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57-462: Tschaika were either 24 m (79 ft) (Ganz ("Full") Tschaika) or 12 m (39 ft) (Halb ("Half") Tschaika) in length, operated by sail or oars . Between 30 and 50 men were in service, commanded by an officer, with a helmsman, an armourer, a drummer, two bowsmen, and up to 36 oarsmen. Chaikas were between 18–20 m (59–66 ft) in length, 3–3.5 m (9.8–11.5 ft) in width, and 3.5–4 m (11–13 ft) in depth. The bottom of

114-401: A rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle , central angle , and external angle are all equal (90°). A square with vertices ABCD would be denoted ◻ {\displaystyle \square } ABCD . A quadrilateral is a square if and only if it is any one of the following: A square is a special case of

171-438: A rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles), and therefore has all the properties of all these shapes, namely: A square has Schläfli symbol {4}. A truncated square, t{4},

228-444: A rhombus . These two forms are duals of each other, and have half the symmetry order of the square. d2 is the symmetry of an isosceles trapezoid , and p2 is the symmetry of a kite . g2 defines the geometry of a parallelogram . Only the g4 subgroup has no degrees of freedom, but can be seen as a square with directed edges . Every acute triangle has three inscribed squares (squares in its interior such that all four of

285-436: A chaika was carved out of a single tree trunk , with sides built out of wooden planks. To protect the boat from enemy guns or from sinking, reed bales were tied to the gunwales of the boat. One such boat could carry around 50 to 60 men and up to 6 falconets (small cannon). Some chaikas also had two steering oars , so that the boat never needed turning around in order to switch direction. A similar, but larger boat used by

342-401: A combination of woven materials—including canvas or polyester cloth, laminated membranes or bonded filaments, usually in a three- or four-sided shape. A sail provides propulsive force via a combination of lift and drag, depending on its angle of attack , its angle with respect to the apparent wind . Apparent wind is the air velocity experienced on the moving craft and is the combined effect of

399-447: A horizontal or vertical radius of r . The square is therefore the shape of a topological ball according to the L 1 distance metric . The following animations show how to construct a square using a compass and straightedge . This is possible as 4 = 2 , a power of two . The square has Dih 4 symmetry, order 8. There are 2 dihedral subgroups: Dih 2 , Dih 1 , and 3 cyclic subgroups: Z 4 , Z 2 , and Z 1 . A square

456-405: A lateral force, resisted by the underwater foils, ice runners, or wheels of the sailing craft. For apparent wind angles aligned with the entry point of the sail, the sail acts as an airfoil and lift is the predominant component of propulsion. For apparent wind angles behind the sail, lift diminishes and drag increases as the predominant component of propulsion. For a given true wind velocity over

513-414: A line or a hook may pass, as on Bermuda mainsails. Fore-and-aft sails may have tell-tales —pieces of yarn, thread or tape that are affixed to sails—to help visualize airflow over their surfaces. The lines that attach to and control sails are part of the running rigging and differ between square and fore-and-aft rigs. Some rigs shift from one side of the mast to the other, e.g. the dipping lug sail and

570-439: A mast to support the airfoil and are beyond the scope of this article. Sailing craft employ two types of rig, the square rig and the fore-and-aft rig . The square rig carries the primary driving sails on horizontal spars , which are perpendicular or square , to the keel of the vessel and to the masts. These spars are called yards and their tips, beyond the lifts , are called the yardarms . A ship mainly so rigged

627-561: A mast. They are typically raised by a line, called a halyard , and their angle with respect to the wind is usually controlled by a line, called a sheet . In use, they may be designed to be curved in both directions along their surface, often as a result of their curved edges. Battens may be used to extend the trailing edge of a sail beyond the line of its attachment points. Other non-rotating airfoils that power sailing craft include wingsails , which are rigid wing-like structures, and kites that power kite-rigged vessels , but do not employ

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684-404: A property is that of a three by six rectangle. In classical times , the second power was described in terms of the area of a square, as in the above formula. This led to the use of the term square to mean raising to the second power. The area can also be calculated using the diagonal d according to In terms of the circumradius R , the area of a square is since the area of the circle

741-420: A sail is defined by its edges and corners in the plane of the sail, laid out on a flat surface. The edges may be curved, either to extend the sail's shape as an airfoil or to define its shape in use. In use, the sail becomes a curved shape, adding the dimension of depth or draft . Sail characteristics derive, in part, from the design, construction and the attributes of the fibers, which are woven together to make

798-471: A sail to reinforce it, or to fix the sail into a groove in the boom, in the mast, or in the luff foil of a roller-furling jib. They may have stiffening features, called battens , that help shape the sail, when full length, or just the roach, when present. They may have a variety of means of reefing them (reducing sail area), including rows of short lines affixed to the sail to wrap up unused sail, as on square and gaff rigs, or simply grommets through which

855-582: A shape that does not lie flat. Conventional sail panels are sewn together. Sails are tensile structures, so the role of a seam is to transmit a tensile load from panel to panel. For a sewn textile sail this is done through thread and is limited by the strength of the thread and the strength of the hole in the textile through which it passes. Sail seams are often overlapped between panels and sewn with zig-zag stitches that create many connections per unit of seam length. Whereas textiles are typically sewn together, other sail materials may be ultrasonically welded ,

912-400: A square and reconnecting by its two diagonals. It has half the symmetry of the square, Dih 2 , order 4. It has the same vertex arrangement as the square, and is vertex-transitive . It appears as two 45-45-90 triangles with a common vertex, but the geometric intersection is not considered a vertex. A crossed square is sometimes likened to a bow tie or butterfly . the crossed rectangle

969-417: A square's vertices lie on a side of the triangle, so two of them lie on the same side and hence one side of the square coincides with part of a side of the triangle). In a right triangle two of the squares coincide and have a vertex at the triangle's right angle, so a right triangle has only two distinct inscribed squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of

1026-402: A square. The coordinates for the vertices of a square with vertical and horizontal sides, centered at the origin and with side length 2 are (±1, ±1), while the interior of this square consists of all points ( x i , y i ) with −1 < x i < 1 and −1 < y i < 1 . The equation specifies the boundary of this square. This equation means " x or y , whichever

1083-401: A technique whereby high frequency ultrasonic acoustic vibrations are locally applied to workpieces being held together under pressure to create a solid state weld . It is commonly used for plastics , and especially for joining dissimilar materials . Sails feature reinforcements of fabric layers where lines attach at grommets or cringles . A bolt rope may be sewn onto the edges of

1140-473: Is π R 2 , {\displaystyle \pi R^{2},} the square fills 2 / π ≈ 0.6366 {\displaystyle 2/\pi \approx 0.6366} of its circumscribed circle . In terms of the inradius r , the area of the square is hence the area of the inscribed circle is π / 4 ≈ 0.7854 {\displaystyle \pi /4\approx 0.7854} of that of

1197-425: Is a transcendental number rather than an algebraic irrational number ; that is, it is not the root of any polynomial with rational coefficients. In non-Euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles. In spherical geometry , a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry,

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1254-401: Is a special case of many lower symmetry quadrilaterals: These 6 symmetries express 8 distinct symmetries on a square. John Conway labels these by a letter and group order. Each subgroup symmetry allows one or more degrees of freedom for irregular quadrilaterals . r8 is full symmetry of the square, and a1 is no symmetry. d4 is the symmetry of a rectangle , and p4 is the symmetry of

1311-438: Is an octagon , {8}. An alternated square, h{4}, is a digon , {2}. The square is the n = 2 case of the families of n - hypercubes and n - orthoplexes . The perimeter of a square whose four sides have length ℓ {\displaystyle \ell } is and the area A is Since four squared equals sixteen, a four by four square has an area equal to its perimeter. The only other quadrilateral with such

1368-412: Is called a square-rigger . A fore-and-aft rig consists of sails that are set along the line of the keel rather than perpendicular to it. Vessels so rigged are described as fore-and-aft rigged . The invention of the sail was a technological advance of equal or even greater importance than the invention of the wheel. It has been suggested by some that it has the significance of the development of

1425-401: Is larger, equals 1." The circumradius of this square (the radius of a circle drawn through the square's vertices) is half the square's diagonal, and is equal to 2 . {\displaystyle {\sqrt {2}}.} Then the circumcircle has the equation Alternatively the equation can also be used to describe the boundary of a square with center coordinates ( a , b ), and

1482-448: Is related, as a faceting of the rectangle, both special cases of crossed quadrilaterals . The interior of a crossed square can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise. A square and a crossed square have the following properties in common: It exists in the vertex figure of a uniform star polyhedra , the tetrahemihexahedron . The K 4 complete graph

1539-471: Is usually a "flow through" structure) and a number of intervisible islands create both an invitation to travel and an environment where advanced navigation techniques are not needed. Alongside this, the Nile has a northward flowing current with a prevailing wind in the opposite direction, so giving the potential to drift in one direction and sail in the other. Many do not consider sails to have been used before

1596-433: Is very little stress at the tack, whereas head sails (spinnakers and jibs) are more likely to be tri-radial, because they are tensioned at their corners. Higher performance sails may be laminated, constructed directly from multiple plies of filaments , fibers , taffetas , and films , instead of woven textiles that are adhered together. Molded sails are laminated sails formed over a curved mold and adhered together into

1653-572: The caravel in Northern European waters from about 1440 made lateen sails familiar in this part of the world. Additionally, lateen sails were used for the mizzen on early three-masted ships, playing a significant role in the development of the full-rigged ship . It did not, however, provide much of the propulsive force of these vessels – rather serving as a balancing sail that was needed for some manoeuvres in some sea and wind conditions. The extensive amount of contemporary maritime art showing

1710-399: The linear mass density of fibers). Cross-cut sails have the panels sewn parallel to one another, often parallel to the foot of the sail, and are the least expensive of the two sail constructions. Triangular cross-cut sail panels are designed to meet the mast and stay at an angle from either the warp or the weft (on the bias ) to allow stretching along the luff, but minimize stretching on

1767-504: The 11th into the 19th centuries. Materials used in sails, as of the 21st century, include nylon for spinnakers, where light weight and elastic resistance to shock load are valued and a range of fibers, used for triangular sails, that includes Dacron , aramid fibers including Kevlar , and other liquid crystal polymer fibers including Vectran . Woven materials, like Dacron, may specified as either high or low tenacity , as indicated, in part by their denier count (a unit of measure for

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1824-618: The 5th millennium BCE. Others consider sails to have been invented much earlier. Archaeological studies of the Cucuteni-Trypillian culture ceramics show use of sailing boats from the sixth millennium BCE onwards. Excavations of the Ubaid period (c. 6000–4300 BCE) in Mesopotamia provide direct evidence of sailing boats. Sails from ancient Egypt are depicted around 3200 BCE, where reed boats sailed upstream against

1881-585: The River Nile 's current. Ancient Sumerians used square rigged sailing boats at about the same time, and it is believed they established sea trading routes as far away as the Indus valley . Greeks and Phoenicians began trading by ship by around 1200 BCE. V-shaped square rigs with two spars that come together at the hull were the ancestral sailing rig of the Austronesian peoples before they developed

1938-623: The Zaporozhian Cossacks for both transport and warfare was called a baidak . This article about a type of ship or boat is a stub . You can help Misplaced Pages by expanding it . This Ukraine -related article is a stub . You can help Misplaced Pages by expanding it . Sail A sail is a tensile structure , which is made from fabric or other membrane materials, that uses wind power to propel sailing craft, including sailing ships , sailboats , windsurfers , ice boats , and even sail-powered land vehicles . Sails may be made from

1995-410: The angle of attack diverges from the apparent wind as a sailing craft turns downwind, the more drag increases and lift decreases as propulsive forces, until a sail going downwind is predominated by drag forces. Sails are unable to generate propulsive force if they are aligned too closely to the wind. Sails may be attached to a mast , boom or other spar or may be attached to a wire that is suspended by

2052-432: The angles of such a square are larger than a right angle. Larger spherical squares have larger angles. In hyperbolic geometry , squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger hyperbolic squares have smaller angles. Examples: A crossed square is a faceting of the square, a self-intersecting polygon created by removing two opposite edges of

2109-454: The following. Sails on high-performance sailing craft. Sails on craft subject to low forward resistance and high lateral resistance typically have full-length battens. square#Adjective In Euclidean geometry , a square is a regular quadrilateral , which means that it has four straight sides of equal length and four equal angles (90- degree angles, π/2 radian angles, or right angles ). It can also be defined as

2166-444: The force component in the direction of the apparent wind and lift , the force component normal (90°) to the apparent wind. Depending on the alignment of the sail with the apparent wind, lift or drag may be the predominant propulsive component. Total aerodynamic force also resolves into a forward, propulsive, driving force, resisted by the medium through or over which the craft is passing (e.g., through water, air, or over ice, sand) and

2223-503: The fore-and-aft crab claw , tanja and junk rigs . The date of introduction of these later Austronesian sails is disputed. Lateen sails emerged by around the 2nd century CE in the Mediterranean. They did not become common until the 5th century, when there is evidence that the Mediterranean square sail (which had been in wide use throughout the classical period ) was undergoing a simplification of its rigging components. Both

2280-480: The increasing popularity of the lateen and the changes to the contemporary square rig are suggested to be cost saving measures, reducing the number of expensive components needed to fit out a ship. It has been a common and erroneous presumption among maritime historians that lateen had significantly better sailing performance than the square rig of the same period. Analysis of voyages described in contemporary accounts and also in various replica vessels demonstrates that

2337-432: The islands of Maritime Southeast Asia , then later sailed further onwards to Micronesia , Island Melanesia , Polynesia , and Madagascar , eventually settling a territory spanning half the globe. The proto- Austronesian words for sail, lay(r) , and some other rigging parts date to about 3000 BCE when this group began their Pacific expansion. Austronesian rigs are distinctive in that they have spars supporting both

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2394-533: The lateen mizzen on 16th and 17th century ships often has the sail furled. Practical experience on the Duyfken replica confirmed the role of the lateen mizzen. Austronesian invention of catamarans , outriggers , and the bi-sparred triangular crab claw sails enabled their ships to sail for vast distances in open ocean. It led to the Austronesian Expansion . From Taiwan, they rapidly settled

2451-401: The lateen. The lines can be categorized as those that support the sail, those that shape it, and those that control its angle to the wind. Fore-and-aft rigged vessels have rigging that supports, shapes, and adjusts the sails to optimize their performance in the wind, which include the following lines: Square-rigged vessels require more controlling lines than fore-and-aft rigged ones, including

2508-422: The luff and foot, where the fibers are aligned with the edges of the sail. Radial sails have panels that "radiate" from corners in order to efficiently transmit stress and are typically of higher performance than cross-cut sails. A bi-radial sail has panels radiating from two of three corners; a tri-radial sail has panels radiating from all three corners. Mainsails are more likely to be bi-radial, since there

2565-482: The neolithic lifestyle or the first establishment of cities. Yet it is not known when or where this invention took place. Much of the early development of water transport is believed to have occurred in two main "nursery" areas of the world: Island Southeast Asia and the Mediterranean region. In both of these you have warmer waters, so that use of rafts is possible without the risk of hypothermia (a raft

2622-585: The performance of square rig and lateen were very similar. Lateen provided a cheaper rig to build and maintain, with no degradation of performance. The lateen was adopted by Arab seafarers (usually in the sub-type: the settee sail ), but the date is uncertain, with no firm evidence for their use in the Western Indian Ocean before 1500 CE. There is, however, good iconographic evidence of square sails being used by Arab, Persian and Indian ships in this region in, for instance, 1519. The popularity of

2679-537: The rest of Austronesia , crab claw sails were mainly for double-outrigger ( trimarans ) and double-hulled ( catamarans ) boats, which remained stable even leeward. In western Island Southeast Asia , later square sails also evolved from the crab claw sail, the tanja and the junk rig , both of which retained the Austronesian characteristic of having more than one spar supporting the sail. Aerodynamic forces on sails depend on wind speed and direction and

2736-443: The sail cloth. There are several key factors in evaluating a fiber for suitability in weaving a sail-cloth: initial modulus , breaking strength (tenacity) , creep , and flex strength . Both the initial cost and its durability of the material define its cost-effectiveness over time. Traditionally, sails were made from flax or cotton canvas , although Scandinavian, Scottish and Icelandic cultures used woolen sails from

2793-445: The speed and direction of the craft. The direction that the craft is traveling with respect to the true wind (the wind direction and speed over the surface) is called the "point of sail". The speed of the craft at a given point of sail contributes to the apparent wind ( V A ), the wind speed and direction as measured on the moving craft. The apparent wind on the sail creates a total aerodynamic force, which may be resolved into drag ,

2850-400: The square. Because it is a regular polygon , a square is the quadrilateral of least perimeter enclosing a given area. Dually, a square is the quadrilateral containing the largest area within a given perimeter. Indeed, if A and P are the area and perimeter enclosed by a quadrilateral, then the following isoperimetric inequality holds: with equality if and only if the quadrilateral is

2907-551: The surface, a sail can propel a craft to a higher speed, on points of sail when the entry point of the sail is aligned with the apparent wind, than it can with the entry point not aligned, because of a combination of the diminished force from airflow around the sail and the diminished apparent wind from the velocity of the craft. Because of limitations on speed through the water, displacement sailboats generally derive power from sails generating lift on points of sail that include close-hauled through broad reach (approximately 40° to 135° off

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2964-525: The triangle's longest side. The fraction of the triangle's area that is filled by the square is no more than 1/2. Squaring the circle , proposed by ancient geometers , is the problem of constructing a square with the same area as a given circle , by using only a finite number of steps with compass and straightedge . In 1882, the task was proven to be impossible as a consequence of the Lindemann–Weierstrass theorem , which proves that pi ( π )

3021-489: The true wind velocity with the velocity of the sailing craft. Angle of attack is often constrained by the sailing craft's orientation to the wind or point of sail . On points of sail where it is possible to align the leading edge of the sail with the apparent wind, the sail may act as an airfoil , generating propulsive force as air passes along its surface, just as an airplane wing generates lift , which predominates over aerodynamic drag retarding forward motion. The more that

3078-545: The upper and lower edges of the sails (and sometimes in between). The sails were also made from salt-resistant woven leaves, usually from pandan plants. Crab claw sails used with single-outrigger ships in Micronesia , Island Melanesia , Polynesia , and Madagascar were intrinsically unstable when tacking leeward. To deal with this, Austronesians in these regions developed the shunting technique in sailing, in conjunction with uniquely reversible single-outriggers. In

3135-652: The various combinations of sail proposed for a sailing ship . Sail plans may vary for different wind conditions—light to heavy. Both square-rigged and fore-and-aft rigged vessels have been built with a wide range of configurations for single and multiple masts with sails and with a variety of means of primary attachment to the craft, including: High-performance yachts, including the International C-Class Catamaran , have used or use rigid wing sails , which perform better than traditional soft sails but are more difficult to manage. A rigid wing sail

3192-405: The wind). Because of low friction over the surface and high speeds over the ice that create high apparent wind speeds for most points of sail, iceboats can derive power from lift further off the wind than displacement boats. Each rig is configured in a sail plan , appropriate to the size of the sailing craft. A sail plan is a set of drawings, usually prepared by a naval architect which shows

3249-424: Was used by Stars and Stripes , the defender which won the 1988 America's Cup , and by USA-17 , the challenger which won the 2010 America's Cup . USA 17' s performance during the 2010 America's Cup races demonstrated a velocity made good upwind of over twice the wind speed and downwind of over 2.5 times the wind speed and the ability to sail as close as 20 degrees off the apparent wind. The shape of

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