User:Kurzon/sandbox

${\displaystyle R={\frac {mv}{qB}}}$

${\displaystyle BR={\frac {mv}{q}}=390,000{\text{ C/sm m}}}$

${\displaystyle {\frac {q}{m}}=6000}$

${\displaystyle {\frac {m}{q}}={\frac {1}{6000}}}$

${\displaystyle v={\frac {q}{m}}{\text{ C/kg}}\times 390,000{\text{ kg/s2 A m}}=2.34\times 10^{9}{\text{ cm/s}}}$

This section presents an alternative method to find the relation between the impact parameter and deflection angle in a single-atom encounter, using a force-centric approach as opposed to the energy-centric one that Rutherford used.

The scattering geometry is shown in this diagram^{[22][23]: 106}

The impact parameter b is the distance between the alpha particle's initial trajectory and a parallel line that goes through the nucleus. Smaller values of b bring the particle closer to the atom so it feels more deflection force resulting in a larger deflection angle θ.^[24]: 82 The goal is to find the relationship between b and the deflection angle.

The alpha particle's path is a hyperbola and the net change in momentum ${\displaystyle \Delta {\vec {P}}}$ runs along the axis of symmetry. From the geometry in the diagram and the magnitude of the initial and final momentum vectors, ${\displaystyle |{\vec {P}}_{i}|=|{\vec {P}}_{f}|=mv}$, the magnitude of ${\displaystyle \Delta {\vec {P}}}$ can be related to the deflection angle:^[23]: 111

$${\displaystyle \Delta P=2mv\cdot \sin {\frac {\theta }{2}}}$$

A second formula for ${\displaystyle \Delta P}$ involving b will give the relationship to the deflection angle. The net change in momentum can also be found by adding small increments to momentum all along the trajectory using the integral

$${\displaystyle \Delta P=\int \limits _{0}^{\infty }{\frac {kq_{\text{a}}q_{\text{g}}}{r^{2}}}\cdot \cos \varphi \cdot \mathrm {\mathrm {d} } t}$$

where ${\displaystyle r}$ is the distance between the alpha particle and the centre of the nucleus and ${\displaystyle \varphi }$ is its angle from the axis of symmetry. These two are the polar coordinates of the alpha particle at time ${\displaystyle t}$. q_a is the charge of the alpha particle, q_g is the charge of the atomic nucleus, and k is the Coulomb constant. The Coulomb force exerted along the line between the alpha particle and the atom is ${\displaystyle {\tfrac {kq_{\text{a}}q_{\text{g}}}{r^{2}}}}$and the factor ${\displaystyle \cos \varphi }$ gives that part of the force causing deflection.

The polar coordinates r and φ depend on t in the integral, but they must be related to each other as they both vary as the particle moves. Changing the variable and limits of integration from t to φ makes this connection explicit:^[23]: 112

$${\displaystyle \Delta P=\int \limits _{-{\frac {\pi -\theta }{2}}}^{\frac {\pi -\theta }{2}}{\frac {kq_{\text{a}}q_{\text{g}}}{r^{2}}}\cdot \cos \varphi \cdot {\frac {\mathrm {d} t}{\mathrm {d} \varphi }}\cdot \mathrm {d} \varphi }$$

The factor ${\displaystyle {\tfrac {\mathrm {d} t}{\mathrm {d} \varphi }}={\tfrac {1}{\omega }}}$ is the reciprocal of the angular velocity the particle. Since the force is only along the line between the particle and the atom, the angular momentum, which is proportional to the angular velocity, is constant:

$${\displaystyle mvb=mr^{2}\omega =mr^{2}{\frac {\mathrm {d} \varphi }{\mathrm {d} t}}}$$

This law of conservation of angular momentum gives a formula for ${\displaystyle {\tfrac {\mathrm {d} t}{\mathrm {d} \varphi }}}$:

$${\displaystyle {\frac {\mathrm {d} t}{\mathrm {d} \varphi }}={\frac {r^{2}}{vb}}}$$

Replacing ${\displaystyle {\tfrac {\mathrm {d} t}{\mathrm {d} \varphi }}}$ in the integral for ΔP simultaneously eliminates the dependence on r:

$${\displaystyle \Delta P=\int \limits _{-{\frac {\pi -\theta }{2}}}^{\frac {\pi -\theta }{2}}{\frac {kq_{\text{a}}q_{\text{g}}}{vb}}\cdot \cos \varphi \cdot \mathrm {d} \varphi }$$

$${\displaystyle ={\frac {kq_{\text{a}}q_{\text{g}}}{vb}}\left(\sin \left[{\frac {\pi -\theta }{2}}\right]-\sin \left[-{\frac {\pi -\theta }{2}}\right]\right)}$$

Applying the trigonometric identities ${\displaystyle \sin({\tfrac {\pi }{2}}-\theta )=\cos \theta }$ and ${\displaystyle \sin(\theta \pm {\tfrac {\pi }{2}})=\pm \cos \theta }$ to simplify this result gives the second formula for ${\displaystyle \Delta P}$:

$${\displaystyle \Delta P={\frac {kq_{\text{a}}q_{\text{g}}}{vb}}\cdot 2\cos {\frac {\theta }{2}}}$$

We now have two equations for ${\displaystyle \Delta P}$, which we can solve for θ:

$${\displaystyle \Delta P={\frac {kq_{\text{a}}q_{\text{g}}}{vb}}\cdot 2\cos {\frac {\theta }{2}}=2mv\cdot \sin {\frac {\theta }{2}}}$$

$${\displaystyle \theta =2\arctan \left({\frac {kq_{\text{a}}q_{\text{g}}}{mv^{2}b}}\right)}$$

Using the following values, we will examine an example where an alpha particle passes through a gold atom:

• q_g = positive charge of the gold atom = 79 q_e = 1.26×10⁻¹⁷ C
• q_a = charge of the alpha particle = 2 q_e = 3.20×10⁻¹⁹ C
• v = speed of the alpha particle = 1.53×10⁷ m/s
• m = mass of the alpha particle = 6.64×10⁻²⁷ kg
• k = Coulomb constant = 8.987×10⁹ N·m²/C²

When the alpha particle passes close to the nucleus barely missing it, such that the impact parameter b is equal to the radius of a gold nucleus (7×10⁻¹⁵ m), the estimated deflection angle θ will be 2.56 radians (147°). If the alpha particle grazes the edge of the atom, with b therefore being equal to 1.44×10⁻¹⁰ m, the estimated deflection is a tiny 0.0003 radians (0.02°).^{[23]: 109 [25]}

$${\displaystyle {\bar {\theta }}_{1}={\frac {16}{5}}\cdot {\frac {kq_{e}q_{e}}{m_{e}v_{e}^{2}}}\cdot {\frac {1}{R}}\cdot {\sqrt {\frac {3N}{2}}}\approx 0.00084{\text{ radians or }}0.048{\text{ degrees}}}$$

where

• q_g = positive charge of the gold atom = 79 e = 1.26×10⁻¹⁷ C
• q_a = charge of the alpha particle = 2 e = 3.20×10⁻¹⁹ C
• q_e = elementary charge = 1.602×10⁻¹⁹ C
• R = radius of the gold atom = 1.44×10⁻¹⁰ m
• v = speed of the alpha particle = 1.53×10⁷ m/s
• v_e = speed of the beta particle = 2.7×10⁸ m/s
• m = mass of the alpha particle = 6.64×10⁻²⁷ kg
• m_e = mass of the beta particle = 9.11×10⁻³¹ kg
• k = Coulomb constant = 8.987×10⁹ N·m²/C²
• N = number of electrons in the gold atom = 79

The average angle by which an alpha particle should be deflected by the positive sphere of the atom was simply given by Thomson as:

$${\displaystyle {\bar {\theta }}_{2}={\frac {\pi }{4}}\cdot {\frac {kq_{e}q_{g}}{m_{e}v_{e}^{2}}}\cdot {\frac {1}{R}}\approx 0.0015{\text{ radians or 0.086 degrees}}}$$

The net deflection per atom combines the two equations:

$${\displaystyle {\bar {\theta }}={\sqrt {{\bar {\theta }}_{1}^{2}+{\bar {\theta }}_{2}^{2}}}\approx 0.097{\text{ degrees}}}$$

$${\displaystyle e^{-(90/9.7)^{2}}\approx e^{-86}\approx 10^{-37}}$$

At age 17, Slim convinced a girlfriend named in his memoir as "June" to work as a prostitute for him. His second customer recognized the girl and informed her father, and the father in turn contacted the police. Slim was sentenced to 12 to 18 months in prison for "carnal knowledge and abuse". June's father used his influence to prevent Slim from being charged with "pandering" because he did not want his daughter to be labelled a prostitute. Slim served his sentence in Wisconsin Green Bay Reformatory.^[26]

Slim returned to Milwaukee after being released. Four and a half months after being paroled, a man named "Weeping" paid Slim $500 to have sex with a woman named "Pepper" with the intent to take photographs of the couple in bed and blackmail Pepper. But after Slim did the deed and was paid, he was arrested and accused of stealing the money from Pepper's house. Pepper testified against Slim at his trial, and Slim was convicted of burglary and sentenced to two years in prison, which he served in Waupun State Prison. He was released three months early for good behavior. Slim never figured out why Weeping and Pepper framed him.^[27]

Chapter 15 - Slim was arrested on an outstanding federal warrant.

Slim was convicted of armed robbery and sentenced to one year in a workhouse.

In Thomson's model of scattering the average angle by which an alpha particle should be deflected by the positive sphere of the atom is^{[28][29]: 268}

$${\displaystyle {\bar {\theta }}_{2}={\frac {\pi }{4}}\cdot {\frac {kq_{a}q_{g}}{mv^{2}R}}}$$

Neither Thomson nor Rutherford explained how this equation was developed, but here an educated guess is made.^[30]

In 1906, Thomson provided an equation which models how a beta particle should be deflected by an atomic electron in a close encounter:^[31]

$${\displaystyle \tan {\frac {\theta _{e}}{2}}={\frac {kq_{e}q_{e}}{m'v^{2}b}}}$$

This then-standard application of hyperbolic orbits for trajectories in a central potential^[32]: 86 was also used in Rutherford's more famous 1911 paper^[33] (a full explanation is available in the article on the Rutherford scattering experiments). The factor ${\displaystyle m'}$, the reduced mass equal to ${\displaystyle {\tfrac {m_{1}m_{2}}{m_{1}+m_{2}}}}$ where m₁ and m₂ are the masses of the two colliding particles, enters the model when the two-body coordinates are written as the equivalent one-body problem.^[24]: 59 q_e is the elementary charge and b is the impact parameter.

An alpha particle passing by the positive sphere with a radius R equal to that of a gold atom, just close enough to graze its edge, will experience the sphere's electric field at its strongest.^[34]: 107 This occurs for an impact parameter b equal to the radius R as shown here:

Using Thomson's equation from above to model this collision gives:

$${\displaystyle \theta _{2}=2\arctan \left({\frac {kq_{a}q_{g}}{mv^{2}b}}\right)\approx 0.02{\text{ degrees}}}$$

Unlike Thomson's electron-electron collision, no correction for recoil is needed here because the gold atom is nearly 20 times as heavy as the alpha particle. The equation shows that the maximum deflection caused by the positive sphere will be very small. But what of the average deflection ${\displaystyle {\bar {\theta }}_{2}}$ over the whole sphere?

Consider an alpha particle passing through the positive sphere of a gold atom, with its initial trajectory at a lateral distance b from the center.

Inside a sphere of uniformly distributed positive charge the force exerted on the alpha particle at any point along its path through the sphere is^{[35][34]: 106}

$${\displaystyle F={\frac {kq_{a}q_{g}}{r^{2}}}\cdot {\frac {r^{3}}{R^{3}}}}$$

The lateral component of this force is

$${\displaystyle F_{y}={\frac {kq_{a}q_{g}}{r^{2}}}\cdot {\frac {r^{3}}{R^{3}}}\cdot \cos \varphi ={\frac {bkq_{a}q_{g}}{R^{3}}}}$$

The lateral change in momentum p_y is therefore

$${\displaystyle \Delta p_{y}=F_{y}t={\frac {bkq_{a}q_{g}}{R^{3}}}\cdot {\frac {2L}{v}}}$$

The deflection angle ${\displaystyle \theta _{2}}$ is given by

$${\displaystyle \tan \theta _{2}={\frac {\Delta p_{y}}{p_{x}}}={\frac {bkq_{a}q_{g}}{R^{3}}}\cdot {\frac {2L}{v}}\cdot {\frac {1}{mv}}}$$

where p_x is the average horizontal momentum, which is first reduced then restored as horizontal force switches direction as the alpha particle goes across the sphere. Since we already know the deflection is very small, we can treat ${\displaystyle \tan \theta _{2}}$ as being equal to ${\displaystyle \theta _{2}}$.

To find the average deflection angle ${\displaystyle {\bar {\theta }}_{2}}$, we must average b and L across the entire sphere:

$${\displaystyle {\bar {\theta }}_{2}={\frac {1}{\pi R^{2}}}\int _{0}^{R}{\frac {bkq_{a}q_{g}}{R^{3}}}\cdot {\frac {2{\sqrt {R^{2}-b^{2}}}}{v}}\cdot {\frac {1}{mv}}\cdot 2\pi b\cdot \mathrm {d} b}$$

$${\displaystyle ={\frac {\pi }{4}}\cdot {\frac {kq_{a}q_{g}}{mv^{2}R}}}$$

This matches Thomson's formula in his 1910 paper.

B = the impact parameter where the distance of closest approach r_A is equal to the average distance between electrons d.

${\displaystyle {\frac {B^{2}}{d^{2}}}=1-2{\frac {q}{d}}}$

Greco-Roman wrestling was boring to watch. Fights usually lasted several hours if not more, and looked like a boring shoving match to spectators. Beekman p. 25

"That wrestling did not follow a similar course [as boxing] toward respectability and honest competition derived from the unique circumstances that developed in the decades bookending the turn of the twentieth century." p 27

• Nobody could replace Gotch
• Carnival culture

As he grew older, the Greco-Roman wrestling champion William Muldoon introduced time limits, usually of one hour, to his matches. The match would end in a draw on a timeout. This made Muldoon more able to defend his title from younger challengers who had more stamina. Beekman p. 32-33

In the late nineteenth century, competitive wrestlers switched from Greco-Roman to catch wrestling. Catch wrestling was more quick, violent, and exciting. Beekman p. 36

In the late nineteenth century, wrestling waned in popularity, and pro wrestlers toured the country more frequently to compensate. They therefore encountered each other more often on tour, which gave them opportunities to plan matches with each other in advance, both for scheduling convenience and to reduce the risk of injury. Beekman p. 39

"The shift toward wrestlers working in collusion, and the development of the catch style, emerged from the carnival subculture" Beekman p. 39

Carnival operators would hire boxers and wrestlers to challenge paying attendees to fights. If the challenger lasted fifteen minutes with the champion, he won a prize. Wrestlers thus had to obtain quick victories, and catch wrestlers did this better than Greco-Roman wrestlers. Beekman p. 39-40

Carnival operators often staged rigged matches between the champion and a "stick" in the audience. The stick would win, making the champion look beatable, thereby duping paying customers into challenging the champion. This kind of scam fostered a swindler mentality among wrestlers, and developed the art of staging wrestling matches presented as genuine. Beekman p. 40

"A 1905 National Police Gazette editorial posited that ‘‘nine out of ten [wrestling] bouts ... are prearranged affairs.’’ Despite this, undoubtedly correct, assertion" Beekman p. 40

In the early 20th century, many states in America banned boxing over concerns of rigged matches. Many out-of-work boxers turned to professional wrestling. Beekman p. 41

"The success of these boxers-turned-wrestlers was a model for later wrestling promoters, who actively sought out washed-up fighters such as Joe Louis, Primo Carnera, and Jack Dempsey to add luster to the grappling game" Beekman p 42

"With no wrestler able to generate the excitement of Frank Gotch and the attendance figures dwindling, professional wrestling faced a dire circumstance. To survive as a economically viable operation, the sport fundamentally altered. No longer a legitimate sporting contest, wrestling became pure entertainment under the guise of an athletic endeavor." p 52

"[Jack] Curley, however, faced difficulties in sustaining his gains because of the lack of prominent eastern wrestlers. The Plains, which produced Gotch, Burns, and Stecher, remained the locus of the sport. To create a vast and sustainable wrestling empire, Curley needed to develop ties to the wrestling powers of the Midwest." p 53

"Most important, they recognized that through cooperative effort promoters could dominate the sport and effectively eliminate the bargaining power of independent-minded wrestlers. As the controlling force in wrestling, promoters could maximize profits by carefully establishing new stars and through selective scheduling of matches. For this plan to succeed, ‘‘works’’ had to be an integral part of professional wrestling" p 54

"For wrestling, a sport lacking home teams or an established ‘‘season,’’ the development of personas was an essential aspect for drawing fans to matches in which they had no vested, personal interest." p 64

"Although no hard rules existed for determining personas, promoters usually pushed handsome or former college star wrestlers as clean-wrestling faces, while older, fatter, or foreign-born (who became somewhat less common thanks to the immigration laws of the 1920s) wrestlers often became heels." p 64

"By the early 1930s, promoters across the country adopted the technique [of personas], and it became a standard aspect of professional wrestling." p 64

"To make matters worse, recent events [in the late 1930s] had shattered public assurance in the honesty of wrestling." P 69 suggests many fans back then thought pro wrestling was genuine

"Wrestlers of Thesz’s skills, however, were rare. Many worried promoters did not have any wrestlers under contract who combined mat skills with drawing power like the handsome young Missourian. [...] Faced with declining revenues, the promoters made the fateful decision to focus on developing wrestlers who possessed drawing power, with increasingly little regard given to knowledge of holds." p 71

"Recognizing that much of the public now viewed professional wrestling as an entertainment form rather than an honest sport, the promoters simply gave the public what they believed it wanted." p 71

" Matches became more comical and outlandish as promoters introduced gimmick matches and bizarre wrestling personas" p 72

Dmitry Grigoryev; Anastasia Batkhina; Lucian Gideon Conway III; Alivia Zubrod (2022). "Authoritarian Attitudes in Russia: Right-Wing Authoritarianism and Social Dominance Orientation in the Modern Russian Context". Asian Journal of Social Psychology. doi:10.1111/ajsp.12523.

p. 39: "In addressing the vulnerability of the DRV internal situation, one finds. a subsistence level agricultural economy operating on a marginal basis. There is a small economic infrastructure and only a modest (and highly valued) industrial capacity. The population is rigidly controlled, is largely rural and is already accustomed to an extremely austere living standard."

p. 40: "Most important, perhaps, was the feeling that the Viet Cong might well be able to continue operating in SVN for a considerable period of time using existing stockpiles, captured stores and weapons, and levies on the country, despite destruction of major military and industrial facilities in NVN. Cited were examples of the VC provisioning from the larder of RVN villages."

p. 133: "The North Vietnamese made every effort to disperse their supplies and equipment and profitable targets became progressively more difficult to locate."

p. 137: "The basic economy (primarily agricultural) remained intact even though the eight primary industrial targets (5-10% of the total worth of the country) had been destroyed."

p. 134: "Intelligence reports indicated that the supplies had been positioned by the CPR and that they were far in excess of the needs of the Pathet Lao."

p. 158: "Soviet and Bloc shipping continues to arrive at North Vietnamese ports with vitally needed supplies and equipment."

p. 158: "The VC has continued mining operations in SVN along roads and railroads with good effect."

p. 167: "Prior to destruction of the final industrial targets in the DRV, the United States used the UK and Canadians to presure Hanoi into halting support of the VC and PL insurgencies. As in previous instances they were informed that such conversations were useless. If anything they were more useless than previously since there was very little remaining for the Fascist murderers to destroy in the DRV and all the people of the SEA were united in their determination to throw off capitalist shackles."

p. 187: "I think the answer to that is the eight year war against the French when the Vie-t Minh didn't control any of the cities or have the industrial, small industrial complex that they have now. They still proceeded to progress during the eight years and eventually win the war."

p. 190: "We [RED] develop pretty good techniques for making basically hostile people perform regardless of what's happening to them."

p. 194: "We have no consensus on what would happen if we initiated a bombing campaign on North Vietnam."

p. 196: "I would think, as a military judgment, that strikes against military targets or even industrial targets are not going to cut off the Viet Cong activity suddenly. They will have too much in hand, too much in stock piles. Their needs are quite primitive in any event. They are too primitive for such strikes to have the same effect on their society and their armed forces that similar strikes would have on ours. We have gotten too sophisticated and we need too much, as the J-4 would be the first to testify, in order to exist and even more to operate."

Fawcett (2009), How to Lose a War, p. 28: "Hanoi only had to send 10 to 15 tons of supplies per day down the Ho Chi Minh Trail to support its war effort in the South. The Viet Cong obtained most of its supplies locally."

Bill Fawcett (2009). How to Lose a War: More Foolish Plans and Great Military Blunders. Harper Collins. ISBN 9780061900709.

McMaster (1998), Dereliction of Duty, chpt. 4: "Rusk, agreeing with McNamara, believed that graduated pressure would never present “Peking or Moscow with enough of a change in the situation to require them to make a major decision… in terms of intervening in [Vietnam].” Rusk believed that applying force in carefully controlled gradations would help to “limit the war to Viet Nam.”"

McMaster (1998), Dereliction of Duty, chpt. 4: "McNamara’s strategy of graduated pressure seemed to “solve” the president’s problem of not losing Vietnam while maintaining the image that he was reluctant to escalate the war. If the Chiefs had successfully pressed with the president their position that the United States needed to act forcefully to defeat the North, they might have forced a difficult choice between war and withdrawal from South Vietnam."

McMaster (1998), Dereliction of Duty, chpt. 5: "The outcome of the game was eerily prophetic. [...] McNamara sent to the president, however, only those assessments that supported his conception of prosecuting the conflict in Vietnam. Robert McNamara was not interested in the outcome of SIGMA I [...] the SIGMA test, largely a subjective evaluation based on military experience and diplomatic expertise, did not appeal to McNamara’s penchant for systematic and quantitative analysis."

McMaster (1998), Dereliction of Duty, chpt. 8: "The growing consensus behind the strategic concept of graduated pressure overpowered SIGMA II’s unpromising conclusions because the president and his advisers were unwilling to risk either disengagement or escalation. In their minds the rash application of force could be disastrous and lead, in the worst-case scenario, to nuclear war with the Soviet Union. Doing nothing would lead to defeat in South Vietnam and an associated loss of credibility that could undermine the West’s alliance structure and result in defeat in the Cold War."

25⁄300

²⁵⁄₃₀₀

25⁄300

5+25⁄300

Where did Roberts get his training/inspiration in wargaming?

Parkin (2019) Ch 7: "Roberts’ naval career continued on a promising, if unorthodox trajectory when, following sorties to fit out Australia’s first aircraft carrier and a trip down the Danube, he was made a game designer for the Royal Navy. In July 1935, a few days after he was promoted to the rank of commander, Roberts joined the tactical school at Portsmouth. Here naval captains and their senior staff played wargames, hyper-evolved military-themed board games staged on floors painted to look like giant chessboards. Distant cousins to commercial board games such as Battleship and Risk, these wargames were intended to explore and rehearse lifelike combat situations, a crucible in which tactics could be tested, analysed, and refined. It was work to which Roberts took an immediate liking."

Parkin (2019) Ch 7: "The progenitor of the wargame on which Roberts based his games in Portsmouth was Fred Jane, a failed novelist who, in 1898, published the rules of a boardgame-style naval wargame in the Engineering Journal. Later that year, his books, Jane Naval Wargame and Fighting Ships, provided a formal set of rules, scorecards and ship diagrams, which were subsequently adapted by the navy. The game, which used scale ship models, a squared board and even some ping-pong-like bats to fire projectiles, was notable for its flexibility and realism. Jane tested the game aboard warships docked in Portsmouth Harbour and, four years later, a modified version was issued to HM Ships for training. It was a version of the Jane Naval Wargame that Roberts adapted at his posting in Portsmouth, more than three decades later."

Parkin (2019) Ch 8: "Churchill’s aide [Admiral Cecil Usborne] believed that Roberts, who had shown himself to be a talented strategist in Portsmouth and an enthusiastic proponent of games as a way to prepare for war, was the ideal person to evolve anti-U-boat tactics. Moreover, as a gifted communicator he was qualified to train escort commanders in those tactics."

The wargames that Roberts' played in 1935-37 at Portsmouth did not feature submarines

Parkin (2019) Ch 7: "Despite the fact that during the First World War the Germans had used submarines to great effect to disrupt the convoys bringing food and supplies to Great Britain, neither U-boats nor convoys featured in the wargames of 1935. [...] ‘Submarines were not mentioned,’ Roberts wrote of the games he was tasked with designing. ‘Nor were convoys and attacks on them. Nobody connected Hitler’s rise … to the possibility of another Battle of the Atlantic. Nor did I, to be absolutely fair.’"

When was Roberts put in charge of WATU?

Parkin (2019) Ch 8: "On the first day of 1942, Roberts was told to report to the Admiralty offices with an overnight bag. On arrival he met two of the navy’s most senior officers, the Second Sea Lord, Sir Charles Little, and Admiral Cecil Usborne, the former director of naval intelligence, now an aide to Winston Churchill. Usborne was responsible for overseeing the development of anti-U-boat weapons. To Roberts’ astonishment, the men began to describe, ‘most clearly’, the true extent of Britain’s ongoing losses in the Atlantic, and the Allied force’s miserable performance in battling the U-boats."

Parkin (2019) Ch 8: "Usborne motioned Roberts out of the office, and the two men went to the canteen to eat. There, over the course of two hours, Usborne explained what was needed of Roberts. He was to take the train to Liverpool, and report to Noble at the new Western Approaches HQ, which had been established in a building called Derby House, nicknamed ‘the Citadel’. He was to take charge of a large room on the top floor. Roberts would be assigned a group of young staff. Then, using any and every means necessary, he and his staff were to get to work on the U-boat problem."

Parkin (2019) Ch 10: "Roberts disembarked the train at Liverpool station in the early hours of 2nd January 1942."

WATU location

Parkin (2019) Ch 10: "Roberts was to be given the entire top floor of Derby House, recently vacated by Tate & Lyle sugar company, comprising eight rooms."

Wargame design

Parkin (2019) Ch 11: "The floor in the centre of the room was covered in brown linoleum, painted with white gridlines and punctuated with tiny wooden models, some of which had been fashioned from wood taken from HMS Nelson, an armoured cruiser built in the 1870s that had been scrapped in 1910."

Parkin (2019) Ch 11: "The convoy ships, the prize in play for both sides, would automatically plod on at each turn of the game toward their destination, the battle raging around them, just as at sea. Next, Roberts explained the rules of the game. Players were given two minutes in which to submit their orders for the next ‘turn’, to replicate the urgency of a real battlefield. The movements of the U-boats were drawn in green5 chalk on the floor, a colour chosen as it was impossible to make out against the floor’s tint when viewed from an angle. This ensured the U-boat positions were undetectable to the players peering through the canvas screens. The escort ships’ movements would then be added to the floor in white chalk, which was, in contrast to the green markings, legible to those peeking from the canvas holes. Turn by turn the pieces would move around the floor, as the escort ships dashed to the site of an explosion to drop depth charges, and the U-boats performed their feints and dodges in an effort to pick off convoy ships, while evading the escort."

Parkin (2019) Ch 11: "As Okell surveyed the floor, Roberts explained that each white line was spaced ten inches apart, representing one nautical mile, while the counters represented ships and surfaced German U-boats."

Raspberry

Parkin (2019), A Game of Birds and Wolves. Ch 11: "If the U-boats were firing from outside the perimeter of the convoy, how had Annavore, which was in the centre of the convoy, been sunk? Might it be possible, he wondered, that the U-boat had attacked the ship from inside the columns of the convoy? There was, he reasoned, a simple way to prove his theory."

Parkin (2019), A Game of Birds and Wolves. Ch 11: "Between them, Roberts and the two Wrens began to plot different scenarios that might have enabled the U-boat to sneak into the convoy without being detected. Only one checked out: the U-boat had entered the columns of the convoy from behind. And it must have done so on the surface, where it was able to travel at a faster speed than the ships. By approaching from astern, where the lookouts rarely checked, the U-boat would be able to slip inside the convoy undetected, fire at close range, then submerge in order to get away."

Parkin (2019), A Game of Birds and Wolves. Ch 11: "With the U-boat tactic abruptly unveiled, Roberts wanted to try out some potential countermeasures that might foil the plan. The four returned to the game room. Roberts assumed the role of the U-boat captain, and Laidlaw and Okell played as Walker’s escort ships. The countermeasure revealed itself immediately. Rather than splay out from the convoy at speed, dropping depth charges at random, Laidlaw and Okell lined the escort ships up around the convoy. While the convoy continued on its way, each escort ship performed a triangular sweep, listening for U-boats on the ASDIC."

Effects of WATU

Parkin (2019), A Game of Birds and Wolves. Ch 12: "Still, the work was exhilarating, especially when the first fruits of WATU’s work began to be seen in summer 1942, when escort ships sank four times as many U-boats as the previous month, beginning an upward trend that would continue, broadly, for the rest of the year."

The obvious advantage of wargaming is that it allows the military to conduct training and research in a safe and relatively cheap way.

In 2018, the US Navy spent $3.35 million on wargaming,^[45].

Another advantage of wargames is that it allows the military to develop the skills and theories of its officers without the enemy noticing and adapting. A problem that any military faces when learning through hard experience – i.e. actual warfare – is that as it gets better at fighting the enemy, the enemy will adapt in turn, modifying their own armaments and tactics to maintain their edge. This problem doesn't exist with wargaming, because if the real enemy cannot participate in the wargame, he cannot know what ideas were developed.^[46]

Wargames can also teach trainees skills and theories faster than field experience, because wargames can greatly compress the timespan of a conflict. A campaign that might take months to wage in a real war might take only hours or days to simulate in a wargame.^[47]

Wargames can be used to experiment with new tactical and strategic ideas. For instance, in the 1920s the US Navy conceived the circular formation, in which a capital ship such as a battleship or aircraft carrier is surrounded by a circle of smaller support ships to maximize defence against aircraft and submarines. After initial testing in wargames, the Navy developed the idea further through field exercises.

Wargames can be used to develop theories of how to best use a new weapon system before it's used in an actual war. Wargaming can help a military develop the best tactics, the logistical demands, the optimal command structure, etc. For instance, in World War I, the British deployed tanks (their recent invention) and learned how to use them through experience on the battlefield. The consequence of this was that as British tank tactics and strategies improved, the Germans kept pace, developing counter-measures. During the inter-war years, the German army used wargames (along with field exercises) to develop more advanced tank doctrines that would take the French by surprise in 1939. Whereas French tanks were attached to infantry or cavalry units, the Germans organized their tanks into dedicated corps (panzerkorps) which moved and fought with great speed and efficiency.

Wargames cannot be used to predict the outcomes of wars, or even battles, as one might forecast the weather. However, they can identify a range of likely outcomes and the circumstances that lead to them. Wargames can help planners decide which armaments to produce, design contingencies for likely enemy responses, identify important strategic locations, etc.

If a wargame cannot teach a student specific tactics and strategies, they can at least train students to become better at devising tactics and strategies. For instance, in the years leading up to World War 2, the US Navy knew little of the capabilities of Japanese warships, and consequently could not provide accurate models for its wargames. Instead, instructors used made-up models for Japanese warships, and challenged the players to discover the capabilities of the virtual Japanese in the course of the game itself, and then devise appropriate tactics and strategies on the fly. Navy officers became quite good at this kind of improvisation, and during World War 2, when they could finally test the real Japanese in combat, they could size up the enemy and devise new tactics very quickly.^[48]

Peter Perla argues that using wargames is more akin to historical research than science. By that he means that the outcomes of all these simulated battles and campaigns are to be studied in the same way one would study the actual history of warfare.

Benefits of wargames for training

• They stimulate discussion

Perla (1990) harvp error: multiple targets (4×): CITEREFPerla1990 (help): "This is especially important for professional games, whose objectives tend to be more specific than those of commercial games."

Perla (1990) harvp error: multiple targets (4×): CITEREFPerla1990 (help): "Unlike those in the wargaming hobby, professional wargamers work in a relatively closed society. One organization's games are not freely available for all to try, critique, and modify. Professional wargame designers may document their games (usually in classified publications), but they seldom describe the design process they employed to create them."

Creveld (2013) harvp error: multiple targets (2×): CITEREFCreveld2013 (help): "Still following Dunnigan, who has extensive experience in working both in the commercial world and with the military, wargames used by the military tend to suffer from several problems. One is the need to satisfy the requirements of many different user organizations each of which does not wish to buy the game off the shelf but actively attempts to pull it in its own direction. Often the outcome is great complexity and compromises that end up, like the famous camel that was created by a committee, by satisfying nobody. Adding more and more features in the name of “realism” also causes the cost to go up, ultimately leading to diminishing returns. Much of the data that goes into the programs is classified: as a result, checking on whether it is correct is difficult, and errors, once they have crept in, tend to stay.61 Secrecy also makes it hard to update the games as needed. Finally, those who design, manufacture, and market games in the commercial world are obliged to pay attention to users’ demands, such as ease of play and creating a good interface between player and game. Their counterparts working in, or for, the military, are not nearly as affected by these concerns. On occasion this can lead to bad games that people simply do not want to play."

• What resources did the NWC allocate to wargaming?
• How were the insights developed in wargames transmitted to the Navy?

WW2

Caffrey (2019), p. 55 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "Apparently the former tsarist officers who came over to the Red Army during Russia’s civil war brought imperial Russia’s wargaming techniques with them."

Caffrey (2019), p. 55 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "Terrain models were common for even very large operations, and a wargame typically comprised a single turn. The slow, detailed adjudication of these wargames that was optimal for decision support was poorly suited to developing the thinking skills of Soviet officers."

Caffrey (2019), p. 61-62 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "Soviet games typically centered on terrain models. Using each side’s plans for the entire mission, the umpires, using incredibly detailed and cumbersome procedures, would the adjudicate the operation all at once, all the way to its conclusion. Only then would the two teams be called back and walked through the operation, step by step. Essentially, these were one-move wargames."

Caffrey (2019), p. 63 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "The defeat of the Axis powers ushered in an eclipse of wargaming. Obviously, the former Axis nations ceased wargaming. Within the United States, gaming dropped almost as steeply. Only inside the Soviet Union did wargaming expand and become more rigorous."

Cold War

Caffrey (2019), p. 74 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "...immediately after World War II, wargaming at the Naval War College dropped to about 10 percent of its prewar levels. However, as early as 1947 the College increased its use of wargaming with the addition of a game-intensive logistics course."

Caffrey (2019), p. 78 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "If the British were less than thorough in their data collection, the Soviets were obsessive. Even before the cessation of hostilities, they launched a massive effort to collect and compile operational data from their part of World War II, the “Great Patriotic War,” to increase the validity of their wargaming."

Vietnam

Caffrey (2019), p. 85 harvp error: multiple targets (3×): CITEREFCaffrey2019 (help): "But the largest impact was achieved in the East, by Soviet-style wargames. The Soviets opened their service schools to the officers of satellite and other communist countries. Wargaming constituted a very significant part of their curriculum. The North Vietnamese applied the methods they learned in the USSR with effective results. Using Soviet methods, they wargamed each of their attacks against the South Vietnamese and their allies, from firefights to major battles. Familiarity with the plans the Soviet method produced allowed the communists to coordinate fairly complicated attacks without radios: subordinate commanders remembered a plan’s timetable and executed it by their wristwatches."

• 1937: $612 (AFI $13,706)
• 1938: $4,530 (AFI $103,612)
• 1939: $8,612.21 (AFI $199,338)
• 1940: $38,080.42 (AFI $875,126)
• 1941: $56,573.48 (AFI $1,238,345)
• 1942: $63,776.46 (AFI $1,256,695)
• 1943: $63,776.46 (AFI $1,144,067)
• 1944: $57,638.52 (AFI $1,054,164)
• 1945: $48,794.46 (AFI $872,618)
• 1946: $49,938.58 (AFI $824,498)
• 1947: $11,148.82 (AFI $160,752)
• TOTAL: AFI $5,875,001

TOTAL 5,885,419

363,722

SUM: $7729215

rounded : SUM: $7,700,000

Superman (1978)

• budget: $55 million (AFI $271,492,347)
• box office: $300 million ($1,480,867,347)

Man of Steel 2013

• budget: $225 million ($310,982,143)
• box office: $668 million ($923,271,429)

Batman v Superman 2016

• budget: $263 million ($352,818,220)
• box office: $873.6 mil ($1,171,946,755)