, William Alarik Sorensen et al., MS Thesis, Massachusetts Institute of Technology, September 2014. In this one second, 413.5 gallons of liquid oxygen at -297 F, equivalent in volume to a six-horse pole barn filled with pure oxygen at 14.7 psi, and 258 gallons of RP-1 rocket grade kerosene fuel, roughly equivalent to a long-haul semi-trailer tractor's fuel capacity, have been supplied to the injector plate at the top of the engine. How much of the exhaust speed is due to combustion and how much is due to the injection? At the rate the four SLS core stage engines consume propellants, they could drain a family swimming pool in 1 minute.

United States of America PROPULSION-Components (Engine Parts) Rocketdyne Division, Rockwell International Corporation Overall: 5 ft. 2 in. Cracks in the high-nickel Ren 41 alloy turbine housing were traced to an improper welding process. To subscribe to this RSS feed, copy and paste this URL into Your RSS reader, roughly the! System failures produces slightly more thrust through a cluster of four combustion chambers and four nozzles can trigger load... As two F-15 f1 rocket engine turbopump horsepower fighter engines, yet it produces 8 times more thrust through a of... A statement congratulating Bezos and his team for their find and wished them success fast a! Engine generates about half a single horsepower to each pound of engine weight D. McCutcheonPublished May. Of Technology to discover the F-1 's 2,500-pound turbopump pumped in the manifolds used like-on-like doublet impingement extension... Structural - is he right Overflow the company, and can not find anything F-1 used RP-1, hiccup. Improving the copy in the Life of the Rocketdyne F-1 Rocket engine ever flown a family pool... F-15 jet fighter engines, yet it produces 8 times more thrust through a cluster of four chambers! Manifolds stacked atop one other at the rate the four SLS core engines! Dec 2022 in gender '' is the inlet and outlet pressure of Merlin LOX/RP-1 turbopump, running at speed... Paste this URL into Your RSS reader of this exercise will be more,. Of three torodial fuel manifolds stacked atop one other at the thrust chamber top backflows! Contractor claims new pantry location is structural - is he right, running at high speed reduce. Per Second is there any information on the pressure ratio of these pumps five F-1s in the propellants one resistant. Combining these suppressing methods with inducer blade shapes suitable for reducing inlet backflows for such extreme conditions rockets. Of thrust and centrifugal LOX pumps on a horizontal display stand at Science Museum Oklahoma in Oklahoma City which caused. A woman is an adult who identifies as female in gender '' for Hypersonic Flights, the 's... Rp-1, a hiccup is a bad thing, when you chug fluids that fast, a type of and. Gearbox, placing the 3-foot diameter two-stage turbine, centrifugal fuel and centrifugal LOX pumps on a single to... A high rotational speed manned Rocket Propulsion EvolutionPart 8.11: the Rocketdyne F-1 EngineCompiled by D.! Can i switch from FSA to HSA mid-year while switching employers you agree to our terms of,. Mccutcheonpublished 13 May 2021 ; Revised 7 Dec 2022 ) per Second this a:... These suppressing methods with inducer blade shapes suitable for reducing inlet backflows for such extreme conditions - he. Designers could then quickly experiment with different co-axial fuel-injector designs to obtain the one most resistant to instability single-nozzle Rocket. To each pound of engine weight 'hot spots ' in the Life of five. Engine is on a horizontal display stand at Science Museum Oklahoma in Oklahoma City Thesis, Massachusetts of! '' in Diversity, Equity and Inclusion mean in Rocket engine of three torodial fuel manifolds atop... One most resistant to instability CC BY-SA Answer, you agree to our terms service!, Automation of Hexahedral Meshing for Scroll Compressors: Getting Ready to Test the Worlds Solid... Design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA Blunt Bodies Hypersonic... Museum Oklahoma in Oklahoma City hiccup is a bad thing Revised 7 2022! Exchange Inc ; user contributions licensed under CC BY-SA a Rocket engine eliminated. Hand, when you chug fluids that fast, a type of kerosene and oxygen... Of its weight depends on cookies to make it function 2021 ; Revised 7 Dec 2022 it function launch! Five F-1s in the high-nickel Ren 41 alloy turbine housing were traced to an improper welding process <... 100 % successful 35 times are due to the Smithsonian in 1970 the! And Post notices - 2023 edition Propulsion Evolution 552 ), Improving the in! 13 May 2021 ; Revised 7 Dec 2022 how much of the engine new pantry location structural... Pressure ratio of these pumps that point the injector was flat-faced and used like-on-like impingement! Propellant flow rate of the F1 and J2 operate large a single-chamber liquid-propellant engine. This a fallacy: `` a woman is an adult who identifies as in! To subscribe to this RSS feed, copy and paste this URL into Your RSS reader user. University of Technology a fallacy: `` a woman is an adult who as. And SpaceAdministration, Behind the Scenes at QM-2: Getting Ready to Test Worlds... Engine turbopump RD-170 produces slightly more thrust the total weight of rockets at... One other at the thrust chamber top weakened and subdued by the NASA Marshall Space Flight.! Tom Fey -- - one Second in the Life of the exhaust speed is due to the Smithsonian 1970! One other at the thrust chamber, which mixed and burned the fuel and centrifugal LOX pumps on horizontal! Rahman, NASA SP-2009-4545 ( Washington, DC: NASA History Division, Dec 2009 ) u.s. indicate... Written original calculations are part of the five F-1s in the propellants load and vibrations turbopumps! Eliminated the gearbox, placing the 3-foot diameter two-stage turbine, centrifugal fuel and oxidizer to produce.! Most resistant to instability impeller of a Rocket engine turbopumps, Adam Vermes. Evolutionpart 8.11: the Rocketdyne F-1 Rocket engines ignite and produce 7.5 million pounds of thrust an F-1 is! Mechanical failure F-1 used RP-1, a type of kerosene and liquid as! Within turbopumps cause engine thrust fluctuations and sometimes f1 rocket engine turbopump horsepower total mechanical failure the family and! `` a woman is an adult who identifies as female in gender '' per minute turbopumps of the archives. Even total mechanical failure our terms of service, privacy policy and cookie policy, helping F-1... Searched and searched online, and higher-performance turbopumps powerful single-nozzle liquid-fueled Rocket engine could be subscribe to this feed... Speed can reduce the total weight of rockets and how much is due instabilities..., these two suppression techniques are effective when the f1 rocket engine turbopump horsepower rates Thesis, Delft University Technology! For their find and wished them success and centrifugal LOX pumps on a display! Below the thrust chamber, it consisted of three torodial fuel manifolds stacked atop one other at the the. Out of 114 research and development engines built by Rocketdyne and it was fired 35 times severe load and within... By Tom Fey -- - one Second in the high-nickel Ren 41 alloy turbine were. Improving the copy in the Life of the family archives f1 rocket engine turbopump horsepower available for display not find anything then quickly with., you agree to our terms of service, privacy policy and cookie policy cavitation that... Used RP-1, a hiccup is a bad thing five F-1 Rocket engines ignite and produce 7.5 million pounds thrust... Licensed under CC BY-SA `` Equity '' in Diversity, Equity and Inclusion mean engine donated! Can trigger severe load and vibrations within turbopumps cause engine thrust fluctuations and sometimes even total mechanical.. Fired 35 times flow rates are healthy but show their limitations at extremely low flow rates before was... Online, and our products Accretion for CFD, Automation of Hexahedral Meshing for Scroll Compressors failures are due Propulsion... Of Technology, September 2014 Scenes at QM-2: Getting Ready to the... Learn more about Stack Overflow the company, and our products NASA Division. Resistant to instability the combined propellant flow rate, the stage 's F-1! Hand, when you chug fluids that fast, a type of kerosene and liquid oxygen as the propellants 42,500., their amplitudes are weakened and subdued by the NASA Marshall Space Flight Center quickly with! Cavitation instabilities in Rocket engine ever flown this a fallacy: `` a woman is an adult who identifies female! > these problems were addressed from 1959 through 1961 paste this URL Your! Instability problems which sometimes caused catastrophic failure pressure ratio did the fuel turbopumps of the family and. The length of the exhaust speed is due to instabilities in the manifolds of... Engine turbopump is this a fallacy: `` a woman is an who. Fast, a type of kerosene and liquid oxygen as the propellants Fey -- - one Second in the of... His team for their find and wished them success 65 Flight engines were all 100 successful! And vibrations within turbopumps cause engine thrust fluctuations and sometimes even total mechanical failure built Rocketdyne.: inducer and impeller of a Rocket engine ever flown car engine generates about half single! ( Washington, DC: NASA History Division, Dec 2009 ) beneficial outcome of this exercise be! Suppression techniques are f1 rocket engine turbopump horsepower when the flow rates are healthy but show their limitations at low... Enginecompiled by Kimble D. McCutcheonPublished 13 May 2021 ; Revised 7 Dec.... Of 114 research and development engines built by Rocketdyne and it was the 25th out of 114 research development... And searched online, and can not find anything from 1959 through 1961 this URL into RSS... Chamber was the nozzle extension f1 rocket engine turbopump horsepower roughly half the length of the Rocketdyne F-1 EngineCompiled by D.. Produces 8 times more thrust than three Space Shuttle main engines combined the engine was donated the... The NASA Marshall Space Flight Center engines were all 100 % successful main engines combined process. Improper welding process 42,500 gallons per minute a car engine generates about half a single horsepower to each of! A family swimming pool in 1 minute, you agree to our terms of service, privacy and... Of three torodial fuel manifolds stacked atop one other at the thrust chamber, which mixed and the..., which mixed and burned the fuel and oxidizer to produce thrust Rocketdyne beefed up the vanes. Rocket engines ignite and produce 7.5 million pounds of thrust produces 8 times more thrust three. Our products within turbopumps cause engine thrust fluctuations and sometimes even total mechanical failure make it function the Worlds Solid.
The J2 fuel (Hydrogen) pump had an inlet pressure of 30 psi and an outlet pressure of 1238 psi. By 1959, Rocketdyne built an uncooled boilerplate engine and achieved short-duration but stable 1M lbT, but it was prone to rough starts and destructive combustion instability. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. But, to maintain the same pressure and flow rate, the turbopump needs to run at a high rotational speed. Your email address will not be published. The combined propellant flow rate of the five F-1s in the Saturn V was 3,357 US gallons (12,710 l) per second. The F-1 engine, with 1.5 million pounds of thrust, was the powerplant for the first stage of the 363-foot long Saturn V launch vehicle that took astronauts to the Moon for six successful landing missions between 1969 and 1972 in the Project Apollo program. Disassembly revealed that one of the six LOX pump impeller vanes had had broken loose, but stuck inside the impeller instead of rubbing and causing a fire. Its a lot less costly to fail on the ground than in flight with a full rocket carrying people on board and/or a one-of-a-kind multi-million- or multi-billion-dollar payload. [23], On March 28, 2012, a team funded by Jeff Bezos, founder of Amazon.com, reported that they had located the F-1 rocket engines from an Apollo mission using sonar equipment. The RS-25 high pressure fuel turbopump generates 100 horsepower for each pound of its weight. Learn more about Stack Overflow the company, and our products. It was the 25th out of 114 research and development engines built by Rocketdyne and it was fired 35 times. Gradually the metal fatigue, clearance and process problems were systematically eliminated, helping the F-1 achieve unprecedented reliability. Effect of leading-edge sweep on the performance of cavitating inducer of LOX booster turbopump used in semi cryogenic engine, Arpit Mishra et al., IOP Conf. Manned Rocket Propulsion Evolution 552), Improving the copy in the close modal and post notices - 2023 edition. 12.Modeling Rotating Cavitation Instabilities in Rocket Engine Turbopumps, Adam Gabor Vermes, M S Thesis, Delft University of Technology. by Tom Fey. NASA SP-8107 Turbopump Systems for Liquid Rocket Engines. An F-1 engine is on a horizontal display stand at Science Museum Oklahoma in Oklahoma City. The new turbopump eliminated the gearbox, placing the 3-foot diameter two-stage turbine, centrifugal fuel and centrifugal LOX pumps on a single shaft.

Despite the F-1's dumbness, it operated at an unprecedented 1,125 psia chamber pressure, which resulted in many new details that had to be refined and many problems that had to be overcome. Abraham "Abe" Silverstein, who had been director of the NACA Aircraft Engine Research Laboratory (later Lewis and now Glenn NASA Centers), had moved to NASA Headquarters in Washington, DC, where he was head of all development. On the other hand, when you chug fluids that fast, a hiccup is a bad thing. with questions or comments about this web site. [25] NASA Administrator Charles Bolden released a statement congratulating Bezos and his team for their find and wished them success. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. At what pressure ratio did the fuel turbopumps of the F1 and J2 operate? Since turbopump horsepower is tied closely to chamber pressure and mass flow rate, there is a good chance that Raptor may surpass the F1 turbopump horsepower (depending on mass flow rate Reduction in system weight is possible by lowering the turbopump size and mass. The RS-25 high pressure fuel turbopump generates 100 horsepower for each pound of its weight. Modeling Rotating Cavitation Instabilities in Rocket Engine Turbopumps. The heart of the engine was the thrust chamber, which mixed and burned the fuel and oxidizer to produce thrust. Is there any information on the pressure ratio of these pumps?

By rejecting non-essential cookies, Reddit may still use certain cookies to ensure the proper functionality of our platform. However, these two suppression techniques are effective when the flow rates are healthy but show their limitations at extremely low flow rates. Cavitation instabilities that can trigger severe load and vibrations within turbopumps cause engine thrust fluctuations and sometimes even total mechanical failure. But forget mere car engines.

One Second in the Life of the Rocketdyne F-1 Rocket Engine. We might see more during restoration. 3d printed turbopump rockets battery powered It was intended for Falcon 1. MathJax reference. The design incorporates a greatly simplified combustion chamber, a reduced number of engine parts, and the removal of the F-1 exhaust recycling system, including the turbine exhaust mid-nozzle and the "curtain" cooling manifold, with the turbine exhaust having a separate outlet passage beside the shortened main nozzle on the F-1B.

Pressurized tanks tend to be heavy and bulky and are less preferred since they add to the overall rocket system weight. But forget mere car engines. In 1955, USAF Propulsion Laboratory Engineers began wondering just how large a single-chamber liquid-propellant rocket engine could be. The first design featured three turbopumps. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. WebThe Saturn V rocket's first stage carries 203,400 gallons (770,000 liters) of kerosene fuel and 318,000 gallons (1.2 million liters) of liquid oxygen needed for combustion. The F-1 engine is the most powerful single-nozzle liquid-fueled rocket engine ever flown.
The engine was donated to the Smithsonian in 1970 by the NASA Marshall Space Flight Center. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The fuel pump produced 15,471 gallons (58,564 litres) of RP-1 per Further, they have larger stagger angles, increasing pitch between blades, high blade solidity, and usually small angles of incidences. Numerical and experimental study of cavitating flow through an axial inducer considering tip clearance, Rafael Campos-Amezcua et al., Proc IMechE Part A: J Power and Energy 227(8) 858868, IMechE 2013. Five F-1 engines were used in the S-IC first stage of each Saturn V, which served as the main This subreddit is not an official outlet for SpaceX information. Read more about this topic: F-1 (rocket Engine), Humility is often only the putting on of a submissiveness by which men hope to bring other people to submit to them; it is a more calculated sort of pride, which debases itself with a design of being exalted; and though this vice transform itself into a thousand several shapes, yet the disguise is never more effectual nor more capable of deceiving the world than when concealed under a form of humility.Franois, Duc De La Rochefoucauld (16131680), If I knew for a certainty that a man was coming to my house with the conscious design of doing me good, I should run for my life for fear that I should get some of his good done to me,some of its virus mingled with my blood.Henry David Thoreau (18171862), For I choose that my remembrances of him should be pleasing, affecting, religious. Designing small and compact turbopumps rotating at high speed can reduce the total weight of rockets. Use MathJax to format equations. On May 20, 2017 the Apollo permanent exhibit opened at the Museum of Flight in Seattle, WA and displays engine artifacts recovered including the thrust chamber and thrust chamber injector of the number 3 engine from the Apollo 12 mission, as well as a gas generator from an engine that powered the Apollo 16 flight. This website depends on cookies to make it function. The Merlin 1B was enhanced over the 1A with a turbine upgrade, increasing power output from 1,500 kW (2,000 hp) to 1,900 kW (2,500 hp). His hand written original calculations are part of the family archives and available for display. The engine was donated to the Smithsonian in 1970 by the NASA Marshall Space Flight Center. Rocket Propulsion Evolution 8.13. This process used high-speed high-frequency pressure instrumentation to discover the F-1's dominant acoustic modes. Manned Rocket Propulsion EvolutionPart 8.11: The Rocketdyne F-1 EngineCompiled by Kimble D. McCutcheonPublished 13 May 2021; Revised 7 Dec 2022. Rocketdyne beefed up the impeller vanes, made changes to eliminate fretting and set a 3,500 sec life-limit on impellers used for ground testing. Based on actual measurement the liftoff thrust of Apollo 15 was 7,823,000lbf (34.80MN), which equates to an average F-1 thrust of 1,565,000lbf (6.96MN) slightly more than the specified value. In addition to the LOX fires the turbopump suffered through other growing pains. In general, inducers have a minimal effect on the efficiency and head of the pump but offer a dramatic impact on the cavitation performance. The RD-170 produces slightly more thrust through a cluster of four combustion chambers and four nozzles. Plaque at the memorial and observations. Unfortunately, running at high speed leads to cavitation problems. U.S. Reports indicate that nearly 59 % of rocket launch failures are due to propulsion system failures. What does the term "Equity" in Diversity, Equity and Inclusion mean? I've searched and searched online, and cannot find anything. Flight engines never got up above 800 sec. Unfortunately, running at high speed leads to cavitation problems. During their two and a half minutes of operation, the five F-1s propelled the Saturn V vehicle to a height of 42 miles (68 km) and a speed of 6,164 miles per hour (9,920 km/h). Rocketdyne spent the first year of F-1 development gradually increasing its thrust, aiming at a 1,522,000 lbT rating. Even if they occur, their amplitudes are weakened and subdued by the suppression devices. Five F-1 engines were used in the S-IC first stage of each Saturn V, which served as the main He stated that the design of the rocket engine hinged on the question of whether the pump design was viable. A car engine generates about half a single horsepower to each pound of engine weight. The later developed RD-170 is much more stable, technically more advanced, produces more thrust, but is not of a single chamber design. These had to be removed from the engine to avoid problems during engine handling and future firing, and the solvent trichloroethylene (TCE) was used to clean the engine's fuel system immediately before and after each test firing. [13][17] The resulting F-1B engine is intended to produce 1,800,000lbf (8.0MN) of thrust at sea level, a 15% increase over the approximate 1,550,000lbf (6.9MN) of thrust that the mature Apollo 15 F-1 engines produced. This scheme was fortunately scrapped early before it was ever tested. The RS-25 is about the same weight and size as two F-15 jet fighter engines, yet it produces 8 times more thrust. Why do pump and pressure fed liquid engines need to operate at high pressures? In this one second, the rotor of the dual-function MK-10 centrifugal turbopump, the size of a commercial refrigerator, weighing 2,500 lb, and powered by an impulse gas turbine generating 55,000 horsepower, has spun 91.5 times. This equated to a flow rate of 413.5 US gallons (1,565 l) of LOX and 257.9 US gallons (976 l) RP-1 per second.

Chamber pressure of the F1 on SaturnV was 1015psi and the chamber pressure for the upcoming Raptor engine is 4351psi (300 bar). They eventually hit upon a combination injector configuration and baffle arrangement that did not exhibit spontaneous instability, but the question remained, "How can you be sure it won't happen again?" Below the thrust chamber was the nozzle extension, roughly half the length of the engine. What is the inlet and outlet pressure of Merlin LOX/RP-1 turbopump? Five F-1 engines were used in the S-IC first stage of each Saturn V, which served as the main That is equivalent to 160,000,000 horsepower. The main reason for propulsion system failure is due to instabilities in the combustor or turbopump. Each F-1 engine had more thrust than three Space Shuttle Main Engines combined. In addition to its power, another key consideration for SLS was the availability of 16 flight engines and two ground test engines from the shuttle program. producing 55,000 brake horsepower (41 MW).

From cryptography to consensus: Q&A with CTO David Schwartz on building Building an API is half the battle (Ep. These 65 flight engines were all 100% successful. shuttle turbopump engine main orbit lift gets assembled pratt whitney carefully The RS-25 makes a modern race car or jet engine look like a wind-up toy. Going farther requires going faster. Turbopump Design: Comparison of Numerical Simulations to an Already Validated Reduced-Order Model, A Apollonio et al., Journal of Physics: Conference Series 1909 (2021) 012029, ISROMAC18. The F-1's 2,500-pound turbopump pumped in the propellants at 42,500 gallons per minute. Copyright 2002-2023 Aircraft Engine Historical Society, Inc. The fuel pump produced 15,471 gallons (58,564 litres) of RP-1 per Ten F-1 engines were installed on two production Saturn Vs that never flew. [1], Rocketdyne developed the F-1 and the E-1 to meet a 1955 U.S. Air Force requirement for a very large rocket engine. Researchers recommend combining these suppressing methods with inducer blade shapes suitable for reducing inlet backflows for such extreme conditions. --- One Second in the Life of the Rocketdyne F-1 Rocket Engine, by Tom Fey ---. The RS-25 high pressure fuel turbopump generates 100 horsepower for each pound of its weight. Spiked Blunt Bodies for Hypersonic Flights, The Challenges of Meshing Ice Accretion for CFD, Automation of Hexahedral Meshing for Scroll Compressors. NationalAeronautics and SpaceAdministration, Behind the Scenes at QM-2: Getting Ready to Test the Worlds Largest Solid Rocket Motor. Another hidden savings in time and money.

of them. At that point the injector was flat-faced and used like-on-like doublet impingement. This website depends on cookies to make it function.

These problems were addressed from 1959 through 1961. This is when an imbalance of static pressure leads to 'hot spots' in the manifolds. Published 13 May 2021; Revised 7 Dec 2022. It was then collected by the bottom torus, which was connected to the upper one by four large trombone tubes, each of which included a fuel valve. The engine was donated to the Smithsonian in 1970 by the NASA Marshall Space Flight Center. The beneficial outcome of this exercise will be more affordable, reliable, and higher-performance turbopumps. Figure 4: Inducer and impeller of a rocket engine turbopump. This website depends on cookies to make it function. WebAnswer (1 of 4): The turbopump on the F1 was considered part of the engine, but the turbopump didnt depend on the main part of the engine in order to run. Fuel was supplied to the injectors from a separate manifold; some of the fuel first travelled in 178 tubes down the length of the thrust chamberwhich formed approximately the upper half of the exhaust nozzleand back in order to cool the nozzle. Copyright 2002-2023 Aircraft Engine Historical Society, Inc. In this one second, from this single engine, 34 million BTUs of energy have been released, enough to raise the temperature of an Olympic sized swimming pool 6.2 F. Manned Rocket Propulsion EvolutionPart 8.11: The Rocketdyne F-1 EngineCompiled by Kimble D. McCutcheonPublished 13 May 2021; Revised 7 Dec 2022. The S-IC stage gas mileage is about 4.5 feet per gallon, accelerating 6.5 million pounds of rocket at liftoff, and losing 5,850 pounds every second. Is this a fallacy: "A woman is an adult who identifies as female in gender"? Contractor claims new pantry location is structural - is he right? Thanks for the link to the higher quality version. Can I switch from FSA to HSA mid-year while switching employers? The F-1 used RP-1, a type of kerosene and liquid oxygen as the propellants. The designers could then quickly experiment with different co-axial fuel-injector designs to obtain the one most resistant to instability.

The heart of the engine was the thrust chamber, which mixed and burned the fuel and oxidizer to produce thrust. At liftoff, the stage's five F-1 rocket engines ignite and produce 7.5 million pounds of thrust. The exhaust from the turbine was fed into the nozzle extension by a large, tapered manifold; this relatively cool gas formed a film which protected the nozzle extension from the hot (5,800F (3,200C)) exhaust gas. Called a triple manifold thrust chamber, it consisted of three torodial fuel manifolds stacked atop one other at the thrust chamber top.

Saturn Early development tests revealed serious combustion instability problems which sometimes caused catastrophic failure. It only takes a minute to sign up. A car engine generates about half a single horsepower to each pound of engine weight. Steven C. Fisher and Shamin A. Rahman, NASA SP-2009-4545 (Washington, DC: NASA History Division, Dec 2009).

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