title: Pearl

text: The Hindu tradition describes the sacred Nine Pearls which were first documented in the Garuda Purana, one of the books of the Hindu scriptures. Ayurveda contains references to pearl powder as a stimulant of digestion and to treat mental ailments. According to Marco Polo, the kings of Malabar wore a necklace of 108 rubies and pearls which was given from one generation of kings to the next. The reason was that every king had to say 108 prayers every morning and every evening. At least until the beginning of the 20th century it was a Hindu custom to present a completely new, undrilled pearl and pierce it during the wedding ceremony.


title: Pearl

text: The Pearl, which can be transliterated to "Moti", a type of "Mani" from Sanskrit, is also associated with many Hindu deities, the most famous being the Kaustubha that Lord Vishnu wears on his chest.


title: Pearl

text: The Hebrew word פְּנִינִים 'pearl(s)' appears in several places in the Hebrew Bible (Job 28:18; Proverbs 3:15; 8:11; 20:15; 31:10; Lamentations 4:7), although its etymology is unclear.


title: Pearl

text: In a Christian New Testament parable (Matthew 13:45–46), Jesus compared the Kingdom of Heaven to a "pearl of great price". "Again, the kingdom of heaven is like unto a merchant man, seeking goodly (fine) pearls: Who, when he had found one pearl of great price, went and sold all that he had, and bought it."


title: Pearl

text: The twelve gates of the New Jerusalem are reportedly each made of a single pearl in Revelation 21:21, that is, the Pearly Gates. "And the twelve gates were twelve pearls: every several gate was of one pearl: and the street of the city was pure gold, as it were transparent glass."


title: Pearl

text: Holy things are compared to pearls in Matthew 7:6: "Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you."


title: Pearl

text: Pearls are also found in numerous references showing the wickedness and pride of a people, as in Revelation 18:16. "And saying, Alas, alas, that great city, that was clothed in fine linen, in purple, and scarlet, and decked with gold, and precious stones, and pearls!"


title: Pearl

text: 22:23 God will admit those who believe and work righteous deeds, to Gardens beneath which rivers flow: they shall be adorned therein with bracelets of gold and pearls; and their garments there will be of silk.


title: Pearl

text: 35:33 Gardens of Eternity will they enter: therein will they be adorned with bracelets of gold, silver and pearls; and their garments there will be of silk.


title: Pearl

text: The metaphor of a pearl appears in the longer Hymn of the Pearl, a poem respected for its high literary quality, and use of layered theological metaphor, found within one of the texts of Gnosticism.


title: Pearl

text: The Pearl of Great Price is a book of scripture in the Church of Jesus Christ of Latter-day Saints (LDS Church) and some other Latter Day Saint denominations.


title: Tank

text: A tank is an armoured fighting vehicle intended as a primary offensive weapon in front-line ground combat. Tank designs are a balance of heavy firepower, strong armour, and good battlefield mobility provided by tracks and a powerful engine; usually their main armament is mounted in a turret. They are a mainstay of modern 20th and 21st century ground forces and a key part of combined arms combat.


title: Tank

text: Modern tanks are versatile mobile land weapons platforms whose main armament is a large-caliber tank gun mounted in a rotating gun turret, supplemented by machine guns or other ranged weapons such as anti-tank guided missiles or rocket launchers. They have heavy vehicle armour which provides protection for the crew, the vehicle's munition storage, fuel tank and propulsion systems. The use of tracks rather than wheels provides improved operational mobility which allows the tank to overcome rugged terrain and adverse conditions such as mud and ice/snow better than wheeled vehicles, and thus be more flexibly positioned at advantageous locations on the battlefield. These features enable the tank to perform well in a variety of intense combat situations, simultaneously both offensively (with direct fire from their powerful main gun) and defensively (as fire support and defilade for friendly troops due to the near invulnerability to common infantry small arms and good resistance against heavier weapons, although anti-tank weapons used in 2022, some of them man-portable, have demonstrated the ability to destroy older generations of tanks with single shots), all while maintaining the mobility needed to exploit changing tactical situations. Fully integrating tanks into modern military forces spawned a new era of combat: armoured warfare.


title: Tank

text: Until the arrival of the main battle tank, tanks were typically categorized either by weight class (light, medium, heavy or superheavy tanks) or doctrinal purpose (breakthrough-, cavalry-, infantry-, cruiser-, or reconnaissance tanks). Some being larger and very heavily armoured and with large guns, while others are smaller, lightly armoured, and equipped with a smaller caliber and lighter gun. These smaller tanks move over terrain with speed and agility and can perform a reconnaissance role in addition to engaging enemy targets. The smaller, faster tank would not normally engage in battle with a larger, heavily armoured tank, except during a surprise flanking manoeuvre.


title: Tank

text: The word "tank" was first applied to the British "landships" in 1915, before they entered service, to keep their nature secret.


title: Tank

text: On 24 December 1915, a meeting took place of the Inter-Departmental Conference (including representatives of the Director of Naval Construction's Committee, the Admiralty, the Ministry of Munitions, and the War Office). Its purpose was to discuss the progress of the plans for what were described as "Caterpillar Machine Gun Destroyers or Land Cruisers." In his autobiography, Albert Gerald Stern (Secretary to the Landship Committee, later head of the Mechanical Warfare Supply Department) says that at that meeting "Mr. (Thomas J.) Macnamara (M.P., and Parliamentary and Financial Secretary to the Admiralty) then suggested, for secrecy's sake, to change the title of the Landship Committee. Mr. d'Eyncourt agreed that it was very desirable to retain secrecy by all means, and proposed to refer to the vessel as a "Water Carrier". In Government offices, committees and departments are always known by their initials. For this reason I, as Secretary, considered the proposed title totally unsuitable. In our search for a synonymous term, we changed the word "Water Carrier" to "Tank," and became the "Tank Supply" or "T.S." Committee. That is how these weapons came to be called Tanks," and incorrectly added, "and the name has now been adopted by all countries in the world."


title: Tank

text: Colonel Ernest Swinton, who was secretary to the meeting, says that he was instructed to find a non-committal word when writing his report of the proceedings. In the evening he discussed it with a fellow officer, Lt-Col Walter Dally Jones, and they chose the word "tank". "That night, in the draft report of the conference, the word 'tank' was employed in its new sense for the first time." Swinton's "Notes on the Employment of Tanks", in which he uses the word throughout, was published in January 1916.


title: Tank

text: This appears to be an imperfect recollection. He says that the name problem arose "when we shipped the first two vehicles to France the following year" (August 1916), but by that time the name "tank" had been in use for eight months. The tanks were labelled "With Care to Petrograd," but the belief was encouraged that they were a type of snowplough.


title: Tank

text: The term "tank" is used throughout the English speaking world, but other countries use different terminology. In France, the second country to use tanks in battle, the word "tank" or "tanque" was adopted initially, but was then, largely at the insistence of Colonel J.B.E. Estienne, rejected in favour of "char d'assaut" ("assault vehicle") or simply "char" ("vehicle"). During World War I, German sources tended to refer to British tanks as "Tanks" and to their own as "Kampfwagen". Later, tanks became referred to as "Panzer" (lit. "armour"), a shortened form of the full term ""Panzerkampfwagen"", literally "armoured fighting vehicle". In the Arab world, tanks are called "Dabbāba" (after a type of siege engine). In Italian, a tank is a ""carro armato"" (lit. "armed wagon"), without reference to its armour. Norway uses the term "stridsvogn" and Sweden the similar "stridsvagn" (lit. "battle wagon", also used for "chariots"), whereas Denmark uses "kampvogn" (lit. fight wagon). Finland uses "panssarivaunu" (armoured wagon), although "tankki" is also used colloquially. The Polish name "czołg", derived from verb "czołgać się" ("to crawl"), is used, depicting the way of machine's movement and its speed. In Hungarian the tank is called "harckocsi" (combat wagon), albeit "tank" is also common. In Japanese, the term is taken from Chinese and used, and this term is likewise borrowed into Korean as "jeoncha" (전차/戰車); more recent Chinese literature uses the English derived 坦克 "tǎnkè" (tank) as opposed to 戰車 "zhànchē" (battle vehicle) used in earlier days.


title: Tank

text: The modern tank is the result of a century of development from the first primitive armoured vehicles, due to improvements in technology such as the internal combustion engine, which allowed the rapid movement of heavy armoured vehicles. As a result of these advances, tanks underwent tremendous shifts in capability in the years since their first appearance. Tanks in World War I were developed separately and simultaneously by Great Britain and France as a means to break the deadlock of trench warfare on the Western Front. The first British prototype, nicknamed Little Willie, was constructed at William Foster & Co. in Lincoln, England in 1915, with leading roles played by Major Walter Gordon Wilson who designed the gearbox and hull, and by William Tritton of William Foster and Co., who designed the track plates. This was a prototype of a new design that would become the British Army's Mark I tank, the first tank used in combat in September 1916 during the Battle of the Somme. The name "tank" was adopted by the British during the early stages of their development, as a security measure to conceal their purpose (see etymology). While the British and French built thousands of tanks in World War I, Germany was unconvinced of the tank's potential, and did not have enough resources, thus it built only twenty.


title: Tank

text: Tanks of the interwar period evolved into the much larger and more powerful designs of World War II. Important new concepts of armoured warfare were developed; the Soviet Union launched the first mass tank/air attack at Khalkhin Gol (Nomonhan) in August 1939, and later developed the T-34, one of the predecessors of the main battle tank. Less than two weeks later, Germany began their large-scale armoured campaigns that would become known as blitzkrieg ("lightning war") – massed concentrations of tanks combined with motorized and mechanized infantry, artillery and air power designed to break through the enemy front and collapse enemy resistance.


title: Tank

text: The widespread introduction of high-explosive anti-tank warheads during the second half of World War II led to lightweight infantry-carried anti-tank weapons such as the Panzerfaust, which could destroy some types of tanks. Tanks in the Cold War were designed with these weapons in mind, and led to greatly improved armour types during the 1960s, especially composite armour. Improved engines, transmissions and suspensions allowed tanks of this period to grow larger. Aspects of gun technology changed significantly as well, with advances in shell design and aiming technology.


title: Tank

text: During the Cold War, the main battle tank concept arose and became a key component of modern armies. In the 21st century, with the increasing role of asymmetrical warfare and the end of the Cold War, that also contributed to the increase of cost-effective anti-tank rocket propelled grenades (RPGs) worldwide and its successors, the ability of tanks to operate independently has declined. Modern tanks are more frequently organized into combined arms units which involve the support of infantry, who may accompany the tanks in infantry fighting vehicles, and supported by reconnaissance or ground-attack aircraft.


title: Tank

text: The tank is the 20th century realization of an ancient concept: that of providing troops with mobile protection and firepower. The internal combustion engine, armour plate, and continuous track were key innovations leading to the invention of the modern tank.


title: Tank

text: Many sources imply that Leonardo da Vinci and H.G. Wells in some way foresaw or "invented" the tank. Leonardo's late 15th century drawings of what some describe as a "tank" show a man-powered, wheeled vehicle with cannons all around it. However the human crew would not have enough power to move it over larger distance, and usage of animals was problematic in a space so confined. In the 15th century, Jan Žižka built armoured wagons containing cannons and used them effectively in several battles. The continuous "caterpillar" track arose from attempts to improve the mobility of wheeled vehicles by spreading their weight, reducing ground pressure, and increasing their traction. Experiments can be traced back as far as the 17th century, and by the late nineteenth they existed in various recognizable and practical forms in several countries.


title: Tank

text: It is frequently claimed that Richard Lovell Edgeworth created a caterpillar track. It is true that in 1770 he patented a "machine, that should carry and lay down its own road", but this was Edgeworth's choice of words. His own account in his autobiography is of a horse-drawn wooden carriage on eight retractable legs, capable of lifting itself over high walls. The description bears no similarity to a caterpillar track. Armoured trains appeared in the mid-19th century, and various armoured steam and petrol-engined vehicles were also proposed.


title: Tank

text: The machines described in Wells' 1903 short story "The Land Ironclads" are a step closer, insofar as they are armour-plated, have an internal power plant, and are able to cross trenches. Some aspects of the story foresee the tactical use and impact of the tanks that later came into being. However, Wells' vehicles were driven by steam and moved on pedrail wheels, technologies that were already outdated at the time of writing. After seeing British tanks in 1916, Wells denied having "invented" them, writing, "Yet let me state at once that I was not their prime originator. I took up an idea, manipulated it slightly, and handed it on." It is, though, possible that one of the British tank pioneers, Ernest Swinton, was subconsciously or otherwise influenced by Wells' tale.


title: Tank

text: The first combinations of the three principal components of the tank appeared in the decade before World War One. In 1903, Captain Léon René Levavasseur of the French artillery proposed mounting a field gun in an armoured box on tracks. Major William E. Donohue, of the British Army's Mechanical Transport Committee, suggested fixing a gun and armoured shield on a British type of track-driven vehicle. The first armoured car was produced in Austria in 1904. However, all were restricted to rails or reasonably passable terrain. It was the development of a practical caterpillar track that provided the necessary independent, all-terrain mobility.


title: Tank

text: In a memorandum of 1908, Antarctic explorer Robert Falcon Scott presented his view that man-hauling to the South Pole was impossible and that motor traction was needed. Snow vehicles did not yet exist however, and so his engineer Reginald Skelton developed the idea of a caterpillar track for snow surfaces. These tracked motors were built by the Wolseley Tool and Motor Car Company in Birmingham, tested in Switzerland and Norway, and can be seen in action in Herbert Ponting's 1911 documentary film of Scott's Antarctic Terra Nova Expedition). Scott died during the expedition in 1912, but expedition member and biographer Apsley Cherry-Garrard credited Scott's "motors" with the inspiration for the British World War I tanks, writing: "Scott never knew their true possibilities; for they were the direct ancestors of the 'tanks' in France".


title: Tank

text: In 1911, a Lieutenant Engineer in the Austrian Army, Günther Burstyn, presented to the Austrian and Prussian War Ministries plans for a light, three-man tank with a gun in a revolving turret, the so-called Burstyn-Motorgeschütz. In the same year an Australian civil engineer named Lancelot de Mole submitted a basic design for a tracked, armoured vehicle to the British War Office. In Russia, Vasiliy Mendeleev designed a tracked vehicle containing a large naval gun. All of these ideas were rejected and, by 1914, forgotten (although it was officially acknowledged after the war that de Mole's design was at least the equal to the initial British tanks). Various individuals continued to contemplate the use of tracked vehicles for military applications, but by the outbreak of the War no one in a position of responsibility in any army gave much thought to tanks.


title: Tank

text: From late 1914 a small number of middle-ranking British Army officers tried to persuade the War Office and the Government to consider the creation of armoured vehicles. Amongst their suggestions was the use of caterpillar tractors, but although the Army used many such vehicles for towing heavy guns, it could not be persuaded that they could be adapted as armoured vehicles. The consequence was that early tank development in the United Kingdom was carried out by the Royal Navy.


title: Tank

text: As the result of an approach by Royal Naval Air Service officers who had been operating armoured cars on the Western Front, the First Lord of the Admiralty, Winston Churchill, formed the Landship Committee, on 20 February 1915. The Director of Naval Construction for the Royal Navy, Eustace Tennyson d'Eyncourt, was appointed to head the Committee in view of his experience with the engineering methods it was felt might be required; the two other members were naval officers, and a number of industrialists were engaged as consultants. So many played a part in its long and complicated development that it is not possible to name any individual as the sole inventor of the tank.


title: Tank

text: However leading roles were played by Lt Walter Gordon Wilson R.N. who designed the gearbox and developed practical tracks and by William Tritton whose agricultural machinery company, William Foster & Co. in Lincoln, Lincolnshire, England built the prototypes. On 22 July 1915, a commission was placed to design a machine that could cross a trench 4 ft wide. Secrecy surrounded the project with the designers locking themselves in a room at the White Hart Hotel in Lincoln. The committee's first design, Little Willie, ran for the first time in September 1915 and served to develop the form of the track but an improved design, better able to cross trenches, swiftly followed and in January 1916 the prototype, nicknamed "Mother", was adopted as the design for future tanks. The first order for tanks was placed on 12 February 1916, and a second on 21 April. Fosters built 37 (all "male"), and Metropolitan Railway Carriage and Wagon Company, of Birmingham, 113 (38 "male" and 75 "female"), a total of 150. Production models of "Male" tanks (armed with naval cannon and machine guns) and "Females" (carrying only machine-guns) would go on to fight in history's first tank action at the Somme in September 1916. Great Britain produced about 2,600 tanks of various types during the war. The first tank to engage in battle was designated "D1", a British Mark I Male, during the Battle of Flers-Courcelette (part of the wider Somme offensive) on 15 September 1916. Bert Chaney, a nineteen-year-old signaller with the 7th London Territorial Battalion, reported that "three huge mechanical monsters such as [he] had never seen before" rumbled their way onto the battlefield, "frightening the Jerries out of their wits and making them scuttle like frightened rabbits." When the news of the first use of the tanks emerged, Prime Minister David Lloyd George commented,


title: Tank

text: Whilst several experimental machines were investigated in France, it was a colonel of artillery, J.B.E. Estienne, who directly approached the Commander-in-Chief with detailed plans for a tank on caterpillar tracks, in late 1915. The result was two largely unsatisfactory types of tank, 400 each of the Schneider and Saint-Chamond, both based on the Holt Tractor.


title: Tank

text: The following year, the French pioneered the use of a full 360° rotation turret in a tank for the first time, with the creation of the Renault FT light tank, with the turret containing the tank's main armament. In addition to the traversable turret, another innovative feature of the FT was its engine located at the rear. This pattern, with the gun located in a mounted turret and the engine at the back, has become the standard for most succeeding tanks across the world even to this day. The FT was the most numerous tank of the war; over 3,000 were made by late 1918.


title: Tank

text: Germany fielded very few tanks during World War I, and started development only after encountering British tanks on the Somme. The A7V, the only type made, was introduced in March 1918 with just 20 being produced during the war. The first tank "versus" tank action took place on 24 April 1918 at the Second Battle of Villers-Bretonneux, France, when three British Mark IVs met three German A7Vs. Captured British Mk IVs formed the bulk of Germany's tank forces during World War I; about 35 were in service at any one time. Plans to expand the tank programme were under way when the War ended.


title: Tank

text: The United States Tank Corps used tanks supplied by France and Great Britain during World War I. Production of American-built tanks had just begun when the War came to an end. Italy also manufactured two Fiat 2000s towards the end of the war, too late to see service. Russia independently built and trialed two prototypes early in the War; the tracked, two-man Vezdekhod and the huge Lebedenko, but neither went into production. A tracked self-propelled gun was also designed but not produced.


title: Tank

text: Although tank tactics developed rapidly during the war, piecemeal deployments, mechanical problems, and poor mobility limited the military significance of the tank in World War I, and the tank did not fulfil its promise of rendering trench warfare obsolete. Nonetheless, it was clear to military thinkers on both sides that tanks in some way could have a significant role in future conflicts.


title: Tank

text: In the interwar period tanks underwent further mechanical development. In terms of tactics, J.F.C. Fuller's doctrine of spearhead attacks with massed tank formations was the basis for work by Heinz Guderian in Germany, Percy Hobart in Britain, Adna R. Chaffee, Jr., in the US, Charles de Gaulle in France, and Mikhail Tukhachevsky in the USSR. Liddell Hart held a more moderate view that all arms – cavalry, infantry and artillery – should be mechanized and work together. The British formed the all-arms Experimental Mechanized Force to test the use of tanks with supporting forces.


title: Tank

text: In the Second World War only Germany would initially put the theory into practice on a large scale, and it was their superior tactics and French blunders, not superior weapons, that made the "blitzkrieg" so successful in May 1940. For information regarding tank development in this period, see tank development between the wars.


title: Tank

text: Germany, Italy and the Soviet Union all experimented heavily with tank warfare during their clandestine and "volunteer" involvement in the Spanish Civil War, which saw some of the earliest examples of successful mechanized combined arms —such as when Republican troops, equipped with Soviet-supplied tanks and supported by aircraft, eventually routed Italian troops fighting for the Nationalists in the seven-day Battle of Guadalajara in 1937. However, of the nearly 700 tanks deployed during this conflict, only about 64 tanks representing the "Franco" faction and 331 from the "Republican" side were equipped with cannon, and of those 64 nearly all were World War I vintage Renault FT tanks, while the 331 Soviet supplied machines had 45mm main guns and were of 1930s manufacture. The balance of "Nationalist" tanks were machine gun armed. The primary lesson learned from this war was that machine gun armed tanks had to be equipped with cannon, with the associated armour inherent to modern tanks.


title: Tank

text: The five-month-long war between the Soviet Union and the Japanese 6th Army at "Khalkhin Gol" (Nomonhan) in 1939 brought home some lessons. In this conflict, the Soviets fielded over two thousand tanks, to the around 73 cannon armed tanks deployed by the Japanese, the major difference being that Japanese armour were equipped with diesel engines as opposed to the Russian tanks equipped with petrol engines. After General Georgy Zhukov inflicted a defeat on the Japanese 6th Army with his massed combined tank and air attack, the Soviets learned a lesson on the use of gasoline engines, and quickly incorporated those newly found experiences into their new T-34 medium tank during World War II.


title: Tank

text: Prior to World War II, the tactics and strategy of deploying tank forces underwent a revolution. In August 1939, Soviet General Georgy Zhukov used the combined force of tanks and airpower at Nomonhan against the Japanese 6th Army; Heinz Guderian, a tactical theoretician who was heavily involved in the formation of the first independent German tank force, said "Where tanks are, the front is", and this concept became a reality in World War II. Guderian's armoured warfare ideas, combined with Germany's existing doctrines of "Bewegungskrieg" ("maneuver warfare") and infiltration tactics from World War I, became the basis of blitzkrieg in the opening stages of World War II.


title: Tank

text: During World War II, the first conflict in which armoured vehicles were critical to battlefield success, the tank and related tactics developed rapidly. armoured forces proved capable of tactical victory in an unprecedentedly short amount of time, yet new anti-tank weaponry showed that the tank was not invulnerable. During the Invasion of Poland, tanks performed in a more traditional role in close cooperation with infantry units, but in the Battle of France deep independent armoured penetrations were executed by the Germans, a technique later called "blitzkrieg". Blitzkrieg used innovative combined arms tactics and radios in all of the tanks to provide a level of tactical flexibility and power that surpassed that of the Allied armour. The French Army, with tanks equal or superior to the German tanks in both quality and quantity, employed a linear defensive strategy in which the armoured cavalry units were made subservient to the needs of the infantry armies to cover their entrenchment in Belgium. In addition, they lacked radios in many of their tanks and headquarters, which limited their ability to respond to German attacks.


title: Tank

text: In accordance with blitzkrieg methods, German tanks bypassed enemy strongpoints and could radio for close air support to destroy them, or leave them to the infantry. A related development, motorized infantry, allowed some of the troops to keep up with the tanks and create highly mobile combined arms forces. The defeat of a major military power within weeks shocked the rest of the world, spurring tank and anti-tank weapon development.


title: Tank

text: The North African Campaign also provided an important battleground for tanks, as the flat, desolate terrain with relatively few obstacles or urban environments was ideal for conducting mobile armoured warfare. However, this battlefield also showed the importance of logistics, especially in an armoured force, as the principal warring armies, the German Afrika Korps and the British Eighth Army, often outpaced their supply trains in repeated attacks and counter-attacks on each other, resulting in complete stalemate. This situation would not be resolved until 1942, when during the Second Battle of El Alamein, the Afrika Korps, crippled by disruptions in their supply lines, had 95% of its tanks destroyed and was forced to retreat by a massively reinforced Eighth Army, the first in a series of defeats that would eventually lead to the surrender of the remaining Axis forces in Tunisia.


title: Tank

text: When Germany launched its invasion of the Soviet Union, Operation Barbarossa, the Soviets had a superior tank design, the T-34. A lack of preparations for the Axis surprise attack, mechanical problems, poor training of the crews and incompetent leadership caused the Soviet machines to be surrounded and destroyed in large numbers. However, interference from Adolf Hitler, the geographic scale of the conflict, the dogged resistance of the Soviet combat troops, and the Soviets' massive advantages in manpower and production capability prevented a repeat of the German successes of 1940. Despite early successes against the Soviets, the Germans were forced to up-gun their Panzer IVs, and to design and build both the larger and more expensive Tiger heavy tank in 1942, and the Panther medium tank the following year. In doing so, the "Wehrmacht" denied the infantry and other support arms the production priorities that they needed to remain equal partners with the increasingly sophisticated tanks, in turn violating the principle of combined arms they had pioneered. Soviet developments following the invasion included upgunning the T-34, development of self-propelled anti-tank guns such as the SU-152, and deployment of the IS-2 in the closing stages of the war, with the T-34 being the most produced tank of World War II, totalling up to some 65,000 examples by May 1945.


title: Tank

text: Much like the Soviets, when entering World War II six months later (December 1941), the United States' mass production capacity enabled it to rapidly construct thousands of relatively cheap M4 Sherman medium tanks. A compromise all round, the Sherman was reliable and formed a large part of the Anglo-American ground forces, but in a tank-versus-tank battle was no match for the Panther or Tiger. Numerical and logistical superiority and the successful use of combined arms allowed the Allies to overrun the German forces during the Battle of Normandy. Upgunned versions with the 76 mm gun M1 and the 17-pounder were introduced to improve the M4's firepower, but concerns about protection remained—despite the apparent armour deficiencies, a total of some 42,000 Shermans were built and delivered to the Allied nations using it during the war years, a total second only to the T-34.


title: Tank

text: Tank hulls were modified to produce flame tanks, mobile rocket artillery, and combat engineering vehicles for tasks including mine-clearing and bridging. Specialized self-propelled guns, most of which could double as tank destroyers, were also both developed by the Germans—with their "Sturmgeschütz", "Panzerjäger" and "Jagdpanzer" vehicles—and the "Samokhodnaya ustanovka" families of AFV's for the Soviets: such turretless, casemate-style tank destroyers and assault guns were less complex, stripped down tanks carrying heavy guns, solely firing forward. The firepower and low cost of these vehicles made them attractive but as manufacturing techniques improved and larger turret rings made larger tank guns feasible, the gun turret was recognized as the most effective mounting for the main gun to allow movement in a different direction from firing, enhancing tactical flexibility.


title: Tank

text: During the Cold War, tension between the Warsaw Pact countries and North Atlantic Treaty Organization (NATO) countries created an arms race that ensured that tank development proceeded largely as it had during World War II. The essence of tank designs during the Cold War had been hammered out in the closing stages of World War II. Large turrets, capable suspension systems, greatly improved engines, sloped armour and large-caliber (90 mm and larger) guns were standard. Tank design during the Cold War built on this foundation and included improvements to fire control, gyroscopic gun stabilization, communications (primarily radio) and crew comfort and saw the introduction of laser rangefinders and infrared night vision equipment. armour technology progressed in an ongoing race against improvements in anti-tank weapons, especially antitank guided missiles like the TOW.


title: Tank

text: Medium tanks of World War II evolved into the "main battle tank" (MBT) of the Cold War and took over the majority of tank roles on the battlefield. This gradual transition occurred in the 1950s and 1960s due to anti-tank guided missiles, sabot ammunition and high-explosive anti-tank warheads. World War II had shown that the speed of a light tank was no substitute for armour & firepower and medium tanks were vulnerable to newer weapon technology, rendering them obsolete.


title: Tank

text: In a trend started in World War II, economies of scale led to serial production of progressively upgraded models of all major tanks during the Cold War. For the same reason many upgraded post-World War II tanks and their derivatives (for example, the T-55 and T-72) remain in active service around the world, and even an obsolete tank may be the most formidable weapon on battlefields in many parts of the world. Among the tanks of the 1950s were the British Centurion and Soviet T-54/55 in service from 1946, and the US M48 from 1951. These three vehicles formed the bulk of the armoured forces of NATO and the Warsaw Pact throughout much of the Cold War. Lessons learned from tanks such as the Leopard 1, M48 Patton series, Chieftain, and T-72 led to the contemporary Leopard 2, M1 Abrams, Challenger 2, C1 Ariete, T-90 and Merkava IV.


title: Tank

text: Tanks and anti-tank weapons of the Cold War era saw action in a number of proxy wars like the Korean War, Vietnam War, Indo-Pakistani War of 1971, Soviet–Afghan War and Arab-Israeli conflicts, culminating with the Yom Kippur War. The T-55, for example, has seen action in no fewer than 32 conflicts. In these wars the U.S. or NATO countries and the Soviet Union or China consistently backed opposing forces. Proxy wars were studied by Western and Soviet military analysts and provided a contribution to the Cold War tank development process.


title: Tank

text: The role of tank vs. tank combat is becoming diminished. Tanks work in concert with infantry in urban warfare by deploying them ahead of the platoon. When engaging enemy infantry, tanks can provide covering fire on the battlefield. Conversely, tanks can spearhead attacks when infantry are deployed in personnel carriers.


title: Tank

text: Tanks were used to spearhead the initial US invasion of Iraq in 2003. As of 2005, there were 1,100 M1 Abrams used by the United States Army in the course of the Iraq War, and they have proven to have an unexpectedly high level of vulnerability to roadside bombs. A relatively new type of remotely detonated mine, the explosively formed penetrator has been used with some success against American armoured vehicles (particularly the Bradley fighting vehicle). However, with upgrades to their armour in the rear, M1s have proven invaluable in fighting insurgents in urban combat, particularly at the Battle of Fallujah, where the US Marines brought in two extra brigades.


title: Tank

text: Israeli Merkava tanks contain features that enable them to support infantry in low intensity conflicts (LIC) and counter-terrorism operations. Such features are the rear door and rear corridor, enabling the tank to carry infantry and embark safely; the IMI APAM-MP-T multi-purpose ammunition round, advanced C4IS systems and recently: TROPHY active protection system which protects the tank from shoulder-launched anti-tank weapons. During the Second Intifada further modifications were made, designated as "Merkava Mk. 3d Baz LIC".


title: Tank

text: In terms of firepower, the focus of 2010s-era R&D was increased detection capability such as thermal imagers, automated fire control systems for the guns and increased muzzle energy from the gun to improve range, accuracy and armour penetration. The most mature future gun technology is the electrothermal-chemical gun. The XM291 electrothermal-chemical tank gun has gone through successful multiple firing sequences on a modified American M8 Armored Gun System chassis. To improve tank protection, one field of research involves making the tank invisible to radar by adapting stealth technologies originally designed for aircraft. Improvements to camouflage or and attempts to render it invisible through active camouflage, which changes according to where the tank is located, are being pursued. Research is also ongoing in electromagnetic armour systems to disperse or deflect incoming shaped charges, as well as various forms of active protection systems to prevent incoming projectiles (RPGs, missiles, etc.) from striking the tank.


title: Tank

text: Mobility may be enhanced in future tanks by the use of diesel-electric or turbine-electric series hybrid drives—first used in a primitive, gasoline-engined form with Porsche's "Elefant" German tank destroyer of 1943—improving fuel efficiency while reducing the size and weight of the power plant. Furthermore, advances in gas turbine technology, including the use of advanced recuperators, have allowed for reduction in engine volume and mass to less than 1 m and 1 metric ton, respectively, while maintaining fuel efficiency similar to that of a diesel engine. In line with the new doctrine of network-centric warfare, the 2010s-era modern battle tank shows increasing sophistication in its electronics and communication systems. The future of tanks has been challenged by the proliferation of relatively inexpensive anti tank guided missiles and rockets during the Russo-Ukrainian War.


title: Tank

text: The three traditional factors determining a tank's capability effectiveness are its "firepower", "protection", and "mobility". Firepower is the ability of a tank's crew to identify, engage, and destroy enemy tanks and other targets using its large-caliber cannon. Protection is the degree to which the tank's armour, profile and camouflage enables the tank crew to evade detection, protect themselves from enemy fire, and retain vehicle functionality during and after combat. Mobility includes how well the tank can be transported by rail, sea, or air to the operational staging area; from the staging area by road or over terrain towards the enemy; and tactical movement by the tank over the battlefield during combat, including traversing of obstacles and rough terrain. The variations of tank designs have been determined by the way these three fundamental features are blended. For instance, in 1937, the French doctrine focused on firepower and protection more than mobility because tanks worked in intimate liaison with the infantry. There was also the case of the development of a heavy cruiser tank, which focused on armour and firepower to challenge Germany's Tiger and Panther tanks.


title: Tank

text: Tanks have been classified by weight, role, or other criteria, that has changed over time and place. Classification is determined by the prevailing theories of armoured warfare, which have been altered in turn by rapid advances in technology. No one classification system works across all periods or all nations; in particular, weight-based classification is inconsistent between countries and eras.


title: Tank

text: In World War I, the first tank designs focused on crossing wide trenches, requiring very long and large vehicles, such as the British Mark I; these became classified as heavy tanks. Tanks that fulfilled other combat roles were smaller, like the French Renault FT; these were classified as light tanks or tankettes. Many late-war and inter-war tank designs diverged from these according to new, though mostly untried, concepts for future tank roles and tactics. Tank classifications varied considerably according to each nation's own tank development, such as "cavalry tanks", "fast tanks", and "breakthrough tanks".


title: Tank

text: During World War II, many tank concepts were found unsatisfactory and discarded, mostly leaving the more multi-role tanks; these became easier to classify. Tank classes based on weight (and the corresponding transport and logistical needs) led to new definitions of heavy and light tank classes, with medium tanks covering the balance of those between. The British maintained cruiser tanks, focused on speed, and infantry tanks that traded speed for more armour. Tank destroyers are tanks or other armoured fighting vehicles specifically designed to defeat enemy tanks. Assault guns are armoured fighting vehicles that could combine the roles of infantry tanks and tank destroyers. Some tanks were converted to flame tanks, specializing on close-in attacks on enemy strongholds with flamethrowers. As the war went on, tanks tended to become larger and more powerful, shifting some tank classifications and leading to super-heavy tanks.


title: Tank

text: Experience and technology advances during the Cold War continued to consolidate tank roles. With the worldwide adoption of the modern main battle tank designs, which favour a modular universal design, most other classifications are dropped from modern terminology. All main battle tanks tend to have a good balance of speed, armour, and firepower, even while technology continues to improve all three. Being fairly large, main battle tanks can be complemented with light tanks, armoured personnel carriers, infantry fighting vehicles or similar relatively lighter armoured fighting vehicles, typically in the roles of armoured reconnaissance, amphibious or air assault operations, or against enemies lacking main battle tanks.


title: Tank

text: The main weapon of modern tanks is typically a single, large-caliber cannon mounted in a fully traversing (rotating) gun turret. The typical modern tank gun is a smoothbore weapon capable of firing a variety of ammunition, including armour-piercing kinetic energy penetrators (KEP), also known as armour-piercing discarding sabot (APDS), and/or armour-piercing fin-stabilized discarding sabot (APFSDS) and high-explosive anti-tank (HEAT) shells, and/or high-explosive squash head (HESH) and/or anti-tank guided missiles (ATGM) to destroy armoured targets, as well as high-explosive (HE) shells for shooting at "soft" targets (unarmoured vehicles or troops) or fortifications. Canister shot may be used in close or urban combat situations where the risk of hitting friendly forces with shrapnel from HE rounds is unacceptably high.


title: Tank

text: A gyroscope is used to stabilise the main gun, allowing it to be effectively aimed and fired at the "short halt" or on the move. Modern tank guns are also commonly fitted with insulating thermal sleeves to reduce gun-barrel warping caused by uneven thermal expansion, bore evacuators to minimise gun firing fumes entering the crew compartment and sometimes muzzle brakes to minimise the effect of recoil on accuracy and rate of fire.


title: Tank

text: Traditionally, target detection relied on visual identification. This was accomplished from within the tank through telescopic periscopes; often, however, tank commanders would open up the hatch to view the outside surroundings, which improved situational awareness but incurred the penalty of vulnerability to sniper fire. Though several developments in target detection have taken place, these methods are still common practice. In the 2010s, more electronic target detection methods are available.


title: Tank

text: In some cases spotting rifles were used to confirm proper trajectory and range to a target. These spotting rifles were mounted co-axially to the main gun, and fired tracer ammunition ballistically matched to the gun itself. The gunner would track the movement of the tracer round in flight, and upon impact with a hard surface, it would give off a flash and a puff of smoke, after which the main gun was immediately fired. However this slow method has been mostly superseded by laser rangefinding equipment.


title: Tank

text: Modern tanks also use sophisticated light intensification and thermal imaging equipment to improve fighting capability at night, in poor weather and in smoke. The accuracy of modern tank guns is pushed to the mechanical limit by computerized fire-control systems. A fire-control system uses a laser rangefinder to determine the range to the target, a thermocouple, anemometer and wind vane to correct for weather effects and a muzzle referencing system to correct for gun-barrel temperature, warping and wear. Two sightings of a target with the range-finder enable calculation of the target movement vector. This information is combined with the known movement of the tank and the principles of ballistics to calculate the elevation and aim point that maximises the probability of hitting the target.


title: Tank

text: Usually, tanks carry smaller caliber armament for short-range defense where fire from the main weapon would be ineffective or wasteful, for example when engaging infantry, light vehicles or close air support aircraft. A typical complement of secondary weapons is a general-purpose machine gun mounted coaxially with the main gun, and a heavier anti-aircraft-capable machine gun on the turret roof. Some tanks also have a hull-mounted machine gun. These weapons are often modified variants of those used by infantry, and so use the same kinds of ammunition.


title: Tank

text: The measure of a tank's protection is the combination of its ability to avoid detection (due to having a low profile and through the use of camouflage), to avoid being hit by enemy fire, its resistance to the effects of enemy fire, and its capacity to sustain damage whilst still completing its objective, or at least protecting its crew. This is done by a variety of countermeasures, such as armour plating and reactive defenses, as well as more complex ones such as heat-emissions reduction.


title: Tank

text: In common with most unit types, tanks are subject to additional hazards in dense wooded and urban combat environments which largely negate the advantages of the tank's long-range firepower and mobility, limit the crew's detection capabilities and can restrict turret traverse. Despite these disadvantages, tanks retain high survivability against previous-generation rocket-propelled grenades aimed at the most-armoured sections.


title: Tank

text: However, as effective and advanced as armour plating has become, tank survivability against newer-generation tandem-warhead anti-tank missiles is a concern for military planners. Tandem-warhead RPGs use two warheads to fool active protection systems; a first dummy warhead is fired first, to trigger the active defenses, with the real warhead following it. For example, the RPG-29 from the 1980s is able to penetrate the frontal hull armour of the Challenger II and also managed to damage a M1 Abrams. As well, even tanks with advanced armour plating can have their tracks or gear cogs damaged by RPGs, which may render them immobile or hinder their mobility. Despite all of the advances in armour plating, a tank with its hatches open remains vulnerable to Molotov cocktail (gasoline bombs) and grenades. Even a "buttoned up" tank may have components which are vulnerable to Molotov cocktails, such as optics, extra gas cans and extra ammunition stored on the outside of the tank.


title: Tank

text: A tank avoids detection using the doctrine of countermeasures known as CCD: camouflage (looks the same as the surroundings), concealment (cannot be seen) and deception (looks like something else).


title: Tank

text: Camouflage can include disruptive painted shapes on the tank to break up the distinctive appearance and silhouette of a tank. Netting or actual branches from the surrounding landscape are also used. Prior to development of infrared technology, tanks were often given a coating of camouflage paint that, depending on environmental region or season, would allow it to blend in with the rest of its environment. A tank operating in wooded areas would typically get a green and brown paintjob; a tank in a winter environment would get white paint (often mixed with some darker colors); tanks in the desert often get khaki paintjobs.


title: Tank

text: The Russian Nakidka camouflage kit was designed to reduce the optical, thermal, infrared, and radar signatures of a tank, so that acquisition of the tank would be difficult. According to Nii Stali, the designers of Nakidka, Nakidka would reduce the probabilities of detection via "visual and near-IR bands by 30%, the thermal band by 2–3-fold, radar band by 6-fold, and radar-thermal band to near-background levels.


title: Tank

text: Concealment can include hiding the tank among trees or digging in the tank by having a combat bulldozer dig out part of a hill, so that much of the tank will be hidden. A tank commander can conceal the tank by using "hull down" approaches to going over upward-sloping hills, so that she or he can look out the commander's cupola without the distinctive-looking main cannon cresting over the hill. Adopting a turret-down or hull-down position reduces the visible silhouette of a tank as well as providing the added protection of a position in defilade.


title: Tank

text: Working against efforts to avoid detection is the fact that a tank is a large metallic object with a distinctive, angular silhouette that emits copious heat and engine noise. A tank that is operating in cold weather or which needs to use its radio or other communications or target-detecting electronics will need to start its engine regularly to maintain its battery power, which will create engine noise. Consequently, it is difficult to effectively camouflage a tank in the absence of some form of cover or concealment (e.g., woods) it can hide its hull behind. The tank becomes easier to detect when moving (typically, whenever it is in use) due to the large, distinctive auditory, vibration and thermal signature of its engine and power plant. Tank tracks and dust clouds also betray past or present tank movement.


title: Tank

text: Switched-off tanks are vulnerable to infra-red detection due to differences between the thermal conductivity and therefore heat dissipation of the metallic tank and its surroundings. At close range the tank can be detected even when powered down and fully concealed due to the column of warmer air above the tank and the smell of diesel or gasoline. Thermal blankets slow the rate of heat emission and some thermal camouflage nets use a mix of materials with differing thermal properties to operate in the infra-red as well as the visible spectrum.


title: Tank

text: Grenade launchers can rapidly deploy a smoke screen that is opaque to infrared light, to hide it from the thermal viewer of another tank. In addition to using its own grenade launchers, a tank commander could call in an artillery unit to provide smoke cover. Some tanks can produce a smoke screen.


title: Tank

text: Sometimes camouflage and concealment are used at the same time. For example, a camouflage-painted and branch-covered tank (camouflage) may be hidden in a behind a hill or in a dug-in-emplacement (concealment).


title: Tank

text: Some armoured recovery vehicles (often tracked, tank chassis-based "tow trucks" for tanks) have dummy turrets and cannons. This makes it less likely that enemy tanks will fire on these vehicles. Some armies have fake "dummy" tanks made of wood which troops can carry into position and hide behind obstacles. These "dummy" tanks may cause the enemy to think that there are more tanks than are actually possessed.


title: Tank

text: To effectively protect the tank and its crew, tank armour must counter a wide variety of antitank threats. Protection against kinetic energy penetrators and high-explosive anti-tank (HEAT) shells fired by other tanks is of primary importance, but tank armour also aims to protect against infantry mortars, grenades, rocket-propelled grenades, anti-tank guided missiles, anti-tank mines, anti-tank rifles, bombs, direct artillery hits, and (less often) nuclear, biological and chemical threats, any of which could disable or destroy a tank or its crew.


title: Tank

text: Steel armour plate was the earliest type of armour. The Germans pioneered the use of face hardened steel during World War II and the Soviets also achieved improved protection with sloped armour technology. World War II developments led to the obsolescence of homogeneous steel armour with the development of shaped-charge warheads, exemplified by the Panzerfaust and bazooka infantry-carried weapons which were effective, despite some early success with spaced armour. Magnetic mines led to the development of anti-magnetic paste and paint. From WWII to the modern era, troops have added improvised armour to tanks while in combat settings, such as sandbags or pieces of old armour plating.


title: Tank

text: British tank researchers took the next step with the development of Chobham armour, or more generally composite armour, incorporating ceramics and plastics in a resin matrix between steel plates, which provided good protection against HEAT weapons. High-explosive squash head warheads led to anti-spall armour linings, and kinetic energy penetrators led to the inclusion of exotic materials like a matrix of depleted uranium into a composite armour configuration.


title: Tank

text: Reactive armour consists of small explosive-filled metal boxes that detonate when hit by the metallic jet projected by an exploding HEAT warhead, causing their metal plates to disrupt it. Tandem warheads defeat reactive armour by causing the armour to detonate prematurely. Modern reactive armour protects itself from Tandem warheads by having a thicker front metal plate to prevent the precursor charge from detonating the explosive in the reactive armour. Reactive armours can also reduce the penetrative abilities of kinetic energy penetrators by deforming the penetrator with the metal plates on the Reactive armour, thereby reducing its effectiveness against the main armour of the tank.


title: Tank

text: The latest generation of protective measures for tanks are active protection systems. The term "active" is used to contrast these approaches with the armour used as the primary protective approach in earlier tanks.


title: Tank

text: The mobility of a tank is described by its battlefield or tactical mobility, its operational mobility, and its strategic mobility.


title: Tank

text: Tank agility is a function of the weight of the tank due to its inertia while manoeuvring and its ground pressure, the power output of the installed power plant and the tank transmission and track design. In addition, rough terrain effectively limits the tank's speed through the stress it puts on the suspension and the crew. A breakthrough in this area was achieved during World War II when improved suspension systems were developed that allowed better cross-country performance and limited firing on the move. Systems like the earlier Christie or later torsion-bar suspension developed by Ferdinand Porsche dramatically improved the tank's cross-country performance and overall mobility.


title: Tank

text: Tanks are highly mobile and able to travel over most types of terrain due to their continuous tracks and advanced suspension. The tracks disperse the weight of the vehicle over a large area, resulting in less ground pressure. A tank can travel at approximately across flat terrain and up to on roads, but due to the mechanical strain this places on the vehicle and the logistical strain on fuel delivery and tank maintenance, these must be considered "burst" speeds that invite mechanical failure of engine and transmission systems. Consequently, wheeled tank transporters and rail infrastructure is used wherever possible for long-distance tank transport. The limitations of long-range tank mobility can be viewed in sharp contrast to that of wheeled armoured fighting vehicles. The majority of blitzkrieg operations were conducted at the pedestrian pace of , and that was only achieved on the roads of France.


title: Tank

text: The tank's power plant supplies kinetic energy to move the tank, and electric power via a generator to components such as the turret rotation motors and the tank's electronic systems. The tank power plant has evolved from predominantly petrol and adapted large-displacement aeronautical or automotive engines during World Wars I and II, through diesel engines to advanced multi-fuel diesel engines, and powerful (per unit weight) but fuel-hungry gas turbines in the T-80 and M1 Abrams.


title: Tank

text: Strategic mobility is the ability of the tanks of an armed force to arrive in a timely, cost effective, and synchronized fashion. For good strategic mobility transportability by air is important, which means that weight and volume must be kept within the designated transport aircraft capabilities. Nations often stockpile enough tanks to respond to any threat without having to make more tanks as many sophisticated designs can only be produced at a relatively low rate. The US for instance keeps 6,000 MBTs in storage.


title: Tank

text: In the absence of combat engineers, most tanks are limited to fording small rivers. The typical fording depth for MBTs is approximately , being limited by the height of the engine air intake and driver's position. Modern tanks such as the Russian T-90 and the German Leopard 1 and Leopard 2 tanks can ford to a depth of when properly prepared and equipped with a snorkel to supply air for the crew and engine. Tank crews usually have a negative reaction towards deep fording but it adds considerable scope for surprise and tactical flexibility in water crossing operations by opening new and unexpected avenues of attack.


title: Tank

text: Amphibious tanks are specially designed or adapted for water operations, such as by including snorkels and skirts, but they are rare in modern armies, being replaced by purpose-built amphibious assault vehicles or armoured personnel carriers in amphibious assaults. Advances such as the EFA mobile bridge and armoured vehicle-launched scissors bridges have also reduced the impediment to tank advance that rivers posed in World War II.


title: Tank

text: Most modern tanks most often have four crew members, or three if an auto-loader is installed. These are the:


title: Tank

text: Operating a tank is a team effort. For example, the loader is assisted by the rest of the crew in stowing ammunition. The driver is assisted in maintaining the automotive features.


title: Tank

text: Historically, crews have varied from just two members to a dozen. First World War tanks were developed with immature technologies; in addition to the crew needed to man the multiple guns and machine guns, up to four crewmen were needed to drive the tank: the driver, acting as the vehicle commander and manning the brakes, drove via orders to his gears-men; a co-driver operated the gearbox and throttle; and two gears-men, one on each track, steered by setting one side or the other to idle, allowing the track on the other side to slew the tank to one side. Pre-World War II French tanks were noted for having a two-man crew, in which the overworked commander had to load and fire the gun in addition to commanding the tank.


title: Tank

text: With World War II the multi-turreted tanks proved impracticable, and as the single turret on a low hull design became standard, crews became standardized around a crew of four or five. In those tanks with a fifth crew member, usually three were located in the turret (as described above) while the fifth was most often seated in the hull next to the driver, and operated the hull machine gun in addition to acting as a co-driver or radio operator. Well-designed crew stations, giving proper considerations to comfort and ergonomics, are an important factor in the combat effectiveness of a tank, as it limits fatigue and speeds up individual actions.


title: Tank

text: A noted author on the subject of tank design engineering, Richard Ogorkiewicz, outlined the following basic engineering sub-systems that are commonly incorporated into tank's technological development:


title: Tank

text: To the above can be added unit communication systems and electronic anti-tank countermeasures, crew ergonomic and survival systems (including flame suppression), and provision for technological upgrading.


title: Tank

text: Few tank designs have survived their entire service lives without some upgrading or modernization, particularly during wartime, including some that have changed almost beyond recognition, such as the latest Israeli Magach versions.


title: Tank

text: The characteristics of a tank are determined by the performance criteria required for the tank. The obstacles that must be traversed affect the vehicles front and rear profiles. The terrain that is expected to be traversed determines the track ground pressure that may be allowed to be exerted for that particular terrain.


title: Tank

text: Tank design is a compromise between its technological and budgetary constraints and its tactical capability requirements. It is not possible to maximise firepower, protection and mobility simultaneously while incorporating the latest technology and retain affordability for sufficient procurement quantity to enter production.


title: Tank

text: For example, in the case of tactical capability requirements, increasing protection by adding armour will result in an increase in weight and therefore decrease in mobility; increasing firepower by installing a larger gun will force the designer team to increase armour, the therefore weight of the tank by retaining same internal volume to ensure crew efficiency during combat. In the case of the Abrams MBT which has good firepower, speed and armour, these advantages are counterbalanced by its engine's notably high fuel consumption, which ultimately reduces its range, and in a larger sense its mobility.


title: Tank

text: Since the Second World War, the economics of tank production governed by the complexity of manufacture and cost, and the impact of a given tank design on logistics and field maintenance capabilities, have also been accepted as important in determining how many tanks a nation can afford to field in its force structure.


title: Tank

text: Some tank designs that were fielded in significant numbers, such as Tiger I and M60A2 proved to be too complex or expensive to manufacture, and made unsustainable demands on the logistics services support of the armed forces. The "affordability of the design" therefore takes precedence over the combat capability requirements.


title: Tank

text: Nowhere was this principle illustrated better than during the Second World War when two Allied designs, the T-34 and the M4 Sherman, although both simple designs which accepted engineering compromises, were used successfully against more sophisticated designs by Germany that were more complex and expensive to produce, and more demanding on overstretched logistics of the Wehrmacht. Given that a tank crew will spend most of its time occupied with maintenance of the vehicle, engineering simplicity has become the primary constraint on tank design since the Second World War despite advances in mechanical, electrical and electronics technologies.


title: Tank

text: Since the Second World War, tank development has incorporated experimenting with significant mechanical changes to the tank design while focusing on technological advances in the tank's many subsystems to improve its performance. However, a number of novel designs have appeared throughout this period with mixed success, including the Soviet IT-1 and T-64 in firepower, and the Israeli Merkava and Swedish S-tank in protection, while for decades the US's M551 remained the only light tank deployable by parachute.


title: Tank

text: Commanding and coordinating tanks in the field has always been subject to particular problems, particularly in the area of communications, but in modern armies these problems have been partially alleviated by networked, integrated systems that enable communications and contribute to enhanced situational awareness.


title: Tank

text: armoured bulkheads, engine noise, intervening terrain, dust and smoke, and the need to operate "buttoned up" (with hatches closed) are severe detriments to communication and lead to a sense of isolation for small tank units, individual vehicles, and tank crew. Radios were not then portable or robust enough to be mounted in a tank, although Morse code transmitters were installed in some Mark IVs at Cambrai as messaging vehicles. Attaching a field telephone to the rear would become a practice only during the next war. During World War I when these failed or were unavailable, situation reports were sent back to headquarters by some crews releasing carrier pigeons through loopholes or hatches and communications between vehicles was accomplished using hand signals, handheld semaphore flags which continued in use in the Red Army/Soviet Army through the Second and Cold wars, or by foot or horse-mounted messengers.


title: Tank

text: From the beginning, the German military stressed wireless communications, equipping their combat vehicles with radios, and drilled all units to rely on disciplined radio use as a basic element of tactics. This allowed them to respond to developing threats and opportunities during battles, giving the Germans a notable tactical advantage early in the war; even where Allied tanks initially had better firepower and armour, they generally lacked individual radios. By mid-war, Western Allied tanks adopted full use of radios, although Russian use of radios remained relatively limited.


title: Tank

text: On the modern battlefield an intercom mounted in the crew helmet provides internal communications and a link to the radio network, and on some tanks an external intercom on the rear of the tank provides communication with co-operating infantry. Radio networks employ radio voice procedure to minimize confusion and "chatter".


title: Tank

text: A recent development in AFV equipment and doctrine is integration of information from the fire control system, laser rangefinder, Global Positioning System and terrain information via hardened military specification electronics and a battlefield network to display information on enemy targets and friendly units on a monitor in the tank. The sensor data can be sourced from nearby tanks, planes, UAVs or, in the future infantry (such as the US Future Force Warrior project). This improves the tank commander's situational awareness and ability to navigate the battlefield and select and engage targets. In addition to easing the reporting burden by automatically logging all orders and actions, orders are sent via the network with text and graphical overlays. This is known as Network-centric warfare by the US, Network Enabled Capability (UK) or Digital Army Battle Management System צי"ד (Israel). Advanced battle tanks, including the K-2 Black Panther, have taken up the first major step forward in adopting a fully radar integrated Fire Control System which allows it to detect tanks from a further distance and identify it as a friend-or-foe as well as increasing the tank's accuracy as well as its capability to lock onto tanks.


title: Tank

text: Performing situational awareness and communication is the one of four primary MBT functions in the 21st century.


title: Tank

text: To improve the crew's situational awareness MBTs use circular review system with a combination of Augmented reality and Artificial Intelligence technologies.


title: Tank

text: Further advancements in tank defense systems have led to the development of active protection systems. These involve either one of two options:


title: Radioactive decay

text: Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay (), beta decay (), and gamma decay (), all of which involve emitting one or more particles. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the electromagnetism and nuclear force. A fourth type of common decay is electron capture, in which an unstable nucleus captures an inner electron from one of the electron shells. The loss of that electron from the shell results in a cascade of electrons dropping down to that lower shell resulting in emission of discrete X-rays from the transitions. A common example is iodine-125 commonly used in medical settings.


title: Radioactive decay

text: Radioactive decay is a stochastic (i.e. random) process at the level of single atoms. According to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed. However, for a significant number of identical atoms, the overall decay rate can be expressed as a decay constant or as half-life. The half-lives of radioactive atoms have a huge range; from nearly instantaneous to far longer than the age of the universe.


title: Radioactive decay

text: The decaying nucleus is called the "parent radionuclide" (or "parent radioisotope"), and the process produces at least one "daughter nuclide". Except for gamma decay or internal conversion from a nuclear excited state, the decay is a nuclear transmutation resulting in a daughter containing a different number of protons or neutrons (or both). When the number of protons changes, an atom of a different chemical element is created.


title: Radioactive decay

text: By contrast there are radioactive decay processes that do not result in a nuclear transmutation. The energy of an excited nucleus may be emitted as a gamma ray in a process called gamma decay, or that energy may be lost when the nucleus interacts with an orbital electron causing its ejection from the atom, in a process called internal conversion. Another type of radioactive decay results in products that vary, appearing as two or more "fragments" of the original nucleus with a range of possible masses. This decay, called spontaneous fission, happens when a large unstable nucleus spontaneously splits into two (or occasionally three) smaller daughter nuclei, and generally leads to the emission of gamma rays, neutrons, or other particles from those products.


title: Radioactive decay

text: In contrast, decay products from a nucleus "with spin" may be distributed "non-isotropically" with respect to that spin direction. Either because of an external influence such as an electromagnetic field, or because the nucleus was produced in a dynamic process that constrained the direction of its spin, the anisotropy may be detectable. Such a parent process could be a previous decay, or a nuclear reaction.


title: Radioactive decay

text: For a summary table showing the number of stable and radioactive nuclides, see radionuclide. There are 28 naturally occurring chemical elements on Earth that are radioactive, consisting of 34 radionuclides (6 elements have 2 different radionuclides) that date before the time of formation of the Solar System. These 34 are known as primordial nuclides. Well-known examples are uranium and thorium, but also included are naturally occurring long-lived radioisotopes, such as potassium-40.


title: Radioactive decay

text: Another 50 or so shorter-lived radionuclides found on Earth such as radium-226 and radon-222, are the products of decay chains that began with the primordial nuclides, or are the product of ongoing cosmogenic processes, such as the production of carbon-14 from nitrogen-14 in the atmosphere by cosmic rays. Radionuclides may also be produced artificially in particle accelerators or nuclear reactors, resulting in 650 of these with half-lives of over an hour, and several thousand more with even shorter half-lives. (See List of nuclides for a list of these sorted by half-life.)


title: Radioactive decay

text: Radioactivity was discovered in 1896 by scientists Henri Becquerel and Marie Curie, while working with phosphorescent materials. These materials glow in the dark after exposure to light, and he suspected that the glow produced in cathode ray tubes by X-rays might be associated with phosphorescence. Becquerel wrapped a photographic plate in black paper and placed various phosphorescent salts on it. All results were negative until he used uranium salts. The uranium salts caused a blackening of the plate in spite of the plate being wrapped in black paper. These radiations were given the name "Becquerel Rays".


title: Radioactive decay

text: It soon became clear that the blackening of the plate had nothing to do with phosphorescence, as the blackening was also produced by non-phosphorescent salts of uranium and by metallic uranium. It became clear from these experiments that there was a form of invisible radiation that could pass through paper and was causing the plate to react as if exposed to light.


title: Radioactive decay

text: At first, it seemed as though the new radiation was similar to the then recently discovered X-rays. Further research by Becquerel, Ernest Rutherford, Paul Villard, Pierre Curie, Marie Curie, and others showed that this form of radioactivity was significantly more complicated. Rutherford was the first to realize that all such elements decay in accordance with the same mathematical exponential formula. Rutherford and his student Frederick Soddy were the first to realize that many decay processes resulted in the transmutation of one element to another. Subsequently, the radioactive displacement law of Fajans and Soddy was formulated to describe the products of alpha and beta decay.


title: Radioactive decay

text: The early researchers also discovered that many other chemical elements, besides uranium, have radioactive isotopes. A systematic search for the total radioactivity in uranium ores also guided Pierre and Marie Curie to isolate two new elements: polonium and radium. Except for the radioactivity of radium, the chemical similarity of radium to barium made these two elements difficult to distinguish.


title: Radioactive decay

text: Marie and Pierre Curie's study of radioactivity is an important factor in science and medicine. After their research on Becquerel's rays led them to the discovery of both radium and polonium, they coined the term "radioactivity" to define the emission of ionizing radiation by some heavy elements. (Later the term was generalized to all elements.) Their research on the penetrating rays in uranium and the discovery of radium launched an era of using radium for the treatment of cancer. Their exploration of radium could be seen as the first peaceful use of nuclear energy and the start of modern nuclear medicine.


title: Radioactive decay

text: The discovery of X‑rays by Wilhelm Röntgen in 1895 led to widespread experimentation by scientists, physicians, and inventors. Many people began recounting stories of burns, hair loss and worse in technical journals as early as 1896. In February of that year, Professor Daniel and Dr. Dudley of Vanderbilt University performed an experiment involving X-raying Dudley's head that resulted in his hair loss. A report by Dr. H.D. Hawks, of his suffering severe hand and chest burns in an X-ray demonstration, was the first of many other reports in "Electrical Review".


title: Radioactive decay

text: Other experimenters, including Elihu Thomson and Nikola Tesla, also reported burns. Thomson deliberately exposed a finger to an X-ray tube over a period of time and suffered pain, swelling, and blistering. Other effects, including ultraviolet rays and ozone, were sometimes blamed for the damage, and many physicians still claimed that there were no effects from X-ray exposure at all.


title: Radioactive decay

text: Despite this, there were some early systematic hazard investigations, and as early as 1902 William Herbert Rollins wrote almost despairingly that his warnings about the dangers involved in the careless use of X-rays were not being heeded, either by industry or by his colleagues. By this time, Rollins had proved that X-rays could kill experimental animals, could cause a pregnant guinea pig to abort, and that they could kill a foetus. He also stressed that "animals vary in susceptibility to the external action of X-light" and warned that these differences be considered when patients were treated by means of X-rays.


title: Radioactive decay

text: However, the biological effects of radiation due to radioactive substances were less easy to gauge. This gave the opportunity for many physicians and corporations to market radioactive substances as patent medicines. Examples were radium enema treatments, and radium-containing waters to be drunk as tonics. Marie Curie protested against this sort of treatment, warning that "radium is dangerous in untrained hands." Curie later died from aplastic anaemia, likely caused by exposure to ionizing radiation. By the 1930s, after a number of cases of bone necrosis and death of radium treatment enthusiasts, radium-containing medicinal products had been largely removed from the market (radioactive quackery).


title: Radioactive decay

text: Only a year after Röntgen's discovery of X rays, the American engineer Wolfram Fuchs (1896) gave what is probably the first protection advice, but it was not until 1925 that the first International Congress of Radiology (ICR) was held and considered establishing international protection standards. The effects of radiation on genes, including the effect of cancer risk, were recognized much later. In 1927, Hermann Joseph Muller published research showing genetic effects and, in 1946, was awarded the Nobel Prize in Physiology or Medicine for his findings.


title: Radioactive decay

text: The second ICR was held in Stockholm in 1928 and proposed the adoption of the röntgen unit, and the International X-ray and Radium Protection Committee (IXRPC) was formed. Rolf Sievert was named Chairman, but a driving force was George Kaye of the British National Physical Laboratory. The committee met in 1931, 1934, and 1937.


title: Radioactive decay

text: After World War II, the increased range and quantity of radioactive substances being handled as a result of military and civil nuclear programs led to large groups of occupational workers and the public being potentially exposed to harmful levels of ionising radiation. This was considered at the first post-war ICR convened in London in 1950, when the present International Commission on Radiological Protection (ICRP) was born.


title: Radioactive decay

text: Since then the ICRP has developed the present international system of radiation protection, covering all aspects of radiation hazards.


title: Radioactive decay

text: In 2020, Hauptmann and other 15 international researchers of eight nations, among which: Institutes of Biostatistics, Registry Research, Centers of Cancer Epidemiology, Radiation Epidemiology, and then also U.S. National Cancer Institute (NCI), International Agency for Research on Cancer (IARC) and Radiation Effects Research Foundation of Hiroshima studied definitively through meta-analysis the damage resulting from the "low doses" that have afflicted the populations of survivors of the atomic bombings of Hiroshima and Nagasaki and also in numerous accidents of nuclear plants that have occurred in the world. These scientists reported, in JNCI Monographs: Epidemiological Studies of Low Dose Ionizing Radiation and Cancer Risk, that the new epidemiological studies directly support excess cancer risks from low-dose ionizing radiation. In 2021, Italian researcher Venturi reported the first correlations between radio-caesium and pancreatic cancer with the role of caesium in biology and in pancreatitis and in diabetes of pancreatic origin.


title: Radioactive decay

text: The International System of Units (SI) unit of radioactive activity is the becquerel (Bq), named in honor of the scientist Henri Becquerel. One Bq is defined as one transformation (or decay or disintegration) per second.


title: Radioactive decay

text: An older unit of radioactivity is the curie, Ci, which was originally defined as "the quantity or mass of radium emanation in equilibrium with one gram of radium (element)". Today, the curie is defined as disintegrations per second, so that 1 curie (Ci) = .


title: Radioactive decay

text: For radiological protection purposes, although the United States Nuclear Regulatory Commission permits the use of the unit curie alongside SI units, the European Union European units of measurement directives required that its use for "public health ... purposes" be phased out by 31 December 1985.


title: Radioactive decay

text: The effects of ionizing radiation are often measured in units of gray for mechanical or sievert for damage to tissue.


title: Radioactive decay

text: Early researchers found that an electric or magnetic field could split radioactive emissions into three types of beams. The rays were given the names alpha, beta, and gamma, in increasing order of their ability to penetrate matter. Alpha decay is observed only in heavier elements of atomic number 52 (tellurium) and greater, with the exception of beryllium-8 (which decays to two alpha particles). The other two types of decay are observed in all the elements. Lead, atomic number 82, is the heaviest element to have any isotopes stable (to the limit of measurement) to radioactive decay. Radioactive decay is seen in all isotopes of all elements of atomic number 83 (bismuth) or greater. Bismuth-209, however, is only very slightly radioactive, with a half-life greater than the age of the universe; radioisotopes with extremely long half-lives are considered effectively stable for practical purposes.


title: Radioactive decay

text: In analysing the nature of the decay products, it was obvious from the direction of the electromagnetic forces applied to the radiations by external magnetic and electric fields that alpha particles carried a positive charge, beta particles carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was clear that alpha particles were much more massive than beta particles. Passing alpha particles through a very thin glass window and trapping them in a discharge tube allowed researchers to study the emission spectrum of the captured particles, and ultimately proved that alpha particles are helium nuclei. Other experiments showed beta radiation, resulting from decay and cathode rays, were high-speed electrons. Likewise, gamma radiation and X-rays were found to be high-energy electromagnetic radiation.


title: Radioactive decay

text: The relationship between the types of decays also began to be examined: For example, gamma decay was almost always found to be associated with other types of decay, and occurred at about the same time, or afterwards. Gamma decay as a separate phenomenon, with its own half-life (now termed isomeric transition), was found in natural radioactivity to be a result of the gamma decay of excited metastable nuclear isomers, which were in turn created from other types of decay.


title: Radioactive decay

text: Although alpha, beta, and gamma radiations were most commonly found, other types of emission were eventually discovered. Shortly after the discovery of the positron in cosmic ray products, it was realized that the same process that operates in classical beta decay can also produce positrons (positron emission), along with neutrinos (classical beta decay produces antineutrinos). In a more common analogous process, called electron capture, some proton-rich nuclides were found to capture their own atomic electrons instead of emitting positrons, and subsequently, these nuclides emit only a neutrino and a gamma ray from the excited nucleus (and often also Auger electrons and characteristic X-rays, as a result of the re-ordering of electrons to fill the place of the missing captured electron). These types of decay involve the nuclear capture of electrons or emission of electrons or positrons, and thus acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of nucleons. This consequently produces a more stable (lower energy) nucleus.


title: Radioactive decay

text: A hypothetical process of positron capture, analogous to electron capture, is theoretically possible in antimatter atoms, but has not been observed, as complex antimatter atoms beyond antihelium are not experimentally available. Such a decay would require antimatter atoms at least as complex as beryllium-7, which is the lightest known isotope of normal matter to undergo decay by electron capture.


title: Radioactive decay

text: Shortly after the discovery of the neutron in 1932, Enrico Fermi realized that certain rare beta-decay reactions immediately yield neutrons as an additional decay particle, so called beta-delayed neutron emission. Neutron emission usually happens from nuclei that are in an excited state, such as the excited O* produced from the beta decay of N. The neutron emission process itself is controlled by the nuclear force and therefore is extremely fast, sometimes referred to as "nearly instantaneous". Isolated proton emission was eventually observed in some elements. It was also found that some heavy elements may undergo spontaneous fission into products that vary in composition. In a phenomenon called cluster decay, specific combinations of neutrons and protons other than alpha particles (helium nuclei) were found to be spontaneously emitted from atoms.


title: Radioactive decay

text: Other types of radioactive decay were found to emit previously seen particles but via different mechanisms. An example is internal conversion, which results in an initial electron emission, and then often further characteristic X-rays and Auger electrons emissions, although the internal conversion process involves neither beta nor gamma decay. A neutrino is not emitted, and none of the electron(s) and photon(s) emitted originate in the nucleus, even though the energy to emit all of them does originate there. Internal conversion decay, like isomeric transition gamma decay and neutron emission, involves the release of energy by an excited nuclide, without the transmutation of one element into another.


title: Radioactive decay

text: Rare events that involve a combination of two beta-decay-type events happening simultaneously are known (see below). Any decay process that does not violate the conservation of energy or momentum laws (and perhaps other particle conservation laws) is permitted to happen, although not all have been detected. An interesting example discussed in a final section, is bound state beta decay of rhenium-187. In this process, the beta electron-decay of the parent nuclide is not accompanied by beta electron emission, because the beta particle has been captured into the K-shell of the emitting atom. An antineutrino is emitted, as in all negative beta decays.


title: Radioactive decay

text: Radionuclides can undergo a number of different reactions. These are summarized in the following table. A nucleus with mass number "A" and atomic number "Z" is represented as ("A", "Z"). The column "Daughter nucleus" indicates the difference between the new nucleus and the original nucleus. Thus, ("A" − 1, "Z") means that the mass number is one less than before, but the atomic number is the same as before.


title: Radioactive decay

text: If energy circumstances are favorable, a given radionuclide may undergo many competing types of decay, with some atoms decaying by one route, and others decaying by another. An example is copper-64, which has 29 protons, and 35 neutrons, which decays with a half-life of hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay to the other particle, which has opposite isospin. This particular nuclide (though not all nuclides in this situation) is more likely to decay through beta plus decay (%) than through electron capture (%). The excited energy states resulting from these decays which fail to end in a ground energy state, also produce later internal conversion and gamma decay in almost 0.5% of the time.


title: Radioactive decay

text: More common in heavy nuclides is competition between alpha and beta decay. The daughter nuclides will then normally decay through beta or alpha, respectively, to end up in the same place.


title: Radioactive decay

text: Radioactive decay results in a reduction of summed rest mass, once the released energy (the "disintegration energy") has escaped in some way. Although decay energy is sometimes defined as associated with the difference between the mass of the parent nuclide products and the mass of the decay products, this is true only of rest mass measurements, where some energy has been removed from the product system. This is true because the decay energy must always carry mass with it, wherever it appears (see mass in special relativity) according to the formula "E" = "mc". The decay energy is initially released as the energy of emitted photons plus the kinetic energy of massive emitted particles (that is, particles that have rest mass). If these particles come to thermal equilibrium with their surroundings and photons are absorbed, then the decay energy is transformed to thermal energy, which retains its mass.


title: Radioactive decay

text: Decay energy, therefore, remains associated with a certain measure of the mass of the decay system, called invariant mass, which does not change during the decay, even though the energy of decay is distributed among decay particles. The energy of photons, the kinetic energy of emitted particles, and, later, the thermal energy of the surrounding matter, all contribute to the invariant mass of the system. Thus, while the sum of the rest masses of the particles is not conserved in radioactive decay, the "system" mass and system invariant mass (and also the system total energy) is conserved throughout any decay process. This is a restatement of the equivalent laws of conservation of energy and conservation of mass.


title: Radioactive decay

text: The "decay rate", or "activity", of a radioactive substance is characterized by the following time-independent parameters:


title: Radioactive decay

text: Although these are constants, they are associated with the statistical behavior of populations of atoms. In consequence, predictions using these constants are less accurate for minuscule samples of atoms.


title: Radioactive decay

text: In principle a half-life, a third-life, or even a (1/√2)-life, can be used in exactly the same way as half-life; but the mean life and half-life have been adopted as standard times associated with exponential decay.


title: Radioactive decay

text: where "N" is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.


title: Radioactive decay

text: The mathematics of radioactive decay depend on a key assumption that a nucleus of a radionuclide has no "memory" or way of translating its history into its present behavior. A nucleus does not "age" with the passage of time. Thus, the probability of its breaking down does not increase with time but stays constant, no matter how long the nucleus has existed. This constant probability may differ greatly between one type of nucleus and another, leading to the many different observed decay rates. However, whatever the probability is, it does not change over time. This is in marked contrast to complex objects that do show aging, such as automobiles and humans. These aging systems do have a chance of breakdown per unit of time that increases from the moment they begin their existence.


title: Radioactive decay

text: Aggregate processes, like the radioactive decay of a lump of atoms, for which the single-event probability of realization is very small but in which the number of time-slices is so large that there is nevertheless a reasonable rate of events, are modelled by the Poisson distribution, which is discrete. Radioactive decay and nuclear particle reactions are two examples of such aggregate processes. The mathematics of Poisson processes reduce to the law of exponential decay, which describes the statistical behaviour of a large number of nuclei, rather than one individual nucleus. In the following formalism, the number of nuclei or the nuclei population "N", is of course a discrete variable (a natural number)—but for any physical sample "N" is so large that it can be treated as a continuous variable. Differential calculus is used to model the behaviour of nuclear decay.


title: Radioactive decay

text: Consider the case of a nuclide that decays into another by some process (emission of other particles, like electron neutrinos and electrons e as in beta decay, are irrelevant in what follows). The decay of an unstable nucleus is entirely random in time so it is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any instant in time. Therefore, given a sample of a particular radioisotope, the number of decay events expected to occur in a small interval of time is proportional to the number of atoms present , that is


title: Radioactive decay

text: Particular radionuclides decay at different rates, so each has its own decay constant . The expected decay is proportional to an increment of time, :


title: Radioactive decay

text: The negative sign indicates that decreases as time increases, as the decay events follow one after another. The solution to this first-order differential equation is the function:


title: Radioactive decay

text: where is the constant number of particles throughout the decay process, which is equal to the initial number of nuclides since this is the initial substance.


title: Radioactive decay

text: The number of decays observed over a given interval obeys Poisson statistics. If the average number of decays is , the probability of a given number of decays is


title: Radioactive decay

text: Now consider the case of a chain of two decays: one nuclide decaying into another by one process, then decaying into another by a second process, i.e. "". The previous equation cannot be applied to the decay chain, but can be generalized as follows. Since decays into , "then" decays into , the activity of adds to the total number of nuclides in the present sample, "before" those nuclides decay and reduce the number of nuclides leading to the later sample. In other words, the number of second generation nuclei increases as a result of the first generation nuclei decay of , and decreases as a result of its own decay into the third generation nuclei . The sum of these two terms gives the law for a decay chain for two nuclides:


title: Radioactive decay

text: The rate of change of , that is , is related to the changes in the amounts of and , can increase as is produced from and decrease as produces .


title: Radioactive decay

text: The subscripts simply refer to the respective nuclides, i.e. is the number of nuclides of type ; is the initial number of nuclides of type ; is the decay constant for – and similarly for nuclide . Solving this equation for gives:


title: Radioactive decay

text: as shown above for one decay. The solution can be found by the integration factor method, where the integrating factor is . This case is perhaps the most useful since it can derive both the one-decay equation (above) and the equation for multi-decay chains (below) more directly.


title: Radioactive decay

text: For the general case of any number of consecutive decays in a decay chain, i.e. , where is the number of decays and is a dummy index (), each nuclide population can be found in terms of the previous population. In this case , , ..., . Using the above result in a recursive form:


title: Radioactive decay

text: In all of the above examples, the initial nuclide decays into just one product. Consider the case of one initial nuclide that can decay into either of two products, that is ' and ' in parallel. For example, in a sample of potassium-40, 89.3% of the nuclei decay to calcium-40 and 10.7% to argon-40. We have for all time :


title: Radioactive decay

text: which is constant, since the total number of nuclides remains constant. Differentiating with respect to time:


title: Radioactive decay

text: where is the initial number of nuclide A. When measuring the production of one nuclide, one can only observe the total decay constant . The decay constants and determine the probability for the decay to result in products or as follows:


title: Radioactive decay

text: The above equations can also be written using quantities related to the number of nuclide particles in a sample;


title: Radioactive decay

text: where = is the Avogadro constant, is the molar mass of the substance in kg/mol, and the amount of the substance is in moles.


title: Radioactive decay

text: the equation indicates that the decay constant has units of , and can thus also be represented as 1/, where is a characteristic time of the process called the "time constant".


title: Radioactive decay

text: In a radioactive decay process, this time constant is also the mean lifetime for decaying atoms. Each atom "lives" for a finite amount of time before it decays, and it may be shown that this mean lifetime is the arithmetic mean of all the atoms' lifetimes, and that it is , which again is related to the decay constant as follows:


title: Radioactive decay

text: This form is also true for two-decay processes simultaneously "", inserting the equivalent values of decay constants (as given above)


title: Radioactive decay

text: A more commonly used parameter is the half-life . Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions: