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51-571: In plan view the almost crescent shape of the leading edge is similar to the Discus but is tapered in three stages. An entirely new wing section is used. The dihedral towards the tips was greatly increased compared with the Discus. Winglets are an optional extra. A version with a narrow fuselage is called the Discus-2a and the wider fuselage version is called the 2b. The fuselage was specifically designed to be highly crash resistant. In U.S. Air Force service

102-429: A test . The test consists of calcium carbonate plates arranged in a fivefold symmetric pattern. The test of certain species of sand dollar have slits called lunules that can help the animal stay embedded in the sand to stop it from being swept away by an ocean wave. In living individuals, the test is covered by a skin of velvet -textured spines which are covered with very small hairs ( cilia ). Coordinated movements of

153-434: A few different reasons. When a predator is near, certain species of sand dollar larvae will split themselves in half in a process they use to asexually clone themselves when sensing danger. The cloning process can take up to 24 hours and creates larvae that are 2/3 smaller than their original size which can help conceal them from the predator. The larvae of these sand dollars clone themselves when they sense dissolved mucus from

204-616: A five-petaled garden flower . The Caribbean sand dollar or inflated sea biscuit, Clypeaster rosaceus , is thicker in height than most. In Spanish-speaking areas of the Americas, the sand dollar is most often known as galleta de mar (sea cookie ); the translated term is often encountered in English. In the folklore of Georgia in the United States, sand dollars were believed to represent coins lost by mermaids . Sand dollars diverged from

255-629: A general purpose airfoil that finds wide application, and pre–dates the NACA system, is the Clark-Y . Today, airfoils can be designed for specific functions by the use of computer programs. The various terms related to airfoils are defined below: The geometry of the airfoil is described with a variety of terms : The shape of the airfoil is defined using the following geometrical parameters: Some important parameters to describe an airfoil's shape are its camber and its thickness . For example, an airfoil of

306-451: A predatory fish. The larvae exposed to this mucus from the predatory fish respond to the threat by cloning themselves. This process doubles their population and halves their size which allows them to better escape detection by the predatory fish but may make them more vulnerable to attacks from smaller predators like crustaceans. Sand dollars will also clone themselves during normal asexual reproduction. Larvae will undergo this process when food

357-437: A sharp leading edge. All have a sharp trailing edge . The air deflected by an airfoil causes it to generate a lower-pressure "shadow" above and behind itself. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle , so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. In some situations (e.g., inviscid potential flow )

408-421: A subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil chord, and an inner region, around the nose, that asymptotically match each other. As the flow in the outer region is dominated by classical thin airfoil theory, Morris's equations exhibit many components of thin airfoil theory. In thin airfoil theory, the width of the (2D) airfoil is assumed negligible, and

459-401: Is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point of maximum thickness back from the leading edge. Supersonic airfoils are much more angular in shape and can have a very sharp leading edge, which is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness close to

510-511: Is plentiful or temperature conditions are optimal. Cloning may also occur to make use of the tissues that are normally lost during metamorphosis. The flattened test of the sand dollar allows it to burrow into the sand and remain hidden from sight from potential predators. Predators of the sand dollar are the fish species cod, flounder, sheepshead and haddock. These fish will prey on sand dollars even through their tough exterior. Sand dollars have spines on their bodies that help them to move around

561-401: Is the position at which the pitching moment M ′ does not vary with a change in lift coefficient: ∂ ( C M ′ ) ∂ ( C L ) = 0 . {\displaystyle {\frac {\partial (C_{M'})}{\partial (C_{L})}}=0{\text{.}}} Thin-airfoil theory shows that, in two-dimensional inviscid flow,

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612-495: The Biot–Savart law , the vorticity γ( x ) produces a flow field w ( x ) = 1 2 π ∫ 0 c γ ( x ′ ) x − x ′ d x ′ , {\displaystyle w(x)={\frac {1}{2\pi }}\int _{0}^{c}{\frac {\gamma (x')}{x-x'}}\,dx'{\text{,}}} oriented normal to

663-1287: The change of variables x = c ⋅ 1 + cos ⁡ ( θ ) 2 , {\displaystyle x=c\cdot {\frac {1+\cos(\theta )}{2}},} and then expanding both dy ⁄ dx and γ( x ) as a nondimensionalized Fourier series in θ with a modified lead term: d y d x = A 0 + A 1 cos ⁡ ( θ ) + A 2 cos ⁡ ( 2 θ ) + … γ ( x ) = 2 ( α + A 0 ) ( sin ⁡ θ 1 + cos ⁡ θ ) + 2 A 1 sin ⁡ ( θ ) + 2 A 2 sin ⁡ ( 2 θ ) + … . {\displaystyle {\begin{aligned}&{\frac {dy}{dx}}=A_{0}+A_{1}\cos(\theta )+A_{2}\cos(2\theta )+\dots \\&\gamma (x)=2(\alpha +A_{0})\left({\frac {\sin \theta }{1+\cos \theta }}\right)+2A_{1}\sin(\theta )+2A_{2}\sin(2\theta )+\dots {\text{.}}\end{aligned}}} The resulting lift and moment depend on only

714-648: The convolution equation ( α − d y d x ) V = − w ( x ) = − 1 2 π ∫ 0 c γ ( x ′ ) x − x ′ d x ′ , {\displaystyle \left(\alpha -{\frac {dy}{dx}}\right)V=-w(x)=-{\frac {1}{2\pi }}\int _{0}^{c}{\frac {\gamma (x')}{x-x'}}\,dx'{\text{,}}} which uniquely determines it in terms of known quantities. An explicit solution can be obtained through first

765-406: The endoskeleton through which podia for gas exchange project from the body. The mouth of the sand dollar is located on the bottom of its body at the center of the petal-like pattern. Unlike other urchins, the bodies of sand dollars also display secondary front-to-back bilateral symmetry with no morphological distinguishing features between males and females. The anus of sand dollars is located at

816-411: The trailing edge angle . The slope is greatest if the angle is zero; and decreases as the angle increases. For a wing of finite span, the aspect ratio of the wing also significantly influences the slope of the curve. As aspect ratio decreases, the slope also decreases. Thin airfoil theory is a simple theory of airfoils that relates angle of attack to lift for incompressible, inviscid flows . It

867-663: The 1/4 chord point will thus be C M ( 1 / 4 c ) = − π / 4 ( A 1 − A 2 ) . {\displaystyle C_{M}(1/4c)=-\pi /4(A_{1}-A_{2}){\text{.}}} From this it follows that the center of pressure is aft of the 'quarter-chord' point 0.25 c , by Δ x / c = π / 4 ( ( A 1 − A 2 ) / C L ) . {\displaystyle \Delta x/c=\pi /4((A_{1}-A_{2})/C_{L}){\text{.}}} The aerodynamic center

918-463: The 1980s revealed the practicality and usefulness of laminar flow wing designs and opened the way for laminar-flow applications on modern practical aircraft surfaces, from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic designs. Schemes have been devised to define airfoils – an example is the NACA system . Various airfoil generation systems are also used. An example of

969-685: The Discus-2b is known as the TG-15B . The Discus-2 has also been successful though the competition from the Rolladen-Schneider LS8 and the Alexander Schleicher ASW 28 has meant that the Discus-2 has not sold in such great numbers as its predecessor, which went unchallenged for many years. A version with an 18-metre span, with the option of smaller wing tips to fly as a Standard Class glider,

1020-409: The NACA 4-digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness. Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are: In two-dimensional flow around a uniform wing of infinite span, the slope of the lift curve is determined primarily by

1071-605: The aerodynamic center is at the quarter-chord position. Sand dollar See text. Sand dollars (also known as sea cookies or snapper biscuits in New Zealand and Brazil , or pansy shells in South Africa ) are species of flat, burrowing sea urchins belonging to the order Clypeasteroida . Some species within the order, not quite as flat, are known as sea biscuits . Sand dollars can also be called "sand cakes" or "cake urchins". The term "sand dollar" derives from

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1122-428: The airfoil at x . Since the airfoil is an impermeable surface , the flow w ( x ) {\displaystyle w(x)} must balance an inverse flow from V . By the small-angle approximation , V is inclined at angle α- dy ⁄ dx relative to the blade at position x , and the normal component is correspondingly (α- dy ⁄ dx ) V . Thus, γ( x ) must satisfy

1173-466: The airfoil generates a circulation around the blade, which can be modeled as a vortex sheet of position-varying strength γ( x ) . The Kutta condition implies that γ( c )=0 , but the strength is singular at the bladefront, with γ( x )∝ 1 ⁄ √ x for x ≈ 0 . If the main flow V has density ρ , then the Kutta–Joukowski theorem gives that

1224-399: The airfoil itself replaced with a 1D blade along its camber line, oriented at the angle of attack α . Let the position along the blade be x , ranging from 0 at the wing's front to c at the trailing edge; the camber of the airfoil, dy ⁄ dx , is assumed sufficiently small that one need not distinguish between x and position relative to the fuselage. The flow across

1275-511: The appearance of the tests (skeletons) of dead individuals after being washed ashore. The test lacks its velvet-like skin of spines and has often been bleached white by sunlight . To beachcombers of the past, this suggested a large, silver coin, such as the old Spanish dollar , which had a diameter of 38–40 mm. Other names for the sand dollar include sand cakes, pansy shells, snapper biscuits, cake urchins, and sea cookies. In South Africa, they are known as pansy shells from their suggestion of

1326-510: The back rather than at the top as in most urchins, with many more bilateral features appearing in some species. These result from the adaptation of sand dollars, in the course of their evolution , from creatures that originally lived their lives on top of the seabed ( epibenthos ) to creatures that burrow beneath it ( endobenthos ). According to World Register of Marine Species : Sand dollars can be found in temperate and tropical zones along all continents. Sand dollars live in waters below

1377-407: The chord line.) Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is: Thin airfoil theory assumes the air is an inviscid fluid so does not account for the stall of the airfoil, which usually occurs at an angle of attack between 10° and 15° for typical airfoils. In the mid-late 2000s, however, a theory predicting the onset of leading-edge stall

1428-403: The design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering. A lift and drag curve obtained in wind tunnel testing is shown on the right. The curve represents an airfoil with a positive camber so some lift is produced at zero angle of attack. With increased angle of attack, lift increases in a roughly linear relation, called the slope of

1479-598: The first few terms of this series. The lift coefficient satisfies C L = 2 π ( α + A 0 + A 1 2 ) = 2 π α + 2 ∫ 0 π d y d x ⋅ ( 1 + cos ⁡ θ ) d θ {\displaystyle C_{L}=2\pi \left(\alpha +A_{0}+{\frac {A_{1}}{2}}\right)=2\pi \alpha +2\int _{0}^{\pi }{{\frac {dy}{dx}}\cdot (1+\cos \theta )\,d\theta }} and

1530-405: The following important properties of airfoils in two-dimensional inviscid flow: As a consequence of (3), the section lift coefficient of a thin symmetric airfoil of infinite wingspan is: (The above expression is also applicable to a cambered airfoil where α {\displaystyle \alpha \!} is the angle of attack measured relative to the zero-lift line instead of

1581-457: The freestream velocity). The lift on an airfoil is primarily the result of its angle of attack . Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge , while those designed for supersonic flight tend to be slimmer with

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1632-791: The laminar flow, making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under certain conditions, insect debris on the wing will cause the loss of small regions of laminar flow as well. Before NASA's research in the 1970s and 1980s the aircraft design community understood from application attempts in the WW II era that laminar flow wing designs were not practical using common manufacturing tolerances and surface imperfections. That belief changed after new manufacturing methods were developed with composite materials (e.g. laminar-flow airfoils developed by Professor Franz Wortmann for use with wings made of fibre-reinforced plastic ). Machined metal methods were also introduced. NASA's research in

1683-594: The leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic speeds. Generally such transonic airfoils and also the supersonic airfoils have a low camber to reduce drag divergence . Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing. Movable high-lift devices, flaps and sometimes slats , are fitted to airfoils on almost every aircraft. A trailing edge flap acts similarly to an aileron; however, it, as opposed to an aileron, can be retracted partially into

1734-433: The lift curve. At about 18 degrees this airfoil stalls , and lift falls off quickly beyond that. The drop in lift can be explained by the action of the upper-surface boundary layer , which separates and greatly thickens over the upper surface at and past the stall angle. The thickened boundary layer's displacement thickness changes the airfoil's effective shape, in particular it reduces its effective camber , which modifies

1785-433: The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta–Joukowski theorem . The wings and stabilizers of fixed-wing aircraft , as well as helicopter rotor blades, are built with airfoil-shaped cross sections. Airfoils are also found in propellers, fans , compressors and turbines . Sails are also airfoils, and

1836-518: The mean low tide line, on or just beneath the surface of sandy and muddy areas. The common sand dollar, Echinarachnius parma , can be found in the Northern Hemisphere from the intertidal zone to the depths of the ocean, while the keyhole sand dollars (three species of the genus Mellita ) can be found on many a wide range of coasts in and around the Caribbean Sea . The spines on

1887-747: The moment coefficient C M = − π 2 ( α + A 0 + A 1 − A 2 2 ) = − π 2 α − ∫ 0 π d y d x ⋅ cos ⁡ ( θ ) ( 1 + cos ⁡ θ ) d θ . {\displaystyle C_{M}=-{\frac {\pi }{2}}\left(\alpha +A_{0}+A_{1}-{\frac {A_{2}}{2}}\right)=-{\frac {\pi }{2}}\alpha -\int _{0}^{\pi }{{\frac {dy}{dx}}\cdot \cos(\theta )(1+\cos \theta )\,d\theta }{\text{.}}} The moment about

1938-478: The ocean floor, in part to their preference for soft bottom areas, which are convenient for their reproduction . The sexes are separate and, as with most echinoids, gametes are released into the water column and go through external fertilization . The nektonic larvae metamorphose through several stages before the skeleton or test begins to form, at which point they become benthic . In 2008, biologists discovered that sand dollar larvae will clone themselves for

1989-523: The other irregular echinoids, namely the cassiduloids , during the early Jurassic , with the first true sand dollar genus, Togocyamus , arising during the Paleocene . Soon after Togocyamus , more modern-looking groups emerged during the Eocene . Sand dollars are small in size, averaging from 80 to 100 mm (3 to 4 inches). As with all members of the order Clypeasteroida, they possess a rigid skeleton called

2040-486: The overall flow field so as to reduce the circulation and the lift. The thicker boundary layer also causes a large increase in pressure drag , so that the overall drag increases sharply near and past the stall point. Airfoil design is a major facet of aerodynamics . Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better suit frequent inverted flight as in an aerobatic airplane. In

2091-404: The region of the ailerons and near a wingtip a symmetric airfoil can be used to increase the range of angles of attack to avoid spin – stall . Thus a large range of angles can be used without boundary layer separation . Subsonic airfoils have a round leading edge, which is naturally insensitive to the angle of attack. The cross section is not strictly circular, however: the radius of curvature

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2142-400: The somewhat flattened topside and underside of the animal allow it to burrow or creep through the sediment when looking for shelter or food. Fine, hair-like cilia cover these tiny spines. Sand dollars usually eat algae and organic matter found along the ocean floor, though some species will tip on their side to catch organic matter floating in ocean currents. Sand dollars frequently gather on

2193-652: The spines enable sand dollars to move across the seabed. The velvety spines of live sand dollars appear in a variety of colors—green, blue, violet, or purple—depending on the species. Individuals which are very recently dead or dying (moribund) are sometimes found on beaches with much of the external morphology still intact. Dead individuals are commonly found with their empty test devoid of all surface material and bleached white by sunlight. The bodies of adult sand dollars, like those of other echinoids , display radial symmetry . The petal-like pattern in sand dollars consists of five paired rows of pores. The pores are perforations in

2244-458: The total lift force F is proportional to ρ V ∫ 0 c γ ( x ) d x {\displaystyle \rho V\int _{0}^{c}\gamma (x)\,dx} and its moment M about the leading edge proportional to ρ V ∫ 0 c x γ ( x ) d x . {\displaystyle \rho V\int _{0}^{c}x\;\gamma (x)\,dx.} From

2295-471: The underwater surfaces of sailboats, such as the centerboard , rudder , and keel , are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils/hydrofoils, common examples being bird wings, the bodies of fish, and the shape of sand dollars . An airfoil-shaped wing can create downforce on an automobile or other motor vehicle, improving traction . When

2346-441: The wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience drag and also an aerodynamic force perpendicular to the wind. This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag. Airfoils are used in

2397-505: The wing if not used. A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the Navier–Stokes equations in the linear regime shows that a negative pressure gradient along the flow has the same effect as reducing the speed. So with the maximum camber in the middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising speed is possible. However, some surface contamination will disrupt

2448-440: The working fluid are called hydrofoils . When oriented at a suitable angle, a solid body moving through a fluid deflects the oncoming fluid (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: lift ( perpendicular to the remote freestream velocity ) and drag ( parallel to

2499-427: Was devised by German mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan . Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for

2550-574: Was launched in 2004 and designated Discus-2c. When fitted with a small sustaining engine (turbo) it is designated Discus-2cT. Data from Schempp-Hirth General characteristics Performance Aircraft of comparable role, configuration, and era Related lists Aerofoil An airfoil ( American English ) or aerofoil ( British English ) is a streamlined body that is capable of generating significantly more lift than drag . Wings, sails and propeller blades are examples of airfoils. Foils of similar function designed with water as

2601-418: Was proposed by Wallace J. Morris II in his doctoral thesis. Morris's subsequent refinements contain the details on the current state of theoretical knowledge on the leading-edge stall phenomenon. Morris's theory predicts the critical angle of attack for leading-edge stall onset as the condition at which a global separation zone is predicted in the solution for the inner flow. Morris's theory demonstrates that

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