A gear train or gear set is a machine element of a mechanical system formed by mounting two or more gears on a frame such that the teeth of the gears engage.
68-416: The Armstrong Siddeley Mamba was a British turboprop engine produced by Armstrong Siddeley in the late 1940s and 1950s, producing around 1,500 effective horsepower (1,100 kW). Armstrong Siddeley gas turbine engines were named after snakes . The Mamba was a compact engine with a 10-stage axial compressor , six combustion chambers and a two-stage power turbine. The epicyclic reduction gearbox
136-400: A Pratt & Whitney Canada PT6 , and an under-speed governor on a Honeywell TPE331 . The turboprop is also distinguished from other kinds of turbine engine in that the fuel control unit is connected to the governor to help dictate power. To make the engine more compact, reverse airflow can be used. On a reverse-flow turboprop engine, the compressor intake is at the aft of the engine, and
204-424: A propelling nozzle . Air enters the intake and is compressed by the compressor. Fuel is then added to the compressed air in the combustor, where the fuel-air mixture then combusts . The hot combustion gases expand through the turbine stages, generating power at the point of exhaust. Some of the power generated by the turbine is used to drive the compressor and electric generator . The gases are then exhausted from
272-701: A Swiss-Mamba SM-1 is displayed at the Flieger-Flab-Museum Dübendorf in Swizterland and another Mamba can be seen at the Aviation Heritage Museum (Western Australia) . Data from Aircraft engines of the World 1957 Related development Related lists Turboprop A turboprop is a turbine engine that drives an aircraft propeller . A turboprop consists of an intake , reduction gearbox , compressor , combustor , turbine , and
340-510: A bombing raid. In 1941, the engine was abandoned due to war, and the factory converted to conventional engine production. The first mention of turboprop engines in the general public press was in the February 1944 issue of the British aviation publication Flight , which included a detailed cutaway drawing of what a possible future turboprop engine could look like. The drawing was very close to what
408-400: A gear train has two gears. The input gear (also known as the drive gear or driver ) transmits power to the output gear (also known as the driven gear ). The input gear will typically be connected to a power source, such as a motor or engine. In such an example, the output of torque and rotational speed from the output (driven) gear depend on the ratio of the dimensions of the two gears or
476-442: A governor, and overspeed governor, and a fuel-topping governor. The governor works in much the same way a reciprocating engine propeller governor works, though a turboprop governor may incorporate beta control valve or beta lift rod for beta operation and is typically located in the 12 o'clock position. There are also other governors that are included in addition depending on the model, such as an overspeed and fuel topping governor on
544-410: A mode typically consisting of zero to negative thrust, is used for all ground operations aside from takeoff. The Beta mode is further broken down into 2 additional modes, Beta for taxi and Beta plus power. Beta for taxi as the name implies is used for taxi operations and consists of all pitch ranges from the lowest alpha range pitch, all the way down to zero pitch, producing very little to zero-thrust and
612-464: A pitch circle radius of 2 in (51 mm), the angular speed ratio R A B {\displaystyle R_{AB}} is 2, which is sometimes written as 2:1. Gear A turns at twice the speed of gear B . For every complete revolution of gear A (360°), gear B makes half a revolution (180°). In addition, consider that in order to mesh smoothly and turn without slipping, these two gears A and B must have compatible teeth. Given
680-581: A small amount of air by a large degree, a low disc loading (thrust per unit disc area) increases the aircraft's energy efficiency , and this reduces the fuel use. Propellers work well until the flight speed of the aircraft is high enough that the airflow past the blade tips reaches the speed of sound. Beyond that speed, the proportion of the power that drives the propeller that is converted to propeller thrust falls dramatically. For this reason turboprop engines are not commonly used on aircraft that fly faster than 0.6–0.7 Mach , with some exceptions such as
748-575: A test-bed not intended for production. It first flew on 20 September 1945. From their experience with the Trent, Rolls-Royce developed the Rolls-Royce Clyde , the first turboprop engine to receive a type certificate for military and civil use, and the Dart , which became one of the most reliable turboprop engines ever built. Dart production continued for more than fifty years. The Dart-powered Vickers Viscount
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#1732837767127816-407: Is called an idler gear. Sometimes, a single idler gear is used to reverse the direction, in which case it may be referred to as a reverse idler . For instance, the typical automobile manual transmission engages reverse gear by means of inserting a reverse idler between two gears. Idler gears can also transmit rotation among distant shafts in situations where it would be impractical to simply make
884-485: Is coupled to the turbine through a reduction gear that converts the high RPM /low torque output to low RPM/high torque. This can be of two primary designs, free-turbine and fixed. A free-turbine turboshaft found on the Pratt & Whitney Canada PT6 , where the gas generator is not connected to the propeller. This allows for propeller strike or similar damage to occur without damaging the gas generator and allowing for only
952-476: Is equal to twice the thickness of a tooth, In the United States, the diametral pitch P {\displaystyle P} is the number of teeth on a gear divided by the pitch diameter; for SI countries, the module m {\displaystyle m} is the reciprocal of this value. For any gear, the relationship between the number of teeth, diametral pitch or module, and pitch diameter
1020-440: Is equivalently determined by the ratio of the number of teeth: In other words, the [angular] speed ratio is inversely proportional to the radius of the pitch circle and the number of teeth of gear A , and directly proportional to the same values for gear B . The gear ratio also determines the transmitted torque. The torque ratio T R A B {\displaystyle {\mathrm {TR} }_{AB}} of
1088-405: Is given by This shows that if the output gear B has more teeth than the input gear A , then the gear train amplifies the input torque. In this case, the gear train is called a speed reducer and since the output gear must have more teeth than the input gear, the speed reducer amplifies the input torque. When the input gear rotates faster than the output gear, then the gear train amplifies
1156-495: Is given by: Since the pitch diameter is related to circular pitch as this means Rearranging, we obtain a relationship between diametral pitch and circular pitch: For a pair of meshing gears, the angular speed ratio , also known as the gear ratio , can be computed from the ratio of the pitch radii or the ratio of the number of teeth on each gear. Define the angular speed ratio R A B {\displaystyle R_{AB}} of two meshed gears A and B as
1224-425: Is not connected directly to either the motor or the output shaft and only transmits power between the input and output gears. There is a third gear (Gear B ) partially shown in the upper-right corner of the photo. Assuming that gear is connected to the machine's output shaft, it is the output or driven gear. Considering only gears A and I , the gear ratio between the idler and the input gear can be calculated as if
1292-407: Is that it can also be used to generate reverse thrust to reduce stopping distance on the runway. Additionally, in the event of an engine failure, the propeller can be feathered , thus minimizing the drag of the non-functioning propeller. While the power turbine may be integral with the gas generator section, many turboprops today feature a free power turbine on a separate coaxial shaft. This enables
1360-424: Is the diameter of a gear's pitch circle, measured through that gear's rotational centerline, and the pitch radius r {\displaystyle r} is the radius of the pitch circle. The distance between the rotational centerlines of two meshing gears is equal to the sum of their respective pitch radii. The circular pitch p {\displaystyle p} is the distance, measured along
1428-399: Is the gear ratio of the gear train, the input torque T A {\displaystyle T_{A}} applied to the input gear A and the output torque T B {\displaystyle T_{B}} on the output gear B are related by the same gear or speed ratio. The torque ratio of a gear train is also known as its mechanical advantage ; as demonstrated,
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#17328377671271496-421: Is typically accessed by moving the power lever to a beta for taxi range. Beta plus power is a reverse range and produces negative thrust, often used for landing on short runways where the aircraft would need to rapidly slow down, as well as backing operations and is accessed by moving the power lever below the beta for taxi range. Due to the pilot not being able to see out of the rear of the aircraft for backing and
1564-616: The P-3 Orion , and the C-130 Hercules military transport aircraft. The first turbine-powered, shaft-driven helicopter was the Kaman K-225 , a development of Charles Kaman 's K-125 synchropter , which used a Boeing T50 turboshaft engine to power it on 11 December 1951. December 1963 saw the first delivery of Pratt & Whitney Canada's PT6 turboprop engine for the then Beechcraft 87, soon to become Beechcraft King Air . 1964 saw
1632-830: The Piper Meridian , Socata TBM , Pilatus PC-12 , Piaggio P.180 Avanti , Beechcraft King Air and Super King Air . In April 2017, there were 14,311 business turboprops in the worldwide fleet. Between 2012 and 2016, the ATSB observed 417 events with turboprop aircraft, 83 per year, over 1.4 million flight hours: 2.2 per 10,000 hours. Three were "high risk" involving engine malfunction and unplanned landing in single‑engine Cessna 208 Caravans , four "medium risk" and 96% "low risk". Two occurrences resulted in minor injuries due to engine malfunction and terrain collision in agricultural aircraft and five accidents involved aerial work: four in agriculture and one in an air ambulance . Jane's All
1700-590: The Tupolev Tu-114 can reach 470 kn (870 km/h; 540 mph). Large military aircraft , like the Tupolev Tu-95 , and civil aircraft , such as the Lockheed L-188 Electra , were also turboprop powered. The Airbus A400M is powered by four Europrop TP400 engines, which are the second most powerful turboprop engines ever produced, after the 11 MW (15,000 hp) Kuznetsov NK-12 . In 2017,
1768-403: The Tupolev Tu-95 . However, propfan engines, which are very similar to turboprop engines, can cruise at flight speeds approaching 0.75 Mach. To maintain propeller efficiency across a wide range of airspeeds, turboprops use constant-speed (variable-pitch) propellers. The blades of a constant-speed propeller increase their pitch as aircraft speed increases. Another benefit of this type of propeller
1836-578: The south-pointing chariot of China. Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. The pitch circle of a given gear is determined by the tangent point contact between two meshing gears; for example, two spur gears mesh together when their pitch circles are tangent, as illustrated. The pitch diameter d {\displaystyle d}
1904-519: The Soviet Union had the technology to create the airframe for a jet-powered strategic bomber comparable to Boeing's B-52 Stratofortress , they instead produced the Tupolev Tu-95 Bear, powered with four Kuznetsov NK-12 turboprops, mated to eight contra-rotating propellers (two per nacelle) with supersonic tip speeds to achieve maximum cruise speeds in excess of 575 mph, faster than many of
1972-837: The UK at the Midland Air Museum , Coventry Airport , Warwickshire , the Royal Air Force Museum Cosford and the East Midlands Aeropark . Another example is to be found at the Hertha Ayrton STEM Centre at Sheffield Hallam University, UK and a Mamba Mk 110 (serial number 654606 - ZP3043, possibly originally installed in a Short Seamew ) is on loan from the Rolls-Royce Heritage Trust to BAE Systems at Farnborough Airport , Hampshire . Overseas,
2040-467: The World's Aircraft . 2005–2006. Reduction gear Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission of rotation from one gear to the next. Features of gears and gear trains include: The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and
2108-420: The additional expansion in the turbine system, the residual energy in the exhaust jet is low. Consequently, the exhaust jet produces about 10% of the total thrust. A higher proportion of the thrust comes from the propeller at low speeds and less at higher speeds. Turboprops have bypass ratios of 50–100, although the propulsion airflow is less clearly defined for propellers than for fans. The propeller
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2176-414: The amount of debris reverse stirs up, manufacturers will often limit the speeds beta plus power may be used and restrict its use on unimproved runways. Feathering of these propellers is performed by the propeller control lever. The constant-speed propeller is distinguished from the reciprocating engine constant-speed propeller by the control system. The turboprop system consists of 3 propeller governors ,
2244-437: The angular rotation of all the gears in the gear train are defined by the angle of the input gear. The input torque T A {\displaystyle T_{A}} acting on the input gear A is transformed by the gear train into the output torque T B {\displaystyle T_{B}} exerted by the output gear B . Let R A B {\displaystyle R_{AB}} be
2312-433: The distant gears larger to bring them together. Not only do larger gears occupy more space, the mass and rotational inertia ( moment of inertia ) of a gear is proportional to the square of its radius. Instead of idler gears, a toothed belt or chain can be used to transmit torque over distance. If a simple gear train has three gears, such that the input gear A meshes with an intermediate gear I which in turn meshes with
2380-419: The drive gear ( A ) must make 1.62 revolutions to turn the output gear ( I ) once. It also means that for every one revolution of the driver ( A ), the output gear ( I ) has made 13 ⁄ 21 = 1 ⁄ 1.62 , or 0.62, revolutions. The larger gear ( I ) turns slower. The third gear in the picture ( B ) has N B = 42 {\displaystyle N_{B}=42} teeth. Now consider
2448-403: The driver and driven gear. If the driver gear moves in the clockwise direction, then the driven gear also moves in the clockwise direction with the help of the idler gear. In the photo, assume the smallest gear (Gear A , in the lower right corner) is connected to the motor, which makes it the drive gear or input gear. The somewhat larger gear in the middle (Gear I ) is called an idler gear. It
2516-407: The exhaust is situated forward, reducing the distance between the turbine and the propeller. Unlike the small-diameter fans used in turbofan engines, the propeller has a large diameter that lets it accelerate a large volume of air. This permits a lower airstream velocity for a given amount of thrust. Since it is more efficient at low speeds to accelerate a large amount of air by a small degree than
2584-493: The first jet aircraft and comparable to jet cruising speeds for most missions. The Bear would serve as their most successful long-range combat and surveillance aircraft and symbol of Soviet power projection through to the end of the 20th century. The USA used turboprop engines with contra-rotating propellers, such as the Allison T40 , on some experimental aircraft during the 1950s. The T40-powered Convair R3Y Tradewind flying-boat
2652-546: The first deliveries of the Garrett AiResearch TPE331 , (now owned by Honeywell Aerospace ) on the Mitsubishi MU-2 , making it the fastest turboprop aircraft for that year. In contrast to turbofans , turboprops are most efficient at flight speeds below 725 km/h (450 mph; 390 knots) because the jet velocity of the propeller (and exhaust) is relatively low. Modern turboprop airliners operate at nearly
2720-458: The future Rolls-Royce Trent would look like. The first British turboprop engine was the Rolls-Royce RB.50 Trent , a converted Derwent II fitted with reduction gear and a Rotol 7 ft 11 in (2.41 m) five-bladed propeller. Two Trents were fitted to Gloster Meteor EE227 — the sole "Trent-Meteor" — which thus became the world's first turboprop-powered aircraft to fly, albeit as
2788-403: The gear ratio and speed ratio of a gear train also give its mechanical advantage. The mechanical advantage M A {\displaystyle \mathrm {MA} } of a pair of meshing gears for which the input gear A has N A {\displaystyle N_{A}} teeth and the output gear B has N B {\displaystyle N_{B}} teeth
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2856-412: The gear ratio for the subset consisting of gears I and B , with the idler gear I serving as the input and third gear B serving as the output. The gear ratio between the idler ( I ) and third gear ( B ) R I B {\displaystyle R_{IB}} is thus or 2:1. The final gear ratio of the compound system is 1.62×2≈3.23. For every 3.23 revolutions of the smallest gear A ,
2924-415: The gear ratios of the two subsets are multiplied: Notice that this gear ratio is exactly the same as for the case when the gears A and B engage directly. The intermediate gear provides spacing but does not affect the gear ratio. For this reason it is called an idler gear. The same gear ratio is obtained for a sequence of idler gears and hence an idler gear is used to provide the same direction to rotate
2992-424: The gear train is defined as the ratio of its output torque to its input torque. Using the principle of virtual work , the gear train's torque ratio is equal to the gear ratio, or speed ratio, of the gear train. Again, assume we have two gears A and B , with subscripts designating each gear and gear A serving as the input gear. For this analysis, consider a gear train that has one degree of freedom, which means
3060-524: The gear train. The speed ratio R A B {\displaystyle R_{AB}} of the gear train can be rearranged to give the magnitude of angular velocity of the output gear in terms of the input gear velocity. Rewriting in terms of a common angular velocity, The principle of virtual work states the input force on gear A and the output force on gear B using applied torques will sum to zero: This can be rearranged to: Since R A B {\displaystyle R_{AB}}
3128-458: The gears will come into contact with every tooth on the other gear before encountering the same tooth again. This results in less wear and longer life of the mechanical parts. A non-hunting gear set is one where the teeth counts are insufficiently prime. In this case, some particular gear teeth will come into contact with particular opposing gear teeth more times than others, resulting in more wear on some teeth than others. The simplest example of
3196-437: The idler gear was the output gear. The input gear A in this two-gear subset has 13 teeth ( N A {\displaystyle N_{A}} ) and the idler gear I has 21 teeth ( N I {\displaystyle N_{I}} ). Therefore, the gear ratio for this subset R A I {\displaystyle R_{AI}} is This is approximately 1.62 or 1.62:1. At this ratio, it means
3264-468: The input torque. Conversely, if the output gear has fewer teeth than the input gear, then the gear train reduces the input torque; in other words, when the input gear rotates slower than the output gear, the gear train reduces the input torque. A hunting gear set is a set of gears where the gear teeth counts are relatively prime on each gear in an interfacing pair. Since the number of teeth on each gear have no common factors , then any tooth on one of
3332-657: The most widespread turboprop airliners in service were the ATR 42 / 72 (950 aircraft), Bombardier Q400 (506), De Havilland Canada Dash 8 -100/200/300 (374), Beechcraft 1900 (328), de Havilland Canada DHC-6 Twin Otter (270), Saab 340 (225). Less widespread and older airliners include the BAe Jetstream 31 , Embraer EMB 120 Brasilia , Fairchild Swearingen Metroliner , Dornier 328 , Saab 2000 , Xian MA60 , MA600 and MA700 , Fokker 27 and 50 . Turboprop business aircraft include
3400-436: The number of teeth N {\displaystyle N} : The thickness t {\displaystyle t} of each tooth, measured through the pitch circle, is equal to the gap between neighboring teeth (also measured through the pitch circle) to ensure the teeth on adjacent gears, cut to the same tooth profile, can mesh without interference. This means the circular pitch p {\displaystyle p}
3468-490: The output gear B , then the pitch circle of the intermediate gear rolls without slipping on both the pitch circles of the input and output gears. This yields the two relations The speed ratio of the overall gear train is obtained by multiplying these two equations for each pair ( A / I and I / B ) to obtain This is because the number of idler gear teeth N I {\displaystyle N_{I}} cancels out when
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#17328377671273536-442: The pitch circle, between one tooth and the corresponding point on an adjacent tooth. The number of teeth N {\displaystyle N} per gear is an integer determined by the pitch circle and circular pitch. The circular pitch p {\displaystyle p} of a gear can be defined as the circumference of the pitch circle using its pitch radius r {\displaystyle r} divided by
3604-485: The power section (turbine and gearbox) to be removed and replaced in such an event, and also allows for less stress on the start during engine ground starts. Whereas a fixed shaft has the gearbox and gas generator connected, such as on the Honeywell TPE331 . The propeller itself is normally a constant-speed (variable pitch) propeller type similar to that used with larger aircraft reciprocating engines , except that
3672-522: The propeller to rotate freely, independent of compressor speed. Alan Arnold Griffith had published a paper on compressor design in 1926. Subsequent work at the Royal Aircraft Establishment investigated axial compressor-based designs that would drive a propeller. From 1929, Frank Whittle began work on centrifugal compressor-based designs that would use all the gas power produced by the engine for jet thrust. The world's first turboprop
3740-403: The propeller-control requirements are very different. Due to the turbine engine's slow response to power inputs, particularly at low speeds, the propeller has a greater range of selected travel in order to make rapid thrust changes, notably for taxi, reverse, and other ground operations. The propeller has 2 modes, Alpha and Beta. Alpha is the mode for all flight operations including takeoff. Beta,
3808-749: The ratio of the magnitude of their respective angular velocities: Here, subscripts are used to designate the gear, so gear A has a radius of r A {\displaystyle r_{A}} and angular velocity of ω A {\displaystyle \omega _{A}} with N A {\displaystyle N_{A}} teeth, which meshes with gear B which has corresponding values for radius r B {\displaystyle r_{B}} , angular velocity ω B {\displaystyle \omega _{B}} , and N B {\displaystyle N_{B}} teeth. When these two gears are meshed and turn without slipping,
3876-421: The ratio of the tooth counts. In a sequence of gears chained together, the ratio depends only on the number of teeth on the first and last gear. The intermediate gears, regardless of their size, do not alter the overall gear ratio of the chain. However, the addition of each intermediate gear reverses the direction of rotation of the final gear. An intermediate gear which does not drive a shaft to perform any work
3944-585: The same speed as small regional jet airliners but burn two-thirds of the fuel per passenger. Compared to piston engines, their greater power-to-weight ratio (which allows for shorter takeoffs) and reliability can offset their higher initial cost, maintenance and fuel consumption. As jet fuel can be easier to obtain than avgas in remote areas, turboprop-powered aircraft like the Cessna Caravan and Quest Kodiak are used as bush airplanes . Turboprop engines are generally used on small subsonic aircraft, but
4012-428: The same tooth and gap widths, they also must have the same circular pitch p {\displaystyle p} , which means This equation can be rearranged to show the ratio of the pitch circle radii of two meshing gears is equal to the ratio of their number of teeth: Since the angular speed ratio R A B {\displaystyle R_{AB}} depends on the ratio of pitch circle radii, it
4080-401: The speed ratio, then by definition Assuming the gears are rigid and there are no losses in the engagement of the gear teeth, then the principle of virtual work can be used to analyze the static equilibrium of the gear train. Because there is a single degree of freedom, the angle θ of the input gear completely determines the angle of the output gear and serves as the generalized coordinate of
4148-415: The turbine. In contrast to a turbojet or turbofan , the engine's exhaust gases do not provide enough power to create significant thrust, since almost all of the engine's power is used to drive the propeller. Exhaust thrust in a turboprop is sacrificed in favor of shaft power, which is obtained by extracting additional power (beyond that necessary to drive the compressor) from turbine expansion. Owing to
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#17328377671274216-462: The velocity v {\displaystyle v} of the tangent point where the two pitch circles come in contact is the same on both gears, and is given by: Rearranging, the ratio of angular velocity magnitudes is the inverse of the ratio of pitch circle radii: Therefore, the angular speed ratio can be determined from the respective pitch radii: For example, if gear A has a pitch circle radius of 1 in (25 mm) and gear B has
4284-708: Was also developed into the form of the Double Mamba , which was used to power the Fairey Gannet anti-submarine aircraft for the Royal Navy . This was essentially two Mambas lying side-by-side and driving contra-rotating propellers separately through a common gearbox. A turbojet version of the Mamba was developed as the Armstrong Siddeley Adder , by removing the reduction gearbox. Surviving Mambas are on display in
4352-557: Was designed by the Hungarian mechanical engineer György Jendrassik . Jendrassik published a turboprop idea in 1928, and on 12 March 1929 he patented his invention. In 1938, he built a small-scale (100 Hp; 74.6 kW) experimental gas turbine. The larger Jendrassik Cs-1 , with a predicted output of 1,000 bhp, was produced and tested at the Ganz Works in Budapest between 1937 and 1941. It
4420-514: Was incorporated in the propeller spinner. Engine starting was by cartridge. The Ministry of Supply designation was ASMa ( A rmstrong S iddeley Ma mba). The ASMa.3 gave 1,475 ehp and the ASMa.6 was rated at 1,770 ehp. A 500-hour test was undertaken in 1948 and the Mamba was the first turboprop engine to power the Douglas DC-3 , when in 1949, a Dakota testbed was converted to take two Mambas. The Mamba
4488-460: Was of axial-flow design with 15 compressor and 7 turbine stages, annular combustion chamber. First run in 1940, combustion problems limited its output to 400 bhp. Two Jendrassik Cs-1s were the engines for the world's first turboprop aircraft – the Varga RMI-1 X/H . This was a Hungarian fighter-bomber of WWII which had one model completed, but before its first flight it was destroyed in
4556-686: Was operated by the U.S. Navy for a short time. The first American turboprop engine was the General Electric XT31 , first used in the experimental Consolidated Vultee XP-81 . The XP-81 first flew in December 1945, the first aircraft to use a combination of turboprop and turbojet power. The technology of Allison's earlier T38 design evolved into the Allison T56 , used to power the Lockheed Electra airliner, its military maritime patrol derivative
4624-593: Was the first turboprop aircraft of any kind to go into production and sold in large numbers. It was also the first four-engined turboprop. Its first flight was on 16 July 1948. The world's first single engined turboprop aircraft was the Armstrong Siddeley Mamba -powered Boulton Paul Balliol , which first flew on 24 March 1948. The Soviet Union built on German World War II turboprop preliminary design work by Junkers Motorenwerke, while BMW, Heinkel-Hirth and Daimler-Benz also worked on projected designs. While
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