The Cuban Missile Crisis

The Cuban Missile Crisis The Cuban missile crisis began on 14 October, 1962 when an American U-2 spy plane discovered that Premier Nikita Khrushchev of the Soviet Union was attempting to install intermediate-range nuclear-outfitted ballistic missiles in Cuba.  [1]  These warheads would have the capacity to destroy a large portion of the United States and therefore posed an enormous threat. When confronted by this immense threat that could presage nuclear war, the American government was forced to take action in order to diffuse the situation. The complexities of this type of decision-making are intricate, yet explainable and fundamentally predictable thanks to modern methods of analysis. As John F. Kennedy phrased it, The essence of ultimate decision remains impenetrable to the observer-often, indeed, to the decider himselfà ¢Ã¢â€š ¬Ã‚ ¦. There will always be the dark and tangled stretches in the decision-making process-mysterious even to those who may be most intimately involved.  [2]  I would like to unravel the dark and tangled stretches in this process by using game theory to retrodict, or make past predictions of, the different leaders choices throughout the thirteen day span of the Cuban missile crisis. Game Theory Basics When examined through the perspective of the Rational Actor Model, this situation introduces an obvious dilemma. Within this model, governments are treated as the primary actors. The government examines a set of goals, evaluates them according to their utility, then selects the one that has the highest payoff. In this instance, the United States was involved in a nuclear standoff with the Soviet Union. In the time of this imminent threat of mutually assured destruction, the correct action needed to be taken as millions of lives were at stake. Game theory is a branch of analytical mathematics utilized in social science to attempt to mathematically calculate decision-making in strategic situations in which an individuals success in making choices is dependent upon the choices of others.  [3]  It applies to situations (games) where there are two or more parties (called players) each attempting to choose between two or more ways of acting (called strategies). The possible outcomes of a particular game depend on the choices made by all players, and they can be ranked in order of preference by each player. In regards to two-person, two-strategy games, as the Cuban missile crisis resembled, there are combinations of strategies for the players that are more or less stable. This occurs when neither player by departing from its strategy can do any better in the outcome. When both players use these strategies simultaneously, the outcome is known as a Nash equilibrium, named after esteemed game theorist John Nash. A Nash equilibrium does not necessarily produce optimum outcomes for one or both players though. Instead, it can be viewed more as an optimal middle ground in which both players are spared from suffering the worst possible outcome. A Nash equilibrium is essentially what was reached during the Cuban missile crisis. Chicken Game Model In game theory, Chicken is the typical game used to model conflicts in which the players are on a deadly collision course. The game borrowed its namesake from hot rod movies made famous in the 1950s.  [4]  In these movies, the players are two hot rodders and the game is one in which they drive their cars directly at one another, risking a head on collision. If one of them turns away at the last minute, he or she is said to have chickened out and is deemed the loser. However, if neither player decides to turn away, both are vulnerable to losing much more, since it is obvious that they will either be killed or seriously injured in the event of a wreck. In the last possibility of outcomes, if both players decide to turn away, neither gains nor loses anything. The payoffs of Chicken can be explained by this basic diagram: Basic Chicken John go straight turn away Mark go straight -10, -10 5, -5 turn away -5, 5 0, 0 *Matrix format  [5]   This matrix shows that this theoretical game has two Nash equilibria, (5,-5) and (-5,5), one where one hot rodder turns away and the other goes straight and vice versa. However, since there are two Nash equilibria and no predefined Schelling point, which is a solution that a player will tend to use in the absence of communication or substantial knowledge because it seems instinctive, or relevant to them,  [6]  there is no indication of which outcome is more likely. This poses a problem for the hot rodders as well as an equivocation for the game theorist since there is the ever present danger of both players falling into the mutual disaster of a collision. When aligned to the Cuban missile crisis, this mutual disaster is the mutually assured destruction of nuclear war. Application of the Chicken Game Model Thus unfolds a classic game of chicken with the United States behind one wheel, facing off with the Soviet Union behind the other. Before evaluating the end results of the game, however, it is important to first examine the formulation of strategies. Abiding by the theory of moves, it is of the highest importance to anticipate, whilst concurrently trying to condition, the outcomes and consequences of any major decision or choice of action. Therefore, when deciding on a strategy to employ, each alternative must be weighed and projected completely through its causal fallout. This was the most critical aspect of the game for the Kennedy administration. As Defense Secretary McNamara explained about the situation, Its not a military problem that were facing. Its a political problem. Its a problem of holding the Alliance together. Its a problem of properly conditioning Khrushchev for our future moves.  [7]  It cannot be said whether he was directly referencing game theory with this sta tement, but the implications are fitting in the application of such concepts. Many members of the administration and military leaders felt as though their hands were up in the air, or tied behind their backs, because no one was confident enough to make a final decision under these tense and potentially tragic conditions. The wrong decision could have led to the end of the United States of America. Even so, the urgency of the situation made it necessary for the right decision to be made immediately. Ultimately, every minute wasted was a minute longer the Soviets had to make the ballistic missiles operable in Cuba, therefore time and decision were of the essence. Group Decision-making and EXCOMM Group decision is a trustworthy way to make choices because of the benefits the approach produces, as long as social phenomena such as groupthink are avoided. The cooperative planning done by the Executive Committee including Secretary of State Dean Rusk, Attorney General Robert F. Kennedy, John McNamara, Director of Central Intelligence John McCone and the other cabinet members ensured multilateral examination of the situation, fuller consideration of the entire spectrum of relevant points of interest, more ingenuity in the formulation of options and a greater overall sense of awareness and knowledge about the issue. This interplay of a multitude of expertise made an optimum decision likely. Furthermore, group interaction was the most logical approach when considering the negative effects preempted by a solo decision of President Kennedy. Miles Law states that where you stand depends on where you sit.  [8]  Specifically in this case, ones stance on an issue is significantly affected by their role in the government and where they fall into the operational chain of command. A cooperative decision minimized the role interference that could bias the plan of action. Possible Courses of Action After days of deliberation, Kennedy and his advisers came up with six possible options. These options were as follows: 1) Do nothing. Although an option, this course of inaction was not even considered as President Kennedy was sure the domestic fallout would be that of intolerance. 2) Impose diplomatic pressures and negotiate with Khrushchev at a summit. This option was also not popular because it implied that American concessions would be made and President Kennedy was unwilling to show this flexibility out of fear that it would be conveyed as vulnerability. 3) Make a secret appeal to Castro and split Cuba from its ties with the Soviet Union. 4) Send troops to Cuba for a ground invasion. 5) Deploy an air strike on the island in order to destroy the missiles and scare the Soviets of Cuba falling to US control. 6) Implement a blockade of Cuba to keep weapons away. However, whichever method picked had to be carried out without sparking a Soviet reprisal on Berlin.  [9]   After further deliberations, these options were narrowed down to two possible courses of action. Either a naval blockade to prevent the shipment of more missiles or a surgical air strike to destroy existing missiles would be implemented. In response, the Soviets could ultimately only choose between two strategies; either withdraw or maintain the missiles in Cuba. Specifically though, the blockade forced Khrushchev to choose among three immediate alternatives: 1) avoid a showdown by keeping Soviet vessels out of the area 2) submit to the blockade by permitting ships to be stopped and searched and 3) provoke the United States to a first use of force by defying the blockade. The game outcomes look more like this diagram: Applied Chicken Soviet Union withdraw (W) maintain (M) United States blockade (B) 3, 3 2, 4 air strike (A) 4, 2 1, 1 Together these strategies comprise the array of options the players have to choose from. When paired, they result in four possible outcomes, which the players are assumed to rank from one to four, with one being the worst, or least beneficial, and four being the best or most profitable outcome. The first number in the ordered pairs for each outcome is the payoff to the row player (United States), and the second number the payoff to the column player (Soviet Union). It is important to remember though that these rankings of the payoffs are only ordinal, meaning they only rank from best to worst, not incorporating the extent or degree to which a player prefers one outcome to another. Analysis of Applied Chicken Game Model Needless to say, this matrix of strategic choices and payoffs only provides an elementary depiction of the crisis as it unfolded over the thirteen day period. It must be acknowledged that both players considered more than merely the options listed, as well as modifications and augmentations of each. For example, the Soviets demanded the withdrawal of American missiles from Turkey as a quid pro quo  [10]  for withdrawal of their own missiles from Cuba.  [11]  The United States blatantly ignored this request. Even so, it is common belief that the superpowers were indeed on a collision course during the Cuban missile crisis and therefore the Chicken model is appropriate. Alternatively, neither side was forthcoming in undertaking any irreversible action, such as one of the drivers might do in Chicken by allowing the other driver to see him boldly breaking off the steering wheel of his car and coincidentally eliminating the option of maneuvering to avoid collision. It is here that the Chicken game leaves voids in application to the crisis. It can be said that the United States ultimately won by forcing the U.S.S.R. to withdraw their missiles. Per contra, Premier Khrushchev was granted a promise that the U.S. would not invade Cuba. This dual-reward represents a result that is basically a compromise- which does not coincide with game theorys prediction for a game of Chicken. The strategies the compromise consists of do not form any Nash equilibriums. To analyze this, assume that gameplay is at the compromise (3,3) position where the U.S. blockades Cuba and the Soviet Union withdraws its missiles. This outcome is not stable because both players have incentives to deviate to more aggressive strategies. If the U.S.S.R. was to defect by maintaining their missiles, gameplay would shift to (2,4) granting the Soviets a payoff of four. The same, but reverse, would happen if the U.S. decided to change their strategy to an air strike. This symmetry in the table of payoffs presents a recurring problem in interpreting results of a Chicken game- there is more than one equilibrium outcome.  [12]  Furthermore, if the players arrive at the mutually worst (1,1) outcome of nuclear war, both would have undoubtful incentive to move away from it, which makes the strategies associated with (1,1) just like those with (3,3); unstable. Shortfalls of the Chicken Game Model As shown, using Chicken to try to wholly model the Cuban missile crisis is flawed not only because of the instability of the outcomes but also because of the parameters. As it happened, the two superpowers did not select their strategies independently of each other, nor simultaneously as assumed in the Chicken game. The Soviet Union chose their actions in response to the already implemented U.S. quarantine. Additionally, the fact that the United States held the air strike option in reserve in case circumstances necessitated escalation of action shows that the first decision was not considered final, and the U.S. felt they still had strategic options open even after imposing the blockade. Consequently, the Cuban missile crisis can be more appropriately modeled as a game of sequential bargaining where neither player makes a terminal decision, but rather considers different alternatives, and reserves the absolutes in case the opponent should fail to act acceptably. Before the crisis, the Soviets felt they needed to advance their global strategic position, even though they feared that the U.S. might invade Cuba. Khrushchev decided that positioning the missiles was worth that risk. He and his staff rationalized that the Americans if confronted with this fait accompli, or an action that is completed before those affected by it are in a position to query or reverse it, would be deterred from invading Cuba and would not any other severe reprisals.  [13]  Even if they instigated a crisis, they did not see the probability of war being high and therefore they risked antagonizing the United States. Recourse Game Model and Application Accordingly, there is convincing evidence to believe that American policy makers did not see the conflict Chicken-like based on how they considered and ranked possible outcomes. The over-simplicity of using this model was alluded to by historian Philip Zelikow in his analysis of the audio tapes of dialogue within the EXCOMM meetings.  [14]  In order to more thoroughly explain the crisis, I will further apply game theory to the situation by creating a new, modified version of the Chicken game that I will call Recourse. This representation maintains the same strategies given in Chicken, but redistributes the rankings and interpretations of outcomes. These new classifications align more thouroughly with history than those of Chicken: Applied Recourse Soviet Union withdraw (W) maintain (M) United States blockade (B) 3, 3 1, 4 air strike (A) 2, 2 4, 1 In the game of Recourse, the possible outcomes are as follows: B/W: The choice of blockade by the United States and withdrawal by the Soviet Union remains the compromise for both players = (3,3). B/M: In the face of a U.S. blockade, Soviet maintenance of their missiles leads to a Soviet victory (its best outcome) and U.S. capitulation (its worst outcome) = (1,4). A/M: An air strike that destroys the missiles that the Soviets were maintaining is an honorable U.S. action (its best outcome) and thwarts the Soviets (their worst outcome) = (4,1). A/W: An air strike that destroys the missiles that the Soviets were withdrawing is a dishonorable U.S. action (its next-worst outcome) and thwarts the Soviets (their next-worst outcome) = (2,2). Although air strike trumps the Soviet Union at both outcomes (4,1) and (2,2), I view the (2,2) outcome as less harmful to the Soviets. This is because international opinion at the time would condemn an American air strike as an obtrusively offensive move and furthermore a dishonorable action of the United States, especially if there was clear evidence that the U.S.S.R. was in the process of withdrawing their missiles already. If no such evidence existed, however, air strike, possibly supplemented with a ground invasion, would be acceptable action to counter the Soviet missiles. Accuracy of the Recourse Game Model The statements of U.S. policy makers support Recourse. In responding to a letter from Khrushchev, President Kennedy said, If you would agree to remove these weapons systems from Cuba . . . we, on our part, would agree . . . (a) to remove promptly the quarantine measures now in effect and (b) to give assurances against an invasion of Cuba,  [15]  which is consistent with Recourse since (3,3) is preferred to (2,2) by the United States, whereas (4,2) is not preferred to (3,3) in Chicken. If the Soviets maintained their missiles, the United States preferred an air strike to the blockade. As Robert Kennedy, the Attorney General under his brother during the crisis, said, If they did not remove those bases, we would remove them,  [16]  which is consistent with Recourse, since the United States prefers (4,1) to (1,4) but not (1,1) to (2,4) in Chicken. Similarly, it is well known that several of President Kennedys advisers were reluctant to initiate an attack against Cuba without first exhausting less belligerent courses of action that could bring about the removal of the missiles with less risk and greater sensitivity to American ideals and values.  [17]  This is in accordance with the United States tendency to always act ethically and the governments perpetual sensitivity to the worlds perception of America. Pointedly, Robert Kennedy claimed that an immediate attack would be looked upon as a Pearl Harbor in reverse, and it would blacken the name of the United States in the pages of history,  [18]  which is again consistent with Recourse since the United States ranks A/W next worst (2), a dishonorable U.S. action, rather than best (4), a U.S. victory, in Chicken. Actual Gameplay As it happened, at 7:00pm on 22 October, 1962, President Kennedy publicly announced that the United States had discovered Soviet missiles in Cuba and decreed a strict quarantine on all offensive military equipment under shipment to Cuba. Additionally, he demanded that Chairman Khrushchev halt and eliminate this clandestine, reckless and provocative threat to world peace.  [19]  After the ships were deployed, all that was left to do was to await a response. Initially, on 24 October, as anticipated, Khrushchev responded defiantly, saying that he would instruct his ships to ignore the American blockade. However, the next morning, he reconciled and told Kennedy that he no longer wanted to exchange caustic remarks and was ready to resolve the crisis. Khrushchev offered his terms, Give us a pledge not to invade Cuba, and we will remove the missiles, proving that he was genuine when he professed that he was prepared to dismantle the missiles to make Cuba into a zone of peace.  [20]  The Soviet Union feared an American invasion of Cuba and saw the blockade as a heartening gesture that allowed concessions to be made without drastic loss. Essentially, the outcome of this game and the Cuban missile crisis in general can be assessed at 4:2 in favor of the United States. Although neither side literally gained any reward from the outcome, both avoided any significant loss. Since the United States made the initial offer and compelled the Soviet Union to make the next move, therefore inconveniencing Khrushchev into yielding to the conditions set forth by President Kennedy, America emerges as the winner of the game although the payoff was not maximized. Although Recourse creates a fitting model, this explanation of events is neither all-inclusive nor infallible. As with any theory, there are conditions that are assumed to, and must be, static that the reasoning is based upon. And in a dynamic world, these criteria are not always satisfied. There are a multitude of external factors that influence decision making, many of which will be discussed in the following sections as they pertain to the Cuban Missile Crisis and nuclear war in general. Specified Game Theory: Deterrence Theory Game theory can be applied in a more general sense to other primary aspects of nuclear war, the most prominent of them being mutually assured destruction and deterrence. The application of game theory to these concepts has resulted in the derivation of a number of consequential theories which ultimately resolve in the cost-benefit analysis that game theory focuses on. According to the official U.S. Department of Defense definition, Deterrence is a state of mind brought about by the existence of a credible threat of unacceptable counter action.  [21]  This definition captures the main premise for the United States historic reliance on deterrence; however, it does not encompass the entirety of deterrence theory. In general, deterrence is a complex term that universally means persuading an opponent that the costs and consequences of a specific action will outweigh and trump any potential benefits. The concept of persuading an adversary references the significant psychological aspect of deterrence, which is often an interplay of uncertain concessions and threats that may or may not be bluffs or true promises. More specifically, using the word potential when describing the anticipated benefits shows the future-oriented aspect of any deterrent threat, meaning there is the promise of a certain reaction only in response to the undesired decision of another actor (player).  [22]   Capability vs. Credibility According to accredited deterrence theorist Derek Smith, Underlying any deterrent threat are the closely intertwined concepts of capability and credibility.  [23]  The concept of capability is reasonably straightforward and readily quantifiable variable, based on each players arsenal and military forces that are available for use in any engagement; whereas, credibility is a much more complex and qualitative variable, which is defined mostly from the anticipated probability that all available forces will actually be utilized, making it trivial. To clarify, for example, a state may have a promising amassment of armed forces, but if the state is governed by domestic doctrine that forbids their use except for in strict cases of homeland defense, then any strategy or threat of external use of force as deterrence will lack credibility. The Psychology of Commitment Techniques In order to strengthen the perception of an actors resolve, a popular strategy is to use commitment techniques,  [24]  or techniques that increase the costs and losses involved in refusing or failing to act. An everyday example of this type of strategy is if someone tells all of their friends that they are quitting smoking for good. From thence on, their friends will act as a constant source of pressure for them to uphold the obligation (commitment) because they voiced it publicly, and will now be held accountable to it. For a better example, Smith illustrates the military image of burning bridges while in combat to make a retreat impossible, which is an unambiguous method for cementing ones resolve.  [25]   Similarly, in the words of Thomas Schelling, What we have to do is get ourselves into a position where we cannot fail to react as we said we would-where we just cannot help it-or where we would be obliged by some overwhelming cost of not reacting in the manner we had declared.  [26]  In order to illustrate this concept, Shelling makes reference to how, during the Cold War, the United States posted troops in Western Europe to act as a tripwire against Soviet aggression. This was an act that served to fortify resolve, and essentially the United States made the defense of Europe, and their overarching containment strategy a more absolute prospect by effectively eliminating the choice of retreat and abandonment.  [27]   The Paradox of Control and MAD The idea that a player denying himself options can be a productive or beneficial move appears counterintuitive at first. Schelling describes this phenomenon as a paradox that the power to constrain an adversary may depend on the power to bind oneself.  [28]  Reexamining a fundamental game of Chicken is a fitting way of clarifying what is meant by that. If the two drivers are about to start speeding towards each other, it would make an extreme statement if one of the drivers decided to break off his steering wheel and show the other driver. After this, the other driver would have no choice but to give up and turn his car or suffer the tragic collision. Making a bold statement like this can be a very effective way of determining resolve in situations where capability is lacking, however, the important thing to note is that it is always possible that both drivers could choose to make the same decision, which would create an even worse outcome than if the power position had been conceded at the end. The critical factor, then, is actually who is able to make the first move, thereby leaving the remaining with only one last clear chance to avoid catastrophe.  [29]  This catastrophe, in parallel to the Cuban Missile Crisis, is mutually assured destruction. Furthermore, in addition to committing oneself to a specific course of action, there is also the trivial strategy of issuing a threat that leaves something to chance, so that the end decision of whether or not to act is not completely controlled by the player that issued the threat.  [30]  This particular bargaining technique plays on the factor of risk-acceptance, assuming that the opposing side will choose to give in first. Consider the clichà © scenario of one person rocking a boat in order to extract concessions from the scared occupants. Schelling uses the term brinksmanship to describe this strategy, the choice of deliberately letting the situation get somewhat out of hand, just because its being out of hand may be intolerable to the other party and force his accommodation.  [31]  Going back to the Chicken scenario, this would be verisimilar to one of the drivers publicly consuming a large amount of alcohol or other psychoactive substance before stepping into the car, thus creating uncertainty in the other players mind that he would be able to avoid a collision even if he actually wanted to do so. This would likely influence the sober driver to concede unless he really wanted to collide, and thus the daredevil player who intoxicated himself indirectly forced the sober player to capitulate; effecting the outcome he desired by acting outside the bounds of rationality. Deterrence: Rationality of Irrationality In much of the widely accepted literature published on deterrence, this phenomenon is called the rationality of irrationality, since one player can draw coercive power from the prospect of being potentially undeterrable.  [32]  As stated, whilst this strategy is dominantly compelling, it still welcomes tragedy, i.e. mutually assured destruction, by undertaking irrationality even though the opponent could possibly do the same or is expecting rational behavior from the other actor involved in the crisis. Regardless, despite the strategies and techniques that play out systematically and predictably in game theory and in the aforementioned hypothetical examples, it is always important to remember that the concept of deterrence, and the use of deterrence as a strategy, are built on a foundati

Hsbc Case Essay

HSBC is known as the â€Å"World’s local bank†. Originally called the HongKong and Shanghai Banking Corporation Limited, HSBC was established in 1865 to finance the growing trade between China and the United Kingdom. HSBC is now the second largest bank in the world, serving 100 million customers through 9,500 branches in 79 countries. The company is organized by business line (personal financial services; customer finance; commercial banking; corporate investment banking and markets; private banking), as well as by goegraphic segment (Asia-Pacific, U. K. /Eurozone, North America/NAFTA, South America, Middle East). Despite operating in 79 different countries, the bank works hard to maintain a local feel and local knowledge in each area. HSBC’s fundamental operating strategy is to remain close to its customers. As HSBC chairman Sir John Bond said in November 2003, â€Å"Our position as the world’s local bank enables us to approach each country uniquely, blending local knowledge with a worldwide operating platform†. For example, consider HSBC’s local marketing efforts in New York City. To prove to jaded New Yorkers that the London-based financial behemoth was â€Å"the world’s local bank. HSBC held a â€Å"New York City’s Most knowledgeable Cabbie† contest. The winning cabbie gets paid to drive full-time for HSBC for the year, and HSBC customers win, too. Any customer showing an HSBC bankcard, checkbook, or bank statement can get a free ride in the HSBC-branded Bankcab. The campaign demonstrates HSBC’s local knowledge. â€Å"In order to ma ke New Yorkers believe you’re local, you have to act local,† said Renegade Marketing Group’s CEO Drew Neisser. Across the world in Hong Kong, HSBC undertook a different campaign. In the region hit hard by the Severe Acute Respiratory Syndrome (SARS) outbreak, HSBC launched a program to revitalize the local economy. HSBC â€Å"plowed back interest payments† to customers who worked in industries most affected by SARS (cinemas, hotels, restaurants, and travel agencies). The program eased its customers financial burden. The bank also promoted Hong Kong’s commercial sector by offering discounts and rebates for customers who use an HSBC credit card when shopping and dining out, to help businesses affected by the downturn. More than 1,500 local merchants participated in the promotion. In addition to local marketing, HSBC does niche marketing. For example, it found a little-known product area that was growing at 125 percent a year : pet insurance. In December 2003 it announced that it will distribute nationwide per insurance through its HSBC Insurance agency, making the insurance available to its depositors. HSBC also segments demographically. In the United states, the Bank will target the immigrant population, particularly Hispanics, now that it has acquired Bital in Mexico, where many migrants to the United States deposit money. Overall, the bank has been consciously pulling together its worldwide business under a single global brand with the â€Å"World’s local bank† slogan. The aim is to link its international size with close relationships in each of the countries in which it operates. The company spends $600 million annually on global marketing and will likely consolidate and use fewer ad agencies. HSBC will decide who gets the account by giving each agency a â€Å"brand-strategy exercise. † Agencies will be vying for the account by improving on HSBC’s number 37 global brand ranking

Fundaments Operations of Aircraft Propellers

Contents Abstract Introduction Pitch Blades Forced Acting on a Propeller Propellers Types Fixed-Pitch Propeller Ground-Adjustable Variable-Pitch Propeller Constant-Speed Propeller Appendix 1 References Abstract: _This text outlines the fundaments operations and aspects of aircraft propellers. It details the components, forces and workings of a propeller as well as discussing the difference between the different propeller types. _ Introduction: Propeller types are defined by blade pitch as being fixed or variable which will be further detailed later in the text. To fully appreciate the differences and understand the advantages of different pitched propellers we must first consider the fundamental characteristics of propellers. Usually propellers have two, three, or four blades; for high-speed or high-powered airplanes, six or more blades are used. In some cases these propellers have an equal number of opposite rotating blades on the same shaft, and are known as dual-rotation propellers. Small single engine aircraft have the propeller mounted on the front as multi-engine aircraft have them set on the wings. Pitch: What is pitch? Pitch is important as it is the main differential from propeller type to propeller type. Essentially pitch relates to the angle of the blade in respects to a flat plane. It is the helical blade path or simpler the distance the propeller blade covers during a full rotation and the cut it has on the air. Pitch is referred to in two ways, fine and coarse. A fine pitch propeller has a low blade angle, will try to move forward a small distance through the air with each rotation, and will take a ‘small' bite of the air. It requires relatively low power to rotate, allowing high propeller speed to be developed, but achieving only limited airspeed. This is like having a low gear in your automobile. (Brandon 2008) A coarse pitch propeller has a high blade angle, will try to advance a long distance through the air with each rotation, and will take a big ‘bite' of the air. It requires greater power to rotate, limiting the propeller speed that can be developed, but achieving high airspeeds. This is like having a high gear in your automobile. (Brandon 2008) The Blades: The propeller blades are in fact aerofoils producing lift and drag. As the propeller spins the leading edge of the blade cut through the atmosphere and accelerates a tube of air or_ relative airflow _the diameter of the propeller moving the aircraft forward. This rotation is able to work because the propeller blades are designed slightly different to wing aerofoils as they have a small twist in them so that the greatest angle is at the blade root and the smallest at the top, due to the different angle and speed that each section of the blade travels. These _blade _elements are in place at different angles because the linear velocity increase towards the tip of the blade as it has a greater distance to travel, the_ _angles prevent bending making each section advance through the air at the same rate. The blade angles combined with the forward motion and the circular rotation of the propeller keep constant the best angle of attack (AOA). The twist causes the blade path to follow an approximate helical path easiest seen in a linear form. This action is similar to a screw being turned in a solid surface, except that in the case of the propeller a slippage occurs because air is a fluid. Forces Acting on the Propeller: Aircraft that are not jet powered use a propeller which converts the rotational power from an aircrafts engine into aerodynamic forces; thrust power moving the aircraft forward through the atmosphere and propeller torque which acts in the plane of rotation. The plane of rotation is perpendicular to the propeller shaft. Propellers are conventionally placed in front of the engine on the engine drive shaft. During cruising flight the propeller torque balances the engine torque and the thrust balances the aircrafts drag force. The propeller rotates clock wise and when the forces are not balance the torque reaction increases a rolling friction on the aircraft. As the blades produce a thrust force, the thrust force pulls on the thinnest section of the blade attempting to bend the tips. For single engine aircraft with the propeller mounted on the front the clockwise rotation creates a vortex of air or slipstream that flows around and down the fuselage to the rudder which affects the lateral movement of the aircraft or a slight yaw to the left during cruising flight Variable-pitched propellers can have their blade angles/pitch altered and will be further explained. Two different forces experienced in these propellers can affect the blade angle. Centrifugal twisting moment (CTM) Aerodynamic twisting moment (ATM) CTM causes pulling stress at the base of the blade and a twisting force at the pitch change axis produce a finer pitch angle. The blade will want to align itself with the plane of rotation. The relative airflow over the blades produces a total reaction, an ATM where the total reaction is ahead of the pitch change axis, tempting the blade to twist, increasing the blade angle producing a coarser pitch. Windmilling propeller – Occurs when the propeller drives the engine. Caused by; steep dive with no power, sudden reduction in power, engine failure, causing the blades to twist to a finer pitch. Propeller Types: As stated earlier pitch is a main component between propeller functions. Under the classification of fixed and variable pitch propellers there are four common types, fixed-pitch, ground-adjustable, variable-pitch and constant-speed propeller. The first two are fixed propellers as the other two are variable. There are a few versions of variable-pitch propellers that may be seen in the aviation industry, two-position propeller, in flight-adjustable propeller, automatic propeller and the constant-speed propeller. The most commonly used at present will be concentrated on, elaborating on fixed through to the variable propellers and the enhancements of pitch control. Fixed-pitch propeller:_ _ The cheapest and crudest propulsion aero-device is the fixed-pitch propeller. Although it has been superseded many a time it is the most common type of propeller used in sport aviation. The fix-pitch means that the pitch of the propeller is decided by the manufacture, there is only one setting and the performance of the aircraft is confined by the constraint of that one setting. This means to reach the optimum RPM/airspeed the propeller has to function through inefficient speeds. Normally there are two versions, a climb propeller with a fine pitch setting or a cruise propeller with a coarse pitch setting. Ground-adjustable propeller: The pitch for a ground-adjustable propeller is able to be set for the condition of flying the aircraft will be doing but only before the flight. However it is still a fixed propeller as once the pitch is set in cannot be changed during the operation of the aircraft. These propellers are mainly installed on ultra light and experimental aircraft. More usually they are used as a low cost way to try out various pitches to determine the propeller pitch that best suits an aircraft. Variable-pitch propeller :_ _ A variable-pitch propeller is exactly what the name implies; the pitch can be controlled and adjusted in flight to the most efficient setting for a certain phases of flight. Simply during take-off the propeller would be set to a fine pitch allowing the engine to develop reasonable revs and then to a coarser pitch during cruising flight speed. The engine will be ticking over comfortable while the propeller cuts through more air. Combine this with throttle control a wide variety of power settings can be achieved maintaining airspeeds with the limits of the aircrafts engine speeds. This feature of a variable-pitch propeller will provide you with performance advantages, including: Reduced take-off roll and improved climb erformance. Fine pitch allows the engine to reach maximum speed and hence maximum power at low airspeeds. Vital for take-off, climb, and for a go-around on landing. (Brandon, 2008) Improved fuel efficiency and greater range. Coarse pitch allows the desired aircraft speed to be maintained with a lower throttle setting and slower propeller speed, so maintaining efficiency and improving range. (Brandon, 2008) Higher top speed. Coarse pitch will ensure your engine does not over speed while the propeller absorbs high power, producing a higher top speed. (Brandon, 2008) Steeper descent and shorter landing roll. With a fine pitch and low throttle setting, a slow turning propeller is able to add to the aircraft's drag, so slowing the aircraft quicker on landing. (Brandon, 2008) Constant-speed propeller : The constant-speed propeller is a special case of variable pitch, which is considered in a family of its own, and offers particular operating benefits. A constant-speed propeller allows the pilot to control the power just by the throttle once the propeller/engine speed has been optimally selected (actually controlling the absolute pressure of the fuel/air mix in the intake manifold [MAP] which then determines power output). This is controlled by a governor or constant speed unit (CSU) which detects the propeller speed and acts to keep it at the selected engine/propeller speed selected by the pilot and vice versa. If the propeller speed increases then the CSU will increase the pitch a little to bring the speed back within the limits. Thus creating vastly efficient running components during phases of flight (The governor or constant speed unit [CSU]_ may be an electronic device that detects the rotational speed of a slip-ring incorporated in the propeller hub, and controls operation of a servomotor/leadscrew pitch change actuator in the hub assembly. Or, it may be an hydraulic fly-ball governor attached to the engine, using engine oil to operate a hydraulic pitch change piston in the hub assembly. In the first case, the cockpit control device is likely to be knobs and switches. In the hydraulic system, the governor is likely to be cable operated from a cockpit lever — JB. _ (Brandon, 2008) While allowing the pilot to ignore the propeller for most of the time, the pilot must still choose the most appropriate engine/propeller speed for the different phases of flight. Take-off, go-around and landing. A high speed setting is used when maximum power is needed for a short time such as on take-off. The high speed setting may also be used to keep the propeller pitch low during approach and landing, to provide the desired drag and be ready for a go-around should it be required. (Brandon, 2008) Climb and high speed cruise. A medium speed setting is used when high power is needed on a continuous basis, such as during an extended climb, or high speed cruise. (Brandon, 2008) Economic cruise. A low speed setting is used for a comfortable cruise with a low engine speed. This operation produces low fuel consumption and longer range, while the advantages of low noise and low engine wear are also enjoyed. (Brandon, 2008) *Appendix 1: – *Description*s* (ThaiTechnics) Leading Edge of the airfoil is the cutting edge that slices into the air. As the leading edge cuts the air, air flows over the blade face and the camber side. {draw:frame} Blade Face is the surface of the propeller blade that corresponds to the lower surface of an airfoil or flat side, we called Blade Face. {draw:frame} Blade Back / Thrust Face is the curved surface of the airfoil. {draw:frame} Blade Shank (Root) is the section of the blade nearest the hub. Blade Tip is the outer end of the blade farthest from the hub. Plane of Rotation is an imaginary plane perpendicular to the shaft. It is the plane that contains the circle in which the blades rotate. {draw:frame} Blade Angle is formed between the face of an element and the plane of rotation. The blade angle throughout the length of the blade is not the same. The reason for placing the blade element sections at different angles is because the various sections of the blade travel at different speed. Each element must be designed as part of the blade to operate at its own best angle of attack to create thrust when revolving at its best design speed {draw:frame} *Blade Elements* are the airfoil sections joined side by side to form the blade airfoil. These elements are placed at different angles in rotation of the plane of rotation. The reason for placing the blade element sections at different angles is because the various sections of the blade travel at different speeds. The inner part of the blade section travels slower than the outer part near the tip of the blade. If all the elements along a blade is at the same blade angle, the relative wind will not strike the elements at the same angle of attack. This is because of the different in velocity of the blade element due to distance from the centre of rotation. {draw:frame} Relative Wind is the air that strikes and passes over the airfoil as the airfoil is driven through the air. Angle of Attack is the angle between the chord of the element and the relative wind. The best efficiency of the propeller is obtained at an angle of attack around 2 to 4 degrees. Blade Path is the path of the direction of the blade element moves. {draw:frame} Pitch refers to the distance a spiral threaded object moves forward in one revolution. As a wood screw moves forward when turned in wood, same with the propeller move forward when turn in the air. Geometric Pitch is the theoretical distance a propeller would advance in one revolution. {draw:frame} Effective Pitch is the actual distance a propeller advances in one revolution in the air. The effective pitch is always shorter than geometric pitch due to the fact that air is a fluid and always slips*. *

Why Jackie Robinson Was The First Pro Ball Player - 844 Words

During the Gilded age many social class, racial walls and gender bias developed lines walls and boundaries for people. The funny thing about that is as new boundaries, walls and limitations were being built sports and the development of it broke them down or found new ways for the different genders and races to find ways to use sports as an outlet. Women were constantly fighting for their right to be involved in sports and pushing the limits as to what social norm deemed acceptable for them to be allowed to play. Working class women started to compete professionally in rowing competitions; they played crocket and played lawn tennis. The American pastime of baseball was well on its way and all though baseball had a huge racial division as to who could play mainly African Americans not being accepted, but they developed their own league and contrary to the belief that Jackie Robinson was the first pro ball player there was another before him by the name of Moses Fleetwood Walker. Moses was the product of a inter racial relations with a black dad and white mom he also attended college at University of Michigan and was the first African American Pro Baseball player. After that he would venture into entrepreneurism, be a newspaper editor, author as well as an inventor. He was quite the Renaissance man living the American Dream despite social and racial ideologies. Collegiate level sporting really started to take off during this time and the development of anotherShow MoreRelatedThe Racism Of Jackie Robinson1008 Words   |  5 PagesMr. Wallace History Day 12 September 2014 Jackie Robinson He walks into the stadium...hopeful...yet aware of the prejudice exiting in the minds of the ignorant... in the minds of those who do not realize his journey will empower the victims of unjustified hate and he will change history. Jackie Robinson shattered the color barrier in the MLB despite racism that permeated throughout the league and in society in the 1940 s. Jackie Robinson was the first African American to play major league baseballRead MoreAfrican Americans in Baseball1142 Words   |  5 Pagesout of those 17 years. From 1998-2004, only one black player has won the batting title. As a huge baseball fan, I never knew that stat and find it very interesting. The article also entails that black players had won the National League MVP award quite often from 1949-1970. More recently from 1985-2004, black players had won the MVP 11 times, with Barry Bonds winning 6 of the 11. The article then argues if there is any black ball player who will take Barry Bonds’ stardom in Major League BaseballRead MoreInsight to Coach Carter Film7710 Words   |  31 Pages Tension mounted as the Richmond High Oilers faced the upcoming basketball championship. The town was wild with excitement over their undefeated team and the bleachers were filled with cheering fans for every game. No one could imagine that on January 4, 1999 the community would erupt in dissention and so many lives would change forever when Coach Ken Carter padlocked the gym, refusing the players access for failing to keep up their grades. Inspired by a true story, â€Å"Coach Carter† is an inspirationalRead MoreHbr When Your Core Business Is Dying74686 Words   |  299 PagesPA IN DS CK R M WA A 53 www.hbr.org April 2007 58 What Your Leader Expects of You Larry Bossidy 66 Finding Your Next Core Business Chris Zook 78 Promise-Based Management: The Essence of Execution Donald N. Sull and Charles Spinosa 90 The Leadership Team: Complementary Strengths or Conï ¬â€šicting Agendas? Stephen A. Miles and Michael D. Watkins 100 Avoiding Integrity Land Mines Ben W. Heineman, Jr. 20 33 FORETHOUGHT HBR CASE STUDY Why Didn t We KnowRead MoreExploring Corporate Strategy - Case164366 Words   |  658 Pages CASE Ministry of Sound – rapid growth but a questionable future in the music industry. Pharmaceutical Industry – global forces at work in the ethical pharmaceutical industry. TUI – competitive forces in the travel industry. HiFi – how can small players survive changing markets? Amazon (B) – latest developments in a successful dot.com. Formula One – developing the capabilities for competitive success in a hi-tech industry. Manchester United – clash of expectations in the football world. Salvation