text: These CIA Case Officers recruit foreign agents, known as 'assets', to give information to the CIA. There are a wide range of motivations for a person to become an asset; CIA Case Officers are normally sent abroad under a cover identity, most commonly as a diplomat but sometimes under "nonofficial cover" using an assumed identity and having no immunity.


title: Organizational structure of the Central Intelligence Agency

text: One of the CIA's best-known publications, "The World Factbook", is in the public domain and is made freely available without copyright restrictions because it is a work of the United States federal government.


text: CIA's Center for the Study of Intelligence maintains the Agency's historical materials and promotes the study of intelligence as a legitimate and serious discipline. The CIA since 1955 has published an in-house professional journal known as "Studies in Intelligence" that addresses historical, operational, doctrinal, and theoretical aspects of the intelligence profession. The Center also publishes unclassified and declassified "Studies" articles, as well as other books and monographs. A further annotated collection of "Studies" articles was published through Yale University Press under the title "Inside CIA's Private World: Declassified Articles from the Agency's Internal Journal, 1955-1992".


text: In 2002, CIA's Sherman Kent School for Intelligence Analysis began publishing the unclassified "Kent Center Occasional Papers", aiming to offer "an opportunity for intelligence professionals and interested colleagues—in an unofficial and unfettered vehicle—to debate and advance the theory and practice of intelligence analysis."


text: Two offices advise the Director on legality and proper operations. The Office of the General Counsel advises the Director of the Central Intelligence Agency on all legal matters relating to his or her role as CIA director and is the principal source of legal counsel for the CIA.


text: The Office of Inspector General promotes efficiency, effectiveness, and accountability in the administration of Agency activities. The OIG also seeks to prevent and detect fraud, waste, abuse, and mismanagement. The Inspector General is nominated by the President and confirmed by the Senate. The Inspector General, whose activities are independent of those of any other component in the Agency, reports directly to the Director of the Central Intelligence Agency. The OIG conducts inspections, investigations, and audits at Headquarters and in the field, and oversees the Agency-wide grievance-handling system. The OIG provides a semiannual report to the Director of the Central Intelligence Agency which the Director is required by law to submit to the House and Senate Intelligence Committees of Congress within 30 days.


text: In February 2008, the Director of the Central Intelligence Agency, Michael V. Hayden, sent a message to employees that Inspector General John L. Helgerson will accept increased control over the investigations by that office, saying "John has chosen to take a number of steps to heighten the efficiency, assure the quality and increase the transparency of the investigation process". "The Washington Post" suggested this was a response to senior officials who believe the OIG has been too aggressive in looking into counterterrorism programs, including detention programs. The changes were the result of an investigation, begun in April 2007, by one of Hayden's assistants, Robert L. Deitz. There was congressional concern that restrictions on the OIG might have a chilling effect on its effectiveness. Senator Ron Wyden, a Democratic member of the Intelligence Committee, did not disagree with any of Hayden's actions, said the inquiry "should never have happened and can't be allowed to happen again."..."I'm all for the inspector general taking steps that help C.I.A. employees understand his processes, but that can be done without an approach that can threaten the inspector general's independence."


text: The Office of Public Affairs advises the Director of the Central Intelligence Agency on all media, public policy, and employee communications issues relating to his role as CIA director and is the CIA's principal communications focal point for the media, the general public and Agency employees. See CIA influence on public opinion.


text: Talent Acquisition is the office tasked with recruiting. As of July 2018, the Chief of Talent Acquisition is Sheronda Dorsey.


title: New Tube for London

text: The New Tube for London (NTfL) is a type of London Underground train to be built by Siemens as part of its Inspiro family at Siemens's factories in Goole (East Yorkshire) and Vienna, Austria.


title: New Tube for London

text: An initial batch of 94 nine-car trains has been ordered at a cost of £1.5billion to replace 1973 Stock trains on the Piccadilly line, with options for a total of 250 trains allowing replacement of all existing trains on the deep-level Central, Waterloo & City and Bakerloo lines. Trains will enter service from 2025, firstly on the Piccadilly line. Trains will enter service with a train operator but equipped to allow for driverless operation in the future.


title: New Tube for London

text: In the late 1990s, the Labour government initiated a public–private partnership (PPP) to reverse years of underinvestment in London Underground. Under the PPP contracts, two private consortiums (Metronet and Tube Lines) would maintain, renew and upgrade London Underground infrastructure over a period of 30 years from 2003. As part of the upgrade work, new rolling stock was to be ordered.


title: New Tube for London

text: Tube Lines planned to order 93 new Piccadilly line trains, which would enter service by 2014. In January 2007, Tube Lines started the process of ordering new Piccadilly line trains, by querying if train manufacturers would be interested in supplying them. Contract award was anticipated for 2008, and trains would enter service on the Piccadilly line in 2014. Following the delivery of 2009 Stock and S Stock trains in the 2010s, Metronet planned to order 24 new Bakerloo line trains, which would enter service by 2019.


title: New Tube for London

text: However, Metronet collapsed in 2007 after cost overruns, and Transport for London (TfL) bought out the Tube Lines consortium in 2010, formally ending the PPP.


title: New Tube for London

text: Following the collapse of the PPPs, TfL began planning the modernisation of Underground lines not started by the PPP. This project would include the eventual replacement of trains, new signalling and other upgrades to the Piccadilly, Central, Waterloo & City and Bakerloo lines. This would complete the modernisation of Underground lines since the formation of TfL in 2000.


title: New Tube for London

text: According to TfL, existing trains on the Bakerloo and Piccadilly lines are approaching the end of their useful lives, and the 1992 Stock used on the Central and Waterloo & City lines is significantly less reliable than more modern rolling stock.


title: New Tube for London

text: Replacement of these older trains with open gangway rolling stock – similar to the S Stock used on the Underground's subsurface lines – would increase passenger capacity, with new automatic signalling increasing capacity further. Although open gangway train concepts were considered in the late 1990s, the Bombardier 2009 Stock did not utilise this technology. New trains would also have air conditioning, which existing deep-level trains lack.


title: New Tube for London

text: In 2011, Siemens presented "EVO" – a conceptual articulated train with walk-through cars, that would be 30tonnes lighter, consume 17 per cent less energy and have 11 per cent more passenger capacity than existing trains. A mock-up of this Siemens Inspiro design was exhibited at The Crystal between October 2013 and January 2014. Siemens also proposed building the new train in the UK, after being criticised for building the Class 700 Thameslink trains in Germany.


title: New Tube for London

text: New trains would have the potential to be driven automatically without a train operator, which would save operating costs and prevent disruption during strikes. Unattended train operation would require the installation of platform screen doors, a substantial additional cost. The ASLEF and RMT trade unions that represent drivers strongly oppose the introduction of driverless trains, saying it would affect safety.


title: New Tube for London

text: In 2020, a leaked TfL study said that the upgrade work required for unattended train operation - including platform screen doors and a safety walkway in tunnels - would cost around £7billion, concluding that "the financial payback is negative". The study also indicated that automatically driven trains with a member of staff present on board (similar to the Docklands Light Railway) offers "reasonable value for money." However, the Department for Transport has pushed for the introduction of driverless trains as a precondition of any future long term funding deal for TfL.


title: New Tube for London

text: In early 2014, the project was named "New Tube for London" (NTfL) and moved from a feasibility stage to the design and specification stage. A TfL feasibility study showed that new generation trains and re-signalling could increase capacity:


title: New Tube for London

text: Overall, the project is estimated to cost a total of £16billion, with a benefit/cost ratio of 4.2 to 1. The Piccadilly line would be the first to be upgraded, given the age of its rolling stock. Other lines would then be upgraded over a period of around 10 years.


title: New Tube for London

text: In early 2014, TfL invited train manufacturers to make expressions of interest in the "Official Journal of the European Union". TfL also commissioned industrial designers PriestmanGoode to create a conceptual design vision that would be used by the train manufacturers. Unveiled in October 2014 to high acclaim, the design included several features not seen before on the deep level tube, including walk-through carriages and air conditioning.


title: New Tube for London

text: In late 2014, TfL published a shortlist of manufacturers who had expressed an interest in supplying new trains – Alstom, Siemens, Hitachi, CAF and Bombardier. The invitation to tender for the trains was issued in January 2016, with a plan to award the contract in 2016, with trains entering service in 2023. During the tender period, Bombardier and Hitachi formed a joint venture (JV) and CAF chose not to submit a bid. Three bids (Alstom, Siemens, Hitachi/Bombardier JV) were submitted in September 2016. All bidders proposed to construct a UK factory, or use existing UK factories to build the trains.


title: New Tube for London

text: Since TfL could not afford 250 new trains and upgraded signalling, it decided to buy only 94 trains for the Piccadilly line and relegate future train purchases to contract options. In 2019, TfL raised £1billion to buy the Piccadilly line trains by selling and leasing back Class 345 Crossrail trains.


title: New Tube for London

text: In total, 250 trains could be ordered throughout the lifetime of the Deep Tube Upgrade Programme, comprising 100 trains for the Piccadilly line, 40 for the Bakerloo line, 100 for the Central line and 10 for the Waterloo & City line. Future trains would be adapted to meet the requirements of lines, with the potential of active steering of bogies and more/fewer cars per trainset as required.


title: New Tube for London

text: In June 2018, the Siemens Mobility Inspiro design was selected, with 94 trains ordered in a £1.5billion contract. In July 2018, the award was challenged in the High Court by the Hitachi/Bombardier JV. The challenge was unsuccessful; Siemens was awarded the contract in November 2018.


title: New Tube for London

text: Around 50 per cent of the trains will be assembled in a new factory in Goole, East Riding of Yorkshire, with the remainder to be built at an existing Siemens factory in Vienna, Austria while the Goole factory is constructed. In July 2020, Prime Minister Boris Johnson visited the Goole site to mark the start of construction of the factory. Full manufacturing of the trains in Austria was due to commence in August 2021, with first deliveries to London taking place from 2024.


title: New Tube for London

text: Despite the lack of resignalling, the purchase of new trains will still increase the capacity of the Piccadilly line, with 27 trains per hour at peak times by 2027. Trains will enter service with a train operator. However, resignalling of the line could allow for driverless operation in future.


title: New Tube for London

text: Siemens has branded the train "Inspiro London", although some sources have named it "2024 Stock", following the existing naming precedent. , the official name of the train has not been confirmed by TfL.


title: New Tube for London

text: Initially, deliveries were to begin in 2023, with entry into service in 2024. , the delivery schedule had slipped; the trains are expected to enter service on the Piccadilly line in 2025. Improvements to service levels would follow in 2027.


title: Troxler's fading

text: Troxler's fading, also called Troxler fading or the Troxler effect, is an optical illusion affecting visual perception. When one fixates on a particular point for even a short period of time, an unchanging stimulus away from the fixation point will fade away and disappear. Research suggests that at least some portion of the perceptual phenomena associated with Troxler's fading occurs in the brain.


title: Troxler's fading

text: Troxler's fading was first identified by Swiss physician Ignaz Paul Vital Troxler in 1804, who was practicing in Vienna at the time.


title: Troxler's fading

text: Troxler's fading has been attributed to the adaptation of neurons vital for perceiving stimuli in the visual system. It is part of the general principle in sensory systems that unvarying stimuli soon disappear from our awareness. For example, if a small piece of paper is dropped on the inside of one's forearm, it is felt for a short period of time. Soon, however, the sensation fades away. This is because the tactile neurons have adapted and start to ignore the unimportant stimulus. But if one jiggles one's arm up and down, giving varying stimulation, one will continue to feel the paper.


title: Troxler's fading

text: A similar 'sensory fading,' or "filling-in", can be seen of a fixated stimulus when its retinal image is made stationary on the retina (a "stabilized retinal image"). Stabilization can be done in at least three ways.


title: Troxler's fading

text: The Troxler effect is enhanced if the stimulus is small, is of low contrast (or "equiluminant"), or is blurred. The effect is enhanced the further the stimulus is away from the fixation point.


title: Troxler's fading

text: Troxler's fading can occur without any extraordinary stabilization of the retinal image in peripheral vision because the neurons in the visual system beyond the rods and cones have large receptive fields. This means that the small, involuntary eye movements made when fixating on something fail to move the stimulus onto a new cell's receptive field, in effect giving unvarying stimulation. Further experimentation this century by Hsieh and Tse showed that at least some portion of the perceptual fading occurred in the brain, not in the eyes.


title: Spaghetti-tree hoax

text: The spaghetti-tree hoax was a three-minute hoax report broadcast on April Fools' Day 1957 by the BBC current-affairs programme "Panorama", purportedly showing a family in southern Switzerland harvesting spaghetti from the family "spaghetti tree". At the time spaghetti was relatively unknown in the UK, so many British people were unaware that it is made from wheat flour and water; a number of viewers afterwards contacted the BBC for advice on growing their own spaghetti trees. Decades later, CNN called this broadcast "the biggest hoax that any reputable news establishment ever pulled".


title: Spaghetti-tree hoax

text: The news report was produced as an April Fools' Day joke in 1957, and presented a family in the canton of Ticino in southern Switzerland gathering a bumper spaghetti harvest after a mild winter and "virtual disappearance of the spaghetti weevil". Footage of a traditional "Harvest Festival" was aired along with a discussion of the breeding necessary to develop a strain to produce the perfect spaghetti noodle length. Some scenes were filmed at the (now closed) Pasta Foods factory on London Road, St Albans, in Hertfordshire, and at a hotel in Castagnola, Switzerland.


title: Spaghetti-tree hoax

text: "Panorama" cameraman Charles de Jaeger dreamed up the story after remembering how teachers at his school in Austria teased his classmates for being so stupid that if they were told that spaghetti grew on trees, they would believe it. The editor of "Panorama", Michael Peacock, told the BBC in 2014 how he gave de Jaeger a budget of £100 and sent him off. The report was made more believable through its voice-over by respected broadcaster Richard Dimbleby. Peacock said Dimbleby knew they were using his authority to make the joke work, and that Dimbleby loved the idea and went at it eagerly.


title: Spaghetti-tree hoax

text: At the time, 7 million of the 15.8 million homes (about 44%) in Britain had television receivers. Pasta was not an everyday food in 1950s Britain, and it was known mainly from tinned spaghetti in tomato sauce and considered by many to be an exotic delicacy. An estimated eight million people watched the programme on 1 April 1957, and hundreds phoned in the following day to question the authenticity of the story or ask for more information about spaghetti cultivation and how they could grow their own spaghetti trees; the BBC told them to "place a sprig of spaghetti in a tin of tomato sauce and hope for the best".


title: Technology transfer

text: Technology transfer (TT), also called transfer of technology (TOT), is the process of transferring (disseminating) technology from the person or organization that owns or holds it to another person or organization, in an attempt to transform inventions and scientific outcomes into new products and services that benefit society. Technology transfer is closely related to (and may arguably be considered a subset of) knowledge transfer.


title: Technology transfer

text: A comprehensive definition of technology transfer today includes the notion of collaborative process as it became clear that global challenges could be resolved only through the development of global solutions. Knowledge and technology transfer plays a crucial role in connecting innovation stakeholders and moving inventions from creators to public and private users.


title: Technology transfer

text: Intellectual property (IP) is an important instrument of technology transfer, as it establishes an environment conducive to sharing research results and technologies. Analysis in 2003 showed that the context, or environment, and motives of each organization involved will influence the method of technology transfer employed. The motives behind the technology transfer were not necessarily homogenous across organization levels, especially when commercial and government interests are combined. The protection of IP rights enables all parties, including universities and research institutions to ensure ownership of the scientific outcomes of their intellectual activity, and to control the use of IP in accordance with their mission and core values. IP protection gives academic institutions capacity to market their inventions, attract funding, seek industrial partners and assure dissemination of new technologies through means such as licensing or creation of start-ups for the benefit of society.


title: Technology transfer

text: Technology transfers may occur between universities, businesses (of any size, ranging from small, medium, to large), governments, across geopolitical borders, both formally and informally, and both openly and secretly. Often it occurs by concerted effort to share skills, knowledge, technologies, manufacturing methods, samples, and facilities among the participants.


title: Technology transfer

text: While the Technology Transfer process involves many activities, which can be represented in many ways, in reality, technology transfer is a fluid and dynamic process that rarely follows a linear course. Typical steps include:


title: Technology transfer

text: Technology transfer aims to ensure that scientific and technological developments are accessible to a wider range of users who can then further develop and exploit the technology into new products, processes, applications, materials, or services. It is closely related to (and may arguably be considered a subset of) knowledge transfer. Horizontal transfer is the movement of technologies from one area to another.


title: Technology transfer

text: Transfer of technology is primarily horizontal. Vertical transfer occurs when technologies are moved from applied research centers to research and development departments.


title: Technology transfer

text: Spin-outs are used where the host organization does not have the necessary will, resources, or skills to develop new technology. Often these approaches are associated with raising of venture capital (VC) as a means of funding the development process, a practice common in the United States and the European Union. Research spin-off companies are a popular vehicle of commercialization in Canada, where the rate of licensing of Canadian university research remains far below that of the US. Local venture capital organizations such as the Mid-Atlantic Venture Association (MAVA) also sponsor conferences at which investors assess the potential for commercialization of technology.


title: Technology transfer

text: Technology brokers are people who discovered how to bridge the emergent worlds and apply scientific concepts or processes to new situations or circumstances. A related term, used almost synonymously, especially in Europe, is "technology valorisation". While conceptually the practice has been utilized for many years (in ancient times, Archimedes was notable for applying science to practical problems), the present-day volume of research, combined with high-profile failures at Xerox PARC and elsewhere, has led to a focus on the process itself.


title: Technology transfer

text: Whereas technology transfer can involve the dissemination of highly complex technology from capital-intensive origins to low-capital recipients (and can involve aspects of dependency and fragility of systems), it also can involve appropriate technology, not necessarily high-tech or expensive, that is better disseminated, yielding robustness and independence of systems.


title: Technology transfer

text: Technology transfer is also promoted through informal means, such as at conferences organized by various groups, including the Ewing Marion Kauffman Foundation and the Association of University Technology Managers (AUTM), and at "challenge" competitions by organizations such as the Center for Advancing Innovation in Maryland. AUTM represents over 3,100 technology transfer professionals, and more than 800 universities, research centers, hospitals, businesses and government organizations.


title: Technology transfer

text: The most frequently used informal means of technology transfer are through education, studies, professional exchange of opinions, movement of people, seminars, workshops. .


title: Technology transfer

text: There are numerous professional associations and TTO Networks enhancing different forms of collaboration among technology managers in order to facilitate this “informal” transfer of best practices and experiences.


title: Technology transfer

text: In addition to AUTM, other regional and international associations include the Association of European Science and Technology Transfer Professionals (ASTP), the Alliance of Technology Transfer Professionals (ATTP), Licensing Executives Society (LES), Praxis Auril and others. There are also national Technology transfer associations and networks, such as the National Association of Technology Transfer Offices in Mexico (Red OTT Mexico), the Brazilian Forum of Innovation and Technology Transfer Managers (FORTEC), the Alliance of TechTransfer Professionals of the Philippines (AToP), the South African Research and Innovation Management Association (SARIMA), and other associations.


title: Technology transfer

text: They promote cooperation in technology transfer and the exchange of best practices and experiences among professionals, as today international technology transfer is considered one of the most effective ways to bring people together to find solutions to global problems such as COVID-19, climate change or cyber-attacks.


title: Technology transfer

text: Universities and research institutions seeking to partner with industry or other organizations can adopt an institutional intellectual property policy for effective intellectual property management and technology transfer. Such policies provide structure, predictability, and a n environment, in which commercialization partners (industrial sponsors, consultants, non-profit organizations, SMEs, governments) and research stakeholders (researchers, technicians, students, visiting researchers, etc.) can access and share knowledge, technology and IP. National IP strategies are measures taken by a government to realize its IP policy objectives.


title: Technology transfer

text: A research result may be of scientific and commercial interest, but patents are normally only issued for practical processes, and so someone—not necessarily the researchers—must come up with a specific practical process. Another consideration is commercial value; for example, while there are many ways to accomplish nuclear fusion, the ones of commercial value are those that generate more energy than they require to operate. The process to commercially exploit research varies widely. It can involve licensing agreements or setting up joint ventures and partnerships to share both the risks and rewards of bringing new technologies to market. Other corporate vehicles, e.g. spin-outs, are used where the host organization does not have the necessary will, resources, or skills to develop new technology. Often these approaches are associated with raising of venture capital (VC) as a means of funding the development process, a practice more common in the United States than in the European Union, which has a more conservative approach to VC funding. Research spin-off companies are a popular vehicle of commercialisation in Canada, where the rate of licensing of Canadian university research remains far below that of the US.


title: Technology transfer

text: Many universities and research institutions, and governmental organizations now have an Office of Technology Transfer (TTO, also known as "Tech Transfer" or "TechXfer") dedicated to identifying research that has potential commercial interest and strategies for how to exploit it. Technology Transfer Offices are usually created within a university in order to manage IP assets of the university, and the transfer of knowledge and technology to industry. Sometimes, their mandate includes any interaction or contractual relation with the private sector, or other responsibilities, depending on the mission of the institutions. Common names for such offices differ. Some examples include Technology Licensing Office (TLO), Technology Management Office, Research Contracts and IP Services Office, Technology Transfer Interface, Industry Liaisons Office, IP and Technology Management Office, and Nucleus of Technological Innovation.


title: Technology transfer

text: Technology transfer offices may work on behalf of research institutions, governments, and even large multinationals. Where start-ups and spin-outs are the clients, commercial fees are sometimes waived in lieu of an equity stake in the business. As a result of the potential complexity of the technology transfer process, technology transfer organizations are often multidisciplinary, including economists, engineers, lawyers, marketers and scientists. The dynamics of the technology transfer process have attracted attention in their own right, and there are several dedicated societies and journals.


title: Technology transfer

text: Technology and Innovation Support Centers (TISCs) help innovators access patent information, scientific and technical literature and search tools and databases and make more effective use of these resources to promote innovation, technology transfer, commercialization and utilization of technologies. The WIPO TISCs program currently supports over 80 countries. WIPO supports its member states in establishing and developing TISCs in universities and other institutions in numerous countries around the world. Services offered by TISCs may include:


title: Technology transfer

text: Science and technology parks (STP) are territories usually affiliated with a university or a research institution, which accommodate and foster the growth of companies based therein through technology transfer and open innovation.


title: Technology transfer

text: Technology business incubators (TBIs) are organizations that help startup companies and individual entrepreneurs develop their businesses by providing a range of services, including training, brokering and financing.


title: Technology transfer

text: Intellectual Property marketplaces are Internet-based platforms that allow innovators to connect with potential partners and/or clients. For example, online platform WIPO GREEN enable collaborations in specific areas of knowledge transfer and facilitate matchmaking between technology providers and technology seekers.


title: Technology transfer

text: There has been a marked increase in technology transfer intermediaries specialized in their field since 1980, stimulated in large part by the Bayh–Dole Act and equivalent legislation in other countries, which provided additional incentives for research exploitation. Due to the increasing focus on technology transfer there are several forms of intermediary institutions at work in this sector, from TTOs to IP 'trolls' that act outside the Bayh–Dole Act provisions. Due to the risk of exploitation, intellectual property policy, training and systems support for technology transfer by government, research institutes and universities, have been international and regionally-focused organisation, such as the World Intellectual Property Organisation and the European Union.


title: Technology transfer

text: The U.S. government's annual budget funds over $100 billion in research and development activity, which leads to a continuous pipeline of new inventions and technologies from within government laboratories. Through legislation including the Bayh–Dole Act, Congress encourages the private sector to use those technologies with commercial potential through technology transfer mechanisms such as Cooperative Research and Development Agreements, Patent License Agreements, Educational Partnership Agreements, and state/local government partnerships.


title: Technology transfer

text: The term “partnership intermediary” means an agency of a state or local government—or a nonprofit entity owned, chartered, funded, or operated by or on behalf of a state or local government—that assists, counsels, advises, evaluates, or otherwise cooperates with small business firms; institutions of higher education defined in section 201(a) of the Higher Education Act of 1965 (20 USC § 1141 [a]); or educational institutions within the meaning of section 2194 of Title 10, United States Code, that need or can make demonstrably productive use of technology-related assistance from a federal laboratory, including state programs receiving funds under cooperative agreements entered into under section 5121 of the Omnibus Trade and Competitiveness Act of 1988 (15 USC § 2781).


title: Technology transfer

text: Technology transfer had a direct impact on contributing to global public health issues, by enabling global access to COVID-19 vaccines. During 2021, vaccine developers concluded over 200 technology transfer agreements. One example was AstraZeneca concluding the licensing and technology transfer agreements on AstraZeneca with the Serum Institute of India and with Daiichi Sankyo of Japan to supply vaccines for COVID-19, which were developed in collaboration with the University of Oxford. In this process Intellectual Property was part of the solution and an important tool for facilitation of affordable global access to COVID 19 treatments – as it was the case in two licensing agreements between Medicines Patent Pool (MPP) and pharmaceutical companies Merck and Pfizer.


title: Technology transfer

text: Despite incentives to move research into production, the practical aspects are sometimes difficult to perform in practice. Using DoD technology readiness levels as a criterion (for example), research tends to focus on TRL (technology readiness level) 1–3 while readiness for production tends to focus on TRL 6–7 or higher. Bridging TRL-3 to TRL-6 has proven to be difficult in some organizations. Attempting to rush research (prototypes) into production (fully tested under diverse conditions, reliable, maintainable, etc.) tends to be more costly and time-consuming than expected.


title: Technology transfer

text: Power political and realpolitik incentives in technology transfer are cognized to be negative factors in destructive applications. Technology transfer to dictatorial regimes is thought to be disruptive for the scientific purposes.


title: Pride (In the Name of Love)

text: "Pride (In the Name of Love)" is a song by Irish rock band U2. It is the second track on the band's 1984 album, "The Unforgettable Fire", and was released as its lead single in September 1984. The song was produced by Brian Eno and Daniel Lanois. Written about Martin Luther King Jr., "Pride" received mixed critical reviews at the time, but it was a major commercial success for U2 and has since become one of their most popular songs. It appeared on the band's compilation albums "The Best of 1980–1990" and "U218 Singles".


title: Pride (In the Name of Love)

text: In 2004, "Rolling Stone" ranked it 378th on its list of "The 500 Greatest Songs of All Time". The song was included on The Rock and Roll Hall of Fame's 500 Songs that Shaped Rock and Roll list.


title: Pride (In the Name of Love)

text: The melody and the chords for "Pride" were improvised by U2 during a soundcheck prior to a November 1983 concert in Hawaii on the band's War Tour. Guitarist the Edge led the group with a series of chord changes during the soundcheck, but after someone made a mistake, the other members picked up on it and changed course, providing a "new twist" to the improvisation, according to Niall Stokes. After the tour concluded, the group continued to work on the track at lead vocalist Bono's home in a Martello tower in Bray, County Wicklow, where the Edge devised a guitar part for the song. "Pride" was further worked on at Slane Castle during the recording sessions for "The Unforgettable Fire", and was ultimately completed at Windmill Lane Studios.


title: Pride (In the Name of Love)

text: The song had been intended to be based on Ronald Reagan's pride in America's military power, but Stephen B. Oates's book "Let The Trumpet Sound: A Life of Martin Luther King, Jr." and a biography of Malcolm X caused the lyricist Bono to ponder the different sides of the civil rights campaigns, the violent and the non-violent. In subsequent years, Bono has expressed his dissatisfaction with the lyrics, which he describes, along with another "Unforgettable Fire" song, "Bad", as being "left as simple sketches". He says that he was swayed by the Edge and producers Brian Eno and Daniel Lanois, who played down the need to develop the lyrics as they thought their impressionistic nature would give added forcefulness to the song's feeling, particularly when heard by non-English speakers. In "U2 by U2", Bono said: "I looked at how glorious that song was and thought: 'What the fuck is that all about?' It's just a load of vowel sounds ganging up on a great man. It is emotionally very articulate - if you didn't speak English."


title: Pride (In the Name of Love)

text: The song contains the erroneous reference to King's shooting as "Early morning, April 4," when it actually occurred after 6 p.m. Bono acknowledges the error and in live performances he often changes the lyric to "Early evening..."


title: Pride (In the Name of Love)

text: Chrissie Hynde of the Pretenders sang backing vocals on the recording. She was married to Jim Kerr of Simple Minds at the time and she is credited as "Christine Kerr".


title: Pride (In the Name of Love)

text: "Pride" is in the key of B, and is played at a tempo of 106 bpm. The song follows a chord progression of B-E–A–Fm and the solo is B–D–E–E.


title: Pride (In the Name of Love)

text: Three music videos were made. The first was shot in August by director Donald Cammell and features opening and closing shots of the Dublin Docklands area. Two versions of this video exist; black and white and colour (sepia). The band were not satisfied with Cammell's video, and they agreed to their principal photographer, Anton Corbijn, shooting an alternative. The second video was filmed in a basement near London's Heathrow Airport, it features U2 standing sternly in front of a wall under poor lighting conditions. The U2 camp was also unimpressed with this video and a third video is produced by compiling footage shot during "The Unforgettable Fire" recording sessions at Slane Castle. The original (black and white) Cammell video was primarily used in promotion.


title: Pride (In the Name of Love)

text: "Pride" reached number 3 on the UK Singles Chart. The song was the band's first top 40 hit in the United States where it peaked at number 33. It gained considerable US album-oriented rock radio airplay and its video was on heavy rotation on MTV, thus helping U2 continue its commercial breakthrough begun with the "War" album. It reached number 1 in New Zealand, the first time a U2 single topped a country's singles chart.


title: Pride (In the Name of Love)

text: Initial critical reactions to "Pride" were mixed, especially in regards to the lyrics. Robert Christgau in "The Village Voice" complained of "the moralism with the turn-somebody-else's-cheek glorification of Martin Luther King's martyrdom." Meanwhile, Kurt Loder of "Rolling Stone" wrote that Pride' gets over only on the strength of its resounding beat and big, droning bass line, not on the nobility of its lyrics, which are unremarkable." "Cash Box" called it a "rousing anthem" with "powerful vocal and guitar," saying that "Bono’s writing and vocal delivery are pure inspiration as is the pounding rhythm section." The 1984 "Pazz & Jop" poll of 240 music critics ranked "Pride" as the 12th-best single of that year, a higher ranking than the overall album, which finished 29th. The single's ranking remained the highest of any U2 single until "One" achieved 8th in 1992.


title: Pride (In the Name of Love)

text: "Pride" was first played live at the opening show of the Unforgettable Fire Tour on 29 August 1984 in Christchurch, New Zealand. The song has been played at virtually every U2 concert since the Unforgettable Fire Tour, although it was played infrequently on the first and second legs of 2001's Elevation Tour and the second and third legs 2009's U2 360° Tour. Live performances during the 1980s and early 1990s were usually played in the key of B, while since the late 1990s the song has been played in the key of A. , it is the band's most played song with over 770 documented performances, though "I Will Follow" has likely been performed more often. Clips from Martin Luther King speeches are often shown on the various tour video screens during these performances. In 2010, in Brisbane, Australia, the final verse was changed to reflect the 30th anniversary of the assassination of John Lennon (8 December 2010).


title: Pride (In the Name of Love)

text: U2 performed the song, along with "City of Blinding Lights", to upwards of 400,000 people on 18 January 2009 at the concert at the Lincoln Memorial to celebrate the upcoming inauguration of Barack Obama. At the end of the performance Bono asked the audience to sing for King's dream, saying it was "not just an American dream; also an Irish dream, a European dream, an African dream", before referencing it to the Israeli–Palestinian conflict and saying that it was "an Israeli dream, and also a Palestinian dream." The performance of "Pride" closed off with Bono quoting part of King's speech "I Have a Dream," saying "Let freedom ring! Let freedom ring! Let freedom ring! Every village, every hamlet, every state, every city. Let freedom ring!" before seguing into "City of Blinding Lights." Bassist Adam Clayton later said "We were scratching our heads going, 'How does an Irish band get invited to play at the Presidential Inauguration?' Our way in was through a song like 'Pride'. It allowed Obama's people to express the connection without being too overt. It was one of those moments where you know the world is watching, but a healthy amount of anxiety gets your mojo working."


title: Pride (In the Name of Love)

text: Live performances of "Pride" appear on the concert films "Rattle and Hum" (both the album and motion picture), "", "", "", "", "Live from Paris", and "U2 3D".


title: Pride (In the Name of Love)

text: In 1989, "Spin" named the song the 65th-greatest single in history. In 2004, "Rolling Stone" placed the song at number 378 on its list of "The 500 Greatest Songs of All Time"; the song was re-ranked to 388th on the magazine's 2010 version of the list. The Rock and Roll Hall of Fame selected "Pride (In the Name of Love)" as one of 500 Songs that Shaped Rock and Roll. Music television network VH1 ranked the song number 38 on the "100 Greatest Songs of the 80s" countdown in its series "The Greatest". In 2004, "Mojo" placed the song at number 63 on its list of the "100 Epic Rock Tracks".


title: Pride (In the Name of Love)

text: In 2007, the Roots covered "Pride" in a medley with "Sunday Bloody Sunday" for an NAACP dinner honoring Bono. The band also mixed in some of their own "False Media" and bits of Edwin Starr's "War".


title: Hunt–Lauda rivalry

text: The Hunt–Lauda rivalry was an individual sport rivalry that ran from 1973 to 1979 between two Formula One drivers: the British James Hunt and the Austrian Niki Lauda.


title: Hunt–Lauda rivalry

text: While they competed on the track, Hunt readily admitted that the two were good friends from their early days "gypsi(ng) around Europe together" in Formula Three, where they became "mates, not just casual acquaintances." The enduring friendship between the two continued until Hunt's death in 1993.


title: Hunt–Lauda rivalry

text: The Ron Howard film "Rush" was based on this rivalry, including their admiration for each other, though replacing their real-world friendship with a more intense (sometimes even nasty) rivalry, before ending with a warm moment and Lauda's voiceover that Hunt was "among the very few I liked, and even fewer I respected."


title: External ballistics

text: External ballistics or exterior ballistics is the part of ballistics that deals with the behavior of a projectile in flight. The projectile may be powered or un-powered, guided or unguided, spin or fin stabilized, flying through an atmosphere or in the vacuum of space, but most certainly flying under the influence of a gravitational field.


title: External ballistics

text: Gun-launched projectiles may be unpowered, deriving all their velocity from the propellant's ignition until the projectile exits the gun barrel. However, exterior ballistics analysis also deals with the trajectories of rocket-assisted gun-launched projectiles and gun-launched rockets; and rockets that acquire all their trajectory velocity from the interior ballistics of their on-board propulsion system, either a rocket motor or air-breathing engine, both during their boost phase and after motor burnout. External ballistics is also concerned with the free-flight of other projectiles, such as balls, arrows etc.


title: External ballistics

text: When in flight, the main or major forces acting on the projectile are gravity, drag, and if present, wind; if in powered flight, thrust; and if guided, the forces imparted by the control surfaces.


title: External ballistics

text: In small arms external ballistics applications, gravity imparts a downward acceleration on the projectile, causing it to drop from the line of sight. Drag, or the air resistance, decelerates the projectile with a force proportional to the square of the velocity. Wind makes the projectile deviate from its trajectory. During flight, gravity, drag, and wind have a major impact on the path of the projectile, and must be accounted for when predicting how the projectile will travel.


title: External ballistics

text: For medium to longer ranges and flight times, besides gravity, air resistance and wind, several intermediate or meso variables described in the external factors paragraph have to be taken into account for small arms. Meso variables can become significant for firearms users that have to deal with angled shot scenarios or extended ranges, but are seldom relevant at common hunting and target shooting distances.


title: External ballistics

text: For long to very long small arms target ranges and flight times, minor effects and forces such as the ones described in the long range factors paragraph become important and have to be taken into account. The practical effects of these minor variables are generally irrelevant for most firearms users, since normal group scatter at short and medium ranges prevails over the influence these effects exert on projectile trajectories.


title: External ballistics

text: At extremely long ranges, artillery must fire projectiles along trajectories that are not even approximately straight; they are closer to parabolic, although air resistance affects this. Extreme long range projectiles are subject to significant deflections, depending on circumstances, from the line toward the target; and all external factors and long range factors must be taken into account when aiming. In very large-calibre artillery cases, like the Paris Gun, very subtle effects that are not covered in this article can further refine aiming solutions.


title: External ballistics

text: In the case of ballistic missiles, the altitudes involved have a significant effect as well, with part of the flight taking place in a near-vacuum well above a rotating earth, steadily moving the target from where it was at launch time.


title: External ballistics

text: The effect of gravity on a projectile in flight is often referred to as projectile drop or bullet drop. It is important to understand the effect of gravity when zeroing the sighting components of a gun. To plan for projectile drop and compensate properly, one must understand parabolic shaped trajectories.


title: External ballistics

text: In order for a projectile to impact any distant target, the barrel must be inclined to a positive elevation angle relative to the target. This is due to the fact that the projectile will begin to respond to the effects of gravity the instant it is free from the mechanical constraints of the bore. The imaginary line down the center axis of the bore and out to infinity is called the line of departure and is the line on which the projectile leaves the barrel. Due to the effects of gravity a projectile can never impact a target higher than the line of departure. When a positively inclined projectile travels downrange, it arcs below the line of departure as it is being deflected off its initial path by gravity. Projectile/Bullet drop is defined as the vertical distance of the projectile below the line of departure from the bore. Even when the line of departure is tilted upward or downward, projectile drop is still defined as the distance between the bullet and the line of departure at any point along the trajectory. Projectile drop does not describe the actual trajectory of the projectile.


title: External ballistics

text: Knowledge of projectile drop however is useful when conducting a direct comparison of two different projectiles regarding the shape of their trajectories, comparing the effects of variables such as velocity and drag behavior.


title: External ballistics

text: For hitting a distant target an appropriate positive elevation angle is required that is achieved by angling the line of sight from the shooter's eye through the centerline of the sighting system downward toward the line of departure. This can be accomplished by simply adjusting the sights down mechanically, or by securing the entire sighting system to a sloped mounting having a known downward slope, or by a combination of both. This procedure has the effect of elevating the muzzle when the barrel must be subsequently raised to align the sights with the target. A projectile leaving a muzzle at a given elevation angle follows a ballistic trajectory whose characteristics are dependent upon various factors such as muzzle velocity, gravity, and aerodynamic drag. This ballistic trajectory is referred to as the bullet path. If the projectile is spin stabilized, aerodynamic forces will also predictably arc the trajectory slightly to the right, if the rifling employs "right-hand twist." Some barrels are cut with left-hand twist, and the bullet will arc to the left, as a result. Therefore, to compensate for this path deviation, the sights also have to be adjusted left or right, respectively. A constant wind also predictably affects the bullet path, pushing it slightly left or right, and a little bit more up and down, depending on the wind direction. The magnitude of these deviations are also affected by whether the bullet is on the upward or downward slope of the trajectory, due to a phenomenon called "yaw of repose," where a spinning bullet tends to steadily and predictably align slightly off center from its point mass trajectory. Nevertheless, each of these trajectory perturbations are predictable once the projectile aerodynamic coefficients are established, through a combination of detailed analytical modeling and test range measurements.


title: External ballistics

text: Projectile/bullet path analysis is of great use to shooters because it allows them to establish ballistic tables that will predict how much vertical elevation and horizontal deflection corrections must be applied to the sight line for shots at various known distances. The most detailed ballistic tables are developed for long range artillery and are based on six-degree-of-freedom trajectory analysis, which accounts for aerodynamic behavior along the three axial directions—elevation, range, and deflection—and the three rotational directions—pitch, yaw, and spin. For small arms applications, trajectory modeling can often be simplified to calculations involving only four of these degrees-of-freedom, lumping the effects of pitch, yaw and spin into the effect of a yaw-of-repose to account for trajectory deflection. Once detailed range tables are established, shooters can relatively quickly adjust sights based on the range to target, wind, air temperature and humidity, and other geometric considerations, such as terrain elevation differences.


title: External ballistics

text: Projectile path values are determined by both the sight height, or the distance of the line of sight above the bore centerline, and the range at which the sights are zeroed, which in turn determines the elevation angle. A projectile following a ballistic trajectory has both forward and vertical motion. Forward motion is slowed due to air resistance, and in point mass modeling the vertical motion is dependent on a combination of the elevation angle and gravity. Initially, the projectile is rising with respect to the line of sight or the horizontal sighting plane. The projectile eventually reaches its apex (highest point in the trajectory parabola) where the vertical speed component decays to zero under the effect of gravity, and then begins to descend, eventually impacting the earth. The farther the distance to the intended target, the greater the elevation angle and the higher the apex.


title: External ballistics

text: The projectile path crosses the horizontal sighting plane two times. The point closest to the gun occurs while the bullet is climbing through the line of sight and is called the near zero. The second point occurs as the projectile is descending through the line of sight. It is called the far zero and defines the current sight in distance for the gun. Projectile path is described numerically as distances above or below the horizontal sighting plane at various points along the trajectory. This is in contrast to projectile drop which is referenced to the plane containing the line of departure regardless of the elevation angle. Since each of these two parameters uses a different reference datum, significant confusion can result because even though a projectile is tracking well below the line of departure it can still be gaining actual and significant height with respect to the line of sight as well as the surface of the earth in the case of a horizontal or near horizontal shot taken over flat terrain.


title: External ballistics

text: Knowledge of the projectile drop and path has some practical uses to shooters even if it does not describe the actual trajectory of the projectile. For example, if the vertical projectile position over a certain range reach is within the vertical height of the target area the shooter wants to hit, the point of aim does not necessarily need to be adjusted over that range; the projectile is considered to have a sufficiently flat point-blank range trajectory for that particular target. Also known as "battle zero", maximum point-blank range is also of importance to the military. Soldiers are instructed to fire at any target within this range by simply placing their weapon's sights on the center of mass of the enemy target. Any errors in range estimation are tactically irrelevant, as a well-aimed shot will hit the torso of the enemy soldier. The current trend for elevated sights and higher-velocity cartridges in assault rifles is in part due to a desire to extend the maximum point-blank range, which makes the rifle easier to use.


title: External ballistics

text: Mathematical models, such as computational fluid dynamics, are used for calculating the effects of drag or air resistance; they are quite complex and not yet completely reliable, but research is ongoing. The most reliable method, therefore, of establishing the necessary projectile aerodynamic properties to properly describe flight trajectories is by empirical measurement.


title: External ballistics

text: Use of ballistics tables or ballistics software based on the Mayevski/Siacci method and G1 drag model, introduced in 1881, are the most common method used to work with external ballistics. Projectiles are described by a ballistic coefficient, or BC, which combines the air resistance of the bullet shape (the drag coefficient) and its sectional density (a function of mass and bullet diameter).


title: External ballistics

text: The deceleration due to drag that a projectile with mass "m", velocity "v", and diameter "d" will experience is proportional to 1/BC, 1/"m", "v²" and "d²". The BC gives the ratio of ballistic efficiency compared to the standard G1 projectile, which is a fictitious projectile with a flat base, a length of 3.28 calibers/diameters, and a 2 calibers/diameters radius tangential curve for the point.


title: External ballistics

text: The G1 standard projectile originates from the "C" standard reference projectile defined by the German steel, ammunition and armaments manufacturer Krupp in 1881. The G1 model standard projectile has a BC of 1. The French Gâvre Commission decided to use this projectile as their first reference projectile, giving the G1 name.


title: External ballistics

text: Sporting bullets, with a calibre "d" ranging from 0.177 to 0.50 inches (4.50 to 12.7 mm), have G1 BC's in the range 0.12 to slightly over 1.00, with 1.00 being the most aerodynamic, and 0.12 being the least. Very-low-drag bullets with BC's ≥ 1.10 can be designed and produced on CNC precision lathes out of mono-metal rods, but they often have to be fired from custom made full bore rifles with special barrels.


title: External ballistics

text: Sectional density is a very important aspect of a projectile or bullet, and is for a round projectile like a bullet the ratio of frontal surface area (half the bullet diameter squared, times pi) to bullet mass. Since, for a given bullet shape, frontal surface increases as the square of the calibre, and mass increases as the cube of the diameter, then sectional density grows linearly with bore diameter. Since BC combines shape and sectional density, a half scale model of the G1 projectile will have a BC of 0.5, and a quarter scale model will have a BC of 0.25.


title: External ballistics

text: Since different projectile shapes will respond differently to changes in velocity (particularly between supersonic and subsonic velocities), a BC provided by a bullet manufacturer will be an average BC that represents the common range of velocities for that bullet. For rifle bullets, this will probably be a supersonic velocity, for pistol bullets it will probably be subsonic. For projectiles that travel through the supersonic, transonic and subsonic flight regimes BC is not well approximated by a single constant, but is considered to be a function "BC(M)" of the Mach number M; here M equals the projectile velocity divided by the speed of sound. During the flight of the projectile the M will decrease, and therefore (in most cases) the BC will also decrease.


title: External ballistics

text: Most ballistic tables or software takes for granted that one specific drag function correctly describes the drag and hence the flight characteristics of a bullet related to its ballistics coefficient. Those models do not differentiate between wadcutter, flat-based, spitzer, boat-tail, very-low-drag, etc. bullet types or shapes. They assume one invariable drag function as indicated by the published BC.


title: External ballistics

text: Several drag curve models optimized for several standard projectile shapes are however available. The resulting fixed drag curve models for several standard projectile shapes or types are referred to as the:


title: External ballistics

text: How different speed regimes affect .338 calibre rifle bullets can be seen in the .338 Lapua Magnum product brochure which states Doppler radar established G1 BC data. The reason for publishing data like in this brochure is that the Siacci/Mayevski G1 model can not be tuned for the drag behavior of a specific projectile whose shape significantly deviates from the used reference projectile shape. Some ballistic software designers, who based their programs on the Siacci/Mayevski G1 model, give the user the possibility to enter several different G1 BC constants for different speed regimes to calculate ballistic predictions that closer match a bullets flight behavior at longer ranges compared to calculations that use only one BC constant.


title: External ballistics

text: The above example illustrates the central problem fixed drag curve models have. These models will only yield satisfactory accurate predictions as long as the projectile of interest has the same shape as the reference projectile or a shape that closely resembles the reference projectile. Any deviation from the reference projectile shape will result in less accurate predictions. How much a projectile deviates from the applied reference projectile is mathematically expressed by the form factor ("i"). The form factor can be used to compare the drag experienced by a projectile of interest to the drag experienced by the employed reference projectile at a given velocity (range). The problem that the actual drag curve of a projectile can significantly deviate from the fixed drag curve of any employed reference projectile systematically limits the traditional drag resistance modeling approach. The relative simplicity however makes that it can be explained to and understood by the general shooting public and hence is also popular amongst ballistic software prediction developers and bullet manufacturers that want to market their products.


title: External ballistics

text: Another attempt at building a ballistic calculator is the model presented in 1980 by Dr. Arthur J. Pejsa. Dr. Pejsa claims on his website that his method was consistently capable of predicting (supersonic) rifle bullet trajectories within 2.5 mm (0.1 in) and bullet velocities within 0.3 m/s (1 ft/s) out to 914 m (1,000 yd) in theory. The Pejsa model is a closed-form solution.


title: External ballistics

text: The Pejsa model can predict a projectile within a given flight regime (for example the supersonic flight regime) with only two velocity measurements, a distance between said velocity measurements, and a slope or deceleration constant factor. The model allows the drag curve to change slopes (true/calibrate) or curvature at three different points. Down range velocity measurement data can be provided around key inflection points allowing for more accurate calculations of the projectile retardation rate, very similar to a Mach vs CD table. The Pejsa model allows the slope factor to be tuned to account for subtle differences in the retardation rate of different bullet shapes and sizes. It ranges from 0.1 (flat-nose bullets) to 0.9 (very-low-drag bullets). If this slope or deceleration constant factor is unknown a default value of 0.5 is used. With the help of test firing measurements the slope constant for a particular bullet/rifle system/shooter combination can be determined. These test firings should preferably be executed at 60% and for extreme long range ballistic predictions also at 80% to 90% of the supersonic range of the projectiles of interest, staying away from erratic transonic effects. With this the Pejsa model can easily be tuned. A practical downside of the Pejsa model is that accurate projectile specific down range velocity measurements to provide these better predictions can not be easily performed by the vast majority of shooting enthusiasts.


title: External ballistics

text: An average retardation coefficient can be calculated for any given slope constant factor if velocity data points are known and distance between said velocity measurements is known. Obviously this is true only within the same flight regime. With velocity actual speed is meant, as velocity is a vector quantity and speed is the magnitude of the velocity vector. Because the power function does not have constant curvature a simple chord average cannot be used. The Pejsa model uses a weighted average retardation coefficient weighted at 0.25 range. The closer velocity is more heavily weighted. The retardation coefficient is measured in feet whereas range is measured in yards hence 0.25 * 3.0 = 0.75, in some places 0.8 rather than 0.75 is used. The 0.8 comes from rounding in order to allow easy entry on hand calculators. Since the Pejsa model does not use a simple chord weighted average, two velocity measurements are used to find the chord average retardation coefficient at midrange between the two velocity measurements points, limiting it to short range accuracy. In order to find the starting retardation coefficient Dr. Pejsa provides two separate equations in his two books. The first involves the power function. The second equation is identical to the one used to find the weighted average at R / 4; add N * (R/2) where R is the range in feet to the chord average retardation coefficient at midrange and where N is the slope constant factor. After the starting retardation coefficient is found the opposite procedure is used in order find the weighted average at R / 4; the starting retardation coefficient minus N * (R/4). In other words, N is used as the slope of the chord line. Dr. Pejsa states that he expanded his drop formula in a power series in order to prove that the weighted average retardation coefficient at R / 4 was a good approximation. For this Dr. Pejsa compared the power series expansion of his drop formula to some other unnamed drop formula's power expansion to reach his conclusions. The fourth term in both power series matched when the retardation coefficient at 0.25 range was used in Pejsa's drop formula. The fourth term was also the first term to use N. The higher terms involving N where insignificant and disappeared at N = 0.36, which according to Dr. Pejsa was a lucky coincidence making for an exceedingly accurate linear approximation, especially for N's around 0.36. If a retardation coefficient function is used exact average values for any N can be obtained because from calculus it is trivial to find the average of any integrable function. Dr. Pejsa states that the retardation coefficient can be modeled by C * V where C is a fitting coefficient which disappears during the derivation of the drop formula and N the slope constant factor.


title: External ballistics

text: The retardation coefficient equals the velocity squared divided by the retardation rate A. Using an average retardation coefficient allows the Pejsa model to be a closed-form expression within a given flight regime.


title: External ballistics

text: In order to allow the use of a G1 ballistic coefficient rather than velocity data Dr. Pejsa provided two reference drag curves. The first reference drag curve is based purely on the Siacci/Mayevski retardation rate function. The second reference drag curve is adjusted to equal the Siacci/Mayevski retardation rate function at a projectile velocity of 2600 fps (792.5 m/s) using a .30-06 Springfield Cartridge, Ball, Caliber .30 M2 rifle spitzer bullet with a slope or deceleration constant factor of 0.5 in the supersonic flight regime. In other flight regimes the second Pejsa reference drag curve model uses slope constant factors of 0.0 or -4.0. These deceleration constant factors can be verified by backing out Pejsa's formulas (the drag curve segments fits the form V / C and the retardation coefficient curve segments fits the form V / (V / C) = C * V where C is a fitting coefficient). The empirical test data Pejsa used to determine the exact shape of his chosen reference drag curve and pre-defined mathematical function that returns the retardation coefficient at a given Mach number was provided by the US military for the Cartridge, Ball, Caliber .30 M2 bullet. The calculation of the retardation coefficient function also involves air density, which Pejsa did not mention explicitly. The Siacci/Mayevski G1 model uses the following deceleration parametrization (60 °F, 30 inHg and 67% humidity, air density ρ = 1.2209 kg/m). Dr. Pejsa suggests using the second drag curve because the Siacci/Mayevski G1 drag curve does not provide a good fit for modern spitzer bullets. To obtain relevant retardation coefficients for optimal long range modeling Dr. Pejsa suggested using accurate projectile specific down range velocity measurement data for a particular projectile to empirically derive the average retardation coefficient rather than using a reference drag curve derived average retardation coefficient. Further he suggested using ammunition with reduced propellant loads to empirically test actual projectile flight behavior at lower velocities. When working with reduced propellant loads utmost care must be taken to avoid dangerous or catastrophic conditions (detonations) with can occur when firing experimental loads in firearms.


title: External ballistics

text: Although not as well known as the Pejsa model, an additional alternative ballistic model was presented in 1989 by Colonel Duff Manges (U S Army Retired) at the American Defense Preparedness (ADPA) 11th International Ballistic Symposium held at the Brussels Congress Center, Brussels, Belgium, May 9–11, 1989. A paper titled "Closed Form Trajectory Solutions for Direct Fire Weapons Systems" appears in the proceedings, Volume 1, Propulsion Dynamics, Launch Dynamics, Flight Dynamics, pages 665–674. Originally conceived to model projectile drag for 120 mm tank gun ammunition, the novel drag coefficient formula has been applied subsequently to ballistic trajectories of center-fired rifle ammunition with results comparable to those claimed for the Pejsa model.


title: External ballistics

text: The Manges model uses a first principles theoretical approach that eschews "G" curves and "ballistic coefficients" based on the standard G1 and other similarity curves. The theoretical description has three main parts. The first is to develop and solve a formulation of the two dimensional differential equations of motion governing flat trajectories of point mass projectiles by defining mathematically a set of quadratures that permit closed form solutions for the trajectory differential equations of motion. A sequence of successive approximation drag coefficient functions is generated that converge rapidly to actual observed drag data. The vacuum trajectory, simplified aerodynamic, d'Antonio, and Euler drag law models are special cases. The Manges drag law thereby provides a unifying influence with respect to earlier models used to obtain two dimensional closed form solutions to the point-mass equations of motion. The third purpose of this paper is to describe a least squares fitting procedure for obtaining the new drag functions from observed experimental data. The author claims that results show excellent agreement with six degree of freedom numerical calculations for modern tank ammunition and available published firing tables for center-fired rifle ammunition having a wide variety of shapes and sizes.


title: External ballistics

text: A Microsoft Excel application has been authored that uses least squares fits of wind tunnel acquired tabular drag coefficients. Alternatively, manufacturer supplied ballistic trajectory data, or Doppler acquired velocity data can be fitted as well to calibrate the model. The Excel application then employs custom macroinstructions to calculate the trajectory variables of interest. A modified 4th order Runge-Kutta integration algorithm is used. Like Pejsa, Colonel Manges claims center-fired rifle accuracies to the nearest one tenth of an inch for bullet position, and nearest foot per second for the projectile velocity.


title: External ballistics

text: The Proceedings of the 11th International Ballistic Symposium are available through the National Defense Industrial Association (NDIA) at the website http://www.ndia.org/Resources/Pages/Publication_Catalog.aspx .


title: External ballistics

text: There are also advanced professional ballistic models like PRODAS available. These are based on six degrees of freedom (6 DoF) calculations. 6 DoF modeling accounts for x, y, and z position in space along with the projectiles pitch, yaw, and roll rates. 6 DoF modeling needs such elaborate data input, knowledge of the employed projectiles and expensive data collection and verification methods that it is impractical for non-professional ballisticians, but not impossible for the curious, computer literate, and mathematically inclined. Semi-empirical aeroprediction models have been developed that reduced extensive test range data on a wide variety of projectile shapes, normalizing dimensional input geometries to calibers; accounting for nose length and radius, body length, and boattail size, and allowing the full set of 6-dof aerodynamic coefficients to be estimated. Early research on spin-stabilized aeroprediction software resulted in the SPINNER computer program. The FINNER aeroprediction code calculates 6-dof inputs for fin stabilized projectiles. Solids modeling software that determines the projectile parameters of mass, center of gravity, axial and transverse moments of inertia necessary for stability analysis are also readily available, and simple to computer program. Finally, algorithms for 6-dof numerical integration suitable to a 4th order Runge-Kutta are readily available. All that is required for the amateur ballistician to investigate the finer analytical details of projectile trajectories, along with bullet nutation and precession behavior, is computer programming determination. Nevertheless, for the small arms enthusiast, aside from academic curiosity, one will discover that being able to predict trajectories to 6-dof accuracy is probably not of practical significance compared to more simplified point mass trajectories based on published bullet ballistic coefficients. 6 DoF is generally used by the aerospace and defense industry and military organizations that study the ballistic behavior of a limited number of (intended) military issue projectiles. Calculated 6 DoF trends can be incorporated as correction tables in more conventional ballistic software applications.


title: External ballistics

text: Though 6 DoF modeling and software applications are used by professional well equipped organizations for decades, the computing power restrictions of mobile computing devices like (ruggedized) personal digital assistants, tablet computers or smartphones impaired field use as calculations generally have to be done on the fly. In 2016 the Scandinavian ammunition manufacturer Nammo Lapua Oy released a 6 DoF calculation model based ballistic free software named Lapua Ballistics. The software is distributed as a mobile app only and available for Android and iOS devices. The employed 6 DoF model is however limited to Lapua bullets as a 6 DoF solver needs bullet specific drag coefficient (Cd)/Doppler radar data and geometric dimensions of the projectile(s) of interest. For other bullets the Lapua Ballistics solver is limited to and based on G1 or G7 ballistic coefficients and the Mayevski/Siacci method.


title: External ballistics

text: Military organizations have developed ballistic models like the NATO Armament Ballistic Kernel (NABK) for fire-control systems for artillery like the SG2 Shareable (Fire Control) Software Suite (S4) from the NATO Army Armaments Group (NAAG). The NATO Armament Ballistic Kernel is a 4-DoF modified point mass model. This is a compromise between a simple point mass model and a computationally intensive 6-DoF model.


title: External ballistics

text: A six- and seven-degree-of-freedom standard called BALCO has also been developed within NATO working groups. BALCO is a trajectory simulation program based on the mathematical model defined by the NATO Standardization Recommendation 4618. The primary goal of BALCO is to compute high-fidelity trajectories for both conventional axisymmetric and precision-guided projectiles featuring control surfaces. The BALCO trajectory model is a FORTRAN 2003 program that implements the following features:


title: External ballistics

text: For the precise establishment of drag or air resistance effects on projectiles, Doppler radar measurements are required. Weibel 1000e or Infinition BR-1001 Doppler radars are used by governments, professional ballisticians, defence forces and a few ammunition manufacturers to obtain real-world data of the flight behavior of projectiles of their interest. Correctly established state of the art Doppler radar measurements can determine the flight behavior of projectiles as small as airgun pellets in three-dimensional space to within a few millimetres accuracy. The gathered data regarding the projectile deceleration can be derived and expressed in several ways, such as ballistic coefficients (BC) or drag coefficients (C). Because a spinning projectile experiences both precession and nutation about its center of gravity as it flies, further data reduction of doppler radar measurements is required to separate yaw induced drag and lift coefficients from the zero yaw drag coefficient, in order to make measurements fully applicable to 6-dof trajectory analysis.


title: External ballistics

text: Doppler radar measurement results for a lathe-turned monolithic solid .50 BMG very-low-drag bullet (Lost River J40 .510-773 grain monolithic solid bullet / twist rate 1:15 in) look like this:


title: External ballistics

text: The initial rise in the BC value is attributed to a projectile's always present yaw and precession out of the bore. The test results were obtained from many shots not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet's manufacturer Lost River Ballistic Technologies.


title: External ballistics

text: Doppler radar measurement results for a Lapua GB528 Scenar 19.44 g (300 gr) 8.59 mm (0.338 in) calibre very-low-drag bullet look like this:


title: External ballistics

text: This tested bullet experiences its maximum drag coefficient when entering the transonic flight regime around Mach 1.200.


title: External ballistics

text: With the help of Doppler radar measurements projectile specific drag models can be established that are most useful when shooting at extended ranges where the bullet speed slows to the transonic speed region near the speed of sound. This is where the projectile drag predicted by mathematic modeling can significantly depart from the actual drag experienced by the projectile. Further Doppler radar measurements are used to study subtle in-flight effects of various bullet constructions.


title: External ballistics

text: Governments, professional ballisticians, defence forces and ammunition manufacturers can supplement Doppler radar measurements with measurements gathered by telemetry probes fitted to larger projectiles.


title: External ballistics

text: In general, a pointed projectile will have a better drag coefficient (C) or ballistic coefficient (BC) than a round nosed bullet, and a round nosed bullet will have a better C or BC than a flat point bullet. Large radius curves, resulting in a shallower point angle, will produce lower drags, particularly at supersonic velocities. Hollow point bullets behave much like a flat point of the same point diameter. Projectiles designed for supersonic use often have a slightly tapered base at the rear, called a boat tail, which reduces air resistance in flight. The usefulness of a "tapered rear" for long-range firing was well established already by early 1870s, but technological difficulties prevented their wide adoption before well into 20th century. Cannelures, which are recessed rings around the projectile used to crimp the projectile securely into the case, will cause an increase in drag.


title: External ballistics

text: Analytical software was developed by the Ballistics Research Laboratory – later called the Army Research Laboratory – which reduced actual test range data to parametric relationships for projectile drag coefficient prediction. Large caliber artillery also employ drag reduction mechanisms in addition to streamlining geometry. Rocket-assisted projectiles employ a small rocket motor that ignites upon muzzle exit providing additional thrust to overcome aerodynamic drag. Rocket assist is most effective with subsonic artillery projectiles. For supersonic long range artillery, where base drag dominates, base bleed is employed. Base bleed is a form of a gas generator that does not provide significant thrust, but rather fills the low-pressure area behind the projectile with gas, effectively reducing the base drag and the overall projectile drag coefficient.


title: External ballistics

text: A projectile fired at supersonic muzzle velocity will at some point slow to approach the speed of sound. At the transonic region (about Mach 1.2–0.8) the centre of pressure (CP) of most non spherical projectiles shifts forward as the projectile decelerates. That CP shift affects the (dynamic) stability of the projectile. If the projectile is not well stabilized, it cannot remain pointing forward through the transonic region (the projectile starts to exhibit an unwanted precession or coning motion called limit cycle yaw that, if not damped out, can eventually end in uncontrollable tumbling along the length axis). However, even if the projectile has sufficient stability (static and dynamic) to be able to fly through the transonic region and stays pointing forward, it is still affected. The erratic and sudden CP shift and (temporary) decrease of dynamic stability can cause significant dispersion (and hence significant accuracy decay), even if the projectile's flight becomes well behaved again when it enters the subsonic region. This makes accurately predicting the ballistic behavior of projectiles in the transonic region very difficult.


title: External ballistics

text: Because of this, marksmen normally restrict themselves to engaging targets close enough that the projectile is still supersonic.


title: External ballistics

text: In 2015 the American ballistician Bryan Litz introduced the "Extended Long Range" concept to define rifle shooting at ranges where supersonic fired (rifle) bullets enter the transonic region. According to Litz, "Extended Long Range starts whenever the bullet slows to its transonic range. As the bullet slows down to approach Mach 1, it starts to encounter transonic effects, which are more complex and difficult to account for, compared to the supersonic range where the bullet is relatively well-behaved."


title: External ballistics

text: The ambient air density has a significant effect on dynamic stability during transonic transition. Though the ambient air density is a variable environmental factor, adverse transonic transition effects can be negated better by a projectile traveling through less dense air, than when traveling through denser air. Projectile or bullet length also affects limit cycle yaw. Longer projectiles experience more limit cycle yaw than shorter projectiles of the same diameter. Another feature of projectile design that has been identified as having an effect on the unwanted limit cycle yaw motion is the chamfer at the base of the projectile. At the very base, or heel of a projectile or bullet, there is a chamfer, or radius. The presence of this radius causes the projectile to fly with greater limit cycle yaw angles. Rifling can also have a subtle effect on limit cycle yaw. In general faster spinning projectiles experience less limit cycle yaw.


title: External ballistics

text: To circumvent the transonic problems encountered by spin-stabilized projectiles, projectiles can theoretically be guided during flight. The Sandia National Laboratories announced in January 2012 it has researched and test-fired 4-inch (102 mm) long prototype dart-like, self-guided bullets for small-caliber, smooth-bore firearms that could hit laser-designated targets at distances of more than a mile (about 1,610 meters or 1760 yards). These projectiles are not spin stabilized and the flight path can steered within limits with an electromagnetic actuator 30 times per second. The researchers also claim they have video of the bullet radically pitching as it exits the barrel and pitching less as it flies down range, a disputed phenomenon known to long-range firearms experts as “going to sleep”. Because the bullet's motions settle the longer it is in flight, accuracy improves at longer ranges, Sandia researcher Red Jones said. “Nobody had ever seen that, but we’ve got high-speed video photography that shows that it’s true,” he said. Recent testing indicates it may be approaching or already achieved initial operational capability.


title: External ballistics

text: Due to the practical inability to know in advance and compensate for all the variables of flight, no software simulation, however advanced, will yield predictions that will always perfectly match real world trajectories. It is however possible to obtain predictions that are very close to actual flight behavior.


title: External ballistics

text: Ballistic prediction computer programs intended for (extreme) long ranges can be evaluated by conducting field tests at the supersonic to subsonic transition range (the last 10 to 20% of the supersonic range of the rifle/cartridge/bullet combination). For a typical .338 Lapua Magnum rifle for example, shooting standard 16.2 gram (250 gr) Lapua Scenar GB488 bullets at 905 m/s (2969 ft/s) muzzle velocity, field testing of the software should be done at ≈ 1200–1300 meters (1312 - 1422 yd) under International Standard Atmosphere sea level conditions (air density ρ = 1.225 kg/m³). To check how well the software predicts the trajectory at shorter to medium range, field tests at 20, 40 and 60% of the supersonic range have to be conducted. At those shorter to medium ranges, transonic problems and hence unbehaved bullet flight should not occur, and the BC is less likely to be transient. Testing the predictive qualities of software at (extreme) long ranges is expensive because it consumes ammunition; the actual muzzle velocity of all shots fired must be measured to be able to make statistically dependable statements. Sample groups of less than 24 shots may not obtain the desired statistically significant confidence interval.


title: External ballistics

text: Governments, professional ballisticians, defence forces and a few ammunition manufacturers use Doppler radars and/or telemetry probes fitted to larger projectiles to obtain precise real world data regarding the flight behavior of the specific projectiles of their interest and thereupon compare the gathered real world data against the predictions calculated by ballistic computer programs. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. Authorities and projectile manufacturers are generally reluctant to share the results of Doppler radar tests and the test derived drag coefficients (C) of projectiles with the general public.


title: External ballistics

text: Around 2020 more affordable but less capable (amateur) Doppler rader equipment to determine free flight drag coefficients became available for the general public.


title: External ballistics

text: In January 2009 the Scandinavian ammunition manufacturer Nammo/Lapua published Doppler radar test-derived drag coefficient data for most of their rifle projectiles.


title: External ballistics

text: In 2015 the US ammunition manufacturer Berger Bullets announced the use of Doppler radar in unison with PRODAS 6 DoF software to generate trajectory solutions.


title: External ballistics

text: In 2016 US ammunition manufacturer Hornady announced the use of Doppler radar derived drag data in software utilizing a modified point mass model to generate trajectory solutions.


title: External ballistics

text: With the measurement derived C data engineers can create algorithms that utilize both known mathematical ballistic models as well as test specific, tabular data in unison. When used by predictive software like QuickTARGET Unlimited, Lapua Edition, Lapua Ballistics or Hornady 4DOF the Doppler radar test-derived drag coefficient data can be used for more accurate external ballistic predictions.


title: External ballistics

text: Some of the Lapua-provided drag coefficient data shows drastic increases in the measured drag around or below the Mach 1 flight velocity region. This behavior was observed for most of the measured small calibre bullets, and not so much for the larger calibre bullets. This implies some (mostly smaller calibre) rifle bullets exhibited more limit cycle yaw (coning and/or tumbling) in the transonic/subsonic flight velocity regime.


title: External ballistics

text: The information regarding unfavourable transonic/subsonic flight behavior for some of the tested projectiles is important. This is a limiting factor for extended range shooting use, because the effects of limit cycle yaw are not easily predictable and potentially catastrophic for the best ballistic prediction models and software.


title: External ballistics

text: Presented C data can not be simply used for every gun-ammunition combination, since it was measured for the barrels, rotational (spin) velocities and ammunition lots the Lapua testers used during their test firings. Variables like differences in rifling (number of grooves, depth, width and other dimensional properties), twist rates and/or muzzle velocities impart different rotational (spin) velocities and rifling marks on projectiles. Changes in such variables and projectile production lot variations can yield different downrange interaction with the air the projectile passes through that can result in (minor) changes in flight behavior. This particular field of external ballistics is currently (2009) not elaborately studied nor well understood.


title: External ballistics

text: The method employed to model and predict external ballistic behavior can yield differing results with increasing range and time of flight. To illustrate this several external ballistic behavior prediction methods for the Lapua Scenar GB528 19.44 g (300 gr) 8.59 mm (0.338 in) calibre very-low-drag rifle bullet with a manufacturer stated G1 ballistic coefficient (BC) of 0.785 fired at 830 m/s (2723 ft/s) muzzle velocity under International Standard Atmosphere sea level conditions (air density ρ = 1.225 kg/m³), Mach 1 = 340.3 m/s, Mach 1.2 = 408.4 m/s), predicted this for the projectile velocity and time of flight from 0 to 3,000 m (0 to 3,281 yd):


title: External ballistics

text: The table shows the Doppler radar test derived drag coefficients (C) prediction method and the 2017 Lapua Ballistics 6 DoF App predictions produce similar results. The 6 DoF modeling estimates bullet stability ((S) and (S)) that gravitates to over-stabilization for ranges over for this bullet. At the total drop predictions deviate 47.5 cm (19.7 in) or 0.20 mil (0.68 moa) at 50° latitude and up to the total drop predictions are within 0.30 mil (1 moa) at 50° latitude. The 2016 Lapua Ballistics 6 DoF App version predictions were even closer to the Doppler radar test predictions.


title: External ballistics

text: The traditional Siacci/Mayevski G1 drag curve model prediction method generally yields more optimistic results compared to the modern Doppler radar test derived drag coefficients (C) prediction method. At range the differences will be hardly noticeable, but at and beyond the differences grow over 10 m/s (32.8 ft/s) projectile velocity and gradually become significant.


title: External ballistics

text: At range the projectile velocity predictions deviate 25 m/s (82.0 ft/s), which equates to a predicted total drop difference of 125.6 cm (49.4 in) or 0.83 mil (2.87 moa) at 50° latitude.


title: External ballistics

text: The Pejsa drag model closed-form solution prediction method, without slope constant factor fine tuning, yields very similar results in the supersonic flight regime compared to the Doppler radar test derived drag coefficients (C) prediction method. At range the projectile velocity predictions deviate 10 m/s (32.8 ft/s), which equates to a predicted total drop difference of 23.6 cm (9.3 in) or 0.16 mil (0.54 moa) at 50° latitude.


title: External ballistics

text: The G7 drag curve model prediction method (recommended by some manufacturers for very-low-drag shaped rifle bullets) when using a G7 ballistic coefficient (BC) of 0.377 yields very similar results in the supersonic flight regime compared to the Doppler radar test derived drag coefficients (C) prediction method. At range the projectile velocity predictions have their maximum deviation of 10 m/s (32.8 ft/s). The predicted total drop difference at is 0.4 cm (0.16 in) at 50° latitude. The predicted total drop difference at is 45.0 cm (17.7 in), which equates to 0.25 mil (0.86 moa).


title: External ballistics

text: Decent prediction models are expected to yield similar results in the supersonic flight regime. The five example models down to all predict supersonic Mach 1.2 projectile velocities and total drop differences within a 51 cm (20.1 in) bandwidth. In the transonic flight regime at the models predict projectile velocities around Mach 1.0 to Mach 1.1 and total drop differences within a much larger 150 cm (59 in) bandwidth.


title: External ballistics

text: Wind has a range of effects, the first being the effect of making the projectile deviate to the side (horizontal deflection). From a scientific perspective, the "wind pushing on the side of the projectile" is not what causes horizontal wind drift. What causes wind drift is drag. Drag makes the projectile turn into the wind, much like a weather vane, keeping the centre of air pressure on its nose. This causes the nose to be cocked (from your perspective) into the wind, the base is cocked (from your perspective) "downwind." So, (again from your perspective), the drag is pushing the projectile downwind in a nose to tail direction.


title: External ballistics

text: Wind also causes aerodynamic jump which is the vertical component of cross wind deflection caused by lateral (wind) impulses activated during free flight of a projectile or at or very near the muzzle leading to dynamic imbalance. The amount of aerodynamic jump is dependent on cross wind speed, the gyroscopic stability of the bullet at the muzzle and if the barrel twist is clockwise or anti-clockwise. Like the wind direction reversing the twist direction will reverse the aerodynamic jump direction.


title: External ballistics

text: A somewhat less obvious effect is caused by head or tailwinds. A headwind will slightly increase the relative velocity of the projectile, and increase drag and the corresponding drop. A tailwind will reduce the drag and the projectile/bullet drop. In the real world, pure head or tailwinds are rare, since wind is seldom constant in force and direction and normally interacts with the terrain it is blowing over. This often makes ultra long range shooting in head or tailwind conditions difficult.


title: External ballistics

text: The vertical angle (or elevation) of a shot will also affect the trajectory of the shot. Ballistic tables for small calibre projectiles (fired from pistols or rifles) assume a horizontal line of sight between the shooter and target with gravity acting perpendicular to the earth. Therefore, if the shooter-to-target angle is up or down, (the direction of the gravity component does not change with slope direction), then the trajectory curving acceleration due to gravity will actually be less, in proportion to the cosine of the slant angle. As a result, a projectile fired upward or downward, on a so-called "slant range," will over-shoot the same target distance on flat ground. The effect is of sufficient magnitude that hunters must adjust their target hold off accordingly in mountainous terrain. A well known formula for slant range adjustment to horizontal range hold off is known as the Rifleman's rule. The Rifleman's rule and the slightly more complex and less well known Improved Rifleman's rule models produce sufficiently accurate predictions for many small arms applications. Simple prediction models however ignore minor gravity effects when shooting uphill or downhill. The only practical way to compensate for this is to use a ballistic computer program. Besides gravity at very steep angles over long distances, the effect of air density changes the projectile encounters during flight become problematic.


title: External ballistics

text: The mathematical prediction models available for inclined fire scenarios, depending on the amount and direction (uphill or downhill) of the inclination angle and range, yield varying accuracy expectation levels.


title: External ballistics

text: Less advanced ballistic computer programs predict the same trajectory for uphill and downhill shots at the same vertical angle and range. The more advanced programs factor in the small effect of gravity on uphill and on downhill shots resulting in slightly differing trajectories at the same vertical angle and range. No publicly available ballistic computer program currently (2017) accounts for the complicated phenomena of differing air densities the projectile encounters during flight.


title: External ballistics

text: Air pressure, temperature, and humidity variations make up the ambient air density. Humidity has a counter intuitive impact. Since water vapor has a density of 0.8 grams per litre, while dry air averages about 1.225 grams per litre, higher humidity actually decreases the air density, and therefore decreases the drag.


title: External ballistics

text: Precipitation can cause significant yaw and accompanying deflection when a bullet collides with a raindrop. The further downrange such a coincidental collision occurs, the less the deflection on target will be. The weight of the raindrop and bullet also influences how much yaw is induced during such a collision. A big heavy raindrop and a light bullet will yield maximal yaw effect. A heavy bullet colliding with an equal raindrop will experience significant less yaw effect.


title: External ballistics

text: Gyroscopic drift is an interaction of the bullet's mass and aerodynamics with the atmosphere that it is flying in.


title: External ballistics

text: Even in completely calm air, with no sideways air movement at all, a spin-stabilized projectile will experience a spin-induced sideways component, due to a gyroscopic phenomenon known as "yaw of repose." For a right hand (clockwise) direction of rotation this component will always be to the right. For a left hand (counterclockwise) direction of rotation this component will always be to the left.


title: External ballistics

text: This is because the projectile's longitudinal axis (its axis of rotation) and the direction of the velocity vector of the center of gravity (CG) deviate by a small angle, which is said to be the equilibrium yaw or the yaw of repose. The magnitude of the yaw of repose angle is typically less than 0.5 degree. Since rotating objects react with an angular velocity vector 90 degrees from the applied torque vector, the bullet's axis of symmetry moves with a component in the vertical plane and a component in the horizontal plane; for right-handed (clockwise) spinning bullets, the bullet's axis of symmetry deflects to the right and a little bit upward with respect to the direction of the velocity vector, as the projectile moves along its ballistic arc. As the result of this small inclination, there is a continuous air stream, which tends to deflect the bullet to the right. Thus the occurrence of the yaw of repose is the reason for the bullet drifting to the right (for right-handed spin) or to the left (for left-handed spin). This means that the bullet is "skidding" sideways at any given moment, and thus experiencing a sideways component.


title: External ballistics

text: Doppler radar measurement results for the gyroscopic drift of several US military and other very-low-drag bullets at 1000 yards (914.4 m) look like this: