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101-649: This glossary of nautical terms is an alphabetical listing of terms and expressions connected with ships , shipping , seamanship and navigation on water (mostly though not necessarily on the sea). Some remain current, while many date from the 17th to 19th centuries. The word nautical derives from the Latin nauticus , from Greek nautikos , from nautēs : "sailor", from naus : "ship". Further information on nautical terminology may also be found at Nautical metaphors in English , and additional military terms are listed in

202-501: A horseshoe . In the case of a distribution of separate bodies, such as the planets of the Solar System , the center of mass may not correspond to the position of any individual member of the system. The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics . In orbital mechanics ,

303-475: A square sail . They were steered by rudders hung on the sternpost . In contrast, the ship-building tradition of the Mediterranean was of carvel construction  – the fitting of the hull planking to the frames of the hull. Depending on the precise detail of this method, it may be characterised as either "frame first" or "frame-led". In either variant, during construction, the hull shape

404-682: A circle instead of a line. The calculation takes every particle's x coordinate and maps it to an angle, θ i = x i x max 2 π {\displaystyle \theta _{i}={\frac {x_{i}}{x_{\max }}}2\pi } where x max is the system size in the x direction and x i ∈ [ 0 , x max ) {\displaystyle x_{i}\in [0,x_{\max })} . From this angle, two new points ( ξ i , ζ i ) {\displaystyle (\xi _{i},\zeta _{i})} can be generated, which can be weighted by

505-421: A crew headed by a sea captain , with deck officers and engine officers on larger vessels. Special-purpose vessels often have specialized crew if necessary, for example scientists aboard research vessels . Center of mass In physics , the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point ) is the unique point at any given time where

606-590: A deadweight cargo and being sailed and steered." At this time, ships were developing in Asia in much the same way as Europe. Japan used defensive naval techniques in the Mongol invasions of Japan in 1281. It is likely that the Mongols of the time took advantage of both European and Asian shipbuilding techniques. During the 15th century, China's Ming dynasty assembled one of the largest and most powerful naval fleets in

707-548: A few years, steam had replaced many of the sailing ships that had served this route. Even greater fuel efficiency was obtained with triple-expansion steam engines – but this had to wait for higher quality steel to be available to make boilers running at 125 pounds per square inch (860 kPa) in SS Aberdeen (1881) . By this point virtually all routes could be served competitively by steamships. Sail continued with some cargoes, where low costs were more important to

808-738: A floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. Other ancient mathematicians who contributed to the theory of the center of mass include Hero of Alexandria and Pappus of Alexandria . In the Renaissance and Early Modern periods, work by Guido Ubaldi , Francesco Maurolico , Federico Commandino , Evangelista Torricelli , Simon Stevin , Luca Valerio , Jean-Charles de la Faille , Paul Guldin , John Wallis , Christiaan Huygens , Louis Carré , Pierre Varignon , and Alexis Clairaut expanded

909-540: A keel made from a dugout canoe. Their designs were unique, evolving from ancient rafts to the characteristic double-hulled, single-outrigger, and double-outrigger designs of Austronesian ships. In the 2nd century AD, people from the Indonesian archipelago already made large ships measuring over 50 m long and standing 4–7 m out of the water. They could carry 600–1000 people and 250–1000 ton cargo. These ships were known as kunlun bo or k'unlun po (崑崙舶, lit. "ship of

1010-522: A single propeller driven by a diesel or, less usually, gas turbine engine ., but until the mid-19th century they were predominantly square sail rigged. The fastest vessels may use pump-jet engines . Most commercial vessels such as container ships, have full hull-forms (higher Block coefficients ) to maximize cargo capacity. Merchant ships and fishing vessels are usually made of steel, although aluminum can be used on faster craft, and fiberglass or wood on smaller vessels. Commercial vessels generally have

1111-400: A uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. In his work On Floating Bodies , Archimedes demonstrated that the orientation of

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1212-421: Is a feasible route – has generally been cheaper, safer and faster than making the same journey on land. Only the coming of railways in the middle of the 19th century and the growth of commercial aviation in the second half of the 20th century have changed this principle. This applied equally to sea crossings, coastal voyages and use of rivers and lakes. Examples of the consequences of this include

1313-413: Is a particle with its mass concentrated at the center of mass. By selecting the center of gravity as the reference point for a rigid body, the gravity forces will not cause the body to rotate, which means the weight of the body can be considered to be concentrated at the center of mass. The linear and angular momentum of a collection of particles can be simplified by measuring the position and velocity of

1414-422: Is always directly below the rotorhead . In forward flight, the center of mass will move forward to balance the negative pitch torque produced by applying cyclic control to propel the helicopter forward; consequently a cruising helicopter flies "nose-down" in level flight. The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the barycenter . The barycenter

1515-668: Is chosen as the center of mass these equations simplify to p = m v , L = ∑ i = 1 n m i ( r i − R ) × d d t ( r i − R ) + ∑ i = 1 n m i R × v {\displaystyle \mathbf {p} =m\mathbf {v} ,\quad \mathbf {L} =\sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )\times {\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+\sum _{i=1}^{n}m_{i}\mathbf {R} \times \mathbf {v} } where m

1616-468: Is crucial, possibly resulting in severe injury or death if assumed incorrectly. A center of gravity that is at or above the lift point will most likely result in a tip-over incident. In general, the further the center of gravity below the pick point, the safer the lift. There are other things to consider, such as shifting loads, strength of the load and mass, distance between pick points, and number of pick points. Specifically, when selecting lift points, it

1717-428: Is determined by the frames, not the planking. The hull planks are not fastened to each other, only to the frames. These Mediterranean ships were rigged with lateen sails on one or more masts (depending on the size of the vessel) and were steered with a side rudder. They are often referred to as "round ships". Crucially, the Mediterranean and Northern European traditions merged. Cogs are known to have travelled to

1818-399: Is no universally accepted distinction between the two. Ships generally can remain at sea for longer periods of time than boats. A legal definition of ship from Indian case law is a vessel that carries goods by sea. A common notion is that a ship can carry a boat, but not vice versa . A ship is likely to have a full-time crew assigned. A US Navy rule of thumb is that ships heel towards

1919-432: Is something of a colloquialism, but it is in common usage and when gravity gradient effects are negligible, center-of-gravity and mass-center are the same and are used interchangeably. In physics the benefits of using the center of mass to model a mass distribution can be seen by considering the resultant of the gravity forces on a continuous body. Consider a body Q of volume V with density ρ ( r ) at each point r in

2020-542: Is the Late Bronze Age Uluburun shipwreck off the coast of Turkey, dating back to 1300 BC. By 1200 B.C., the Phoenicians were building large merchant ships. In world maritime history, declares Richard Woodman, they are recognized as "the first true seafarers, founding the art of pilotage, cabotage , and navigation" and the architects of "the first true ship, built of planks, capable of carrying

2121-1708: Is the mass at the point r , g is the acceleration of gravity, and k ^ {\textstyle \mathbf {\hat {k}} } is a unit vector defining the vertical direction. Choose a reference point R in the volume and compute the resultant force and torque at this point, F = ∭ Q f ( r ) d V = ∭ Q ρ ( r ) d V ( − g k ^ ) = − M g k ^ , {\displaystyle \mathbf {F} =\iiint _{Q}\mathbf {f} (\mathbf {r} )\,dV=\iiint _{Q}\rho (\mathbf {r} )\,dV\left(-g\mathbf {\hat {k}} \right)=-Mg\mathbf {\hat {k}} ,} and T = ∭ Q ( r − R ) × f ( r ) d V = ∭ Q ( r − R ) × ( − g ρ ( r ) d V k ^ ) = ( ∭ Q ρ ( r ) ( r − R ) d V ) × ( − g k ^ ) . {\displaystyle \mathbf {T} =\iiint _{Q}(\mathbf {r} -\mathbf {R} )\times \mathbf {f} (\mathbf {r} )\,dV=\iiint _{Q}(\mathbf {r} -\mathbf {R} )\times \left(-g\rho (\mathbf {r} )\,dV\,\mathbf {\hat {k}} \right)=\left(\iiint _{Q}\rho (\mathbf {r} )\left(\mathbf {r} -\mathbf {R} \right)dV\right)\times \left(-g\mathbf {\hat {k}} \right).} If

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2222-511: Is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet , or a planet orbits a star , both bodies are actually orbiting a point that lies away from the center of the primary (larger) body. For example, the Moon does not orbit the exact center of the Earth , but a point on a line between

2323-903: Is the sum of the masses of all of the particles. These values are mapped back into a new angle, θ ¯ {\displaystyle {\overline {\theta }}} , from which the x coordinate of the center of mass can be obtained: θ ¯ = atan2 ⁡ ( − ζ ¯ , − ξ ¯ ) + π x com = x max θ ¯ 2 π {\displaystyle {\begin{aligned}{\overline {\theta }}&=\operatorname {atan2} \left(-{\overline {\zeta }},-{\overline {\xi }}\right)+\pi \\x_{\text{com}}&=x_{\max }{\frac {\overline {\theta }}{2\pi }}\end{aligned}}} The process can be repeated for all dimensions of

2424-474: Is the total mass of all the particles, p is the linear momentum, and L is the angular momentum. The law of conservation of momentum predicts that for any system not subjected to external forces the momentum of the system will remain constant, which means the center of mass will move with constant velocity. This applies for all systems with classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More formally, this

2525-1282: Is the unit vector in the vertical direction). Let r 1 , r 2 , and r 3 be the position coordinates of the support points, then the coordinates R of the center of mass satisfy the condition that the resultant torque is zero, T = ( r 1 − R ) × F 1 + ( r 2 − R ) × F 2 + ( r 3 − R ) × F 3 = 0 , {\displaystyle \mathbf {T} =(\mathbf {r} _{1}-\mathbf {R} )\times \mathbf {F} _{1}+(\mathbf {r} _{2}-\mathbf {R} )\times \mathbf {F} _{2}+(\mathbf {r} _{3}-\mathbf {R} )\times \mathbf {F} _{3}=0,} or R × ( − W k ^ ) = r 1 × F 1 + r 2 × F 2 + r 3 × F 3 . {\displaystyle \mathbf {R} \times \left(-W\mathbf {\hat {k}} \right)=\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\mathbf {r} _{3}\times \mathbf {F} _{3}.} This equation yields

2626-434: Is true for any internal forces that cancel in accordance with Newton's Third Law . The experimental determination of a body's center of mass makes use of gravity forces on the body and is based on the fact that the center of mass is the same as the center of gravity in the parallel gravity field near the earth's surface. The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus,

2727-418: Is undefined. This is a correct result, because it only occurs when all particles are exactly evenly spaced. In that condition, their x coordinates are mathematically identical in a periodic system . A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes. Where a gravity field can be considered to be uniform, the mass-center and the center-of-gravity will be

2828-411: Is unknown, but the largest number of jong deployed in an expedition is about 400 jongs, when Majapahit attacked Pasai, in 1350. Until the late 13th or early 14th century, European shipbuilding had two separate traditions. In Northern Europe clinker construction predominated. In this, the hull planks are fastened together in an overlapping manner. This is a "shell first" construction technique, with

2929-416: Is very important to place the center of gravity at the center and well below the lift points. The center of mass of the adult human body is 10 cm above the trochanter (the femur joins the hip). In kinesiology and biomechanics, the center of mass is an important parameter that assists people in understanding their human locomotion. Typically, a human's center of mass is detected with one of two methods:

3030-1141: The ( ξ , ζ ) {\displaystyle (\xi ,\zeta )} plane, these coordinates lie on a circle of radius 1. From the collection of ξ i {\displaystyle \xi _{i}} and ζ i {\displaystyle \zeta _{i}} values from all the particles, the averages ξ ¯ {\displaystyle {\overline {\xi }}} and ζ ¯ {\displaystyle {\overline {\zeta }}} are calculated. ξ ¯ = 1 M ∑ i = 1 n m i ξ i , ζ ¯ = 1 M ∑ i = 1 n m i ζ i , {\displaystyle {\begin{aligned}{\overline {\xi }}&={\frac {1}{M}}\sum _{i=1}^{n}m_{i}\xi _{i},\\{\overline {\zeta }}&={\frac {1}{M}}\sum _{i=1}^{n}m_{i}\zeta _{i},\end{aligned}}} where M

3131-744: The Kunlun people") by the Chinese, and kolandiaphonta by the Greeks. They had 4–7 masts and were able to sail against the wind due to the usage of tanja sails . These ships may have reached as far as Ghana . In the 11th century, a new type of ship called djong or jong was recorded in Java and Bali . This type of ship was built using wooden dowels and treenails, unlike the kunlun bo which used vegetal fibres for lashings. In China, miniature models of ships that feature steering oars have been dated to

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3232-1039: The Multiservice tactical brevity code article. Terms used in other fields associated with bodies of water can be found at Glossary of fishery terms , Glossary of underwater diving terminology , Glossary of rowing terms , and Glossary of meteorology . Also ship's magazine . Also simply main . Also man o' war . Also Med moor and Tahitian mooring . Also messdeck . Also midship Also mizzen . Also moorings . Also mothership and mother-ship . Also motor vessel . Contents:  Top A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also References Also position light or running light Also net layer , net tender , gate ship , or boom defence vessel . Contents:  Top A B C D Ships The word ship has meant, depending on

3333-736: The Red Sea as far as the myrrh -country." Sneferu 's ancient cedar wood ship Praise of the Two Lands is the first reference recorded (2613 BC) to a ship being referred to by name. The ancient Egyptians were perfectly at ease building sailboats. A remarkable example of their shipbuilding skills was the Khufu ship , a vessel 143 feet (44 m) in length entombed at the foot of the Great Pyramid of Giza around 2500 BC and found intact in 1954. The oldest discovered sea faring hulled boat

3434-787: The United Kingdom in the Falkland Islands and the United States in Iraq . The size of the world's fishing fleet is more difficult to estimate. The largest of these are counted as commercial vessels, but the smallest are legion. Fishing vessels can be found in most seaside villages in the world. As of 2004, the United Nations Food and Agriculture Organization estimated 4 million fishing vessels were operating worldwide. The same study estimated that

3535-599: The Warring States period (c. 475–221 BC). By the Han dynasty , a well kept naval fleet was an integral part of the military. Sternpost-mounted rudders started to appear on Chinese ship models starting in the 1st century AD. However, these early Chinese ships were fluvial (riverine), and were not seaworthy. The Chinese only acquired sea-going ship technologies in the 10th-century AD Song dynasty after contact with Southeast Asian k'un-lun po trading ships, leading to

3636-454: The atakebune . In Korea, in the early 15th century during the Joseon era, " Geobukseon "(거북선), was developed. The empire of Majapahit used large ships called jong , built in northern Java, for transporting troops overseas. The jongs were transport ships which could carry 100–2000 tons of cargo and 50–1000 people, 28.99–88.56 meter in length. The exact number of jong fielded by Majapahit

3737-581: The outside of a sharp turn, whereas boats heel towards the inside because of the relative location of the center of mass versus the center of buoyancy . American and British 19th century maritime law distinguished "vessels" from other watercraft; ships and boats fall in one legal category, whereas open boats and rafts are not considered vessels. Starting around the middle of the 18th century, sailing vessels started to be categorised by their type of rig . (Previously they were described by their hull type – for example pink , cat .) Alongside

3838-440: The percentage of the total mass divided between these two particles vary from 100% P 1 and 0% P 2 through 50% P 1 and 50% P 2 to 0% P 1 and 100% P 2 , then the center of mass R moves along the line from P 1 to P 2 . The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, and are termed barycentric coordinates . Another way of interpreting

3939-533: The railway up to and past the early days of the Industrial Revolution . Flat-bottomed and flexible scow boats also became widely used for transporting small cargoes. Mercantile trade went hand-in-hand with exploration, self-financed by the commercial benefits of exploration. During the first half of the 18th century, the French Navy began to develop a new type of vessel known as a ship of

4040-478: The weighted relative position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration . Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words,

4141-911: The Great Lakes, "topping off" when they have exited the Seaway. Similarly, the largest lakers are confined to the Upper Lakes ( Superior , Michigan , Huron , Erie ) because they are too large to use the Seaway locks, beginning at the Welland Canal that bypasses the Niagara River . Since the freshwater lakes are less corrosive to ships than the salt water of the oceans, lakers tend to last much longer than ocean freighters. Lakers older than 50 years are not unusual, and as of 2005, all were over 20 years of age. SS  St. Marys Challenger , built in 1906 as William P Snyder ,

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4242-627: The Lakes. These vessels are traditionally called boats, not ships. Visiting ocean-going vessels are called "salties". Because of their additional beam , very large salties are never seen inland of the Saint Lawrence Seaway . Because the smallest of the Soo Locks is larger than any Seaway lock, salties that can pass through the Seaway may travel anywhere in the Great Lakes. Because of their deeper draft, salties may accept partial loads on

4343-463: The Mediterranean in the 12th and 13th centuries. Some aspects of their designs were being copied by Mediterranean ship-builders early in the 14th century. Iconography shows square sails being used on the mainmast but a lateen on the mizzen, and a sternpost hung rudder replacing the side rudder. The name for this type of vessel was "coche" or, for a larger example, "carrack". Some of these new Mediterranean types travelled to Northern European waters and, in

4444-488: The Northern European tradition is the bottom planking of the cog . Here, the hull planks are not joined to each other and are laid flush (not overlapped). They are held together by fastening to the frames but this is done after the shaping and fitting of these planks. Therefore, this is another case of a "shell first" construction technique. These Northern European ships were rigged with a single mast setting

4545-500: The case of a system of particles P i , i = 1, ...,  n   , each with mass m i that are located in space with coordinates r i , i = 1, ...,  n   , the coordinates R of the center of mass satisfy ∑ i = 1 n m i ( r i − R ) = 0 . {\displaystyle \sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )=\mathbf {0} .} Solving this equation for R yields

4646-414: The center of mass is the particle equivalent of a given object for application of Newton's laws of motion . In the case of a single rigid body , the center of mass is fixed in relation to the body, and if the body has uniform density , it will be located at the centroid . The center of mass may be located outside the physical body , as is sometimes the case for hollow or open-shaped objects, such as

4747-488: The center of mass is the same as the centroid of the volume. The coordinates R of the center of mass of a two-particle system, P 1 and P 2 , with masses m 1 and m 2 is given by R = m 1 r 1 + m 2 r 2 m 1 + m 2 . {\displaystyle \mathbf {R} ={{m_{1}\mathbf {r} _{1}+m_{2}\mathbf {r} _{2}} \over m_{1}+m_{2}}.} Let

4848-406: The center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere. In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry. An experimental method for locating the center of mass is to suspend

4949-493: The center of mass of the whole is the weighted average of the centers. This method can even work for objects with holes, which can be accounted for as negative masses. A direct development of the planimeter known as an integraph, or integerometer, can be used to establish the position of the centroid or center of mass of an irregular two-dimensional shape. This method can be applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult. It

5050-509: The center of the Earth and the Moon, approximately 1,710 km (1,062 miles) below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun . If the masses are more similar, e.g., Pluto and Charon , the barycenter will fall outside both bodies. Knowing the location of the center of gravity when rigging

5151-464: The concept further. Newton's second law is reformulated with respect to the center of mass in Euler's first law . The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space. In

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5252-399: The coordinates R to obtain R = 1 M ∭ Q ρ ( r ) r d V , {\displaystyle \mathbf {R} ={\frac {1}{M}}\iiint _{Q}\rho (\mathbf {r} )\mathbf {r} \,dV,} Where M is the total mass in the volume. If a continuous mass distribution has uniform density , which means that ρ is constant, then

5353-623: The coordinates of the center of mass R * in the horizontal plane as, R ∗ = − 1 W k ^ × ( r 1 × F 1 + r 2 × F 2 + r 3 × F 3 ) . {\displaystyle \mathbf {R} ^{*}=-{\frac {1}{W}}\mathbf {\hat {k}} \times (\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\mathbf {r} _{3}\times \mathbf {F} _{3}).} The center of mass lies on

5454-604: The decline of ocean liners as air travel increased. The rise of container ships from the 1960s onwards dramatically changed the nature of commercial merchant shipping, as containerization led to larger ship sizes, dedicated container routes and the decline of general cargo vessels as well as tramp steaming. The late 20th century also saw a rise in cruise ships for tourism around the world. In 2016, there were more than 49,000 merchant ships , totaling almost 1.8 billion deadweight tons . Of these 28% were oil tankers , 43% were bulk carriers , and 13% were container ships . By 2019,

5555-516: The development of the junks . The earliest historical evidence of boats is found in Egypt during the 4th millennium BCE The Greek historian and geographer Agatharchides had documented ship-faring among the early Egyptians : "During the prosperous period of the Old Kingdom , between the 30th and 25th centuries BC , the river -routes were kept in order, and Egyptian ships sailed

5656-436: The distinction between the center-of-gravity and the mass-center. Any horizontal offset between the two will result in an applied torque. The mass-center is a fixed property for a given rigid body (e.g. with no slosh or articulation), whereas the center-of-gravity may, in addition, depend upon its orientation in a non-uniform gravitational field. In the latter case, the center-of-gravity will always be located somewhat closer to

5757-528: The equations of motion of planets are formulated as point masses located at the centers of mass (see Barycenter (astronomy) for details). The center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system . The concept of center of gravity or weight was studied extensively by the ancient Greek mathematician , physicist , and engineer Archimedes of Syracuse . He worked with simplified assumptions about gravity that amount to

5858-481: The era and the context, either just a large vessel or specifically a ship-rigged sailing ship with three or more masts, each of which is square-rigged . The earliest historical evidence of boats is found in Egypt during the 4th millennium BCE. In 2024, ships had a global cargo capacity of 2.4 billion tons, with the three largest classes being ships carrying dry bulk (43%), oil tankers (28%) and container ships (14%). Ships are typically larger than boats, but there

5959-516: The first three centuries AD. Until recently, it was generally the case that a ship represented the most advanced representation of the technology that any society could achieve. The earliest attestations of ships in maritime transport in Mesopotamia are model ships , which date back to the 4th millennium BC. In archaic texts in Uruk , Sumer , the ideogram for "ship" is attested, but in

6060-584: The first two decades of the 15th century, a few were captured by the English, two of which had previously been under charter to the French. The two-masted rig started to be copied immediately, but at this stage on a clinker hull. The adoption of carvel hulls had to wait until sufficient shipwrights with appropriate skills could be hired, but by late in the 1430s, there were instances of carvel ships being built in Northern Europe, and in increasing numbers over

6161-405: The formula R = ∑ i = 1 n m i r i ∑ i = 1 n m i . {\displaystyle \mathbf {R} ={\sum _{i=1}^{n}m_{i}\mathbf {r} _{i} \over \sum _{i=1}^{n}m_{i}}.} If the mass distribution is continuous with the density ρ( r ) within a solid Q , then

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6262-427: The hull shape being defined by the shaping and fitting of the hull planks. The reinforcing frame s (or ribs) are fitted after the planks. Clinker construction in this era usually used planks that were cleft (split radially from the log) and could be made thinner and stronger per unit of thickness than the sawn logs, thanks to preserving the radial integrity of the grain. An exception to clinker construction in

6363-642: The inscriptions of the kings of Lagash , ships were first mentioned in connection to maritime trade and naval warfare at around 2500–2350 BCE. Austronesian peoples originated in what is now Taiwan . From here, they took part in the Austronesian Expansion . Their distinctive maritime technology was integral to this movement and included catamarans and outriggers . It has been suggested that they had sails some time before 2000 BCE. Their crab claw sails enabled them to sail for vast distances in open ocean. From Taiwan, they rapidly colonized

6464-439: The integral of the weighted position coordinates of the points in this volume relative to the center of mass R over the volume V is zero, that is ∭ Q ρ ( r ) ( r − R ) d V = 0 . {\displaystyle \iiint _{Q}\rho (\mathbf {r} )\left(\mathbf {r} -\mathbf {R} \right)dV=\mathbf {0} .} Solve this equation for

6565-461: The invention of an effective stern gland for the propeller shaft, worked better than paddle wheels . Higher boiler pressures of 60 pounds per square inch (410 kPa) powering compound engines, were introduced in 1865, making long-distance steam cargo vessels commercially viable on the route from England to China – even before the opening of the Suez Canal in 1869. Within

6666-562: The islands of Maritime Southeast Asia , then sailed further onwards to Micronesia , Island Melanesia , Polynesia , and Madagascar , eventually colonizing a territory spanning half the globe. Austronesian sails were made from woven leaves, usually from pandan plants. These were complemented by paddlers, who usually positioned themselves on platforms on the outriggers in the larger boats. Austronesian ships ranged in complexity from simple dugout canoes with outriggers or lashed together to large edge-pegged plank-built boats built around

6767-512: The large grain trade in the Mediterranean during the classical period . Cities such as Rome were totally reliant on the delivery by sailing and human powered (oars) ships of the large amounts of grain needed. It has been estimated that it cost less for a sailing ship of the Roman Empire to carry grain the length of the Mediterranean than to move the same amount 15 miles by road. Rome consumed about 150,000 tons of Egyptian grain each year over

6868-484: The line , featuring seventy-four guns. This type of ship became the backbone of all European fighting fleets. These ships were 56 metres (184 ft) long and their construction required 2,800 oak trees and 40 kilometres (25 mi) of rope; they carried a crew of about 800 sailors and soldiers. During the 19th century the Royal Navy enforced a ban on the slave trade , acted to suppress piracy , and continued to map

6969-404: The main attractive body as compared to the mass-center, and thus will change its position in the body of interest as its orientation is changed. In the study of the dynamics of aircraft, vehicles and vessels, forces and moments need to be resolved relative to the mass center. That is true independent of whether gravity itself is a consideration. Referring to the mass-center as the center-of-gravity

7070-512: The mass of the particle x i {\displaystyle x_{i}} for the center of mass or given a value of 1 for the geometric center: ξ i = cos ⁡ ( θ i ) ζ i = sin ⁡ ( θ i ) {\displaystyle {\begin{aligned}\xi _{i}&=\cos(\theta _{i})\\\zeta _{i}&=\sin(\theta _{i})\end{aligned}}} In

7171-443: The meaning can only be determined by the context. Some large vessels are traditionally called boats , notably submarines . Others include Great Lakes freighters , riverboats , and ferryboats , which may be designed for operation on inland or protected coastal waters. In most maritime traditions ships have individual names , and modern ships may belong to a ship class often named after its first ship. In many documents

7272-463: The object from two locations and to drop plumb lines from the suspension points. The intersection of the two lines is the center of mass. The shape of an object might already be mathematically determined, but it may be too complex to use a known formula. In this case, one can subdivide the complex shape into simpler, more elementary shapes, whose centers of mass are easy to find. If the total mass and center of mass can be determined for each area, then

7373-520: The object. The center of mass will be the intersection of the two lines L 1 and L 2 obtained from the two experiments. Engineers try to design a sports car so that its center of mass is lowered to make the car handle better, which is to say, maintain traction while executing relatively sharp turns. The characteristic low profile of the U.S. military Humvee was designed in part to allow it to tilt farther than taller vehicles without rolling over , by ensuring its low center of mass stays over

7474-416: The other rig types such as schooner and brig , the term "ship" referred to the rig type. In this sense, a ship is a vessel with three or more masts, all of which are square-rigged . For clarity, this may be referred to as a full-rigged ship or a vessel may be described as "ship-rigged". Alongside this rig-specific usage, "ship" continued to have the more general meaning of a large sea-going vessel. Often

7575-741: The particles relative to the center of mass. Let the system of particles P i , i = 1, ..., n of masses m i be located at the coordinates r i with velocities v i . Select a reference point R and compute the relative position and velocity vectors, r i = ( r i − R ) + R , v i = d d t ( r i − R ) + v . {\displaystyle \mathbf {r} _{i}=(\mathbf {r} _{i}-\mathbf {R} )+\mathbf {R} ,\quad \mathbf {v} _{i}={\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+\mathbf {v} .} The total linear momentum and angular momentum of

7676-415: The point of being unable to rotate for takeoff or flare for landing. If the center of mass is behind the aft limit, the aircraft will be more maneuverable, but also less stable, and possibly unstable enough so as to be impossible to fly. The moment arm of the elevator will also be reduced, which makes it more difficult to recover from a stalled condition. For helicopters in hover , the center of mass

7777-466: The principles of naval architecture that require same structural components, their classification is based on their function such as that suggested by Paulet and Presles, which requires modification of the components. The categories accepted in general by naval architects are: Some of these are discussed in the following sections. Freshwater shipping may occur on lakes, rivers and canals. Ships designed for those body of waters may be specially adapted to

7878-461: The process here is the mechanical balancing of moments about an arbitrary point. The numerator gives the total moment that is then balanced by an equivalent total force at the center of mass. This can be generalized to three points and four points to define projective coordinates in the plane, and in space, respectively. For particles in a system with periodic boundary conditions two particles can be neighbours even though they are on opposite sides of

7979-528: The quest for more efficient ships, the end of long running and wasteful maritime conflicts, and the increased financial capacity of industrial powers created more specialized ships and other maritime vessels. Ship types built for entirely new functions that appeared by the 20th century included research ships , offshore support vessels (OSVs), Floating production storage and offloading (FPSOs), Pipe and cable laying ships , drill ships and Survey vessels . The late 20th century saw changes to ships that included

8080-431: The reaction board method is a static analysis that involves the person lying down on that instrument, and use of their static equilibrium equation to find their center of mass; the segmentation method relies on a mathematical solution based on the physical principle that the summation of the torques of individual body sections, relative to a specified axis , must equal the torque of the whole system that constitutes

8181-429: The reference point R is chosen so that it is the center of mass, then ∭ Q ρ ( r ) ( r − R ) d V = 0 , {\displaystyle \iiint _{Q}\rho (\mathbf {r} )\left(\mathbf {r} -\mathbf {R} \right)dV=0,} which means the resultant torque T = 0 . Because the resultant torque is zero the body will move as though it

8282-509: The rest of the century. This hybridisation of Mediterranean and Northern European ship types created the full-rigged ship , a three-masted vessel with a square-rigged foremast and mainmast and a lateen sail on the mizzen. This provided most of the ships used in the Age of Discovery , being able to carry sufficient stores for a long voyage and with a rig suited to the open ocean. Over the next four hundred years, steady evolution and development, from

8383-401: The same. However, for satellites in orbit around a planet, in the absence of other torques being applied to a satellite, the slight variation (gradient) in gravitational field between closer-to and further-from the planet (stronger and weaker gravity respectively) can lead to a torque that will tend to align the satellite such that its long axis is vertical. In such a case, it is important to make

8484-513: The ship name is introduced with a ship prefix being an abbreviation of the ship class, for example "MS" (motor ship) or "SV" (sailing vessel), making it easier to distinguish a ship name from other individual names in a text. "Ship" (along with "nation") is an English word that has retained a female grammatical gender in some usages, which allows it sometimes to be referred to as a "she" without being of female natural gender . For most of history, transport by ship – provided there

8585-524: The shipper than a predictable and rapid journey time. The Second Industrial Revolution in particular led to new mechanical methods of propulsion , and the ability to construct ships from metal triggered an explosion in ship design. These led to the development of long-distance commercial ships and Ocean liners , as well as technological changes including the Marine steam engine , screw propellers, triple expansion engines and others. Factors included

8686-593: The size of contemporary carracks. Before the adoption of carvel construction, the increasing size of clinker-built vessels came to necessitate internal framing of their hulls for strength. Parallel to the development of warships, ships in service of marine fishery and trade also developed in the period between antiquity and the Renaissance. Maritime trade was driven by the development of shipping companies with significant financial resources. Canal barges, towed by draft animals on an adjacent towpath , contended with

8787-418: The space bounded by the four wheels even at angles far from the horizontal . The center of mass is an important point on an aircraft , which significantly affects the stability of the aircraft. To ensure the aircraft is stable enough to be safe to fly, the center of mass must fall within specified limits. If the center of mass is ahead of the forward limit , the aircraft will be less maneuverable, possibly to

8888-500: The starting point of the carrack , gave types such as the galleon , fluit , East Indiaman , ordinary cargo ships, warships, clippers and many more, all based on this three-masted square-rigged type. The transition from clinker to carvel construction facilitated the use of gun ports. As vessels became larger, clinker construction became less practical because of the difficulty of finding commensurately large logs from which to cleave planks. Nonetheless, some clinker vessels approached

8989-1500: The system are p = d d t ( ∑ i = 1 n m i ( r i − R ) ) + ( ∑ i = 1 n m i ) v , {\displaystyle \mathbf {p} ={\frac {d}{dt}}\left(\sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )\right)+\left(\sum _{i=1}^{n}m_{i}\right)\mathbf {v} ,} and L = ∑ i = 1 n m i ( r i − R ) × d d t ( r i − R ) + ( ∑ i = 1 n m i ) [ R × d d t ( r i − R ) + ( r i − R ) × v ] + ( ∑ i = 1 n m i ) R × v {\displaystyle \mathbf {L} =\sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )\times {\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+\left(\sum _{i=1}^{n}m_{i}\right)\left[\mathbf {R} \times {\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+(\mathbf {r} _{i}-\mathbf {R} )\times \mathbf {v} \right]+\left(\sum _{i=1}^{n}m_{i}\right)\mathbf {R} \times \mathbf {v} } If R

9090-615: The system to determine the complete center of mass. The utility of the algorithm is that it allows the mathematics to determine where the "best" center of mass is, instead of guessing or using cluster analysis to "unfold" a cluster straddling the periodic boundaries. If both average values are zero, ( ξ ¯ , ζ ¯ ) = ( 0 , 0 ) {\displaystyle \left({\overline {\xi }},{\overline {\zeta }}\right)=(0,0)} , then θ ¯ {\displaystyle {\overline {\theta }}}

9191-440: The system. This occurs often in molecular dynamics simulations, for example, in which clusters form at random locations and sometimes neighbouring atoms cross the periodic boundary. When a cluster straddles the periodic boundary, a naive calculation of the center of mass will be incorrect. A generalized method for calculating the center of mass for periodic systems is to treat each coordinate, x and y and/or z , as if it were on

9292-442: The vertical line L , given by L ( t ) = R ∗ + t k ^ . {\displaystyle \mathbf {L} (t)=\mathbf {R} ^{*}+t\mathbf {\hat {k}} .} The three-dimensional coordinates of the center of mass are determined by performing this experiment twice with the object positioned so that these forces are measured for two different horizontal planes through

9393-430: The volume. In a parallel gravity field the force f at each point r is given by, f ( r ) = − d m g k ^ = − ρ ( r ) d V g k ^ , {\displaystyle \mathbf {f} (\mathbf {r} )=-dm\,g\mathbf {\hat {k}} =-\rho (\mathbf {r} )\,dV\,g\mathbf {\hat {k}} ,} where dm

9494-516: The widths and depths of specific waterways. Examples of freshwater waterways that are navigable in part by large vessels include the Danube , Mississippi , Rhine , Yangtze and Amazon Rivers, and the Great Lakes . Lake freighters , also called lakers, are cargo vessels that ply the Great Lakes . The most well-known is SS  Edmund Fitzgerald , the latest major vessel to be wrecked on

9595-519: The world for the diplomatic and power projection voyages of Zheng He . Elsewhere in Japan in the 15th century, one of the world's first iron-clads, "Tekkōsen" ( 鉄甲船 ), literally meaning "iron ships", was also developed. In Japan, during the Sengoku era from the 15th century to 17th century, the great struggle for feudal supremacy was fought, in part, by coastal fleets of several hundred boats, including

9696-490: The world's 29 million fishermen caught 85,800,000 tonnes (84,400,000 long tons ; 94,600,000 short tons ) of fish and shellfish that year. In 2023, the number of ships globally grew by 3.4%. In 2024, new ships are increasingly being built with alternative fuel capability to increase sustainability and reduce carbon emissions. Alternative ship fuels include LNG , LPG , methanol , biofuel , ammonia and hydrogen among others. Because ships are constructed using

9797-419: The world's fleet included 51,684 commercial vessels with gross tonnage of more than 1,000 tons , totaling 1.96 billion tons. Such ships carried 11 billion tons of cargo in 2018, a sum that grew by 2.7% over the previous year. In terms of tonnage, 29% of ships were tankers , 43% are bulk carriers , 13% container ships and 15% were other types. In 2008, there were 1,240 warships operating in

9898-501: The world, not counting small vessels such as patrol boats . The United States accounted for 3 million tons worth of these vessels, Russia 1.35 million tons, the United Kingdom 504,660 tons and China 402,830 tons. The 20th century saw many naval engagements during the two world wars , the Cold War , and the rise to power of naval forces of the two blocs. The world's major powers have recently used their naval power in cases such as

9999-691: The world. Ships and their owners grew with the 19th century Industrial Revolution across Europe and North America, leading to increased numbers of oceangoing ships, as well as other coastal and canal based vessels. Through more than half of the 19th century and into the early years of the 20th century, steam ships coexisted with sailing vessels. Initially, steam was only viable on shorter routes, typically transporting passengers who could afford higher fares and mail. Steam went through many developmental steps that gave greater fuel efficiency, thereby increasingly making steamships commercially competitive with sail. Screw propulsion, which relied, among other things, on

10100-604: Was regularly used by ship builders to compare with the required displacement and center of buoyancy of a ship, and ensure it would not capsize. An experimental method to locate the three-dimensional coordinates of the center of mass begins by supporting the object at three points and measuring the forces, F 1 , F 2 , and F 3 that resist the weight of the object, W = − W k ^ {\displaystyle \mathbf {W} =-W\mathbf {\hat {k}} } ( k ^ {\displaystyle \mathbf {\hat {k}} }

10201-1102: Was the oldest laker still working on the Lakes until its conversion into a barge starting in 2013. Similarly, E.M. Ford , built in 1898 as Presque Isle , was sailing the lakes 98 years later in 1996. As of 2007 E.M. Ford was still afloat as a stationary transfer vessel at a riverside cement silo in Saginaw, Michigan . Merchant ships are ships used for commercial purposes and can be divided into four broad categories: fishing vessels , cargo ships , passenger ships , and special-purpose ships. The UNCTAD review of maritime transport categorizes ships as: oil tankers, bulk (and combination) carriers, general cargo ships, container ships, and "other ships", which includes " liquefied petroleum gas carriers, liquefied natural gas carriers, parcel (chemical) tankers, specialized tankers, reefers , offshore supply, tugs, dredgers , cruise , ferries , other non-cargo". General cargo ships include "multi-purpose and project vessels and roll-on/roll-off cargo". Modern commercial vessels are typically powered by

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