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53-397: The Fenestron differs from a conventional open tail rotor by being integrally housed within the tail boom, and like the conventional tail rotor it replaces, functions to counteract the torque generated by the main rotor . While conventional tail rotors typically have between two and six blades, Fenestrons have between seven and eighteen blades; these may have variable angular spacing so that

106-534: A force is allowed to act through a distance, it is doing mechanical work . Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass , the work W can be expressed as W = ∫ θ 1 θ 2 τ   d θ , {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta ,} where τ

159-753: A Fenestron for their Guimbal Cabri G2 , a compact reciprocating engine-powered rotorcraft. Chinese Harbin Aircraft Industry Group use Fenestron in Z-19 reconnaissance/attack helicopter. American Bell Textron in Bell 360 Invictus proposed helicopter design intended to meet the United States Army requirement for a Future Attack Reconnaissance Aircraft . The Fenestron's disadvantages are those common to all ducted fans when compared to propellers. They include: Torque In physics and mechanics , torque

212-480: A MoU with Small Industries Development Bank of India (SIDBI) to finance civil helicopter purchases in India. Historical emblems of the company: Some of the helicopters were renamed in 2015, resembling Airbus airplane naming. When the division changed its name from Eurocopter Group to Airbus Helicopters in 2014 the trade names of the products were changed (applied by 1 January 2016) to reflect this. Suffixes, as well as

265-430: A body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque, which is applied by the screwdriver rotating around its axis . A force of three newtons applied two metres from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum. The term torque (from Latin torquēre , 'to twist')

318-702: A considerable number of light, intermediate, and medium weight helicopters have used the Fenestron as an anti-torque tail rotor. Such implementations can be found on many of Eurocopter's helicopter range, such as the Eurocopter EC120 Colibri , EC130 ECO Star , EC135 (and EC635 , the military version of the EC135), EC145 , the AS365 N/N3 Dauphin (also built as the HH-65 Dolphin , a dedicated variant used by

371-509: A decade with a conventional tail rotor. During the 2010s, multinational helicopter manufacturer Airbus Helicopters (a rebranded version of the Eurocopter entity) developed the Fenestron further for their new H160 , a medium-twin sized rotorcraft; in this revision, the fan duct was intentionally sloped by 12 degrees to achieve improved performance and greater stability when being operated with higher payloads and flown at lower speeds. A Fenestron

424-765: A result of the merger of Aérospatiale and DASA in 2000, which founded Airbus , Eurocopter, now rebranded Airbus Helicopters , became a wholly-owned subsidiary of Airbus. The new aerospace corporation in 2000 also incorporated CASA of Spain, which itself had a history of helicopter-related activities dating back to Talleres Loring , including local assembly of the Bo105 . Today, Airbus Helicopters has four main plants in Europe ( Marignane and La Courneuve in France, and Donauwörth and Kassel in Germany), plus 32 subsidiaries and participants around

477-762: A single point particle is: L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } where p is the particle's linear momentum and r is the position vector from the origin. The time-derivative of this is: d L d t = r × d p d t + d r d t × p . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {p} .} This result can easily be proven by splitting

530-648: Is a general proof for point particles, but it can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass. In physics , rotatum is the derivative of torque with respect to time P = d τ d t , {\displaystyle \mathbf {P} ={\frac {\mathrm {d} {\boldsymbol {\tau }}}{\mathrm {d} t}},} where τ

583-459: Is better to use a term which treats this action as a single definite entity than to use terms like " couple " and " moment ", which suggest more complex ideas. The single notion of a twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage. Today, torque is referred to using different vocabulary depending on geographical location and field of study. This article follows

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636-762: Is determined by the right-hand rule. Therefore any force directed parallel to the particle's position vector does not produce a torque. The magnitude of torque applied to a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols: τ = r × F ⟹ τ = r F ⊥ = r F sin ⁡ θ {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp }=rF\sin \theta } where The SI unit for torque

689-457: Is normally paired with a larger vertical stabiliser unit that also performs the role of compensating for torque; this configuration has the effect of reducing wear on the Fenestron blades and transmission system, which in turn leads to maintenance savings. Furthermore, the adoption of larger diameter units, while posing some engineering challenges, normally increases their efficiency and decreases their power requirements. Advanced implementations of

742-646: Is registered as having been filed during May 1943. At that time, Weir had been participated in development work for the Cierva Autogiro Company , who was the holding company for the patent. In concept, the invention was to function as a viable replacement for the conventional tail rotor arrangement, aiming to produce improvements in both safety and performance upon such equipped rotorcraft. However, this early work in Britain would not directly lead to any released product by Cierva making use of this innovation. Instead,

795-562: Is said to have been suggested by James Thomson and appeared in print in April, 1884. Usage is attested the same year by Silvanus P. Thompson in the first edition of Dynamo-Electric Machinery . Thompson motivates the term as follows: Just as the Newtonian definition of force is that which produces or tends to produce motion (along a line), so torque may be defined as that which produces or tends to produce torsion (around an axis). It

848-425: Is the moment of inertia of the body and ω is its angular speed . Power is the work per unit time , given by P = τ ⋅ ω , {\displaystyle P={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where P is power, τ is torque, ω is the angular velocity , and ⋅ {\displaystyle \cdot } represents

901-405: Is the newton-metre (N⋅m). For more on the units of torque, see § Units . The net torque on a body determines the rate of change of the body's angular momentum , τ = d L d t {\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}} where L is the angular momentum vector and t

954-410: Is the rotational analogue of linear force . It is also referred to as the moment of force (also abbreviated to moment ). The symbol for torque is typically τ {\displaystyle {\boldsymbol {\tau }}} , the lowercase Greek letter tau . When being referred to as moment of force, it is commonly denoted by M . Just as a linear force is a push or a pull applied to

1007-1748: Is time. For the motion of a point particle, L = I ω , {\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},} where I = m r 2 {\textstyle I=mr^{2}} is the moment of inertia and ω is the orbital angular velocity pseudovector. It follows that τ n e t = I 1 ω 1 ˙ e 1 ^ + I 2 ω 2 ˙ e 2 ^ + I 3 ω 3 ˙ e 3 ^ + I 1 ω 1 d e 1 ^ d t + I 2 ω 2 d e 2 ^ d t + I 3 ω 3 d e 3 ^ d t = I ω ˙ + ω × ( I ω ) {\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=I_{1}{\dot {\omega _{1}}}{\hat {\boldsymbol {e_{1}}}}+I_{2}{\dot {\omega _{2}}}{\hat {\boldsymbol {e_{2}}}}+I_{3}{\dot {\omega _{3}}}{\hat {\boldsymbol {e_{3}}}}+I_{1}\omega _{1}{\frac {d{\hat {\boldsymbol {e_{1}}}}}{dt}}+I_{2}\omega _{2}{\frac {d{\hat {\boldsymbol {e_{2}}}}}{dt}}+I_{3}\omega _{3}{\frac {d{\hat {\boldsymbol {e_{3}}}}}{dt}}=I{\boldsymbol {\dot {\omega }}}+{\boldsymbol {\omega }}\times (I{\boldsymbol {\omega }})} using

1060-451: Is torque, and θ 1 and θ 2 represent (respectively) the initial and final angular positions of the body. It follows from the work–energy principle that W also represents the change in the rotational kinetic energy E r of the body, given by E r = 1 2 I ω 2 , {\displaystyle E_{\mathrm {r} }={\tfrac {1}{2}}I\omega ^{2},} where I

1113-814: Is torque. This word is derived from the Latin word rotātus meaning 'to rotate', but the term rotatum is not universally recognized but is commonly used. There is not a universally accepted lexicon to indicate the successive derivatives of rotatum, even if sometimes various proposals have been made. Using the cross product definition of torque, an alternative expression for rotatum is: P = r × d F d t + d r d t × F . {\displaystyle \mathbf {P} =\mathbf {r} \times {\frac {\mathrm {d} \mathbf {F} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {F} .} Because

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1166-506: Is valid for any type of trajectory. In some simple cases like a rotating disc, where only the moment of inertia on rotating axis is, the rotational Newton's second law can be τ = I α {\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}} where α = ω ˙ {\displaystyle {\boldsymbol {\alpha }}={\dot {\boldsymbol {\omega }}}} . The definition of angular momentum for

1219-624: Is zero because velocity and momentum are parallel, so the second term vanishes. Therefore, torque on a particle is equal to the first derivative of its angular momentum with respect to time. If multiple forces are applied, according Newton's second law it follows that d L d t = r × F n e t = τ n e t . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} _{\mathrm {net} }={\boldsymbol {\tau }}_{\mathrm {net} }.} This

1272-670: The United States Coast Guard , and the license-built Harbin Z-9 ), and the enlarged EC155 (a wider, heavier and more advanced version of the AS365 N/N3 series). Other than Airbus Helicopters and its predecessors, other companies have also made use of Fenestron anti-torque arrangements. One such rotorcraft was the American Boeing/Sikorsky RAH-66 Comanche , a stealthy aerial reconnaissance helicopter which

1325-446: The geometrical theorem of the same name) states that the resultant torques due to several forces applied to about a point is equal to the sum of the contributing torques: Eurocopter Airbus Helicopters SAS (formerly Eurocopter S.A. , trading as Eurocopter Group ) is the helicopter manufacturing division of Airbus . It is the largest in the industry in terms of revenues and turbine helicopter deliveries, holding 48% of

1378-421: The lever's fulcrum (the length of the lever arm ) is its torque. Therefore, torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. In three dimensions, the torque is a pseudovector ; for point particles , it is given by the cross product of the displacement vector and

1431-414: The scalar product . Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. The power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied (this is equivalent to the linear case where the power injected by a force depends only on

1484-461: The Fenestron are provisioned with stators and adjustable weights in order to optimise the blades for a reduction in power required and pitch control loads imposed. During the 2010s, Airbus Helicopters stated that it expected the design of the Fenestron to continue to be refined, in order to suit rotorcraft of increasing tonnages and to enable additional innovations to be made in the field. Through multiple mergers from Sud Aviation to Airbus Helicopters,

1537-544: The Fenestron would only be further developed during the 1960s by an unrelated company. The Fenestron was first practically applied by the French aircraft manufacturer Sud Aviation , who had decided to introduce it upon the second experimental model of their in-development SA 340 (the first prototype had been furnished with a conventional anti-torque tail rotor). The SA 340's Fenestron was designed by French aerodynamicist Paul Fabre; unusually, this unit had its advancing blade set at

1590-590: The Puma retained a conventional tail rotor instead. During the 1990s, a third generation Fenestron was produced by Eurocopter (Aérospatiale's multinational successor), equipped with unevenly-spaced blades in order to optimize its noise levels; this unit was first fitted onto the company's EC135 helicopter, and was later incorporated into the designs of the EC130 and the EC145 , the latter of which having original been produced for over

1643-756: The Russian rotorcraft manufacturer Kamov , the Chinese Harbin Aircraft Industry Group , and the Japanese conglomerate Kawasaki Heavy Industries . The concept of the Fenestron was first patented in Great Britain by the Glaswegian engineering company G. & J. Weir Ltd . It was designed by British aeronautical engineer C. G. Pullin as an improvement to helicopters in British patent number 572417, and

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1696-721: The above expression for work, , gives W = ∫ s 1 s 2 F ⋅ d θ × r {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } The expression inside the integral is a scalar triple product F ⋅ d θ × r = r × F ⋅ d θ {\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} =\mathbf {r} \times \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}} , but as per

1749-439: The definition of torque, and since the parameter of integration has been changed from linear displacement to angular displacement, the equation becomes W = ∫ θ 1 θ 2 τ ⋅ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}{\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}} If

1802-590: The definition used in US physics in its usage of the word torque . In the UK and in US mechanical engineering , torque is referred to as moment of force , usually shortened to moment . This terminology can be traced back to at least 1811 in Siméon Denis Poisson 's Traité de mécanique . An English translation of Poisson's work appears in 1842. A force applied perpendicularly to a lever multiplied by its distance from

1855-411: The derivative of a vector is d e i ^ d t = ω × e i ^ {\displaystyle {d{\boldsymbol {\hat {e_{i}}}} \over dt}={\boldsymbol {\omega }}\times {\boldsymbol {\hat {e_{i}}}}} This equation is the rotational analogue of Newton's second law for point particles, and

1908-422: The design and performance of the Fenestron has been improved by Sud Aviation and its successor companies, as well as by other companies. During the late 1970s, Aérospatiale (which Sud Aviation had merged into) launched a second generation all- composite unit; it primarily featured a reversal of the blade's direction of rotation as well as adopting a 20 per cent larger diameter duct for greater efficiency. This unit

1961-569: The first helicopter certified for full flight in icing conditions (the AS332 Super Puma , in 1984); the first production helicopter with a Fly-by-wire control system (the NHIndustries NH90 , first flown in full FBW mode in 2003); the first helicopter to use a Fly-by-light primary control system (an EC135 testbed, first flown in 2003); and the first ever landing of a helicopter on Mount Everest (achieved by an AS350 B3 in 2005). As

2014-454: The force vector. The direction of the torque can be determined by using the right hand grip rule : if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. It follows that the torque vector is perpendicular to both the position and force vectors and defines the plane in which the two vectors lie. The resulting torque vector direction

2067-568: The infinitesimal linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } is related to a corresponding angular displacement d θ {\displaystyle \mathrm {d} {\boldsymbol {\theta }}} and the radius vector r {\displaystyle \mathbf {r} } as d s = d θ × r {\displaystyle \mathrm {d} \mathbf {s} =\mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } Substitution in

2120-586: The instantaneous speed – not on the resulting acceleration, if any). The work done by a variable force acting over a finite linear displacement s {\displaystyle s} is given by integrating the force with respect to an elemental linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } W = ∫ s 1 s 2 F ⋅ d s {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {s} } However,

2173-404: The noise is distributed over different frequencies. By placing the fan within a duct, several distinct advantages over a conventional tail rotor are obtained, such as a reduction in tip vortex losses and the potential for substantial noise reduction, while also shielding both the tail rotor itself from collision damage and ground personnel from the hazard posed by a traditional spinning rotor. It

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2226-528: The rate of change of force is yank Y {\textstyle \mathbf {Y} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , the expression can be further simplified to: P = r × Y + v × F . {\displaystyle \mathbf {P} =\mathbf {r} \times \mathbf {Y} +\mathbf {v} \times \mathbf {F} .} The law of conservation of energy can also be used to understand torque. If

2279-554: The start of 2014. Eurocopter sold 422 helicopters in 2013 and delivered 497 helicopters that year. In 2014, AH built a concrete cylinder for testing helicopters before first flight. In December 2022, it was announced Airbus Helicopters has acquired the Kassel-Calden -headquartered gearbox and component supplier, ZF Luftfahrttechnik from ZF Friedrichshafen for an undisclosed amount. The business will be rebranded as Airbus Helicopters Technik. In May 2024, Airbus Helicopters signed

2332-489: The top in defiance of conventional practice, but this was reasoned to pose little impact upon this particular helicopter. Fitted accordingly, on 12 April 1968, the SA 340 became the first rotorcraft to fly using a Fenestron tail unit. Having been determined to have been satisfactory, this tail unit was retained and was put into production on a refined model of the rotorcraft, which was designated Aérospatiale SA 341 Gazelle . Over time,

2385-875: The torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e., τ ⋅ d θ = | τ | | d θ | cos ⁡ 0 = τ d θ {\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta } giving W = ∫ θ 1 θ 2 τ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \,\mathrm {d} \theta } The principle of moments, also known as Varignon's theorem (not to be confused with

2438-733: The vectors into components and applying the product rule . But because the rate of change of linear momentum is force F {\textstyle \mathbf {F} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , d L d t = r × F + v × p {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} +\mathbf {v} \times \mathbf {p} } The cross product of momentum p {\displaystyle \mathbf {p} } with its associated velocity v {\displaystyle \mathbf {v} }

2491-476: The world, including those in Fort Erie Canada , Brisbane , Australia, Albacete , Spain and Grand Prairie , USA. Since approximately 2006, Eurocopter has been involved in the planning for the proposed pan-European Future Transport Helicopter project. As of 2014, more than 12,000 Airbus Helicopters were in service with over 3,000 customers in around 150 countries. Eurocopter became Airbus Helicopter at

2544-752: The worldwide market share as of 2020. Its head office is located at Marseille Provence Airport in Marignane , France , near Marseille . The main facilities of Airbus Helicopters are at its headquarters in Marignane, France, and in Donauwörth , Germany, with additional production plants in Spain , Brazil , Canada , Australia , Romania , the United Kingdom and the United States . The company, originally named Eurocopter,

2597-621: Was canceled in 2004. Another example is the Sikorsky S-67 Blackhawk , which, in 1974, had a Fenestron for testing purposes used for 29 flight hours. It was removed in August the same year. Ducted fan tail rotors have also been used in the Russian Kamov Ka-60 medium-lift helicopter, and also on the Japanese military's Kawasaki OH-1 Ninja reconnaissance rotorcraft. French light helicopter manufacturer Hélicoptères Guimbal has also used

2650-566: Was first developed for use on an operational rotorcraft by the French company Sud Aviation (now part of Airbus Helicopters), being first adopted upon the Aérospatiale Gazelle . Since then, the company (and its successors) have installed Fenestrons upon many of their helicopters. Other manufacturers have also made limited use of the Fenestron on some of their own products, including the American aerospace corporations Bell Textron and Boeing ,

2703-477: Was fitted onto the Aérospatiale SA 360 Dauphin , along with its more successful AS365 Dauphin model and its derivatives. While further flight experiments were conducted using an even larger Fenestron upon an SA 330 Puma medium lift helicopter around the same time frame, it was concluded that there were practical limits to how large a helicopter such a configuration would be suited to, and production examples of

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2756-493: Was rebranded Airbus Helicopters on 2 January 2014. Airbus Helicopters was formed in 1992 as Eurocopter S.A. , through the merger of the helicopter divisions of Aérospatiale and DASA . The company's heritage traces back to Blériot and Lioré et Olivier in France and to Messerschmitt and Focke-Wulf in Germany. Aérospatiale held 33% of the world's helicopter market share prior to the merger and DASA, 8%; Eurocopter's ownership

2809-567: Was therefore split 70%–30% between the two parent companies to reflect their respective weight in the new entity. Eurocopter and its predecessor companies have established a wide range of helicopter firsts, including the first production turboshaft -powered helicopter (the Aérospatiale Alouette II of 1955); the introduction of the Fenestron shrouded tail rotor (on the Gazelle of 1968);

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