title: Quantum superposition

text: The numbers that describe the amplitudes for different possibilities define the kinematics, the space of different states. The dynamics describes how these numbers change with time. For a particle that can be in any one of infinitely many discrete positions, a particle on a lattice, the superposition principle tells you how to make a state:


title: Quantum superposition

text: So that the infinite list of amplitudes formula_40 completely describes the quantum state of the particle. This list is called the state vector, and formally it is an element of a Hilbert space, an infinite-dimensional complex vector space. It is usual to represent the state so that the sum of the absolute squares of the amplitudes is one:


title: Quantum superposition

text: For a particle described by probability theory random walking on a line, the analogous thing is the list of probabilities formula_42, which give the probability of any position. The quantities that describe how they change in time are the transition probabilities formula_43, which gives the probability that, starting at x, the particle ends up at y time t later. The total probability of ending up at y is given by the sum over all the possibilities


title: Quantum superposition

text: The condition of conservation of probability states that starting at any x, the total probability to end up "somewhere" must add up to 1:


title: Quantum superposition

text: When no time passes, nothing changes: for 0 elapsed time formula_46, the K matrix is zero except from a state to itself. So in the case that the time is short, it is better to talk about the rate of change of the probability instead of the absolute change in the probability.


title: Quantum superposition

text: The equation for the probabilities is a differential equation that is sometimes called the master equation:


title: Quantum superposition

text: The R matrix is the probability per unit time for the particle to make a transition from x to y. The condition that the K matrix elements add up to one becomes the condition that the R matrix elements add up to zero:


title: Quantum superposition

text: One simple case to study is when the R matrix has an equal probability to go one unit to the left or to the right, describing a particle that has a constant rate of random walking. In this case formula_48 is zero unless y is either "x" + 1, "x", or "x" − 1, when "y" is "x" + 1 or "x" − 1, the "R" matrix has value "c", and in order for the sum of the "R" matrix coefficients to equal zero, the value of formula_53 must be −2"c". So the probabilities obey the discretized diffusion equation:


title: Quantum superposition

text: which, when c is scaled appropriately and the P distribution is smooth enough to think of the system in a continuum limit becomes:


title: Quantum superposition

text: Quantum amplitudes give the rate at which amplitudes change in time, and they are mathematically exactly the same except that they are complex numbers. The analog of the finite time K matrix is called the U matrix:


title: Quantum superposition

text: Since the sum of the absolute squares of the amplitudes must be constant, formula_57 must be unitary:


title: Quantum superposition

text: The Hamiltonian gives the rate at which the particle has an amplitude to go from m to n. The reason it is multiplied by i is that the condition that U is unitary translates to the condition:


title: Quantum superposition

text: which says that H is Hermitian. The eigenvalues of the Hermitian matrix "H" are real quantities, which have a physical interpretation as energy levels. If the factor "i" were absent, the H matrix would be antihermitian and would have purely imaginary eigenvalues, which is not the traditional way quantum mechanics represents observable quantities like the energy.


title: Quantum superposition

text: For a particle that has equal amplitude to move left and right, the Hermitian matrix H is zero except for nearest neighbors, where it has the value "c". If the coefficient is everywhere constant, the condition that "H" is Hermitian demands that the amplitude to move to the left is the complex conjugate of the amplitude to move to the right. The equation of motion for formula_16 is the time differential equation:


title: Quantum superposition

text: In the case in which left and right are symmetric, "c" is real. By redefining the phase of the wavefunction in time, formula_65, the amplitudes for being at different locations are only rescaled, so that the physical situation is unchanged. But this phase rotation introduces a linear term.


title: Quantum superposition

text: which is the right choice of phase to take the continuum limit. When formula_67 is very large and formula_16 is slowly varying so that the lattice can be thought of as a line, this becomes the free Schrödinger equation:


title: Quantum superposition

text: If there is an additional term in the H matrix that is an extra phase rotation that varies from point to point, the continuum limit is the Schrödinger equation with a potential energy:


title: Quantum superposition

text: The analogy between quantum mechanics and probability is very strong, so that there are many mathematical links between them. In a statistical system in discrete time, t=1,2,3, described by a transition matrix for one time step formula_71, the probability to go between two points after a finite number of time steps can be represented as a sum over all paths of the probability of taking each path:


title: Quantum superposition

text: where the sum extends over all paths formula_73 with the property that formula_74 and formula_75. The analogous expression in quantum mechanics is the path integral.


title: Quantum superposition

text: A generic transition matrix in probability has a stationary distribution, which is the eventual probability to be found at any point no matter what the starting point. If there is a nonzero probability for any two paths to reach the same point at the same time, this stationary distribution does not depend on the initial conditions. In probability theory, the probability m for the stochastic matrix obeys detailed balance when the stationary distribution formula_76 has the property:


title: Quantum superposition

text: Detailed balance says that the total probability of going from m to n in the stationary distribution, which is the probability of starting at m formula_78 times the probability of hopping from m to n, is equal to the probability of going from n to m, so that the total back-and-forth flow of probability in equilibrium is zero along any hop. The condition is automatically satisfied when n=m, so it has the same form when written as a condition for the transition-probability R matrix.


title: Quantum superposition

text: When the R matrix obeys detailed balance, the scale of the probabilities can be redefined using the stationary distribution so that they no longer sum to 1:


title: Quantum superposition

text: whose Hamiltonian has the same eigenvalues as those of the R matrix of the statistical system. The eigenvectors are the same too, except expressed in the rescaled basis. The stationary distribution of the statistical system is the "ground state" of the Hamiltonian and it has energy exactly zero, while all the other energies are positive. If H is exponentiated to find the U matrix:


title: Quantum superposition

text: For quantum systems which are invariant under time reversal the Hamiltonian can be made real and symmetric, so that the action of time-reversal on the wave-function is just complex conjugation. If such a Hamiltonian has a unique lowest energy state with a positive real wave-function, as it often does for physical reasons, it is connected to a stochastic system in imaginary time. This relationship between stochastic systems and quantum systems sheds much light on supersymmetry.


title: Quantum superposition

text: Successful experiments involving superpositions of relatively large (by the standards of quantum physics) objects have been performed.


title: Quantum superposition

text: In quantum computing the phrase "cat state" often refers to the GHZ state, the special entangled state of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1; i.e.,


title: Quantum superposition

text: Applying the superposition principle to a quantum mechanical particle, the configurations of the particle are all positions, so the superpositions make a complex wave in space. The coefficients of the linear superposition are a wave which describes the particle as best as is possible, and whose amplitude interferes according to the Huygens principle.


title: Quantum superposition

text: For any physical property in quantum mechanics, there is a list of all the states where that property has some value. These states are necessarily perpendicular to each other using the Euclidean notion of perpendicularity which comes from sums-of-squares length, except that they also must not be i multiples of each other. This list of perpendicular states has an associated value which is the value of the physical property. The superposition principle guarantees that any state can be written as a combination of states of this form with complex coefficients.


title: Quantum superposition

text: Write each state with the value q of the physical quantity as a vector in some basis formula_87, a list of numbers at each value of n for the vector which has value q for the physical quantity. Now form the outer product of the vectors by multiplying all the vector components and add them with coefficients to make the matrix


title: Quantum superposition

text: where the sum extends over all possible values of q. This matrix is necessarily symmetric because it is formed from the orthogonal states, and has eigenvalues q. The matrix A is called the observable associated to the physical quantity. It has the property that the eigenvalues and eigenvectors determine the physical quantity and the states which have definite values for this quantity.


title: Quantum superposition

text: Every physical quantity has a Hermitian linear operator associated to it, and the states where the value of this physical quantity is definite are the eigenstates of this linear operator. The linear combination of two or more eigenstates results in quantum superposition of two or more values of the quantity. If the quantity is measured, the value of the physical quantity will be random, with a probability equal to the square of the coefficient of the superposition in the linear combination. Immediately after the measurement, the state will be given by the eigenvector corresponding to the measured eigenvalue.


title: Quantum superposition

text: It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition. Indeed, this is sometimes regarded as "mysterious", for instance by Richard Feynman. In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted this dissonance between quantum mechanics and classical physics. One modern view is that this mystery is explained by quantum decoherence. A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as "alive" and "dead"). The mechanism that achieves this is a subject of significant research, one mechanism suggests that the state of the cat is entangled with the state of its environment (for instance, the molecules in the atmosphere surrounding it), when averaged over the possible quantum states of the environment (a physically reasonable procedure unless the quantum state of the environment can be controlled or measured precisely) the resulting mixed quantum state for the cat is very close to a classical probabilistic state where the cat has some definite probability to be dead or alive, just as a classical observer would expect in this situation. Another proposed class of theories is that the fundamental time evolution equation is incomplete, and requires the addition of some type of fundamental Lindbladian, the reason for this addition and the form of the additional term varies from theory to theory. A popular theory is Continuous spontaneous localization, where the lindblad term is proportional to the spatial separation of the states, this too results in a quasi-classical probabilistic state.


title: Foreplay

text: Foreplay is a set of emotionally and physically intimate acts between one or more people meant to create sexual arousal and desire for sexual activity. Although foreplay is typically understood as physical sexual activity, nonphysical activities, such as mental or verbal acts, may in some contexts be foreplay. This is typically the reason why foreplay tends to be an ambiguous term and means different things to different people. It can consist of various sexual practices such as kissing, sexual touching, removing clothing, oral sex, sexual games, and role playing.


title: Foreplay

text: Physically, the sexual organs for both partners receive more blood flow and become aroused. For male partners this leads to an erection and for female partners this results in a clitoral erection. When partners experience sexual arousal from the acts of foreplay, their organs that are susceptible to pleasure become highly sensitive to external stimuli all while at the same time releasing bodily fluids that lubricate the organs to prepare for intercourse. These physical events aforementioned are more easily reached by the male partner as compared to the female partner which is possibly due to the potential consequences of pregnancy and motherhood. It is for this reason foreplay has been found to play a critical role for the female partner, as noted by sexologist Dr. William Robinson. Robinson suggests that male partners are able to perform sexual intercourse without the requirement of foreplay. Whereas female partners require longer acts of foreplay to become sufficiently stimulated and pleasured.


title: Foreplay

text: Psychologically, foreplay lowers inhibitions and increases emotional intimacy between partners. Both partners, while performing foreplay, are able to have a mutual experience of understanding and emotions. This mutuality leads to an enhanced sexual experience for both partners.


title: Foreplay

text: From a biological perspective, foreplay may be seen as an act that is costly in regards to reproduction (male animal perspective). Nonetheless, the costliness of foreplay becomes insufficient when it has been noted through biological research that it is a worthwhile strategy to increase fertility rates in both the animal and human kingdom. The increased rates of fertility are due to physical and psychological effects aforementioned which also play a role in the effects of the neurohypophysial hormone. This hormone is capable of increasing the rate production of sperm count within the male during the acts of extensive foreplay and therefore results with the female partner having higher chances of becoming impregnated.


title: Foreplay

text: According to a survey on heterosexual couples about duration of sexual intercourse and foreplay, neither partner in these relationships was satisfied with the duration of foreplay in their relationships. This survey sampled 152 couples who were mainly university educated and satisfied with their sexual life. In this study, and when compared to some larger studies, men were better at perceiving desired sexual intercourse and foreplay duration for their partner. The average times spent on intercourse were 7 minutes and 12 minutes on foreplay for the couples in this survey. Another result of this survey was that the length of desired foreplay for men and women was about the same.


title: Foreplay

text: In a global study of about 12,000 individuals from 27 countries in 6 continents, physical foreplay was rated as "very important" for 63% of men and 60% of women.


title: Foreplay

text: According to a study of individuals in committed romantic relationships, pornography and sexual media usage does not play a role in satisfaction with time spent on foreplay, although other aspects of sexual satisfaction can be impacted by this type of sexual media. This means that foreplay is an important part of the sexual script, and social influences on the sexual script such as pornography and provocative sexual media do not impact foreplay. Time spent on foreplay is an important part of becoming sexually aroused and unique to each individual, and individuals still need the same amount of foreplay in order to become sexually aroused despite what they learn from porn.


title: Foreplay

text: Sexual role-playing or sex games can create sexual interest. These games can be played in a variety of situations, and have been enhanced by technology. This type of extended foreplay can involve SMS messaging (Sexting), phone calls, online chat, or other forms of distance communication, which are intended to stimulate fantasizing about the forthcoming encounter. This tantalization builds up sexual tension.


title: Foreplay

text: A card or board game can be played for foreplay. The objective of the game is for the partners to indulge their fantasies. The loser can, for example, be required to remove clothing or give the winner a sensual foot massage or any other thing that the winner wants to try. A sensuous atmosphere can also be enhanced by candles, drinks, sensual food or suggestive clothing. Even a suggestion of the use of sex toys or the playing of games involving fetish, sexual bondage, blindfolding or sploshing is an indication of sexual interest.


title: Foreplay

text: Some couples create sexual interest by watching erotic and pornographic videos. Role playing may involve the partners wearing costumes, to create and maintain a sexual fantasy. For variety, the partners can make up a (sexual) story together. One of them starts with a sentence and then the other continues until the story becomes sexually explicit, and it provides an opportunity for the partners to express their sexual fantasies. "Strangers for a day" is a role-playing game which consists of the couple playing roles of the first meeting between them. In a public meeting place, the partners pretend to be strangers meeting for the first time. The objective is for them to flirt and seduce the other, without doing or saying anything that they normally would not do or say at a first meeting.


title: Foreplay

text: Tantric foreplay is the first step in the lovemaking session, according to the tantra principles. Tantric sex is against rushing things for the purpose of reaching an orgasm, so tantric foreplay is a way to prepare the body and the mind for the union between the two bodies. The tantric rules say that foreplay must be focused on the preparation before sexual intercourse. Tantric foreplay may include sensual baths between the two partners in a relaxing atmosphere. Fragrance oil and candles may also be used to set up the mood.


title: Foreplay

text: Tantric foreplay is only about giving each other time to connect spiritually and bind. Staring at each other while in a cross-legged position and touching the other's hand palms is a usual foreplay tactic used by tantra practitioners.


title: Foreplay

text: Tantric foreplay may also include Tantra massages. The massage that is applied, according to the tantric philosophy, is not for reaching orgasms but for giving each other pleasure and connecting at a spiritual level.


title: Foreplay

text: There are many historical references to foreplay, with many artistic depictions. The Ancient Indian work "Kama Sutra" mentions different types of embracing, kissing, and marking with nails and teeth. It also mentions BDSM activities such as slapping and moaning as "play". There are also examples of the use of foreplay in marital advice literature that dates back to the early 1900s.


title: Albert II of Belgium

text: Albert II (born 6 June 1934) is a member of the Belgian royal family who reigned as King of the Belgians from 9 August 1993 to 21 July 2013.


title: Albert II of Belgium

text: Albert II is the son of King Leopold III and the last living child of Queen Astrid, born a princess of Sweden. He is the younger brother of the late Grand Duchess Joséphine-Charlotte of Luxembourg and King Baudouin, whom he succeeded upon Baudouin's death in 1993. He married Donna Paola Ruffo di Calabria (now Queen Paola), with whom he had three children. Albert's eldest son, Philippe, is the current King of the Belgians.


title: Albert II of Belgium

text: On 3 July 2013, King Albert II attended a midday session of the Belgian cabinet. He then announced that, on 21 July, Belgian National Day, he would abdicate the throne for health reasons. He was succeeded by his son Philippe on 21 July 2013. Albert II was the fourth monarch to abdicate in 2013, following Pope Benedict XVI, Queen Beatrix of the Netherlands, and Emir Hamad bin Khalifa of Qatar. In so doing, he was also the second Belgian monarch to abdicate, following his father Leopold III who abdicated in 1951, albeit under very different circumstances.


title: Albert II of Belgium

text: Prince Albert was born in Stuyvenberg Castle, Brussels, as the second son and youngest child of King Leopold III and his first wife, Princess Astrid of Sweden. He was second in line to the throne at birth, and was given the title Prince of Liège. Queen Astrid died in a car accident on 29 August 1935, in which King Leopold was lightly injured but survived, when Prince Albert was one year old. The King remarried to Mary Lilian Baels (later became Princess of Réthy) in 1941. The couple produced three children: Prince Alexandre, Princess Marie-Christine and Princess Marie-Esméralda (who is also Albert's goddaughter). Albert and his siblings had a close relationship with their stepmother and they called her "Mother".


title: Albert II of Belgium

text: During World War II, on 10 May 1940, at the time when Belgium was being invaded, Prince Albert, his elder sister Princess Joséphine-Charlotte and his elder brother Prince Baudouin, left the country for France and later Spain. The Prince and the Princess returned to Belgium on 2 August 1940. They continued their studies until 1944, either at Laeken, or at the Castle of Ciergnon in the Ardennes. In June 1944, at the time of the Allied landings, King Leopold, his wife Princess Lilian and the royal children were deported by the Germans to Hirschstein, Germany, and later to Strobl, Austria, where they were liberated by the American Army on 7 May 1945. Owing to the political situation in Belgium, King Leopold and his family moved to the villa "Le Reposoir" in Pregny, Switzerland, when they left Austria in October 1945 and stayed until July 1950. During that time, Prince Albert would continue his education in a secondary school in Geneva. King Leopold III, accompanied by Prince Baudouin and Prince Albert, returned to Belgium on 22 July 1950.


title: Albert II of Belgium

text: In 1958, Albert went to the Vatican to witness the coronation of Pope John XXIII. At a reception at the Belgian Embassy, he met Italian Donna Paola Ruffo di Calabria. Prince Albert proposed marriage to her, to which she accepted. Two months after their meeting, the prince introduced his future wife to his family, and four months later to the press. The couple married on 2 July 1959 and have three children, two sons and a daughter, twelve grandchildren and two great-grandchildren. Their children are:


title: Albert II of Belgium

text: In 1997, the Belgian satirical magazine "Père Ubu" reported that the Belgian sculptor Delphine Boël (born in 1968) was King Albert II's extramarital daughter. It took some years for the Belgian mainstream media to report this news. According to Baroness Sybille de Selys Longchamps, the mother of Delphine, she and Albert shared an 18-year-long relationship into which Delphine was born. In June 2013, Boël summoned the then King, the then Duke of Brabant and the Archduchess of Austria-Este to appear in court. She hoped to use DNA tests to prove that she is the King's daughter. As the King enjoyed complete immunity under the law, Boël decided to summon his elder children as well. After the King's abdication, she abandoned her first suit to introduce a second one only against the King as he was no longer protected by immunity and the first claim would have been judged according to the situation at the time of the introduction of the claim. In March 2017, the Court ruled that her claim was unfounded, and her lawyers said she would take the claim to appeal. On 25 October 2018, the Court of Appeal decided that Delphine Boël is not a descendant of Jacques Boël, and ordered King Albert to undergo DNA testing. His lawyer announced that he would seek further advice about a possible referral to Belgium's Cour de Cassation / Hof van Cassatie. In 2019, the King's lawyer confirmed he would not provide a DNA sample in the case.


title: Albert II of Belgium

text: On 29 May 2019, it was reported by CNN that Albert II had submitted a DNA sample after a Belgian court ruled on 16 May that he would be fined 5,000 euros for each day that he failed to do so, although he would continue to challenge the ruling, according to his attorney, .


title: Albert II of Belgium

text: The results of these DNA samples were released on 27 January 2020 by Alain Berenboom, confirming Delphine Boël as Albert II's daughter. Albert II confirmed this on 27 January 2020 in a press release.


title: Albert II of Belgium

text: "The king will treat all his children as equal," Berenboom said, according to VTM News. "King Albert now has four children."


title: Albert II of Belgium

text: While it was proven that Boël was his biological daughter, her legal status as a daughter was not recognized until a 1 October 2020 ruling of the Brussels Court of Appeal, which also recognized Boël as a princess of Belgium and granted her the new surname of Saxe-Coburg.


title: Albert II of Belgium

text: As the younger brother of the childless King Baudouin, Prince Albert was the heir-presumptive to the throne. Albert's son Philippe was groomed to eventually succeed. On Baudouin's death, Albert was sworn in before parliament, on 9 August 1993, as King of the Belgians.


title: Albert II of Belgium

text: As King, Albert's duties included representing Belgium at home and abroad on state visits, trade missions, and at high level international meetings as well as taking an interest in Belgian society, culture and enterprise.


title: Albert II of Belgium

text: The King had a constitutional role which came into play in 2010–2011 when Belgium's parliament was unable to agree on a government. When the crisis was resolved, Albert swore in the new government.


title: Albert II of Belgium

text: Albert sparked controversy in his December 2012 Christmas speech by comparing modern "populist movements" with those of the 1930s. This was seen by several political commentators, as well as many Flemish politicians, as aimed implicitly at the large Flemish nationalist party, the N-VA. Bart De Wever, the party's leader, called for the King's role in the formation of Belgian governments to be changed in the wake of this comment since he "could no longer see the monarch as playing the constitutional role of referee."


title: Albert II of Belgium

text: On 3 July 2013, 79-year-old King Albert II attended a midday session of the Belgian cabinet, where he revealed his intention to abdicate to Prime Minister Elio Di Rupo and to the deputy prime ministers. According to a letter sent by the King to the Prime Minister and dated 3 July 2013, and which was made public, the King had already broached the topic of his intention to abdicate several times with the Prime Minister, who had asked him to reconsider it. At 6 PM (CET) the King announced in a recorded radio and television speech that on 21 July, Belgium's National Day, he would abdicate the throne for health reasons. He was succeeded by his elder son, Philippe.


title: Albert II of Belgium

text: After his abdication on 21 July 2013 it was decided that he would be styled as "His Majesty" King Albert II, the same form of address granted to his father, Leopold III, after his abdication.


title: Battle of the Atlantic

text: The Battle of the Atlantic, the longest continuous military campaign in World War II, ran from 1939 to the defeat of Nazi Germany in 1945, covering a major part of the naval history of World War II. At its core was the Allied naval blockade of Germany, announced the day after the declaration of war, and Germany's subsequent counter-blockade. The campaign peaked from mid-1940 through to the end of 1943.


title: Battle of the Atlantic

text: The Battle of the Atlantic pitted U-boats and other warships of the German "Kriegsmarine" (Navy) and aircraft of the "Luftwaffe" (Air Force) against the Royal Navy, Royal Canadian Navy, United States Navy, and Allied merchant shipping. Convoys, coming mainly from North America and predominantly going to the United Kingdom and the Soviet Union, were protected for the most part by the British and Canadian navies and air forces. These forces were aided by ships and aircraft of the United States beginning September 13, 1941. The Germans were joined by submarines of the Italian "Regia Marina" (Royal Navy) after Germany's Axis ally Italy entered the war on June 10, 1940.


title: Battle of the Atlantic

text: As an island country, the United Kingdom was highly dependent on imported goods. Britain required more than a million tons of imported material per week in order to survive and fight. In essence, the Battle of the Atlantic involved a tonnage war: the Allied struggle to supply Britain and the Axis attempt to stem the flow of merchant shipping that enabled Britain to keep fighting. Rationing in the United Kingdom was also used with the aim of reducing demand, by reducing wastage and increasing domestic production and equality of distribution. From 1942 onward the Axis also sought to prevent the build-up of Allied supplies and equipment in the British Isles in preparation for the invasion of occupied Europe. The defeat of the U-boat threat was a prerequisite for pushing back the Axis in Western Europe. The outcome of the battle was a strategic victory for the Allies—the German blockade failed—but at great cost: 3,500 merchant ships and 175 warships were sunk in the Atlantic for the loss of 783 U-boats (the majority of them Type VII submarines) and 47 German surface warships, including 4 battleships (, , , and ), 9 cruisers, 7 raiders, and 27 destroyers. Of the U-boats, 519 were sunk by British, Canadian, or other allied forces, while 175 were destroyed by American forces; 15 were destroyed by the Soviets and 73 were scuttled by their crews before the end of the war for various reasons.


title: Battle of the Atlantic

text: The Battle of the Atlantic has been called the "longest, largest, and most complex" naval battle in history. The campaign started immediately after the European War began, during the so-called "Phoney War", and lasted more than five years, until the German surrender in May 1945. It involved thousands of ships in more than 100 convoy battles and perhaps 1,000 single-ship encounters, in a theatre covering millions of square miles of ocean. The situation changed constantly, with one side or the other gaining advantage, as participating countries surrendered, joined and even changed sides in the war, and as new weapons, tactics, counter-measures and equipment were developed by both sides. The Allies gradually gained the upper hand, overcoming German surface-raiders by the end of 1942 and defeating the U-boats by mid-1943, though losses due to U-boats continued until the war's end. British Prime Minister Winston Churchill later wrote "The only thing that really frightened me during the war was the U-boat peril. I was even more anxious about this battle than I had been about the glorious air fight called the 'Battle of Britain'."


title: Battle of the Atlantic

text: On 5 March 1941, First Lord of the Admiralty A. V. Alexander asked Parliament for "many more ships and great numbers of men" to fight "the Battle of the Atlantic", which he compared to the Battle of France, fought the previous summer. The first meeting of the Cabinet's "Battle of the Atlantic Committee" was on March 19. Churchill claimed to have coined the phrase "Battle of the Atlantic" shortly before Alexander's speech, but there are several examples of earlier usage.


title: Battle of the Atlantic

text: Following the use of unrestricted submarine warfare by Germany in the First World War, countries tried to limit or abolish submarines. The effort failed. Instead, the London Naval Treaty required submarines to abide by "cruiser rules", which demanded they surface, search and place ship crews in "a place of safety" (for which lifeboats did not qualify, except under particular circumstances) before sinking them, unless the ship in question showed "persistent refusal to stop...or active resistance to visit or search". These regulations did not prohibit arming merchantmen, but doing so, or having them report contact with submarines (or raiders), made them "de facto" naval auxiliaries and removed the protection of the cruiser rules. This made restrictions on submarines effectively moot.


title: Battle of the Atlantic

text: In 1939, the "Kriegsmarine" lacked the strength to challenge the combined British Royal Navy and French Navy ("Marine Nationale") for command of the sea. Instead, German naval strategy relied on commerce raiding using capital ships, armed merchant cruisers, submarines and aircraft. Many German warships were already at sea when war was declared in September 1939, including most of the available U-boats and the "pocket battleships" ("Panzerschiffe") and which had sortied into the Atlantic in August. These ships immediately attacked British and French shipping. sank the ocean liner within hours of the declaration of war—in breach of her orders not to sink passenger ships. The U-boat fleet, which was to dominate so much of the Battle of the Atlantic, was small at the beginning of the war; many of the 57 available U-boats were the small and short-range Type IIs, useful primarily for minelaying and operations in British coastal waters. Much of the early German anti-shipping activity involved minelaying by destroyers, aircraft and U-boats off British ports.


title: Battle of the Atlantic

text: With the outbreak of war, the British and French immediately began a blockade of Germany, although this had little immediate effect on German industry. The Royal Navy quickly introduced a convoy system for the protection of trade that gradually extended out from the British Isles, eventually reaching as far as Panama, Bombay and Singapore. When the convoy system was first introduced however, Britain's Royal Admiralty strongly opposed the idea. Britain believed that the convoy would be a waste of ships that they could not afford to do, considering they might be needed in battle. Convoys allowed the Royal Navy to concentrate its escorts near the one place the U-boats were guaranteed to be found, the convoys. Each convoy consisted of between 30 and 70 mostly unarmed merchant ships.


title: Battle of the Atlantic

text: Some British naval officials, particularly the First Lord of the Admiralty, Winston Churchill, sought a more 'offensive' strategy. The Royal Navy formed anti-submarine hunting groups based on aircraft carriers to patrol the shipping lanes in the Western Approaches and hunt for German U-boats. This strategy was deeply flawed because a U-boat, with its tiny silhouette, was always likely to spot the surface warships and submerge long before it was sighted. The carrier aircraft were little help; although they could spot submarines on the surface, at this stage of the war they had no adequate weapons to attack them, and any submarine found by an aircraft was long gone by the time surface warships arrived. The hunting group strategy proved a disaster within days. On 14 September 1939, Britain's most modern carrier, , narrowly avoided being sunk when three torpedoes from exploded prematurely. "U-39" was forced to surface and scuttle by the escorting destroyers, becoming the first U-boat loss of the war. Another carrier, , was sunk three days later by .


title: Battle of the Atlantic

text: Escort destroyers hunting for U-boats continued to be a prominent, but misguided, technique of British anti-submarine strategy for the first year of the war. U-boats nearly always proved elusive, and the convoys, denuded of cover, were put at even greater risk.


title: Battle of the Atlantic

text: German success in sinking "Courageous" was surpassed a month later when Günther Prien in penetrated the British base at Scapa Flow and sank the old battleship at anchor, immediately becoming a hero in Germany.


title: Battle of the Atlantic

text: In the South Atlantic, British forces were stretched by the cruise of "Admiral Graf Spee", which sank nine merchant ships of in the South Atlantic and Indian Ocean during the first three months of war. The British and French formed a series of hunting groups including three battlecruisers, three aircraft carriers, and 15 cruisers to seek the raider and her sister "Deutschland", which was operating in the North Atlantic. These hunting groups had no success until "Admiral Graf Spee" was caught off the mouth of the River Plate between Argentina and Uruguay by an inferior British force. After suffering damage in the subsequent action, she took shelter in neutral Montevideo harbour and was scuttled on 17 December 1939.


title: Battle of the Atlantic

text: After this initial burst of activity, the Atlantic campaign quieted down. Admiral Karl Dönitz, commander of the U-boat fleet, had planned a maximum submarine effort for the first month of the war, with almost all the available U-boats out on patrol in September. That level of deployment could not be sustained; the boats needed to return to harbour to refuel, re-arm, re-stock supplies, and refit. The harsh winter of 1939–40, which froze over many of the Baltic ports, seriously hampered the German offensive by trapping several new U-boats in the ice. Hitler's plans to invade Norway and Denmark in the spring of 1940 led to the withdrawal of the fleet's surface warships and most of the ocean-going U-boats for fleet operations in Operation Weserübung.


title: Battle of the Atlantic

text: The resulting Norwegian campaign revealed serious flaws in the magnetic influence pistol (firing mechanism) of the U-boats' principal weapon, the torpedo. Although the narrow fjords gave U-boats little room for manoeuvre, the concentration of British warships, troopships and supply ships provided countless opportunities for the U-boats to attack. Time and again, U-boat captains tracked British targets and fired, only to watch the ships sail on unharmed as the torpedoes exploded prematurely (due to the influence pistol), or hit and failed to explode (because of a faulty contact pistol), or ran beneath the target without exploding (due to the influence feature or depth control not working correctly). Not a single British warship was sunk by a U-boat in more than 20 attacks. As the news spread through the U-boat fleet, it began to undermine morale. The director in charge of torpedo development continued to claim it was the crews' fault. In early 1941, the problems were determined to be due to differences in the earth's magnetic fields at high latitudes and a slow leakage of high-pressure air from the submarine into the torpedo's depth regulation gear. These problems were solved by about March 1941, making the torpedo a formidable weapon. Similar problems plagued the US Navy's Mark 14 torpedo. The US ignored reports of German problems.


title: Battle of the Atlantic

text: Early in the war, Dönitz submitted a memorandum to Grand Admiral Erich Raeder, the German navy's Commander-in-Chief, in which he estimated effective submarine warfare could bring Britain to its knees because of the country's dependence on overseas commerce. He advocated a system known as the "Rudeltaktik" (the so-called "wolf pack"), in which U-boats would spread out in a long line across the projected course of a convoy. Upon sighting a target, they would come together to attack "en masse" and overwhelm any escorting warships. While escorts chased individual submarines, the rest of the "pack" would be able to attack the merchant ships with impunity. Dönitz calculated 300 of the latest "Atlantic Boats" (the Type VII), would create enough havoc among Allied shipping that Britain would be knocked out of the war.


title: Battle of the Atlantic

text: This was in stark contrast to the traditional view of submarine deployment up until then, in which the submarine was seen as a lone ambusher, waiting outside an enemy port to attack ships entering and leaving. This had been a very successful tactic used by British submarines in the Baltic and Bosporus during World War I, but it could not be successful if port approaches were well patrolled. There had also been naval theorists who held that submarines should be attached to a fleet and used like destroyers; this had been tried by the Germans at Jutland with poor results, since underwater communications were in their infancy. (Interwar exercises had proven the idea faulty.) The Japanese also adhered to the idea of a fleet submarine, following the doctrine of Mahan, and never used their submarines either for close blockade or convoy interdiction. The submarine was still looked upon by much of the naval world as "dishonourable", compared to the prestige attached to capital ships. This was true in the "Kriegsmarine" as well; Raeder successfully lobbied for the money to be spent on capital ships instead.


title: Battle of the Atlantic

text: The Royal Navy's main anti-submarine weapon before the war was the inshore patrol craft, which was fitted with hydrophones and armed with a small gun and depth charges. The Royal Navy, like most, had not considered anti-submarine warfare as a tactical subject during the 1920s and 1930s. Unrestricted submarine warfare had been outlawed by the London Naval Treaty; anti-submarine warfare was seen as 'defensive' rather than dashing; many naval officers believed anti-submarine work was drudgery similar to mine sweeping; and ASDIC was believed to have rendered submarines impotent. Although destroyers also carried depth charges, it was expected these ships would be used in fleet actions rather than coastal patrol, so they were not extensively trained in their use. The British, however, ignored the fact that arming merchantmen, as Britain did from the start of the war, removed them from the protection of the "cruiser rules", and the fact that anti-submarine trials with ASDIC had been conducted in ideal conditions.


title: Battle of the Atlantic

text: The German occupation of Norway in April 1940, the rapid conquest of the Low Countries and France in May and June, and the Italian entry into the war on the Axis side in June transformed the war at sea in general and the Atlantic campaign in particular in three main ways:


title: Battle of the Atlantic

text: The completion of Hitler's campaign in Western Europe meant U-boats withdrawn from the Atlantic for the Norwegian campaign now returned to the war on trade. So at the very time the number of U-boats on patrol in the Atlantic began to increase, the number of escorts available for the convoys was greatly reduced. The only consolation for the British was that the large merchant fleets of occupied countries like Norway and the Netherlands came under British control. After the German occupation of Denmark and Norway, Britain occupied Iceland and the Faroe Islands, establishing bases there and preventing a German takeover.


title: Battle of the Atlantic

text: It was in these circumstances that Winston Churchill, who had become Prime Minister on 10 May 1940, first wrote to President Franklin Roosevelt to request the loan of fifty obsolescent US Navy destroyers. This eventually led to the "Destroyers for Bases Agreement" (effectively a sale but portrayed as a loan for political reasons), which operated in exchange for 99-year leases on certain British bases in Newfoundland, Bermuda and the West Indies, a financially advantageous bargain for the United States but militarily beneficial for Britain, since it effectively freed up British military assets to return to Europe. A significant percentage of the US population opposed entering the war, and some American politicians (including the US Ambassador to Britain, Joseph P. Kennedy) believed that Britain and its allies might actually lose. The first of these destroyers were only taken over by their British and Canadian crews in September, and all needed to be rearmed and fitted with ASDIC. It was to be many months before these ships contributed to the campaign.


title: Battle of the Atlantic

text: The early U-boat operations from the French bases were spectacularly successful. This was the heyday of the great U-boat aces like Günther Prien of "U-47", Otto Kretschmer (), Joachim Schepke (), Engelbert Endrass (), Victor Oehrn () and Heinrich Bleichrodt (). U-boat crews became heroes in Germany. From June until October 1940, over 270 Allied ships were sunk: this period was referred to by U-boat crews as "the Happy Time" (""Die Glückliche Zeit""). Churchill would later write: "...the only thing that ever frightened me during the war was the U-boat peril".


title: Battle of the Atlantic

text: The biggest challenge for the U-boats was to find the convoys in the vastness of the ocean. The Germans had a handful of very long-range Focke-Wulf Fw 200 Condor aircraft based at Bordeaux and Stavanger, which were used for reconnaissance. The Condor was a converted civilian airliner—a stop-gap solution for "Fliegerführer Atlantik". Due to ongoing friction between the "Luftwaffe" and "Kriegsmarine", the primary source of convoy sightings was the U-boats themselves. Since a submarine's bridge was very close to the water, their range of visual detection was quite limited.


title: Battle of the Atlantic

text: The best source proved to be the codebreakers of "B-Dienst" who had succeeded in deciphering the British Naval Cypher No. 3, allowing the Germans to estimate where and when convoys could be expected.


title: Battle of the Atlantic

text: In response, the British applied the techniques of operations research to the problem and came up with some counter-intuitive solutions for protecting convoys. They realised that the area of a convoy increased by the square of its perimeter, meaning the same number of ships, using the same number of escorts, was better protected in one convoy than in two. A large convoy was as difficult to locate as a small one. Moreover, reduced frequency also reduced the chances of detection, as fewer large convoys could carry the same amount of cargo, while large convoys take longer to assemble. Therefore, a few large convoys with apparently few escorts were safer than many small convoys with a higher ratio of escorts to merchantmen.


title: Battle of the Atlantic

text: Instead of attacking the Allied convoys singly, U-boats were directed to work in wolf packs ("Rudel") coordinated by radio. The boats spread out into a long patrol line that bisected the path of the Allied convoy routes. Once in position, the crew studied the horizon through binoculars looking for masts or smoke, or used hydrophones to pick up propeller noises. When one boat sighted a convoy, it would report the sighting to U-boat headquarters, shadowing and continuing to report as needed until other boats arrived, typically at night. Instead of being faced by single submarines, the convoy escorts then had to cope with groups of up to half a dozen U-boats attacking simultaneously. The most daring commanders, such as Kretschmer, penetrated the escort screen and attacked from within the columns of merchantmen. The escort vessels, which were too few in number and often lacking in endurance, had no answer to multiple submarines attacking on the surface at night as their ASDIC only worked well against underwater targets. Early British marine radar, working in the metric bands, lacked target discrimination and range. Moreover, corvettes were too slow to catch a surfaced U-boat.


title: Battle of the Atlantic

text: Pack tactics were first used successfully in September and October 1940 to devastating effect, in a series of convoy battles. On September 21, convoy HX 72 of 42 merchantmen was attacked by a pack of four U-boats, which sank eleven ships and damaged two over the course of two nights. In October, the slow convoy SC 7, with an escort of two sloops and two corvettes, was overwhelmed, losing 59% of its ships. The battle for HX 79 in the following days was in many ways worse for the escorts than for SC 7. The loss of a quarter of the convoy without any loss to the U-boats, despite a very strong escort (two destroyers, four corvettes, three trawlers, and a minesweeper) demonstrated the effectiveness of the German tactics against the inadequate British anti-submarine methods. On 1 December, seven German and three Italian submarines caught HX 90, sinking 10 ships and damaging three others. The success of pack tactics against these convoys encouraged Admiral Dönitz to adopt the wolf pack as his primary tactic.


title: Battle of the Atlantic

text: At the end of the year 1940, the Admiralty viewed the number of ships sunk with growing alarm. Damaged ships might survive but could be out of commission for long periods. Two million gross tons of merchant shipping—13 % percent of the fleet available to the British—were under repair and unavailable, which had the same effect in slowing down cross-Atlantic supplies.


title: Battle of the Atlantic

text: Nor were the U-boats the only threat. Following some early experience in support of the war at sea during Operation Weserübung, the "Luftwaffe" began to take a toll of merchant ships. Martin Harlinghausen and his recently established command—"Fliegerführer Atlantik"—contributed small numbers of aircraft to the Battle of the Atlantic from 1941 onwards. These were primarily Fw 200 Condors and (later) Junkers Ju 290s, used for long-range reconnaissance. The Condors also bombed convoys that were beyond land-based fighter cover and thus defenceless. Initially, the Condors were very successful, claiming 365,000 tons of shipping in early 1941. These aircraft were few in number, however, and directly under "Luftwaffe" control; in addition, the pilots had little specialised training for anti-shipping warfare, limiting their effectiveness.


title: Battle of the Atlantic

text: The Germans received help from their allies. From August 1940, a flotilla of 27 Italian submarines operated from the BETASOM base in Bordeaux to attack Allied shipping in the Atlantic, initially under the command of Rear Admiral Angelo Parona, then of Rear Admiral Romolo Polacchini and finally of Ship-of-the-Line Captain Enzo Grossi. The Italian submarines had been designed to operate in a different way than U-boats, and they had a number of flaws that needed to be corrected (for example huge conning towers, slow speed when surfaced, lack of modern torpedo fire control), which meant that they were ill-suited for convoy attacks, and performed better when hunting down isolated merchantmen on distant seas, taking advantage of their superior range and living standards. While initial operation met with little success (only 65343 GRT sunk between August and December 1940), the situation improved gradually over time, and up to August 1943 the 32 Italian submarines that operated there sank 109 ships of 593,864 tons, for 17 subs lost in return, giving them a subs-lost-to-tonnage sunk ratio similar to Germany's in the same period, and higher overall. The Italians were also successful with their use of "human torpedo" chariots, disabling several British ships in Gibraltar.


title: Battle of the Atlantic

text: Despite these successes, the Italian intervention was not favourably regarded by Dönitz, who characterised Italians as "inadequately disciplined" and "unable to remain calm in the face of the enemy". They were unable to co-operate in wolf pack tactics or even reliably report contacts or weather conditions, and their area of operation was moved away from those of the Germans.


title: Battle of the Atlantic

text: Amongst the more successful Italian submarine commanders who operated in the Atlantic were Carlo Fecia di Cossato, commander of the submarine , and Gianfranco Gazzana-Priaroggia, commander of and then of .


title: Battle of the Atlantic

text: ASDIC (also known as SONAR) was a central feature of the Battle of the Atlantic. One crucial development was the integration of ASDIC with a plotting table and weapons (depth charges and later Hedgehog) to make an anti-submarine warfare system.


title: Battle of the Atlantic

text: ASDIC produced an accurate range and bearing to the target, but could be fooled by thermoclines, currents or eddies, and schools of fish, so it needed experienced operators to be effective. ASDIC was effective only at low speeds. Above or so, the noise of the ship going through the water drowned out the echoes.


title: Battle of the Atlantic

text: The early wartime Royal Navy procedure was to sweep the ASDIC in an arc from one side of the escort's course to the other, stopping the transducer every few degrees to send out a signal. Several ships searching together would be used in a line, apart. If an echo was detected, and if the operator identified it as a submarine, the escort would be pointed towards the target and would close at a moderate speed; the submarine's range and bearing would be plotted over time to determine course and speed as the attacker closed to within . Once it was decided to attack, the escort would increase speed, using the target's course and speed data to adjust her own course. The intention was to pass over the submarine, rolling depth charges from chutes at the stern at even intervals, while throwers fired further charges some to either side. The intention was to lay a 'pattern' like an elongated diamond, hopefully with the submarine somewhere inside it. To effectively disable a submarine, a depth charge had to explode within about . Since early ASDIC equipment was poor at determining depth, it was usual to vary the depth settings on part of the pattern.


title: Battle of the Atlantic

text: There were disadvantages to the early versions of this system. Exercises in anti-submarine warfare had been restricted to one or two destroyers hunting a single submarine whose starting position was known, and working in daylight and calm weather. U-boats could dive far deeper than British or American submarines (over ), well below the maximum depth charge setting of British depth charges. More importantly, early ASDIC sets could not look directly down, so the operator lost contact on the U-boat during the final stages of the attack, a time when the submarine would certainly be manoeuvring rapidly. The explosion of a depth charge also disturbed the water, so ASDIC contact was very difficult to regain if the first attack had failed. It enabled the U-boat to change position with impunity.


title: Battle of the Atlantic

text: The belief that ASDIC had solved the submarine problem, the acute budgetary pressures of the Great Depression, and the pressing demands for many other types of rearmament meant little was spent on anti-submarine ships or weapons. Most British naval spending, and many of the best officers, went into the battlefleet. Critically, the British expected, as in the First World War, German submarines would be coastal craft and only threaten harbour approaches. As a result, the Royal Navy entered the Second World War in 1939 without enough long-range escorts to protect ocean-going shipping, and there were no officers with experience of long-range anti-submarine warfare. The situation in Royal Air Force Coastal Command was even more dire: patrol aircraft lacked the range to cover the North Atlantic and could typically only machine-gun the spot where they saw a submarine dive.


title: Battle of the Atlantic

text: Despite their success, U-boats were still not recognised as the foremost threat to the North Atlantic convoys. With the exception of men like Dönitz, most naval officers on both sides regarded surface warships as the ultimate commerce destroyers.


title: Battle of the Atlantic

text: For the first half of 1940, there were no German surface raiders in the Atlantic because the German Fleet had been concentrated for the invasion of Norway. The sole pocket battleship raider, "Admiral Graf Spee", had been stopped at the Battle of the River Plate by an inferior and outgunned British squadron. From the summer of 1940 a small but steady stream of warships and armed merchant raiders set sail from Germany for the Atlantic.


title: Battle of the Atlantic

text: The power of a raider against a convoy was demonstrated by the fate of convoy HX 84, attacked by the pocket battleship on 5 November 1940. "Admiral Scheer" quickly sank five ships and damaged several others as the convoy scattered. Only the sacrifice of the escorting armed merchant cruiser (whose commander, Edward Fegen, was awarded a posthumous Victoria Cross) and failing light allowed the other merchantmen to escape. The British now suspended North Atlantic convoys and the Home Fleet put to sea to try to intercept "Admiral Scheer". The search failed and "Admiral Scheer" disappeared into the South Atlantic. She reappeared in the Indian Ocean the following month.


title: Battle of the Atlantic

text: Other German surface raiders now began to make their presence felt. On Christmas Day 1940, the cruiser attacked the troop convoy WS 5A, but was driven off by the escorting cruisers. "Admiral Hipper" had more success two months later, on 12 February 1941, when she found the unescorted convoy SLS 64 of 19 ships and sank seven of them. In January 1941, the formidable (and fast) battleships and , which outgunned any Allied ship that could catch them, put to sea from Germany to raid the shipping lanes in Operation Berlin. With so many German raiders at large in the Atlantic, the British were forced to provide battleship escorts to as many convoys as possible. This twice saved convoys from slaughter by the German battleships. In February, the old battleship deterred an attack on HX 106. A month later, SL 67 was saved by the presence of .


title: Battle of the Atlantic

text: In May, the Germans mounted the most ambitious raid of all: Operation Rheinübung. The new battleship and the cruiser put to sea to attack convoys. A British fleet intercepted the raiders off Iceland. In the Battle of the Denmark Strait, the battlecruiser was blown up and sunk, but "Bismarck" was damaged and had to run to France. "Bismarck" nearly reached her destination, but was disabled by an airstrike from the carrier "Ark Royal", and then sunk by the Home Fleet the next day. Her sinking marked the end of the warship raids. The advent of long-range search aircraft, notably the unglamorous but versatile PBY Catalina, largely neutralised surface raiders.


title: Battle of the Atlantic

text: In February 1942, "Scharnhorst", "Gneisenau" and "Prinz Eugen" moved from Brest back to Germany in the "Channel Dash". While this was an embarrassment for the British, it was the end of the German surface threat in the Atlantic. The loss of "Bismarck", the destruction of the network of supply ships that supported surface raiders, the repeated damage to the three ships by air raids, the entry of the United States into the war, Arctic convoys, and the perceived invasion threat to Norway had persuaded Hitler and the naval staff to withdraw.


title: Battle of the Atlantic

text: War had come too early for the German naval expansion project Plan Z. Battleships powerful enough to destroy any convoy escort, with escorts able to annihilate the convoy, were never achieved. Although the number of ships the raiders sank was relatively small compared with the losses to U-boats, mines, and aircraft, their raids severely disrupted the Allied convoy system, reduced British imports, and strained the Home Fleet.


title: Battle of the Atlantic

text: The disastrous convoy battles of October 1940 forced a change in British tactics. The most important of these was the introduction of permanent escort groups to improve the co-ordination and effectiveness of ships and men in battle. British efforts were helped by a gradual increase in the number of escort vessels available as the old ex-American destroyers and the new British- and Canadian-built s were now coming into service in numbers. Many of these ships became part of the huge expansion of the Royal Canadian Navy, which grew from a handful of destroyers at the outbreak of war to take an increasing share of convoy escort duty. Others of the new ships were crewed by Free French, Norwegian and Dutch, but these were a tiny minority of the total number, and directly under British command. By 1941 American public opinion had begun to swing against Germany, but the war was still essentially Great Britain and the Empire against Germany.


title: Battle of the Atlantic

text: Initially, the new escort groups consisted of two or three destroyers and half a dozen corvettes. Since two or three of the group would usually be in dock repairing weather or battle damage, the groups typically sailed with about six ships. The training of the escorts also improved as the realities of the battle became obvious. A new base was set up at Tobermory in the Hebrides to prepare the new escort ships and their crews for the demands of battle under the strict regime of Vice-Admiral Gilbert O. Stephenson.


title: Battle of the Atlantic

text: In February 1941, the Admiralty moved the headquarters of Western Approaches Command from Plymouth to Liverpool, where much closer contact with, and control of, the Atlantic convoys was possible. Greater co-operation with supporting aircraft was also achieved. In April, the Admiralty took over operational control of Coastal Command aircraft. At a tactical level, new short-wave radar sets that could detect surfaced U-boats and were suitable for both small ships and aircraft began to arrive during 1941.


title: Battle of the Atlantic

text: The impact of these changes first began to be felt in the battles during the spring of 1941. In early March, Prien in "U-47" failed to return from patrol. Two weeks later, in the battle of Convoy HX 112, the newly formed 3rd Escort Group of four destroyers and two corvettes held off the U-boat pack. "U-100" was detected by the primitive radar on the destroyer , rammed and sunk. Shortly afterwards "U-99" was also caught and sunk, its crew captured. Dönitz had lost his three leading aces: Kretschmer, Prien, and Schepke.


title: Battle of the Atlantic

text: Dönitz now moved his wolf packs further west, in order to catch the convoys before the anti-submarine escort joined. This new strategy was rewarded at the beginning of April when the pack found Convoy SC 26 before its anti-submarine escort had joined. Ten ships were sunk, but another U-boat was lost.


title: Battle of the Atlantic

text: In June 1941, the British decided to provide convoy escort for the full length of the North Atlantic crossing. To this end, the Admiralty asked the Royal Canadian Navy on May 23, to assume the responsibility for protecting convoys in the western zone and to establish the base for its escort force at St. John's, Newfoundland. On June 13, 1941, Commodore Leonard Murray, Royal Canadian Navy, assumed his post as Commodore Commanding Newfoundland Escort Force, under the overall authority of the Commander-in-Chief, Western Approaches, at Liverpool. Six Canadian destroyers and 17 corvettes, reinforced by seven destroyers, three sloops, and five corvettes of the Royal Navy, were assembled for duty in the force, which escorted the convoys from Canadian ports to Newfoundland and then on to a meeting point south of Iceland, where the British escort groups took over.


title: Battle of the Atlantic

text: By 1941, the United States was taking an increasing part in the war, despite its nominal neutrality. In April 1941 President Roosevelt extended the Pan-American Security Zone east almost as far as Iceland. British forces occupied Iceland when Denmark fell to the Germans in 1940; the US was persuaded to provide forces to relieve British troops on the island. American warships began escorting Allied convoys in the western Atlantic as far as Iceland, and had several hostile encounters with U-boats.


title: Battle of the Atlantic

text: In June 1941, the US realised the tropical Atlantic had become dangerous for unescorted American as well as British ships. On May 21, , an American vessel carrying no military supplies, was stopped by west of Freetown, Sierra Leone. After its passengers and crew were allowed thirty minutes to board lifeboats, "U-69" torpedoed, shelled, and sank the ship. The survivors then drifted without rescue or detection for up to eighteen days. When news of the sinking reached the US, few shipping companies felt truly safe anywhere. As "Time" magazine noted in June 1941, "if such sinkings continue, U.S. ships bound for other places remote from fighting fronts, will be in danger. Henceforth the U.S. would either have to recall its ships from the ocean or enforce its right to the free use of the seas."


title: Battle of the Atlantic

text: A Mid-Ocean Escort Force of British, and Canadian, and American destroyers and corvettes was organised following the declaration of war by the United States in December 1941.


title: Battle of the Atlantic

text: At the same time, the British were working on a number of technical developments which would address the German submarine superiority. Though these were British inventions, the critical technologies were provided freely to the US, which then renamed and manufactured them. Likewise, the US provided the British with Catalina flying boats and Liberator bombers that were important contributions to the war effort.


title: Battle of the Atlantic

text: Aircraft ranges were constantly improving, but the Atlantic was far too large to be covered completely by land-based types. A stop-gap measure was instituted by fitting ramps to the front of some of the cargo ships known as "catapult aircraft merchantmen" (CAM ships), equipped with a lone expendable Hurricane fighter aircraft. When a German bomber approached, the fighter was launched off the end of the ramp with a large rocket to shoot down or drive off the German aircraft, the pilot then ditching in the water and – in the best case – recovered by ship. Nine combat launches were made, resulting in the destruction of eight Axis aircraft for the loss of one Allied pilot.


title: Battle of the Atlantic

text: Although CAM ships and their Hurricanes did not down a great number of enemy aircraft, such aircraft were mostly Fw 200 Condors that would often shadow the convoy out of range of the convoy's guns, reporting back the convoy's course and position so that U-boats could then be directed on to the convoy. The CAM ships and their Hurricanes thus justified the cost in fewer ship losses overall.


title: Battle of the Atlantic

text: One of the more important developments was ship-borne direction-finding radio equipment, known as HF/DF (high-frequency direction-finding, or Huff-Duff), which started to be fitted to escorts from February 1942. These sets were common items of equipment by the spring of 1943. HF/DF let an operator determine the direction of a radio signal, regardless of whether the content could be read. Since the wolf pack relied on U-boats reporting convoy positions by radio, there was a steady stream of messages to intercept. An escort could then run in the direction of the signal and attack the U-boat, or at least force it to submerge (causing it to lose contact), which might prevent an attack on the convoy. When two ships fitted with HF/DF accompanied a convoy, a fix on the transmitter's position, not just direction, could be determined. However, the standard approach of anti-submarine warships was immediately to "run-down" the bearing of a detected signal, hoping to spot the U-boat on the surface and make an immediate attack. Range could be estimated by an experienced operator from the signal strength. Usually the target was found visually. If the submarine was slow to dive, the guns were used; otherwise an ASDIC (Sonar) search was started where the swirl of water of a crash-diving submarine was observed. In good visibility a U-boat might try and outrun an escort on the surface whilst out of gun range. Running down the bearing of a HF/DF signal was also used by escort carriers (particularly , operating south of the Azores), sending aircraft along the line of the bearing to force the submarine to submerge by strafing and then attack with depth charges or a FIDO homing torpedo.


title: Battle of the Atlantic

text: The British also made extensive use of shore HF/DF stations, to keep convoys updated with positions of U-boats.


title: Battle of the Atlantic

text: The radio technology behind direction finding was simple and well understood by both sides, but the technology commonly used before the war used a manually-rotated aerial to fix the direction of the transmitter. This was delicate work, took quite a time to accomplish to any degree of accuracy, and since it only revealed the line along which the transmission originated a single set could not determine if the transmission was from the true direction or its reciprocal 180 degrees in the opposite direction. Two sets were required to fix the position. Believing this to still be the case, German U-boat radio operators considered themselves fairly safe if they kept messages short. The British, however, developed an oscilloscope-based indicator which instantly fixed the direction and its reciprocal the moment a radio operator touched his Morse key. It worked simply with a crossed pair of conventional and fixed directional aerials, the oscilloscope display showing the relative received strength from each aerial as an elongated ellipse showing the line relative to the ship. The innovation was a 'sense' aerial, which, when switched in, suppressed the ellipse in the 'wrong' direction leaving only the correct bearing. With this there was hardly any need to triangulate—the escort could just run down the precise bearing provided, estimating range from the signal strength, and use either efficient look-outs or radar for final positioning. Many U-boat attacks were suppressed and submarines sunk in this way—a good example of the great difference apparently minor aspects of technology could make to the battle.


title: Battle of the Atlantic

text: The way Dönitz conducted the U-boat campaign required relatively large volumes of radio traffic between U-boats and headquarters. This was thought to be safe as the radio messages were encrypted using the Enigma cipher machine, which the Germans considered unbreakable. In addition, the "Kriegsmarine" used much more secure operating procedures than the "Heer" (Army) or "Luftwaffe" (Air Force). The machine's three rotors were chosen from a set of eight (rather than the other services' five). The rotors were changed every other day using a system of key sheets and the message settings were different for every message and determined from "bigram tables" that were issued to operators. In 1939, it was generally believed at the British Government Code and Cypher School (GC&CS) at Bletchley Park that naval Enigma could not be broken. Only the head of the German Naval Section, Frank Birch, and the mathematician Alan Turing believed otherwise.


title: Battle of the Atlantic

text: The British codebreakers needed to know the wiring of the special naval Enigma rotors, and the destruction of by in February 1940 provided this information. In early 1941, the Royal Navy made a concerted effort to assist the codebreakers, and on May 9 crew members of the destroyer boarded and recovered her cryptologic material, including bigram tables and current Enigma keys. The captured material allowed all U-boat traffic to be read for several weeks, until the keys ran out; the familiarity codebreakers gained with the usual content of messages helped in breaking new keys.


title: Battle of the Atlantic

text: Throughout the summer and autumn of 1941, Enigma intercepts (combined with HF/DF) enabled the British to plot the positions of U-boat patrol lines and route convoys around them. Merchant ship losses dropped by over two-thirds in July 1941, and the losses remained low until November.


title: Battle of the Atlantic

text: During May 1943, the US Navy began using a 4-rotor bombe machines used drums for the Enigma rotors at 34 times the speed of the early British bombe machines. By September 1944, the US Navy had 121 bombes.


title: Battle of the Atlantic

text: This Allied advantage was offset by the growing numbers of U-boats coming into service. The Type VIIC began reaching the Atlantic in large numbers in 1941; by the end of 1945, 568 had been commissioned. Although the Allies could protect their convoys in late 1941, they were not sinking many U-boats. The Flower-class corvette escorts could detect and defend, but they were not fast enough to attack effectively.


title: Battle of the Atlantic

text: An extraordinary incident occurred when a Coastal Command Hudson of 209 Squadron captured "U-570" on 27 August 1941 about south of Iceland. Squadron Leader J. Thompson sighted the U-boat on the surface, immediately dived at his target, and released four depth charges as the submarine crash dived. The U-boat surfaced again, a number of crewmen appeared on deck, and Thompson engaged them with his aircraft's guns. The crewmen returned to the conning tower while under fire. A few moments later, a white flag and a similarly coloured board were displayed. Thompson called for assistance and circled the German vessel. A Catalina from 209 Squadron took over watching the damaged U-boat until the arrival of the armed trawler "Kingston Agate" under Lt Henry Owen L'Estrange. The following day the U-boat was beached in an Icelandic cove. Although no codes or secret papers were recovered, the British now possessed a complete U-boat. After a refit, "U-570" was commissioned into the Royal Navy as .


title: Battle of the Atlantic

text: In October 1941, Hitler ordered Dönitz to move U-boats into the Mediterranean to support German operations in that theatre. The resulting concentration near Gibraltar resulted in a series of battles around the Gibraltar and Sierra Leone convoys. In December 1941, Convoy HG 76 sailed, escorted by the 36th Escort Group of two sloops and six corvettes under Captain Frederic John Walker, reinforced by the first of the new escort carriers, , and three destroyers from Gibraltar. The convoy was immediately intercepted by the waiting U-boat pack, resulting in a brutal battle. Walker was a tactical innovator, his ships' crews were highly trained and the presence of an escort carrier meant U-boats were frequently sighted and forced to dive before they could get close to the convoy. Over the next five days, five U-boats were sunk (four by Walker's group), despite the loss of "Audacity" after two days. The British lost "Audacity", a destroyer and only two merchant ships. The battle was the first clear Allied convoy victory.


title: Battle of the Atlantic

text: Through dogged effort, the Allies slowly gained the upper hand until the end of 1941. Although Allied warships failed to sink U-boats in large numbers, most convoys evaded attack completely. Shipping losses were high, but manageable.


title: Battle of the Atlantic

text: The attack on Pearl Harbor and the subsequent German declaration of war on the United States had an immediate effect on the campaign. Dönitz promptly planned to attack shipping off the American East Coast. He had only 12 Type IX boats able to reach US waters; half of them had been diverted by Hitler to the Mediterranean. One of the remainder was under repair, leaving only five boats for Operation Drumbeat ("Paukenschlag"), sometimes called by the Germans the "Second happy time."


title: Battle of the Atlantic

text: The US, having no direct experience of modern naval war on its own shores, did not employ a black-out. U-boats simply stood off shore at night and picked out ships silhouetted against city lights. Admiral Ernest King, Commander-in-Chief United States Fleet (Cominch), who disliked the British, initially rejected Royal Navy calls for a coastal black-out or convoy system. King has been criticised for this decision, but his defenders argue the United States destroyer fleet was limited (partly because of the sale of 50 old destroyers to Britain earlier in the war), and King claimed it was far more important that destroyers protect Allied troop transports than merchant shipping. His ships were also busy convoying Lend-Lease material to the Soviet Union, as well as fighting the Japanese in the Pacific. King could not require coastal black-outs—the Army had legal authority over all civil defence—and did not follow advice the Royal Navy (or Royal Canadian Navy) provided that even unescorted convoys would be safer than merchants sailing individually. No troop transports were lost, but merchant ships sailing in US waters were left exposed and suffered accordingly. Britain eventually had to build coastal escorts and provide them to the US in a "reverse Lend Lease", since King was unable (or unwilling) to make any provision himself.


title: Battle of the Atlantic

text: The first U-boats reached US waters on January 13, 1942. By the time they withdrew on February 6, they had sunk 156,939 tonnes of shipping without loss. The first batch of Type IXs was followed by more Type IXs and Type VIIs supported by Type XIV "Milk Cow" tankers which provided refuelling at sea. They sank 397 ships totalling over 2 million tons. (As mentioned previously, not a single troop transport was lost.) In 1943, the United States launched over 11 million tons of merchant shipping; that number declined in the later war years, as priorities moved elsewhere.


title: Battle of the Atlantic

text: In May, King (by this time both Cominch and CNO) finally scraped together enough ships to institute a convoy system. This quickly led to the loss of seven U-boats. The US did not have enough ships to cover all the gaps; the U-boats continued to operate freely during the Battle of the Caribbean and throughout the Gulf of Mexico (where they effectively closed several US ports) until July, when the British-loaned escorts began arriving. These included 24 armed anti-submarine trawlers crewed by the Royal Naval Patrol Service; many had previously been peacetime fishermen. On July 3, 1942, one of these trawlers, HMS "Le Tigre" proved her worth by picking up 31 survivors from the American merchant "Alexander Macomb". Shortly after, "Le Tigre" managed to hunt down the U-boat that had torpedoed the merchant ship, which was then sunk by ; credit was awarded to "Le Tigre". The institution of an interlocking convoy system on the American coast and in the Caribbean Sea in mid-1942 resulted in an immediate drop in attacks in those areas. As a result of the increased coastal convoy escort system, the U-boats' attention was shifted back to the Atlantic convoys. For the Allies, the situation was serious but not critical throughout much of 1942.


title: Battle of the Atlantic

text: Operation Drumbeat had one other effect. It was so successful that Dönitz's policy of economic war was seen, even by Hitler, as the only effective use of the U-boat; he was given complete freedom to use them as he saw fit. Meanwhile, Hitler sacked Raeder after the embarrassing Battle of the Barents Sea, in which two German heavy cruisers were beaten off by half a dozen British destroyers. Dönitz was eventually made Grand Admiral, and all building priorities turned to U-boats.


title: Battle of the Atlantic

text: With the US finally arranging convoys, ship losses to the U-boats quickly dropped, and Dönitz realised his U-boats were better used elsewhere. On July 19, 1942, he ordered the last boats to withdraw from the United States Atlantic coast; by the end of July 1942 he had shifted his attention back to the North Atlantic, where allied aircraft could not provide cover—i.e. the Black Pit. Convoy SC 94 marked the return of the U-boats to the convoys from Canada to Britain. The command centre for the submarines operating in the West, including the Atlantic also changed, moving to a newly constructed command bunker at the Château de Pignerolle just east of Angers on the Loire river. The headquarters was commanded by Hans-Rudolf Rösing.


title: Battle of the Atlantic

text: There were enough U-boats spread across the Atlantic to allow several wolf packs to attack many different convoy routes. Often as many as 10 to 15 boats would attack in one or two waves, following convoys like SC 104 and SC 107 by day and attacking at night. Convoy losses quickly increased and in October 1942, 56 ships of over 258,000 tonnes were sunk in the "air gap" between Greenland and Iceland.


title: Battle of the Atlantic

text: U-boat losses also climbed. In the first six months of 1942, 21 were lost, less than one for every 40 merchant ships sunk. In August and September, 60 were sunk, one for every 10 merchant ships, almost as many as in the previous two years.


title: Battle of the Atlantic

text: On November 19, 1942, Admiral Noble was replaced as Commander-in-Chief of Western Approaches Command by Admiral Sir Max Horton. Horton used the growing number of escorts becoming available to organise "support groups", to reinforce convoys that came under attack. Unlike the regular escort groups, support groups were not directly responsible for the safety of any particular convoy. This gave them much greater tactical flexibility, allowing them to detach ships to hunt submarines spotted by reconnaissance or picked up by HF/DF. Where regular escorts would have to break off and stay with their convoy, the support group ships could keep hunting a U-boat for many hours. One tactic introduced by Captain John Walker was the "hold-down", where a group of ships would patrol over a submerged U-boat until its air ran out and it was forced to the surface; this might take two or three days.


title: Battle of the Atlantic

text: Between February 1942 and July 1945, about 5,000 naval officers played war games at "Western Approaches Tactical Unit". Many game graduates believe that the battle they fought on the linoleum floor is essential to their subsequent victory at sea. In November 1942, Admiral Horton tested "Beta Search" in a wargame. Janet Okell and Jean Laidlaw played the role of the escorts. Five times in a row Okell and Laidlaw sank the submarine of Admiral Horton, the commander-in chief of Western Approaches.


title: Battle of the Atlantic

text: At the start of World War II, the depth charge was the only weapon available to a vessel for destroying a submerged submarine. Depth charges were dropped over the stern and thrown to the side of a warship travelling at speed. Early models of ASDIC/Sonar searched only ahead, astern and to the sides of the anti-submarine vessel that was using it: there was no downward-looking capability. So there was a time lag between the last fix obtained on the submarine and the warship reaching a point above that position. Then the depth charges had to sink to the depth at which they were set to explode. During those two delays, a capable submarine commander would manoeuvre rapidly to a different position and avoid the attack. The depth charges then left an area of disturbed water, through which it was difficult to regain ASDIC/Sonar contact. In response to this problem, one of the solutions developed by the Royal Navy was the ahead-throwing anti-submarine weapon—the first of which was Hedgehog.


title: Battle of the Atlantic

text: Hedgehog was a multiple spigot mortar, which fired contact-fused bombs ahead of the firing ship while the target was still within the ASDIC beam. These started to be installed on anti-submarine ships from late 1942. The warship could approach slowly (as it did not have to clear the area of exploding depth charges to avoid damage) and so its position was less obvious to the submarine commander as it was making less noise. Because hedgehog only exploded if it hit the submarine, if the target was missed, there was no disturbed water to make tracking difficult—and contact had not been lost in the first place.


title: Battle of the Atlantic

text: Squid was an improvement on 'Hedgehog' introduced in late 1943. A three-barrelled mortar, it projected charges ahead or abeam; the charges' firing pistols were automatically set just prior to launch. The more advanced installations had Squid linked to the latest ASDIC sets so that Squid was fired automatically.


title: Battle of the Atlantic

text: Detection by radar-equipped aircraft could suppress U-boat activity over a wide area, but an aircraft attack could only be successful with good visibility. U-boats were relatively safe from aircraft at night for two reasons: 1) radar then in use could not detect them at less than ; 2) flares deployed to illuminate any attack gave adequate warning for evasive manoeuvres. The introduction of the Leigh Light by the British in January 1942 solved the second problem, thereby becoming a significant factor in the Battle for the Atlantic. Developed by RAF officer H. Leigh, it was a powerful and controllable searchlight mounted primarily to Wellington bombers and B-24 Liberators. These aircraft first made contact with enemy submarines using air-to-surface-vessel (ASV) radar. Then, about a from the target, the Leigh Light would be switched on. It immediately and accurately illuminated the enemy, giving U-boat commanders less than 25 seconds to react before they were attacked with depth charges. The first confirmed kill using this technology was "U-502" on July 5, 1942.


title: Battle of the Atlantic

text: The Leigh Light enabled the British to attack enemy subs on the surface at night, forcing German and Italian commanders to remain underwater especially when coming into port at sub bases in the Bay of Biscay. U-boat commanders who survived such attacks reported a particular fear of this weapon system since aircraft could not be seen at night, and the noise of an approaching aircraft was inaudible above the din of the sub's engines. Subsequently, the common practice of surfacing at night to recharge batteries and refresh air was mostly abandoned as it was safer to perform these tasks during daylight hours when enemy planes could be spotted. A drop in Allied shipping losses from 600,000 to 200,000 tons per month was attributed to this device.


title: Battle of the Atlantic

text: By August 1942, U-boats were being fitted with radar detectors to enable them to avoid sudden ambushes by radar-equipped aircraft or ships. The first such receiver, named Metox after its French manufacturer, was capable of picking up the metric radar bands used by the early radars. This not only enabled U-boats to avoid detection by Canadian escorts, which were equipped with obsolete radar sets, but allowed them to track convoys where these sets were in use.


title: Battle of the Atlantic

text: However, it also caused problems for the Germans, as it sometimes detected stray radar emissions from distant ships or planes, causing U-boats to submerge when they were not in actual danger, preventing them from recharging batteries or using their surfaced speed.


title: Battle of the Atlantic

text: Metox provided the U-boat commander with an advantage that had not been anticipated by the British. The Metox set beeped at the pulse rate of the hunting aircraft's radar, approximately once per second. When the radar operator came within of the U-boat, he changed the range of his radar. With the change of range, the radar doubled its pulse repetition frequency and as a result, the Metox beeping frequency also doubled, warning the commander that he had been detected.


title: Battle of the Atlantic

text: In 1941, American intelligence informed Rear Admiral John Henry Godfrey that the UK naval codes could be broken. In March, 1942, the Germans broke Naval Cipher 3, the code for Anglo-American communication. Eighty percent of the Admiralty messages from March, 1942 to June 1943 were read by the Germans. The sinking of Allied merchant ships increased dramatically.


title: Battle of the Atlantic

text: "We had reached a stage when it took one or two days to decrypt the British radio messages. On occasions only a few hours were required. We could sometimes deduce when and how they would take advantage of the gaps in our U-boat dispositions. Our function was to close those gaps just before the convoys were due."


title: Battle of the Atlantic

text: The code breakers of Bletchley Park assigned only two people to evaluate whether the Germans broke the code. After five months, they finally determined that the codes were broken. In August, 1942, the UK Admiralty was informed. However, the Admiralty did not change the codes until June, 1943.


title: Battle of the Atlantic

text: Captain Raymond Dreyer, deputy staff signals officer at Western Approaches, the British HQ for the Battle of the Atlantic in Liverpool, said, "Some of their most successful U-boat pack attacks on our convoys were based on information obtained by breaking our ciphers."


title: Battle of the Atlantic

text: On February 1, 1942, the "Kriegsmarine" switched the U-boats to a new Enigma network (TRITON) that used the new, four-rotor, Enigma machines. This new key could not be read by codebreakers; the Allies no longer knew where the U-boat patrol lines were. This made it far more difficult to evade contact, and the wolf packs ravaged many convoys. This state persisted for ten months. To obtain information on submarine movements the Allies had to make do with HF/DF fixes and decrypts of "Kriegsmarine" messages encoded on earlier Enigma machines. These messages included signals from coastal forces about U-boat arrivals and departures at their bases in France, and the reports from the U-boat training command. From these clues, Commander Rodger Winn's Admiralty Submarine Tracking Room supplied their best estimates of submarine movements, but this information was not enough.


title: Battle of the Atlantic

text: Then on October 30, crewmen from salvaged Enigma material from as she foundered off Port Said. This allowed the codebreakers to break TRITON, a feat credited to Alan Turing. By December 1942, Enigma decrypts were again disclosing U-boat patrol positions, and shipping losses declined dramatically once more.


title: Battle of the Atlantic

text: Following the St Nazaire Raid on 28 March 1942, Raeder decided the risk of further seaborne attack was high and relocated the western command centre for U-boats to the Château de Pignerolle, where a command bunker was built and from where all Enigma radio messages between German command and Atlantic based operational U-boats were transmitted/received. In July 1942, Hans-Rudolf Rösing was appointed as FdU West ("Führer der Unterseeboote West"). Pignerolle became his headquarters.


title: Battle of the Atlantic

text: After Convoy ON 154, winter weather provided a brief respite from the fighting in January before convoys SC 118 and ON 166 in February 1943, but in the spring, convoy battles started up again with the same ferocity. There were so many U-boats on patrol in the North Atlantic, it was difficult for convoys to evade detection, resulting in a succession of vicious battles.


title: Battle of the Atlantic

text: On March 10, 1943, the Germans added a refinement to the U-boat Enigma key, which blinded the Allied codebreakers at Bletchley Park for 9 days. That month saw the battles of convoys UGS 6, HX 228, SC 121, SC 122 and HX 229. One hundred and twenty ships were sunk worldwide, 82 ships of 476,000 tons in the Atlantic, while 12 U-boats were destroyed.


title: Battle of the Atlantic

text: The supply situation in Britain was such that there was talk of being unable to continue the war, with supplies of fuel being particularly low. The situation was so bad that the British considered abandoning convoys entirely. The next two months saw a complete reversal of fortunes.


title: Battle of the Atlantic

text: In April, losses of U-boats increased while their kills fell significantly. Only 39 ships of 235,000 tons were sunk in the Atlantic, and 15 U-boats were destroyed. By May, wolf packs no longer had the advantage and that month became known as Black May in the U-boat Arm ("U-Bootwaffe"). The turning point was the battle centred on slow convoy ONS 5 (April–May 1943). Made up of 43 merchantmen escorted by 16 warships, it was attacked by a pack of 30 U-boats. Although 13 merchant ships were lost, six U-boats were sunk by the escorts or Allied aircraft. Despite a storm which scattered the convoy, the merchantmen reached the protection of land-based air cover, causing Dönitz to call off the attack. Two weeks later, SC 130 saw at least three U-boats destroyed and at least one U-boat damaged for no losses. Faced with disaster, Dönitz called off operations in the North Atlantic, saying, "We had lost the Battle of the Atlantic".


title: Battle of the Atlantic

text: In all, 43 U-boats were destroyed in May, 34 in the Atlantic. This was 25% of German U-boat Arm's total operational strength. The Allies lost 58 ships in the same period, 34 of these (totalling 134,000 tons) in the Atlantic.


title: Battle of the Atlantic

text: The Battle of the Atlantic was won by the Allies in two months. There was no single reason for this; what had changed was a sudden convergence of technologies, combined with an increase in Allied resources.


title: Battle of the Atlantic

text: The mid-Atlantic gap that had previously been unreachable by aircraft was closed by long-range B-24 Liberators. On 18 March 1943, Roosevelt ordered King to transfer 60 Liberators from the Pacific theatre to the Atlantic to combat German U-boats; one of only two direct orders he gave to his military commanders in WWII (the other was regarding Operation Torch). At the May 1943 Trident conference, Admiral King requested General Henry H. Arnold to send a squadron of ASW-configured B-24s to Newfoundland to strengthen the air escort of North Atlantic convoys. General Arnold ordered his squadron commander to engage only in "offensive" search and attack missions and not in the escort of convoys. In June, General Arnold suggested the Navy assume responsibility for ASW operations. Admiral King requested the Army's ASW-configured B-24s in exchange for an equal number of unmodified Navy B-24s. Agreement was reached in July and the exchange was completed in September 1943.


title: Battle of the Atlantic

text: Further air cover was provided by the introduction of merchant aircraft carriers (MAC ships), and later the growing numbers of American-built escort carriers. Primarily flying Grumman F4F Wildcats and Grumman TBF Avengers, they sailed with the convoys and provided much-needed air cover and patrols all the way across the Atlantic.


title: Battle of the Atlantic

text: Larger numbers of escorts became available, both as a result of American building programmes and the release of escorts committed to the North African landings during November and December 1942. In particular, destroyer escorts (DEs) (similar British ships were known as "frigates") were designed to be built economically, compared to fleet destroyers and sloops whose warship-standards construction and sophisticated armaments made them too expensive for mass production. Destroyer escorts and frigates were also better designed for mid-ocean anti-submarine warfare than corvettes, which, although maneuverable and seaworthy, were too short, slow, and inadequately armed to match the DEs. Not only would there be sufficient numbers of escorts to securely protect convoys, they could also form hunter-killer groups (often centered on escort carriers) to aggressively hunt U-boats.


title: Battle of the Atlantic

text: By spring 1943, the British had developed an effective sea-scanning radar small enough to be carried in patrol aircraft armed with airborne depth charges. Centimetric radar greatly improved interception and was undetectable by Metox. Fitted with it, RAF Coastal Command sank more U-boats than any other Allied service in the last three years of the war. During 1943 U-boat losses amounted to 258 to all causes. Of this total, 90 were sunk and 51 damaged by Coastal Command.


title: Battle of the Atlantic

text: Allied air forces developed tactics and technology to make the Bay of Biscay, the main route for France-based U-boats, very dangerous to submarines. The Leigh Light enabled attacks on U-boats recharging their batteries on the surface at night. "Fliegerführer Atlantik" responded by providing fighter cover for U-boats moving into and returning from the Atlantic and for returning blockade runners. Nevertheless, with intelligence coming from resistance personnel in the ports themselves, the last few miles to and from port proved hazardous to U-boats.


title: Battle of the Atlantic

text: Dönitz's aim in this tonnage war was to sink Allied ships faster than they could be replaced; as losses fell and production rose, particularly in the United States, this became impossible.


title: Battle of the Atlantic

text: Beginning in August 1943, the British were allowed to access the harbors at the Portuguese Azores Islands and to operate Allied military aircraft based in the Azores Islands.


title: Battle of the Atlantic

text: Despite U-boat operations in the region (centred in the Atlantic Narrows between Brazil and West Africa) beginning autumn 1940, only in the following year did these start to raise serious concern in Washington. This perceived threat caused the US to decide that the introduction of US forces along Brazil's coast would be valuable. After negotiations with Brazilian Foreign Minister Osvaldo Aranha (on behalf of dictator Getúlio Vargas), these were introduced in second half of 1941.


title: Battle of the Atlantic

text: Germany and Italy subsequently extended their submarine attacks to include Brazilian ships wherever they were, and from April 1942 were found in Brazilian waters. On 22 May 1942, the first Brazilian attack (although unsuccessful) was carried out by Brazilian Air Force aircraft on the . After a series of attacks on merchant vessels off the Brazilian coast by , Brazil officially entered the war on 22 August 1942, offering an important addition to the Allied strategic position in the South Atlantic.