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| {{Image|SR-71 over mtns.jpg|right|250px| SR-71B loaned from the U.S. Air Force for use in high-speed, high-altitude research at the NASA Dryden Flight Research Center, Edwards, California.}} | | {{:{{FeaturedArticleTitle}}}} |
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| The '''[[Lockheed SR-71]]''' (known unofficially as the '''Blackbird''', and by its crews as the '''Habu''' or the '''sled''') was an advanced, long-range, Mach 3 strategic reconnaissance aircraft developed from the Lockheed YF-12A and A-12 aircraft by the Lockheed Skunk Works. The SR-71 line was in service from 1964 to 1998, and it was the world's fastest and highest-flying operational manned aircraft throughout that entire period, an unparalleled achievement in aviation history. The aircraft flew so fast and so high that if the crew detected a surface-to-air missile launch, the standard evasive action was simply to accelerate. Thirteen aircraft are known to have been lost, all from non-combat related reasons.
| | ==Footnotes== |
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| | {{reflist|2}} |
| The SR-71 included many novel and advanced technologies in order to achieve that performance; in particular, due to extensive frictional heating from its high speed, almost everything in the aircraft had to be specially produced; the airframe was built almost entirely of titanium, as operating temperatures were too high for aluminum. It was also one of the first aircraft to be have been built with a reduced radar cross section; however, the aircraft was not completely stealthy, and still had a fairly large radar signature. The chief designer, Kelly Johnson, was the man behind many of its advanced concepts. After his retirement, Ben Rich ran the program.
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| ====History====
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| While the U-2 Dragon Lady reconnaissance aircraft produced immense value when it began to overfly the Soviet Union in 1956, it was accepted that this subsonic, nonstealthy aircraft eventually would be vulnerable to the Soviet air defense network. Indeed, one was shot down in May 1960, ending manned reconnaissance overflights of the Russian landmass. Overhead reconnaissance of the Soviet Union was taken over by satellites, but the SR-71 was already in development.
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| =====Predecessor models=====
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| The A-12 Oxcart, designed for the CIA by Kelly Johnson at the Lockheed Skunk Works, was the precursor of the SR-71. Lockheed used the name "Archangel" for this design, but many documents use Johnson's preferred name for the plane, "the Article." As the design evolved, the internal Lockheed designation went from A-1 to A-12 as configuration changes occurred, such as substantial design changes to reduce the radar cross-section. The first flight took place at Groom Lake, Nevada, on April 25, 1962. It was 'Article 121,' an A-12, but it was equipped with less powerful Pratt & Whitney J75s due to protracted development of the intended Pratt & Whitney J58. The J58s were retrofitted as they became available. The J58s became the standard power plant for all subsequent aircraft in the series (A-12, YF-12, MD-21) as well as the follow-on SR-71 aircraft. Eighteen A-12 aircraft were built in four variations, of which three were YF-12As, prototypes of the planned F-12B interceptor version, and two were the M-21 variant (see below).
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| The Air Force reconnaissance version was originally called the R-12 (see the opening fly page in Paul Crickmore's book ''SR-71, Secret Missions Exposed'', which contains a copy of the original R-12 labeled plan view drawing of the vehicle). However, during the 1964 presidential campaign, Senator Barry Goldwater continually criticized President Lyndon B. Johnson and his administration for falling behind the Soviet Union in the research and development of new weapon systems. Johnson decided to counter this criticism with the public release of the highly classified A-12 program and later the existence of the reconnaissance version.
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| ===== Name and designation =====
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| The USAF had planned to redesignate the A-12 aircraft as the B-71 as the successor to the B-70 Valkyrie, whichhad two test Valkyries flying at Edwards Air Force Base, California. The B-71 would have a nuclear capability of 3 first-generation SRAM's (Short-Range Attack Missiles). The next designation was RS-71 (Reconnaissance-Strike) when the strike capability became an option. However, then USAF Chief of Staff Curtis LeMay preferred the SR designation and wanted the RS-71 to be named SR-71. Before the Blackbird was to be announced by President Johnson on February 29, 1964, LeMay lobbied to modify Johnson's speech to read SR-71 instead of RS-71. The media transcript given to the press at the time still had the earlier RS-71 designation in places, creating the myth that the president had misread the plane's designation.
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| ''[[Lockheed SR-71|.... (read more)]]''
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Latest revision as of 10:19, 11 September 2020
In computational molecular physics and solid state physics, the Born-Oppenheimer approximation is used to separate the quantum mechanical motion of the electrons from the motion of the nuclei. The method relies on the large mass ratio of electrons and nuclei. For instance the lightest nucleus, the hydrogen nucleus, is already 1836 times heavier than an electron. The method is named after Max Born and Robert Oppenheimer[1], who proposed it in 1927.
Rationale
The computation of the energy and wave function of an average-size molecule is a formidable task that is alleviated by the Born-Oppenheimer (BO) approximation.The BO approximation makes it possible to compute the wave function in two less formidable, consecutive, steps. This approximation was proposed in the early days of quantum mechanics by Born and Oppenheimer (1927) and is indispensable in quantum chemistry and ubiquitous in large parts of computational physics.
In the first step of the BO approximation the electronic Schrödinger equation is solved, yielding a wave function depending on electrons only. For benzene this wave function depends on 126 electronic coordinates. During this solution the nuclei are fixed in a certain configuration, very often the equilibrium configuration. If the effects of the quantum mechanical nuclear motion are to be studied, for instance because a vibrational spectrum is required, this electronic computation must be repeated for many different nuclear configurations. The set of electronic energies thus computed becomes a function of the nuclear coordinates. In the second step of the BO approximation this function serves as a potential in a Schrödinger equation containing only the nuclei—for benzene an equation in 36 variables.
The success of the BO approximation is due to the high ratio between nuclear and electronic masses. The approximation is an important tool of quantum chemistry, without it only the lightest molecule, H2, could be handled; all computations of molecular wave functions for larger molecules make use of it. Even in the cases where the BO approximation breaks down, it is used as a point of departure for the computations.
Historical note
The Born-Oppenheimer approximation is named after M. Born and R. Oppenheimer who wrote a paper
[Annalen der Physik, vol. 84, pp. 457-484 (1927)] entitled: Zur Quantentheorie der Molekeln (On the Quantum Theory of Molecules). This paper describes the separation of electronic motion, nuclear vibrations, and molecular rotation. A reader of this paper who expects to find clearly delineated the BO approximation—as it is explained above and in most modern textbooks—will be disappointed. The presentation of the BO approximation is well hidden in Taylor expansions (in terms of internal and external nuclear coordinates) of (i) electronic wave functions, (ii) potential energy surfaces and (iii) nuclear kinetic energy terms. Internal coordinates are the relative positions of the nuclei in the molecular equilibrium and their displacements (vibrations) from equilibrium. External coordinates are the position of the center of mass and the orientation of the molecule. The Taylor expansions complicate the theory tremendously and make the derivations
very hard to follow. Moreover, knowing that the proper separation of vibrations and rotations was not achieved in this work, but only eight years later [by C. Eckart, Physical Review, vol. 46, pp. 383-387 (1935)] (see Eckart conditions), chemists and molecular physicists are not very much motivated to invest much effort into understanding the work by Born and Oppenheimer, however famous it may be. Although the article still collects many citations each year, it is safe to say that it is not read anymore, except maybe by historians of science.