Angle of attack
In fluid dynamics, angle of attack is the angle between a reference line on a body and the vector representing the relative motion between the body and the fluid through which it is moving. Angle of attack is the angle between the oncoming flow; this article focuses on the most common application, the angle of attack of a wing or airfoil moving through air. In aerodynamics, angle of attack specifies the angle between the chord line of the wing of a fixed-wing aircraft and the vector representing the relative motion between the aircraft and the atmosphere. Since a wing can have twist, a chord line of the whole wing may not be definable, so an alternate reference line is defined; the chord line of the root of the wing is chosen as the reference line. Another choice is to use a horizontal line on the fuselage as the reference line; some authors do not use an arbitrary chord line but use the zero lift axis where, by definition, zero angle of attack corresponds to zero coefficient of lift. Some British authors have used the term angle of incidence instead of angle of attack.
However, this can lead to confusion with the term riggers' angle of incidence meaning the angle between the chord of an airfoil and some fixed datum in the airplane. The lift coefficient of a fixed-wing aircraft varies with angle of attack. Increasing angle of attack is associated with increasing lift coefficient up to the maximum lift coefficient, after which lift coefficient decreases; as the angle of attack of a fixed-wing aircraft increases, separation of the airflow from the upper surface of the wing becomes more pronounced, leading to a reduction in the rate of increase of the lift coefficient. The figure shows a typical curve for a cambered straight wing. Cambered airfoils are curved such. A symmetrical wing has zero lift at 0 degrees angle of attack; the lift curve is influenced by the wing shape, including its airfoil section and wing planform. A swept wing has a lower, flatter curve with a higher critical angle; the critical angle of attack is the angle of attack. This is called the "stall angle of attack".
Below the critical angle of attack, as the angle of attack decreases, the lift coefficient decreases. Conversely, above the critical angle of attack, as angle of attack increases, the air begins to flow less smoothly over the upper surface of the airfoil and begins to separate from the upper surface. On most airfoil shapes, as the angle of attack increases, the upper surface separation point of the flow moves from the trailing edge towards the leading edge. At the critical angle of attack, upper surface flow is more separated and the airfoil or wing is producing its maximum lift coefficient; as angle of attack increases further, the upper surface flow becomes more separated and the lift coefficient reduces further. Above this critical angle of attack, the aircraft is said to be in a stall. A fixed-wing aircraft by definition is stalled at or above the critical angle of attack rather than at or below a particular airspeed; the airspeed at which the aircraft stalls varies with the weight of the aircraft, the load factor, the center of gravity of the aircraft and other factors.
However the aircraft always stalls at the same critical angle of attack. The critical or stalling angle of attack is around 15° - 20° for many airfoils; some aircraft are equipped with a built-in flight computer that automatically prevents the aircraft from increasing the angle of attack any further when a maximum angle of attack is reached, regardless of pilot input. This is called the'angle of attack limiter' or'alpha limiter'. Modern airliners that have fly-by-wire technology avoid the critical angle of attack by means of software in the computer systems that govern the flight control surfaces. In takeoff and landing operations from short runways, such as Naval Aircraft Carrier operations and STOL back country flying, aircraft may be equipped with angle of attack or Lift Reserve Indicators; these indicators measure the angle of attack or the Potential of Wing Lift directly and help the pilot fly close to the stalling point with greater precision. STOL operations require the aircraft to be able to operate close to the critical angle of attack during landings and at the best angle of climb during takeoffs.
Angle of attack indicators are used by pilots for maximum performance during these maneuvers since airspeed information is only indirectly related to stall behaviour. Some military aircraft are able to achieve controlled flight at high angles of attack, but at the cost of massive induced drag; this provides the aircraft with great agility. A famous military example is sometimes thought to be Pugachev's Cobra. Although the aircraft experiences high angles of attack throughout the maneuver, the aircraft is not capable of either aerodynamic directional control or maintaining level flight until the maneuver ends; the Cobra is an example of supermaneuvering as the aircraft's wings are well beyond the critical angle of attack for most of the maneuver. Additional aerodynamic surfaces known as "high-lift devices" including leading edge wing root extensions allow fighter aircraft much greater flyable'true' alpha, up to over 45°, compared to about 20° for aircraft without these devices; this can be helpful at high altitudes where slight maneuvering may require high angles of attack due to the low density of air in the upper atmosphere as well as at low speed at low altitude where the margin between level flight AoA and stall AoA is reduced.
The high AoA capability of the aircraft provides a buff
An airfoil or aerofoil is the cross-sectional shape of a wing, blade, or sail. An airfoil-shaped body moved through a fluid process, produces an aerodynamic force; the component of this force perpendicular to the direction of motion is called lift. The component parallel to the direction of motion is called drag. Subsonic flight airfoils have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge with a symmetric curvature of upper and lower surfaces. Foils of similar function designed with water as the working fluid are called hydrofoils; the lift on an airfoil is the result of its angle of attack and shape. When oriented at a suitable angle, the airfoil deflects the oncoming air, resulting in a force on the airfoil in the direction opposite to the deflection; this force can be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack; this "turning" of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other.
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. 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. A fixed-wing aircraft's wings and vertical stabilizers are built with airfoil-shaped cross sections, as are helicopter rotor blades. Airfoils are found in propellers, fans and turbines. Sails are airfoils, the underwater surfaces of sailboats, such as the centerboard and keel, are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and many plants and sessile organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of fish, the shape of sand dollars. An airfoil-shaped wing can create downforce on an automobile or other motor vehicle, improving traction.
Any object, such as a flat plate, a building, or the deck of a bridge, with an angle of attack in a moving fluid will generate an aerodynamic force perpendicular to the flow. Airfoils are more efficient lifting shapes, able to generate more lift than sized flat plates, to generate lift with less drag. 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 linear relation, called the slope of the lift curve. At about 18 degrees this airfoil stalls, lift falls off beyond that; the drop in lift can be explained by the action of the upper-surface boundary layer, which separates and 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 the overall flow field so as to reduce the circulation and the lift.
The thicker boundary layer causes a large increase in pressure drag, so that the overall drag increases 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 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, insensitive to the angle of attack; the cross section is not circular, however: the radius of curvature is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This moves the point of maximum thickness back from the leading edge. Supersonic airfoils are much more angular in shape and can have a sharp leading edge, sensitive to angle of attack.
A supercritical airfoil has its maximum thickness close to the leading edge to have a lot of length to shock the supersonic flow back to subsonic speeds. Such transonic airfoils and 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 and sometimes slats, are fitted to airfoils on every aircraft. A trailing edge flap acts to an aileron. 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 the laminar flow. 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 f
An aircraft is a machine, able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. Common examples of aircraft include airplanes, airships and hot air balloons; the human activity that surrounds aircraft is called aviation. The science of aviation, including designing and building aircraft, is called aeronautics. Crewed aircraft are flown by an onboard pilot, but unmanned aerial vehicles may be remotely controlled or self-controlled by onboard computers. Aircraft may be classified by different criteria, such as lift type, aircraft propulsion and others. Flying model craft and stories of manned flight go back many centuries, however the first manned ascent – and safe descent – in modern times took place by larger hot-air balloons developed in the 18th century; each of the two World Wars led to great technical advances. The history of aircraft can be divided into five eras: Pioneers of flight, from the earliest experiments to 1914.
First World War, 1914 to 1918. Aviation between the World Wars, 1918 to 1939. Second World War, 1939 to 1945. Postwar era called the jet age, 1945 to the present day. Aerostats use buoyancy to float in the air in much the same way, they are characterized by one or more large gasbags or canopies, filled with a low-density gas such as helium, hydrogen, or hot air, less dense than the surrounding air. When the weight of this is added to the weight of the aircraft structure, it adds up to the same weight as the air that the craft displaces. Small hot-air balloons called sky lanterns were first invented in ancient China prior to the 3rd century BC and used in cultural celebrations, were only the second type of aircraft to fly, the first being kites which were first invented in ancient China over two thousand years ago. A balloon was any aerostat, while the term airship was used for large, powered aircraft designs – fixed-wing. In 1919 Frederick Handley Page was reported as referring to "ships of the air," with smaller passenger types as "Air yachts."
In the 1930s, large intercontinental flying boats were sometimes referred to as "ships of the air" or "flying-ships". – though none had yet been built. The advent of powered balloons, called dirigible balloons, of rigid hulls allowing a great increase in size, began to change the way these words were used. Huge powered aerostats, characterized by a rigid outer framework and separate aerodynamic skin surrounding the gas bags, were produced, the Zeppelins being the largest and most famous. There were still no fixed-wing aircraft or non-rigid balloons large enough to be called airships, so "airship" came to be synonymous with these aircraft. Several accidents, such as the Hindenburg disaster in 1937, led to the demise of these airships. Nowadays a "balloon" is an unpowered aerostat and an "airship" is a powered one. A powered, steerable aerostat is called a dirigible. Sometimes this term is applied only to non-rigid balloons, sometimes dirigible balloon is regarded as the definition of an airship.
Non-rigid dirigibles are characterized by a moderately aerodynamic gasbag with stabilizing fins at the back. These soon became known as blimps. During the Second World War, this shape was adopted for tethered balloons; the nickname blimp was adopted along with the shape. In modern times, any small dirigible or airship is called a blimp, though a blimp may be unpowered as well as powered. Heavier-than-air aircraft, such as airplanes, must find some way to push air or gas downwards, so that a reaction occurs to push the aircraft upwards; this dynamic movement through the air is the origin of the term aerodyne. There are two ways to produce dynamic upthrust: aerodynamic lift, powered lift in the form of engine thrust. Aerodynamic lift involving wings is the most common, with fixed-wing aircraft being kept in the air by the forward movement of wings, rotorcraft by spinning wing-shaped rotors sometimes called rotary wings. A wing is a flat, horizontal surface shaped in cross-section as an aerofoil. To fly, air must generate lift.
A flexible wing is a wing made of fabric or thin sheet material stretched over a rigid frame. A kite is tethered to the ground and relies on the speed of the wind over its wings, which may be flexible or rigid, fixed, or rotary. With powered lift, the aircraft directs its engine thrust vertically downward. V/STOL aircraft, such as the Harrier Jump Jet and F-35B take off and land vertically using powered lift and transfer to aerodynamic lift in steady flight. A pure rocket is not regarded as an aerodyne, because it does not depend on the air for its lift. Rocket-powered missiles that obtain aerodynamic lift at high speed due to airflow over their bodies are a marginal case; the forerunner of the fixed-wing aircraft is the kite. Whereas a fixed-wing aircraft relies on its forward speed to create airflow over the wings, a kite is tethered to the ground and relies on the wind blowing over its wings to provide lift. Kites were the first kind of aircraft to fly, were invented in China around 500 BC.
Much aerodynamic research was done with kites before test aircraft, wind tunnels, computer modelling programs became available. The first heavier-than-air craft capable of controlled free-flight were gliders. A glider designed by Geo
A glider or sailplane is a type of glider aircraft used in the leisure activity and sport of gliding. This unpowered aircraft uses occurring currents of rising air in the atmosphere to remain airborne. Gliders are aerodynamically streamlined and are capable of gaining altitude and remaining airborne, maintaining forward motion. Gliders benefit from producing the least drag for any given amount of lift, this is best achieved with long, thin wings, a faired narrow cockpit and a slender fuselage. Aircraft with these features are able to soar - climb efficiently in rising air produced by thermals or hills. In still air, gliders can glide long distances at high speed with a minimum loss of height in between. Gliders have either skids or undercarriage. In contrast hang gliders and paragliders use the pilot's feet for the start of the launch and for the landing; these latter types are described in separate articles, though their differences from gliders are covered below. Gliders are launched by winch or aerotow, though other methods: auto tow and bungee, are used.
Some gliders do not soar and are engineless aircraft towed by another aircraft to a desired destination and cast off for landing. Military gliders are single-use only, are abandoned after landing, having served their purpose. Motor gliders are gliders with engines which can be used for extending a flight and in some cases, for take-off; some high-performance motor gliders may have an engine-driven retractable propeller which can be used to sustain flight. Other motor gliders have enough thrust to launch themselves before the engine is retracted and are known as "self-launching" gliders. Another type is the self-launching "touring motor glider", where the pilot can switch the engine on and off in flight without retracting their propellers. Sir George Cayley's gliders achieved brief wing-borne hops from around 1849. In the 1890s, Otto Lilienthal built gliders using weight shift for control. In the early 1900s, the Wright Brothers built gliders using movable surfaces for control. In 1903, they added an engine.
After World War I gliders were first built for sporting purposes in Germany. Germany's strong links to gliding were to a large degree due to post-WWI regulations forbidding the construction and flight of motorised planes in Germany, so the country's aircraft enthusiasts turned to gliders and were encouraged by the German government at flying sites suited to gliding flight like the Wasserkuppe; the sporting use of gliders evolved in the 1930s and is now their main application. As their performance improved, gliders began to be used for cross-country flying and now fly hundreds or thousands of kilometres in a day if the weather is suitable. Early gliders had the pilot sat on a small seat located just ahead of the wing; these were known as "primary gliders" and they were launched from the tops of hills, though they are capable of short hops across the ground while being towed behind a vehicle. To enable gliders to soar more than primary gliders, the designs minimized drag. Gliders now have smooth, narrow fuselages and long, narrow wings with a high aspect ratio and winglets.
The early gliders were made of wood with metal fastenings and control cables. Fuselages made of fabric-covered steel tube were married to wood and fabric wings for lightness and strength. New materials such as carbon-fiber, fiber glass and Kevlar have since been used with computer-aided design to increase performance; the first glider to use glass-fiber extensively was the Akaflieg Stuttgart FS-24 Phönix which first flew in 1957. This material is still used because of its high strength to weight ratio and its ability to give a smooth exterior finish to reduce drag. Drag has been minimized by more aerodynamic shapes and retractable undercarriages. Flaps are fitted to the trailing edges of the wings on some gliders to minimize the drag from the tailplane at all speeds. With each generation of materials and with the improvements in aerodynamics, the performance of gliders has increased. One measure of performance is the glide ratio. A ratio of 30:1 means that in smooth air a glider can travel forward 30 meters while losing only 1 meter of altitude.
Comparing some typical gliders that might be found in the fleet of a gliding club – the Grunau Baby from the 1930s had a glide ratio of just 17:1, the glass-fiber Libelle of the 1960s increased that to 39:1, modern flapped 18 meter gliders such as the ASG29 have a glide ratio of over 50:1. The largest open-class glider, the eta, has a span of 30.9 meters and has a glide ratio over 70:1. Compare this to the Gimli Glider, a Boeing 767 which ran out of fuel mid-flight and was found to have a glide ratio of 12:1, or to the Space Shuttle with a glide ratio of 4.5:1. Due to the critical role that aerodynamic efficiency plays in the performance of a glider, gliders have aerodynamic features found in other aircraft; the wings of a modern racing glider have a specially designed low-drag laminar flow airfoil. After the wings' surfaces have been shaped by a mold to great accuracy, they are highly polished. Vertical winglets at the ends of the wings are computer-designed to decrease drag and improve handling performance.
Special aerodynamic seals are used at the ailerons and elevator to prevent the flow of air through control surface gaps. Turbulator devices in the form of a zig-zag tape or multiple blow holes positioned in a span-wise line along the wing are used to trip laminar flow air into turbulent flow at a desired location on the wing; this flow control prevents the formation of laminar flow bubbles and ensures t
A fluid flowing past the surface of a body exerts a force on it. Lift is the component of this force, perpendicular to the oncoming flow direction, it contrasts with the drag force, the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow. If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a hydrodynamic force. Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, dirigibles and submarines. Planing lift, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats and water-skis. A fluid flowing past the surface of a body exerts a force on it, it makes no difference whether the fluid is flowing past a stationary body or the body is moving through a stationary volume of fluid.
Lift is the component of this force, perpendicular to the oncoming flow direction. Lift is always accompanied by a drag force, the component of the surface force parallel to the flow direction. Lift is associated with the wings of fixed-wing aircraft, although it is more generated by many other streamlined bodies such as propellers, helicopter rotors, racing car wings, maritime sails, wind turbines in air, by sailboat keels, ship's rudders, hydrofoils in water. Lift is exploited by flying and gliding animals by birds and insects, in the plant world by the seeds of certain trees. While the common meaning of the word "lift" assumes that lift opposes weight, lift can be in any direction with respect to gravity, since it is defined with respect to the direction of flow rather than to the direction of gravity; when an aircraft is cruising in straight and level flight, most of the lift opposes gravity. However, when an aircraft is climbing, descending, or banking in a turn the lift is tilted with respect to the vertical.
Lift may act as downforce in some aerobatic manoeuvres, or on the wing on a racing car. Lift may be horizontal, for instance on a sailing ship; the lift discussed in this article is in relation to airfoils, although marine hydrofoils and propellers share the same physical principles and work in the same way, despite differences between air and water such as density and viscosity. An airfoil is a streamlined shape, capable of generating more lift than drag. A flat plate can generate lift, but not as much as a streamlined airfoil, with somewhat higher drag. There are several ways to explain; some are more physically rigorous than others. For example, there are explanations based directly on Newton’s laws of motion and explanations based on Bernoulli’s principle. Either can be used to explain lift. An airfoil generates lift by exerting a downward force on the air. According to Newton's third law, the air must exert an equal and opposite force on the airfoil, lift; the airflow changes direction as it passes the airfoil and follows a path, curved downward.
According to Newton's second law, this change in flow direction requires a downward force applied to the air by the airfoil. Newton's third law requires the air to exert an upward force on the airfoil. In the case of an airplane wing, the wing exerts a downward force on the air and the air exerts an upward force on the wing; the downward turning of the flow is not produced by the lower surface of the airfoil, the air flow above the airfoil accounts for much of the downward-turning action. Bernoulli's principle states that there is a direct mathematical relationship between the pressure of a fluid and the speed of that fluid, so if one knows the speed at all points within the airflow one can calculate the pressure, vice versa. For any airfoil generating lift, there must be a pressure imbalance, i.e. lower average air pressure on the top than on the bottom. Bernoulli's principle states that this pressure difference must be accompanied by a speed difference. Starting with the flow pattern observed in both theory and experiments, the increased flow speed over the upper surface can be explained in terms of streamtube pinching and conservation of mass.
For incompressible flow, the rate of volume flow must be constant within each streamtube since matter is not created or destroyed. If a streamtube becomes narrower, the flow speed must increase in the narrower region to maintain the constant flow rate, to satisfy the principle of conservation of mass; the upper streamtubes constrict as they flow around the airfoil. Conservation of mass says; the lower streamtubes expand and their flowrate slows. From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower; this pressure difference creates a net aerodynamic force. As explained below under a more comprehensive physical explanation, producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions, thus requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle; the simplified explanations given above are therefore incomplete because they define lift in terms of only one o
A rudder is a primary control surface used to steer a ship, submarine, aircraft, or other conveyance that moves through a fluid medium. On an aircraft the rudder is used to counter adverse yaw and p-factor and is not the primary control used to turn the airplane. A rudder operates by redirecting the fluid past the hull or fuselage, thus imparting a turning or yawing motion to the craft. In basic form, a rudder is a flat plane or sheet of material attached with hinges to the craft's stern, tail, or after end. Rudders are shaped so as to minimize hydrodynamic or aerodynamic drag. On simple watercraft, a tiller—essentially, a stick or pole acting as a lever arm—may be attached to the top of the rudder to allow it to be turned by a helmsman. In larger vessels, pushrods, or hydraulics may be used to link rudders to steering wheels. In typical aircraft, the rudder is operated by pedals via mechanical hydraulics. A rudder is "part of the steering apparatus of a boat or ship, fastened outside the hull", denoting all different types of oars and rudders.
More the steering gear of ancient vessels can be classified into side-rudders and stern-mounted rudders, depending on their location on the ship. A third term, steering oar, can denote both types. In a Mediterranean context, side-rudders are more called quarter-rudders as the term designates more the place where the rudder was mounted. Stern-mounted rudders are uniformly suspended at the back of the ship in a central position. Although some classify a steering oar as a rudder, others argue that the steering oar used in ancient Egypt and Rome was not a true rudder and define only the stern-mounted rudder used in ancient Han China as a true rudder; the steering oar has the capacity to interfere with handling of the sails while it was fit more for small vessels on narrow, rapid-water transport. In regards to the ancient Phoenician use of the steering oar without a rudder in the Mediterranean, Leo Block writes: A single sail tends to turn a vessel in an upwind or downwind direction, rudder action is required to steer a straight course.
A steering oar was used at this time. With a single sail, a frequent movement of the steering oar was required to steer a straight course; the second sail, located forward, could be trimmed to offset the turning tendency of the main sail and minimize the need for course corrections by the steering oar, which would have improved sail performance. The steering oar or steering board is an oversized oar or board to control the direction of a ship or other watercraft prior to the invention of the rudder, it is attached to the starboard side in larger vessels, though in smaller ones it is if attached. Rowing oars set aside for steering appeared on large Egyptian vessels long before the time of Menes. In the Old Kingdom as many as five steering oars are found on each side of passenger boats; the tiller, at first a small pin run through the stock of the steering oar, can be traced to the fifth dynasty. Both the tiller and the introduction of an upright steering post abaft reduced the usual number of necessary steering oars to one each side.
Single steering oars put on the stern can be found in a number of tomb models of the time during the Middle Kingdom when tomb reliefs suggests them employed in Nile navigation. The first literary reference appears in the works of the Greek historian Herodotus, who had spent several months in Egypt: "They make one rudder, this is thrust through the keel" meaning the crotch at the end of the keel. In Iran, oars mounted on the side of ships for steering are documented from the 3rd millennium BCE in artwork, wooden models, remnants of actual boats. Roman navigation used sexillie quarter steering oars that went in the Mediterranean through a long period of constant refinement and improvement, so that by Roman times ancient vessels reached extraordinary sizes; the strength of the steering oar lay in its combination of effectiveness and simpleness. Roman quarter steering oar mounting systems survived intact through the medieval period. By the first half of the 1st century AD, steering gear mounted on the stern were quite common in Roman river and harbour craft as proved from reliefs and archaeological finds.
A tomb plaque of Hadrianic age shows a harbour tug boat in Ostia with a long stern-mounted oar for better leverage. The boat featured a spritsail, adding to the mobility of the harbour vessel. Further attested Roman uses of stern-mounted steering oars includes barges under tow, transport ships for wine casks, diverse other ship types; the well-known Zwammerdam find, a large river barge at the mouth of the Rhine, featured a large steering gear mounted on the stern. According to new research, the advanced Nemi ships, the palace barges of emperor Caligula, may have featured 14 m long rudders; the world's oldest known depiction of a sternpost-mounted rudder can be seen on a pottery model of a Chinese junk dating from the 1st century AD during the Han Dynasty, predating their appearance in the West by a thousand years. In China, miniature models of ships t
Aircraft principal axes
An aircraft in flight is free to rotate in three dimensions: yaw, nose left or right about an axis running up and down. The axes are alternatively designated as vertical and longitudinal respectively; these axes rotate relative to the Earth along with the craft. These definitions were analogously applied to spacecraft when the first manned spacecraft were designed in the late 1950s; these rotations are produced by torques about the principal axes. On an aircraft, these are intentionally produced by means of moving control surfaces, which vary the distribution of the net aerodynamic force about the vehicle's center of gravity. Elevators produce pitch, a rudder on the vertical tail produces yaw, ailerons produce roll. On a spacecraft, the moments are produced by a reaction control system consisting of small rocket thrusters used to apply asymmetrical thrust on the vehicle. Normal axis, or yaw axis — an axis drawn from top to bottom, perpendicular to the other two axes. Parallel to the fuselage station.
Transverse axis, lateral axis, or pitch axis — an axis running from the pilot's left to right in piloted aircraft, parallel to the wings of a winged aircraft. Parallel to the buttock line. Longitudinal axis, or roll axis — an axis drawn through the body of the vehicle from tail to nose in the normal direction of flight, or the direction the pilot faces. Parallel to the waterline; these axes are represented by the letters X, Y and Z in order to compare them with some reference frame named x, y, z. This is made in such a way that the X is used for the longitudinal axis, but there are other possibilities to do it; the yaw axis has its origin at the center of gravity and is directed towards the bottom of the aircraft, perpendicular to the wings and to the fuselage reference line. Motion about this axis is called yaw. A positive yawing motion moves the nose of the aircraft to the right; the rudder is the primary control of yaw. The term yaw was applied in sailing, referred to the motion of an unsteady ship rotating about its vertical axis.
Its etymology is uncertain. The pitch axis has its origin at the center of gravity and is directed to the right, parallel to a line drawn from wingtip to wingtip. Motion about this axis is called pitch. A positive pitching motion lowers the tail; the elevators are the primary control of pitch. The roll axis has its origin at the center of gravity and is directed forward, parallel to the fuselage reference line. Motion about this axis is called roll. An angular displacement about this axis is called bank. A positive rolling motion lowers the right wing; the pilot rolls by decreasing it on the other. This changes the bank angle; the ailerons are the primary control of bank. The rudder has a secondary effect on bank; these axes are not the same. They are geometrical symmetry axes, regardless of the mass distribution of the aircraft. In aeronautical and aerospace engineering intrinsic rotations around these axes are called Euler angles, but this conflicts with existing usage elsewhere; the calculus behind them is similar to the Frenet–Serret formulas.
Performing a rotation in an intrinsic reference frame is equivalent to right-multiplying its characteristic matrix by the matrix of the rotation. The first aircraft to demonstrate active control about all three axes was the Wright brothers' 1902 glider. Aerodynamics Aircraft flight control system Euler angles Fixed-wing aircraft Flight control surfaces Flight dynamics Moving frame Panning Six degrees of freedom Screw theory Triad method Yaw Axis Control as a Means of Improving V/STOL Aircraft Performance. 3D fast walking simulation of biped robot by yaw axis moment compensation Flight control system for a hybrid aircraft in the yaw axis