chronometer.
Conceptually, the process is not complex to understand:
In practice, the mathematical process, called "reduction" of the observation, can be complex for the uninitiated. To the height observed with the sextant, it is necessary to apply a series of corrections to compensate for atmospheric refraction, parallax and other errors. Once this is done, it is necessary to solve a spherical triangle by mathematical and trigonometric methods.
There are many methods to do this. The manual methods use tables (trigonometric, logarithms, etc.) to facilitate the calculations. The introduction of calculators and electronic computers at the end of the 20th century greatly facilitated the calculation, but the creation of GPS made celestial navigation no longer important, relegating it to the background as an alternative method in case of failure of the on-board electronics or as a hobby of scientific interest.
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Navigation and location of the ship by positioning techniques based on the aids provided by global positioning systems, such as GPS, GLONASS, or GALILEO. It is the system most widely spread and easiest to use, in spite of the errors that may arise.
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Navigation and location of the ship by means of the analysis of the data provided by accelerometers and/or gyroscopes located on board, which integrate the accelerations experienced in complex electronic systems, that converted into velocities (in the 3 possible axes of displacement) and according to the observed courses, make it possible to obtain the location of the ship.
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The harbinger of a successful navigation was the dolphin, which is why its representation became the symbol carried by all ships.
More recently, navigation was represented as a woman crowned with ship's sterns whose clothes are agitated by the winds. She rests one hand on a rudder and the other holds the instrument for measuring height. At her feet, the ampoule, the compass, the trident of Neptune and the riches of commerce, while the sea can be seen on the horizon, completed by a lighthouse and traversed by ships at full sail.[10]
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