Range of a projectile
In physics, assuming a flat Earth with a uniform gravity field, no air resistance, a projectile launched with specific initial conditions will have a predictable range. The following applies for ranges. For longer ranges see sub-orbital spaceflight; the maximum horizontal distance traveled by the projectile, neglecting air resistance, can be calculated as follows: d = v 2 2 g sin 2 θ where d is the total horizontal distance travelled by the projectile. V is the velocity at which the projectile is launched g is the gravitational acceleration—usually taken to be 9.81 m/s2 near the Earth's surface θ is the angle at which the projectile is launched y0 is the initial height of the projectileIf y0 is taken to be zero, meaning that the object is being launched on flat ground, the range of the projectile will simplify to: d = v 2 g sin 2 θ Ideal projectile motion states that there is no air resistance and no change in gravitational acceleration. This assumption simplifies the mathematics and is a close approximation of actual projectile motion in cases where the distances travelled are small.
Ideal projectile motion is a good introduction to the topic before adding the complications of air resistance. A launch angle of 45 degrees displaces the projectile the farthest horizontally; this is due to the nature of right triangles. Additionally, from the equation for the range: d = v 2 sin 2 θ g We can see that the range will be maximum when the value of sin 2 θ is the highest. 2 θ has to be 90 degrees. That is to say, θ is 45 degrees. First we examine the case; the horizontal position of the projectile is x = v t cos θ In the vertical direction y = v t sin θ − 1 2 g t 2 We are interested in the time when the projectile returns to the same height it originated. Let tg be any time when the height of the projectile is equal to its initial value. 0 = v t sin θ − 1 2 g t 2 By factoring: t = 0 or t = 2 v sin θ g but t = T = time of flight T = 2 v sin θ g The first solution corresponds to when the projectile is first launched. The second solution is the useful one for determining the range of the projectile.
Plugging this value for into the horizontal equation yields x = 2 v 2 cos θ sin θ g Applying the trigonometric identity sin = sin x cos y + sin y cos x If x and y are same, sin 2 θ = 2 sin θ cos θ allows us to simplify the solution to d = v 2 sin 2 θ g Note that when is 45°, the solution becomes d max = v 2 g Now we will allow to be nonzero. Our equations of motion are now x = v t cos θ and y = y 0 + v t sin θ − 1 2 g t 2 Once again we solv
Stall (fluid dynamics)
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases. This occurs; the critical angle of attack is about 15 degrees, but it may vary depending on the fluid and Reynolds number. Stalls in fixed-wing flight are experienced as a sudden reduction in lift as the pilot increases the wing's angle of attack and exceeds its critical angle of attack. A stall does not mean that the engine have stopped working, or that the aircraft has stopped moving—the effect is the same in an unpowered glider aircraft. Vectored thrust in manned and unmanned aircraft is used to maintain altitude or controlled flight with wings stalled by replacing lost wing lift with engine or propeller thrust, thereby giving rise to post-stall technology; because stalls are most discussed in connection with aviation, this article discusses stalls as they relate to aircraft, in particular fixed-wing aircraft. The principles of stall discussed here translate to foils in other fluids as well.
A stall is a condition in aerodynamics and aviation such that if the angle of attack increases beyond a certain point lift begins to decrease. The angle at which this occurs is called the critical angle of attack; this critical angle is dependent upon the airfoil section or profile of the wing, its planform, its aspect ratio, other factors, but is in the range of 8 to 20 degrees relative to the incoming wind for most subsonic airfoils. The critical angle of attack is the angle of attack on the lift coefficient versus angle-of-attack curve at which the maximum lift coefficient occurs. Stalling is caused by flow separation which, in turn, is caused by the air flowing against a rising pressure. Whitford describes three types of stall, trailing-edge, leading-edge and thin-aerofoil, each with distinctive Cl~alpha features. For the trailing-edge stall separation begins at small angles of attack near the trailing edge of the wing while the rest of the flow over the wing remains attached; as angle of attack increases, the separated regions on the top of the wing increase in size as the flow separation moves forwards and this hinders the ability of the wing to create lift.
This is shown by the reduction in lift-slope on a Cl~alpha curve as the lift nears its maximum value. The separated flow causes buffeting. Beyond the critical angle of attack, separated flow is so dominant that additional increases in angle of attack cause the lift to fall from its peak value. Piston-engined and early jet transports had good stall behaviour with pre-stall buffet warning and, if ignored, a straight nose-drop for a natural recovery. Wing developments that came with the introduction of turbo-prop engines introduced unacceptable stall behaviour. Leading-edge developments on high-lift wings and the introduction of rear-mounted engines and high-set tailplanes on the next generation of jet transports introduced unacceptable stall behaviour; the probability of achieving the stall speed inadvertently, a hazardous event, had been calculated, in 1965, at about once in every 100,000 flights enough to justify the cost of development and incorporation of warning devices, such as stick shakers, devices to automatically provide an adequate nose-down pitch, such as stick pushers.
When the mean angle of attack of the wings is beyond the stall a spin, an autorotation of a stalled wing, may develop. A spin follows departures in roll and pitch from balanced flight. For example, a roll is damped with an unstalled wing but with wings stalled the damping moment is replaced with a propelling moment; the graph shows that the greatest amount of lift is produced as the critical angle of attack is reached. This angle is 17.5 degrees in this case. In particular, for aerodynamically thick airfoils, the critical angle is higher than with a thin airfoil of the same camber. Symmetric airfoils have lower critical angles; the graph shows that, as the angle of attack exceeds the critical angle, the lift produced by the airfoil decreases. The information in a graph of this kind is gathered using a model of the airfoil in a wind tunnel; because aircraft models are used, rather than full-size machines, special care is needed to make sure that data is taken in the same Reynolds number regime as in free flight.
The separation of flow from the upper wing surface at high angles of attack is quite different at low Reynolds number from that at the high Reynolds numbers of real aircraft. High-pressure wind tunnels are one solution to this problem. In general, steady operation of an aircraft at an angle of attack above the critical angle is not possible because, after exceeding the critical angle, the loss of lift from the wing causes the nose of the aircraft to fall, reducing the angle of attack again; this nose drop, independent of control inputs, indicates the pilot has stalled the aircraft. This graph shows the stall angle, yet in practice most pilot operating handbooks or generic flight manuals describe stalling in terms of airspeed; this is because all aircraft are equipped with an airspeed indicator, but fewer aircraft have an angle of attack indicator. An aircraft's stalling speed is published by the manufacturer for a range of weights and flap positions, but the stalling angle of attack is not published.
As speed reduces, angle of attack has to increase to keep lift
A laser designator is a laser light source, used to designate a target. Laser designators provide targeting for laser-guided bombs, missiles, or precision artillery munitions, such as the Paveway series of bombs, AGM-114 Hellfire, or the M712 Copperhead round, respectively; when a target is marked by a designator, the beam does not shine continuously. Instead, a series of coded pulses of laser light are fired; these signals bounce off the target into the sky, where they are detected by the seeker on the laser-guided munition, which steers itself towards the centre of the reflected signal. Unless the people being targeted possess laser detection equipment or can hear aircraft overhead, it is difficult for them to determine if they are being marked. Laser designators work best in clear atmospheric conditions. Cloud cover, rain or smoke can make reliable designation of targets impossible. Laser designators may be mounted on ground vehicles, naval vessels, or handheld; the U. S. Air Force selected the Lockheed Martin's Sniper Advanced Targeting Pod in 2004.
It equipped multiple USAF platforms such as the F-16, F-15E, B-1, B-52, A-10C. It operates on multiple international fighter platforms; the U. S. Navy employ LITENING and ATFLIR targeting pods on a variety of strike aircraft; the Litening II is used by many other of the world’s air forces. The United Kingdom’s Royal Air Force use the Litening III system and the French use the Damocles and ATLIS II. U. S. Air Force Joint Terminal Air Controllers and Marine Corps Forward Air Controllers employ a lightweight device, such as the AN/PED-1 Lightweight Laser Designator Rangefinder, permitting them to designate targets for Close Air Support aircraft flying overhead and in close proximity to friendly forces. Northrop Grumman's LLDR, using an eye-safe laser wavelength, recognizes targets, finds the range to a target, fixes target locations for laser-guided, GPS-guided, conventional munitions; this lightweight, interoperable system uniquely provides range finding and targeting information to other digital battlefield systems allowing the system to provide targeting information for non-guided munitions, or when laser designation is unreliable due to battlefield conditions.
Pakistan Army uses home made laser designator LDR-4. Guidance system Laser sight List of laser articles Targeting pods AN/PEQ-1 SOFLAM Lightweight Laser Designator Rangefinder, Northrop Grumman
Taiwan the Republic of China, is a state in East Asia. Neighbouring states include the People's Republic of China to the west, Japan to the northeast, the Philippines to the south. Taiwan is the most populous state and largest economy, not a member of the United Nations; the island of Taiwan was inhabited by indigenous peoples for thousands of years before the 17th century, when Dutch colonialists opened the island to mass Han immigration. After a brief rule by the Kingdom of Tungning, the island was annexed in 1683 by the Qing dynasty of China, ceded to Japan in 1895. Following the surrender of Japan in 1945, the Republic of China, which had overthrown and succeeded the Qing in 1911, took control of Taiwan; the resumption of the Chinese Civil War led to the loss of the mainland to the Communists and the flight of the ROC government to Taiwan in 1949. Although the ROC government continued to claim to be the legitimate representative of China, since 1950 its effective jurisdiction has been limited to Taiwan and several small islands.
In the early 1960s, Taiwan entered a period of industrialisation. In the 1980s and early 1990s, it changed from a one-party military dictatorship to a multi-party democracy with a semi-presidential system; as a founding member, the ROC represented China in the UN until it was replaced by the PRC in 1971. The PRC has claimed sovereignty over Taiwan and refused diplomatic relations with any country that recognises the ROC; as of 2019, Taiwan maintains official ties with 16 out of 193 UN member states. Most international organisations in which the PRC participates either refuse to grant membership to Taiwan or allow it to participate only as a non-state actor. Most major powers maintain unofficial ties with Taiwan through representative offices and institutions that function as de facto embassies and consulates. In Taiwan, the major political division is between parties favouring eventual Chinese unification and promoting a Chinese identity contrasted with those aspiring to independence and promoting a Taiwanese identity, though both sides have moderated their positions to broaden their appeal.
Taiwan is a high-income advanced economy, with a skilled and educated workforce. It has the 22nd-largest economy in the world, its high-tech industry plays a key role in the global economy, it is urbanised, is one of the most densely populated countries in the world, with most of the population concentrated on the western coast. The state is ranked in terms of civil and political liberties, health care and human development. Various names for the island of Taiwan remain in use today, each derived from explorers or rulers during a particular historical period; the name Formosa dates from 1542, when Portuguese sailors sighted an uncharted island and noted it on their maps as Ilha Formosa. The name Formosa "replaced all others in European literature" and remained in common use among English speakers into the 20th century. In the early 17th century, the Dutch East India Company established a commercial post at Fort Zeelandia on a coastal sandbar called "Tayouan", after their ethnonym for a nearby Taiwanese aboriginal tribe Taivoan people, written by the Dutch and Portuguese variously as Taiouwang, Teijoan, etc.
This name was adopted into the Chinese vernacular as the name of the sandbar and nearby area. The modern word "Taiwan" is derived from this usage, seen in various forms in Chinese historical records; the area occupied by modern-day Tainan represented the first permanent settlement by both European colonists and Chinese immigrants. The settlement grew to be the island's most important trading centre and served as its capital until 1887. Use of the current Chinese name became official as early as 1684 with the establishment of Taiwan Prefecture. Through its rapid development the entire Formosan mainland became known as "Taiwan". In his Daoyi Zhilüe, Wang Dayuan used "Liuqiu" as a name for the island of Taiwan, or the part of it closest to Penghu. Elsewhere, the name was used for the Ryukyu Islands in general or Okinawa, the largest of them; the name appears in the Book of Sui and other early works, but scholars cannot agree on whether these references are to the Ryukyus, Taiwan or Luzon. The official name of the state is the "Republic of China".
Shortly after the ROC's establishment in 1912, while it was still located on the Chinese mainland, the government used the short form "China" to refer to itself, which derives from zhōng and guó, a term which developed under the Zhou dynasty in reference to its royal demesne, the name was applied to the area around Luoyi during the Eastern Zhou and to China's Central Plain before being used as an occasional synonym for the state during the Qing era. During the 1950s and 1960s, after the government had withdrawn to Taiwan upon losing the Chinese Civil War, it was referred to as "Nationalist China" to differentiate it from "Communist China", it was a member of the United Nations representing "China" until 1971, when it lost its seat to the People's Republic of China. Over subsequent decades, the Republic of China has become known as "Taiwan", after the island that comprises 99% of the territory under its control. In some contexts ROC government publications, the name is written as "
Aerodynamics, from Greek ἀήρ aer + δυναμική, is the study of motion of air as interaction with a solid object, such as an airplane wing. It is a sub-field of fluid dynamics and gas dynamics, many aspects of aerodynamics theory are common to these fields; the term aerodynamics is used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight, first demonstrated by Otto Lilienthal in 1891. Since the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies.
Recent work in aerodynamics has focused on issues related to compressible flow and boundary layers and has become computational in nature. Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills, images and stories of flight appear throughout recorded history, such as the Ancient Greek legend of Icarus and Daedalus. Fundamental concepts of continuum and pressure gradients appear in the work of Aristotle and Archimedes. In 1726, Sir Isaac Newton became the first person to develop a theory of air resistance, making him one of the first aerodynamicists. Dutch-Swiss mathematician Daniel Bernoulli followed in 1738 with Hydrodynamica in which he described a fundamental relationship between pressure and flow velocity for incompressible flow known today as Bernoulli's principle, which provides one method for calculating aerodynamic lift. In 1757, Leonhard Euler published the more general Euler equations which could be applied to both compressible and incompressible flows.
The Euler equations were extended to incorporate the effects of viscosity in the first half of the 1800s, resulting in the Navier–Stokes equations. The Navier-Stokes equations are the most general governing equations of fluid flow and but are difficult to solve for the flow around all but the simplest of shapes. In 1799, Sir George Cayley became the first person to identify the four aerodynamic forces of flight, as well as the relationships between them, in doing so outlined the path toward achieving heavier-than-air flight for the next century. In 1871, Francis Herbert Wenham constructed the first wind tunnel, allowing precise measurements of aerodynamic forces. Drag theories were developed by Jean le Rond d'Alembert, Gustav Kirchhoff, Lord Rayleigh. In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight. Otto Lilienthal, the first person to become successful with glider flights, was the first to propose thin, curved airfoils that would produce high lift and low drag.
Building on these developments as well as research carried out in their own wind tunnel, the Wright brothers flew the first powered airplane on December 17, 1903. During the time of the first flights, Frederick W. Lanchester, Martin Kutta, Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics behind thin-airfoil and lifting-line theories as well as work with boundary layers; as aircraft speed increased, designers began to encounter challenges associated with air compressibility at speeds near or greater than the speed of sound. The differences in air flows under such conditions leads to problems in aircraft control, increased drag due to shock waves, the threat of structural failure due to aeroelastic flutter; the ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach, one of the first to investigate the properties of supersonic flow.
William John Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory for flow properties before and after a shock wave, while Jakob Ackeret led the initial work of calculating the lift and drag of supersonic airfoils. Theodore von Kármán and Hugh Latimer Dryden introduced the term transonic to describe flow speeds around Mach 1 where drag increases rapidly; this rapid increase in drag led aerodynamicists and aviators to disagree on whether supersonic flight was achievable until the sound barrier was broken for the first time in 1947 using the Bell X-1 aircraft. By the time the sound barrier was broken, aerodynamicists' understanding of the subsonic and low supersonic flow had matured; the Cold War prompted the design of an ever-evolving line of high performance aircraft. Computational fluid dynamics began as an effort to solve for flow properties around complex objects and has grown to the point where entire aircraft can be designed using computer software, with wind-tunnel tests followed by flight tests to confirm the computer predictions.
Understanding of supersonic and hypersonic aerodynamics has matured since the 1960s, the goals of aerodynamicists have shifted from the behavior of fluid flow to the engineering of a vehicle such that it interacts pedictably with the fluid flow. Designing aircraft for supersonic and hypersonic conditions, as well as the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems, continues to motivate new research in aero
Cloud cover refers to the fraction of the sky obscured by clouds when observed from a particular location. Okta is the usual unit of measurement of the cloud cover; the cloud cover is correlated to the sunshine duration as the least cloudy locales are the sunniest ones while the cloudiest areas are the least sunny places. The global cloud cover averages around 0.68 when analyzing clouds with optical depth larger than 0.1. This value is lower when considering clouds with an optical depth larger than 2, higher when counting subvisible cirrus clouds. Clouds play multiple critical roles in the climate system. In particular, being bright objects in the visible part of the solar spectrum, they efficiently reflect light to space and thus contribute to the cooling of the planet. Cloud cover thus plays an important role in the energetic balance of the atmosphere and a variation of it is a consequence of and to the climate change expected by recent studies. Cloud cover values only vary by 0.03 from year to year, whereas the local, day to day variability in cloud amount rises to 0.3 over the globe.
Most data sets agree on the fact. Lastly, there is a latitudinal variation in the cloud cover, such that around 20°N there are regions with 0.10 less cloudiness than the global mean. The same variation is found 20°S. On the other hand, in the storm regions of the Southern Hemisphere midlatitudes were found to have with 0.15-0.25 more cloudiness than the global mean at 60°S. On average, about 52% of Earth is cloud-covered at any moment; some regions are always cloudy such as the Amazon Rainforest and some others are always clear such as the Sahara Desert. McIntosh, D. H. Meteorological Glossary, Her Majesty's Stationery Office, Met. O. 842, A. P. 897, 319 p. NSDL.arm.gov, Glossary of Atmospheric Terms, From the National Science Digital Library's Atmospheric Visualization Collection. Earthobersvatory.nasa.gov, Monthly maps of global cloud cover from NASA's Earth Observatory International Satellite Cloud Climatology Project, NASA's data products on their satellite observations NASA composite satellite image
Lebanon known as the Lebanese Republic, is a country in Western Asia. It is bordered by Syria to the north and east and Israel to the south, while Cyprus is west across the Mediterranean Sea. Lebanon's location at the crossroads of the Mediterranean Basin and the Arabian hinterland facilitated its rich history and shaped a cultural identity of religious and ethnic diversity. At just 10,452 km2, it is the smallest recognized sovereign state on the mainland Asian continent; the earliest evidence of civilization in Lebanon dates back more than seven thousand years, predating recorded history. Lebanon was the home of the Canaanites/Phoenicians and their kingdoms, a maritime culture that flourished for over a thousand years. In 64 BC, the region came under the rule of the Roman Empire, became one of the Empire's leading centers of Christianity. In the Mount Lebanon range a monastic tradition known as the Maronite Church was established; as the Arab Muslims conquered the region, the Maronites held onto their identity.
However, a new religious group, the Druze, established themselves in Mount Lebanon as well, generating a religious divide that has lasted for centuries. During the Crusades, the Maronites re-established contact with the Roman Catholic Church and asserted their communion with Rome; the ties they established with the Latins have influenced the region into the modern era. The region was ruled by the Ottoman Empire from 1516 to 1918. Following the collapse of the empire after World War I, the five provinces that constitute modern Lebanon came under the French Mandate of Lebanon; the French expanded the borders of the Mount Lebanon Governorate, populated by Maronites and Druze, to include more Muslims. Lebanon gained independence in 1943, establishing confessionalism, a unique, Consociationalism-type of political system with a power-sharing mechanism based on religious communities. Bechara El Khoury, President of Lebanon during the independence, Riad El-Solh, first Lebanese prime minister and Emir Majid Arslan II, first Lebanese minister of defence, are considered the founders of the modern Republic of Lebanon and are national heroes for having led the country's independence.
Foreign troops withdrew from Lebanon on 31 December 1946, although the country was subjected to military occupations by Syria that lasted nearly thirty years before being withdrawn in April 2005 as well as the Israeli military in Southern Lebanon for fifteen years. Despite its small size, the country has developed a well-known culture and has been influential in the Arab world, powered by its large diaspora. Before the Lebanese Civil War, the country experienced a period of relative calm and renowned prosperity, driven by tourism, agriculture and banking; because of its financial power and diversity in its heyday, Lebanon was referred to as the "Switzerland of the East" during the 1960s, its capital, attracted so many tourists that it was known as "the Paris of the Middle East". At the end of the war, there were extensive efforts to revive the economy and rebuild national infrastructure. In spite of these troubles, Lebanon has the 7th highest Human Development Index and GDP per capita in the Arab world after the oil-rich economies of the Persian Gulf.
Lebanon has been a member of the United Nations since its founding in 1945 as well as of the Arab League, the Non-Aligned Movement, Organisation of the Islamic Cooperation and the Organisation internationale de la francophonie. The name of Mount Lebanon originates from the Phoenician root lbn meaning "white" from its snow-capped peaks. Occurrences of the name have been found in different Middle Bronze Age texts from the library of Ebla, three of the twelve tablets of the Epic of Gilgamesh; the name is recorded in Ancient Egyptian as Rmnn, where R stood for Canaanite L. The name occurs nearly 70 times in the Hebrew Bible, as לְבָנוֹן. Lebanon as the name of an administrative unit was introduced with the Ottoman reforms of 1861, as the Mount Lebanon Mutasarrifate, continued in the name of the State of Greater Lebanon in 1920, in the name of the sovereign Republic of Lebanon upon its independence in 1943; the borders of contemporary Lebanon are a product of the Treaty of Sèvres of 1920. Its territory was the core of the Bronze Age Phoenician city-states.
As part of the Levant, it was part of numerous succeeding empires throughout ancient history, including the Egyptian, Babylonian, Achaemenid Persian, Hellenistic and Sasanid Persian empires. After the 7th-century Muslim conquest of the Levant, it was part of the Rashidun, Abbasid Seljuk and Fatimid empires; the crusader state of the County of Tripoli, founded by Raymond IV of Toulouse in 1102, encompassed most of present-day Lebanon, falling to the Mamluk Sultanate in 1289 and to the Ottoman Empire in 1517. With the dissolution of the Ottoman Empire, Greater Lebanon fell under French mandate in 1920, gained independence under president Bechara El Khoury in 1943. Lebanon's history since independence has been marked by alternating periods of political stability and prosperity based on Beirut's position as a regional center for finance and trade, interspersed with political turmoil and