108-603: An airplane ( North American English ) or aeroplane ( British English ), informally plane , is a fixed-wing aircraft that is propelled forward by thrust from a jet engine , propeller , or rocket engine . Airplanes come in a variety of sizes, shapes, and wing configurations . The broad spectrum of uses for airplanes includes recreation , transportation of goods and people, military , and research . Worldwide, commercial aviation transports more than four billion passengers annually on airliners and transports more than 200 billion tonne - kilometers of cargo annually, which
216-417: A basic plane and must then be completed by the builder. Few companies produce planes on a large scale. However, the production of a plane for one company is a process that actually involves dozens, or even hundreds, of other companies and plants, that produce the parts that go into the plane. For example, one company can be responsible for the production of the landing gear, while another one is responsible for
324-682: 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
432-564: A combustion chamber or a solid fuel with oxidizer may burn in the fuel chamber. Whether liquid or solid-fueled, the hot gas is accelerated through a nozzle. In World War II , the Germans deployed the Me 163 Komet rocket-powered aircraft . The first plane to break the sound barrier in level flight was a rocket plane – the Bell X-1 in 1948. The North American X-15 broke many speed and altitude records in
540-736: A first flight. The flight tests continue until the aircraft has fulfilled all the requirements. Then, the governing public agency of aviation of the country authorizes the company to begin production. In the United States, this agency is the Federal Aviation Administration (FAA). In the European Union, European Aviation Safety Agency (EASA); in the United Kingdom it is the Civil Aviation Authority (CAA). In Canada,
648-467: A form of roll control supplied either by wing warping or by ailerons and controlled by its pilot with a joystick and rudder bar. It was an important predecessor of his later Blériot XI Channel -crossing aircraft of the summer of 1909. World War I served as a testbed for the use of the airplane as a weapon. Airplanes demonstrated their potential as mobile observation platforms, then proved themselves to be machines of war capable of causing casualties to
756-412: A frame and made rigid by the lift forces exerted by the airflow over them. Larger aircraft have rigid wing surfaces which provide additional strength. Whether flexible or rigid, most wings have a strong frame to give them their shape and to transfer lift from the wing surface to the rest of the aircraft. The main structural elements are one or more spars running from root to tip, and many ribs running from
864-413: A jet-powered aircraft with a speed of Mach 9.7, nearly 12,100 kilometers per hour (7,500 mph). Whereas jet aircraft use the atmosphere both as a source of oxidant and of mass to accelerate reactively behind the aircraft, rocket aircraft carry the oxidizer on board and accelerate the burned fuel and oxidizer backwards as the sole source of mass for reaction. Liquid fuel and oxidizer may be pumped into
972-548: A long span from side to side but have a short chord (high aspect ratio ). But to be structurally efficient, and hence light weight, a wing must have a short span but still enough area to provide lift (low aspect ratio). North American English North American English is the most generalized variety of the English language as spoken in the United States and Canada . Because of their related histories and cultures, plus
1080-537: A presence in all the major battles of World War II . The first jet aircraft was the German Heinkel He 178 in 1939. The first jet airliner , the de Havilland Comet , was introduced in 1952. The Boeing 707 , the first widely successful commercial jet, was in commercial service for more than 60 years, from 1958 to 2019. First attested in English in the late 19th century (prior to the first sustained powered flight),
1188-416: A propeller creates is determined, in part, by its disk area—the area through which the blades rotate. The limitation on blade speed is the speed of sound ; as when the blade tip exceeds the speed of sound, shock waves decrease propeller efficiency. The rpm required to generate a given tip speed is inversely proportional to the diameter of the propeller. The upper design speed limit for propeller-driven aircraft
SECTION 10
#17328523331491296-476: A shaft through a reduction gearing to the propeller. The propelling nozzle provides a relatively small proportion of the thrust generated by a turboprop. An electric aircraft runs on electric motors with electricity coming from fuel cells , solar cells , ultracapacitors , power beaming , or batteries . Currently, flying electric aircraft are mostly experimental prototypes, including manned and unmanned aerial vehicles , but there are some production models on
1404-426: A single wing plane, a biplane has two stacked one above the other, a tandem wing has two placed one behind the other. When the available engine power increased during the 1920s and 30s and bracing was no longer needed, the unbraced or cantilever monoplane became the most common form of powered type. The wing planform is the shape when seen from above. To be aerodynamically efficient, a wing should be straight with
1512-435: A small and simple engine for high-speed use, such as with missiles. Ramjets require forward motion before they can generate thrust and so are often used in conjunction with other forms of propulsion, or with an external means of achieving sufficient speed. The Lockheed D-21 was a Mach 3+ ramjet-powered reconnaissance drone that was launched from a parent aircraft . A ramjet uses the vehicle's forward motion to force air through
1620-465: A span of 14 m (46 ft). All-up weight was 300 kilograms (660 lb). On 9 October 1890, Ader attempted to fly the Éole . Aviation historians give credit to this effort as a powered take-off and uncontrolled hop of approximately 50 m (160 ft) at a height of approximately 200 mm (7.9 in). Ader's two subsequent machines were not documented to have achieved flight. The American Wright brothers 's flights in 1903 are recognized by
1728-460: A type of rotary aircraft engine, he did not create and fly a powered fixed-wing aircraft. The Frenchman Clement Ader constructed his first of three flying machines in 1886, the Éole . It was a bat-like design run by a lightweight steam engine of his own invention, with four cylinders developing 20 horsepower (15 kW ), driving a four-blade propeller . The engine weighed no more than 4 kilograms per kilowatt (6.6 lb/hp). The wings had
1836-485: Is Mach 0.6. Aircraft designed to go faster than that employ jet engines. Reciprocating engines in aircraft have three main variants, radial , in-line and flat or horizontally opposed engine . The radial engine is a reciprocating type internal combustion engine configuration in which the cylinders "radiate" outward from a central crankcase like the spokes of a wheel and was commonly used for aircraft engines before gas turbine engines became predominant. An inline engine
1944-413: 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
2052-421: Is a reciprocating engine with banks of cylinders, one behind another, rather than rows of cylinders, with each bank having any number of cylinders, but rarely more than six, and may be water-cooled. A flat engine is an internal combustion engine with horizontally-opposed cylinders. A turboprop gas turbine engine consists of an intake, compressor, combustor, turbine, and a propelling nozzle, which provide power from
2160-422: 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
2268-668: 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
SECTION 20
#17328523331492376-468: 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
2484-418: Is less than 1% of the world's cargo movement. Most airplanes are flown by a pilot on board the aircraft, but some are designed to be remotely or computer-controlled such as drones. The Wright brothers invented and flew the first airplane in 1903, recognized as "the first sustained and controlled heavier-than-air powered flight". They built on the works of George Cayley dating from 1799, when he set forth
2592-432: 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
2700-1708: 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
2808-503: 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
2916-903: 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
3024-474: 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
3132-1282: 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
3240-434: 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,
3348-418: 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
Airplane - Misplaced Pages Continue
3456-416: 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:
3564-1141: 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
3672-556: The Fédération Aéronautique Internationale (FAI), the standard-setting and record-keeping body for aeronautics , as "the first sustained and controlled heavier-than-air powered flight". By 1905, the Wright Flyer III was capable of fully controllable, stable flight for substantial periods. The Wright brothers credited Otto Lilienthal as a major inspiration for their decision to pursue manned flight. In 1906,
3780-566: The United States and Canada . In North America, different English dialects of immigrants from England , Scotland , Ireland , and other regions of the British Isles mixed together in the 17th and 18th centuries. These were developed, built upon, and blended together as new waves of immigration, and migration across the North American continent, developed new dialects in new areas, and as these ways of speaking merged with and assimilated to
3888-488: 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 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
3996-538: 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 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
4104-451: The linear and angular momentum of planetary bodies and rigid body dynamics . In orbital mechanics , 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
4212-440: 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
4320-450: The 11th-century English monk Eilmer of Malmesbury ; both experiments injured their pilots. Leonardo da Vinci researched the wing design of birds and designed a man-powered aircraft in his Codex on the Flight of Birds (1502), noting for the first time the distinction between the center of mass and the center of pressure of flying birds. In 1799, George Cayley set forth the concept of
4428-602: The 1920s and 30s, wings could be made heavy and strong enough that bracing was not needed any more. This type of unbraced wing is called a cantilever wing. The number and shape of the wings varies widely on different types. A given wing plane may be full-span or divided by a central fuselage into port (left) and starboard (right) wings. Occasionally, even more wings have been used, with the three-winged triplane achieving some fame in WWI. The four-winged quadruplane and other multiplane designs have had little success. A monoplane has
Airplane - Misplaced Pages Continue
4536-458: The 1960s and pioneered engineering concepts for later aircraft and spacecraft. Military transport aircraft may employ rocket-assisted take offs for short-field situations. Otherwise, rocket aircraft include spaceplanes , like SpaceShipTwo , for travel beyond the Earth's atmosphere and sport aircraft developed for the short-lived Rocket Racing League . Most airplanes are constructed by companies with
4644-902: The American spelling prevails over the British (e.g., tire rather than tyre ). Dialects of American English spoken by United Empire Loyalists who fled the American Revolution (1775–1783) have had a large influence on Canadian English from its early roots. Some terms in North American English are used almost exclusively in Canada and the United States (for example, the terms diaper and gasoline are widely used instead of nappy and petrol ). Although many English speakers from outside North America regard those terms as distinct Americanisms , they are just as common in Canada, mainly due to
4752-711: The Brazilian Alberto Santos-Dumont made what was claimed to be the first airplane flight unassisted by catapult and set the first world record recognized by the Aéro-Club de France by flying 220 meters (720 ft) in less than 22 seconds. This flight was also certified by the FAI. An early aircraft design that brought together the modern monoplane tractor configuration was the Blériot VIII design of 1908. It had movable tail surfaces controlling both yaw and pitch,
4860-614: The Concorde to remove it from service. An aircraft propeller , or airscrew , converts rotary motion from an engine or other power source, into a swirling slipstream which pushes the propeller forwards or backwards. It comprises a rotating power-driven hub, to which are attached two or more radial airfoil -section blades such that the whole assembly rotates about a longitudinal axis. Three types of aviation engines used to power propellers include reciprocating engines (or piston engines), gas turbines , and electric motors . The amount of thrust
4968-590: The Russian Alexander F. Mozhaisky also made some innovative designs. In 1883, the American John J. Montgomery made a controlled flight in a glider. Other aviators who made similar flights at that time were Otto Lilienthal , Percy Pilcher , and Octave Chanute . Sir Hiram Maxim built a craft that weighed 3.5 tons, with a 110-foot (34 m) wingspan that was powered by two 360-horsepower (270 kW) steam engines driving two propellers. In 1894, his machine
5076-484: The air entering the engine must be decelerated to a subsonic speed and then re-accelerated back to supersonic speeds after combustion. An afterburner may be used on combat aircraft to increase power for short periods of time by injecting fuel directly into the hot exhaust gases. Many jet aircraft also use thrust reversers to slow down after landing. A ramjet is a form of jet engine that contains no major moving parts and can be particularly useful in applications requiring
5184-437: The behavior of the aircraft. Computers are used by companies to draw, plan and do initial simulations of the aircraft. Small models and mockups of all or certain parts of the plane are then tested in wind tunnels to verify its aerodynamics. When the design has passed through these processes, the company constructs a limited number of prototypes for testing on the ground. Representatives from an aviation governing agency often make
5292-500: 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
5400-892: The case of international sales, a license from the public agency of aviation or transport of the country where the aircraft is to be used is also necessary. For example, airplanes made by the European company, Airbus , need to be certified by the FAA to be flown in the United States, and airplanes made by U.S.-based Boeing need to be approved by the EASA to be flown in the European Union. Regulations have resulted in reduced noise from aircraft engines in response to increased noise pollution from growth in air traffic over urban areas near airports. Small planes can be designed and constructed by amateurs as homebuilts. Other homebuilt aircraft can be assembled using pre-manufactured kits of parts that can be assembled into
5508-488: 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
SECTION 50
#17328523331495616-406: 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
5724-493: 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
5832-421: 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, 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
5940-454: 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
6048-426: The combustion air, prior to the introduction and ignition of fuel. Rocket motors provide thrust by burning a fuel with an oxidizer and expelling gas through a nozzle. Most jet aircraft use turbofan jet engines, which employ a gas turbine to drive a ducted fan, which accelerates air around the turbine to provide thrust in addition to that which is accelerated through the turbine. The ratio of air passing around
6156-460: 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
6264-477: The concept of the modern airplane (and later built and flew models and successful passenger-carrying gliders ) and the work of German pioneer of human aviation Otto Lilienthal , who, between 1867 and 1896, also studied heavier-than-air flight. Lilienthal's flight attempts in 1891 are seen as the beginning of human flight. Following its limited use in World War I , aircraft technology continued to develop. Airplanes had
6372-503: The concept of the modern wing, his flight attempts in 1891 are seen as the beginning of human flight, the " Lilienthal Normalsegelapparat " is considered to be the first airplane in series production and his work heavily inspired the Wright brothers. In the 1890s, Lawrence Hargrave conducted research on wing structures and developed a box kite that lifted the weight of a man. His box kite designs were widely adopted. Although he also developed
6480-399: 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
6588-623: 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
SECTION 60
#17328523331496696-436: 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
6804-456: The effects of heavy cross-border trade and cultural penetration by the American mass media. The list of divergent words becomes longer if considering regional Canadian dialects, especially as spoken in the Atlantic provinces and parts of Vancouver Island where significant pockets of British culture still remain. There are a considerable number of different accents within the regions of both
6912-479: The end of WWII all-metal aircraft were common. In modern times, increasing use of composite materials has been made. Typical structural parts include: The wings of a fixed-wing aircraft are static planes extending either side of the aircraft. When the aircraft travels forwards, air flows over the wings, which are shaped to create lift. This shape is called an airfoil and is shaped like a bird's wing. Airplanes have flexible wing surfaces which are stretched across
7020-527: The enemy. The earliest known aerial victory with a synchronized machine gun-armed fighter aircraft occurred in 1915, by German Luftstreitkräfte Leutnant Kurt Wintgens . Fighter aces appeared; the greatest (by number of Aerial Combat victories) was Manfred von Richthofen , also known as the Red Baron. Following WWI, aircraft technology continued to develop. Alcock and Brown crossed the Atlantic non-stop for
7128-425: The engine without resorting to turbines or vanes. Fuel is added and ignited, which heats and expands the air to provide thrust. A scramjet is a specialized ramjet that uses internal supersonic airflow to compress, combine with fuel, combust and accelerate the exhaust to provide thrust. The engine operates at supersonic speeds only. The NASA X-43 , an experimental unmanned scramjet, set a world speed record in 2004 for
7236-557: The first time in 1919. The first international commercial flights took place between the United States and Canada in 1919. Airplanes had a presence in all the major battles of World War II . They were an essential component of the military strategies of the period, such as the German Blitzkrieg , The Battle of Britain , and the American and Japanese aircraft carrier campaigns of the Pacific War . The first practical jet aircraft
7344-405: 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
7452-522: The greater American dialect mixture that solidified by the mid-18th century. Below, several major North American English accents are defined by particular characteristics: A majority of North American English (for example, in contrast to British English) includes phonological features that concern consonants, such as rhoticity (full pronunciation of all /r/ sounds), conditioned T-glottalization (with satin pronounced [ˈsæʔn̩] , not [ˈsætn̩] ), T- and D-flapping (with metal and medal pronounced
7560-439: 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
7668-399: The leading (front) to the trailing (rear) edge. Early airplane engines had little power, and lightness was very important. Also, early airfoil sections were very thin, and could not have a strong frame installed within. So, until the 1930s, most wings were too lightweight to have enough strength, and external bracing struts and wires were added. When the available engine power increased during
7776-404: 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
7884-421: The manufacturer or the customer. The structural parts of a fixed-wing aircraft are called the airframe. The parts present can vary according to the aircraft's type and purpose. Early types were usually made of wood with fabric wing surfaces, When engines became available for powered flight around a hundred years ago, their mounts were made of metal. Then as speeds increased more and more parts became metal until by
7992-439: The market. Jet aircraft are propelled by jet engines , which are used because the aerodynamic limitations of propellers do not apply to jet propulsion. These engines are much more powerful than a reciprocating engine for a given size or weight and are comparatively quiet and work well at higher altitude. Variants of the jet engine include the ramjet and the scramjet , which rely on high airspeed and intake geometry to compress
8100-512: 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
8208-402: The modern airplane as a fixed-wing flying machine with separate systems for lift, propulsion, and control. Cayley was building and flying models of fixed-wing aircraft as early as 1803, and he built a successful passenger-carrying glider in 1853. In 1856, Frenchman Jean-Marie Le Bris made the first powered flight, by having his glider "L'Albatros artificiel" pulled by a horse on a beach. Then
8316-463: 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
8424-520: 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
8532-405: The objective of producing them in quantity for customers. The design and planning process, including safety tests, can last up to four years for small turboprops or longer for larger planes. During this process, the objectives and design specifications of the aircraft are established. First the construction company uses drawings and equations, simulations, wind tunnel tests and experience to predict
8640-741: 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
8748-415: 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
8856-461: 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
8964-576: The public agency in charge and authorizing the mass production of aircraft is Transport Canada's Civil Aviation Authority. When a part or component needs to be joined together by welding for virtually any aerospace or defense application, it must meet the most stringent and specific safety regulations and standards. Nadcap , or the National Aerospace and Defense Contractors Accreditation Program sets global requirements for quality, quality management and quality assurance for aerospace engineering. In
9072-401: The radar. The production of such parts is not limited to the same city or country; in the case of large plane manufacturing companies, such parts can come from all over the world. The parts are sent to the main plant of the plane company, where the production line is located. In the case of large planes, production lines dedicated to the assembly of certain parts of the plane can exist, especially
9180-431: 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
9288-429: 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
9396-575: The same), at least one of the LOT vowel mergers (the LOT – PALM merger is completed among virtually all Americans and the LOT – THOUGHT merger among nearly half, while both are completed among virtually all Canadians), and yod-dropping (with tuesday pronounced /ˈtuzdeɪ/ , not /ˈtjuzdeɪ/ ). The last item is more advanced in American English than Canadian English. Center of mass In physics ,
9504-454: The same, as [ˈmɛɾɫ̩] ), L-velarization (with filling pronounced [ˈfɪɫɪŋ] , not [ˈfɪlɪŋ] ), as well as features that concern vowel sounds, such as various vowel mergers before /r/ (so that, Mary , marry , and merry are all commonly pronounced the same ), raising of pre-voiceless /aɪ/ (with price and bright using a higher vowel sound than prize and bride ), the weak vowel merger (with affected and effected often pronounced
9612-401: 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
9720-468: The similarities between the pronunciations (accents), vocabulary, and grammar of American English and Canadian English , the two spoken varieties are often grouped together under a single category. Canadians are generally tolerant of both British and American spellings, with British spellings of certain words (e.g., colour ) preferred in more formal settings and in Canadian print media; for some other words
9828-418: 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
9936-1500: 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
10044-615: 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 }}}
10152-440: 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
10260-600: The term "airplane" is used for powered fixed-wing aircraft. In the United Kingdom and Ireland and most of the Commonwealth , the term "aeroplane" ( / ˈ ɛər ə p l eɪ n / ) is usually applied to these aircraft. Many stories from antiquity involve flight, such as the Greek legend of Icarus and Daedalus , and the Vimana in ancient Indian epics . Around 400 BC in Greece , Archytas
10368-471: 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
10476-406: The turbine to that passing through is called the by-pass ratio . They represent a compromise between turbojet (with no bypass) and turboprop forms of aircraft propulsion (primarily powered with bypass air). Subsonic aircraft, such as airliners, employ high by-pass jet engines for fuel efficiency. Supersonic aircraft , such as jet fighters, use low-bypass turbofans. However at supersonic speeds,
10584-442: 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
10692-430: 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
10800-407: The weights were moved to a single point—their center of mass. In his work On Floating Bodies , Archimedes demonstrated that the orientation of 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
10908-405: The wings and the fuselage. When complete, a plane is rigorously inspected to search for imperfections and defects. After approval by inspectors, the plane is put through a series of flight tests to assure that all systems are working correctly and that the plane handles properly. To meet a particular customer need, the airplane may be customised using components or packages of components provided by
11016-472: The word airplane , like aeroplane , derives from the French aéroplane , which comes from the Greek ἀήρ ( aēr ), "air" and either Latin planus , "level", or Greek πλάνος ( planos ), "wandering". " Aéroplane " originally referred just to the wing, as it is a plane moving through the air. In an example of synecdoche , the word for the wing came to refer to the entire aircraft. In the United States and Canada,
11124-604: 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}} }
11232-405: Was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably steam, said to have flown some 200 m (660 ft). This machine may have been suspended for its flight. Some of the earliest recorded attempts with gliders were those by the 9th-century Andalusian and Arabic-language poet Abbas ibn Firnas and
11340-436: Was studied extensively by the ancient Greek mathematician , physicist , and engineer Archimedes of Syracuse . He worked with simplified assumptions about gravity that amount to 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
11448-518: Was tested with overhead rails to prevent it from rising. The test showed that it had enough lift to take off. The craft was uncontrollable and it is presumed that Maxim realized this because he subsequently abandoned work on it. Between 1867 and 1896, the German pioneer of human aviation Otto Lilienthal developed heavier-than-air flight. He was the first person to make well-documented, repeated, successful gliding flights. Lilienthal's work led to him developing
11556-526: Was the German Heinkel He 178 , which was tested in 1939. In 1943, the Messerschmitt Me 262 , the first operational jet fighter aircraft, went into service in the German Luftwaffe . The first jet airliner , the de Havilland Comet , was introduced in 1952. The Boeing 707 , the first widely successful commercial jet, was in commercial service for more than 50 years, from 1958 to 2010. The Boeing 747
11664-518: Was the world's biggest passenger aircraft from 1970 until it was surpassed by the Airbus A380 in 2005. Supersonic airliner flights , including those of the Concorde , have been limited to over-water flight at supersonic speed because of their sonic boom , which is prohibited over most populated land areas. The high cost of operation per passenger-mile and a deadly crash in 2000 induced the operators of
#148851