Sonnet 116 And John Donne - 1059 Words

William Shakespeare’s â€Å"Sonnet 116† and John Donne’s â€Å"A Valediction: Forbidding Mourning† similarly explore the theme of everlasting true love. However, both poems differ in rhyme scheme, techniques, and meaning. The poets use these tools to convey to the reader that everlasting true love does in fact exist. Although both speak so passionately about said love, only the speaker of Donne’s poem has actually experienced it. While both poems explicate eternal true love, their rhyme scheme differences convey everlasting true love in different manners. Shakespeare’s â€Å"Sonnet 116† follows the Shakespearean sonnet rhyme scheme that goes A-B-A-B-C-D-C-D-E-F-E-F-G-G. It contains three quatrains, and ends with a couplet. Meanwhile, Donne’s â€Å"A†¦show more content†¦The first quatrain introduces divine love by comparing the parting of a lover to death when saying, â€Å"As virtuous men pass mildly away...† ( 1) and, â€Å"So let us melt, and make no noise†¦Ã¢â‚¬  (5). These two lines from the first two quatrains signify that love should not be bothered by distance because divine love is inseparable. The idea that divine love is inseparable is later supported in Line 13-15, which initiates the idea of earthly love by saying, â€Å"Dull sublunary lovers cannot admit absence†. These lines resemble earthly love by contrasting the speakers love to sublunary lovers. Sublunary means belonging to this world, which indicates that those particular lovers belong to earth. Since they belong to earth their love is anything that pertains to the human senses, therefore physical presence is necessary for their love to survive, rendering it temporary. This image of two sides of love cements Donne’s belief that his love is true because his love is so sacred that distance cannot affect it. These ideas of everlasting love are similarly supported by the techniques both poets use, however both poets use different techniques. In Line 8 of â€Å"Sonnet 116†, the Shakespeare personifies love as a guiding star that â€Å"looks on tempests and is never shaken†. The â€Å"tempests† is a metaphor for any obstacle the lovers may face in their relationship, such as arguments and time and illuminates the love that guidesShow MoreRelatedLove And Death By William Shakespeare924 Words   |  4 Pagesor sonnets are about love or death. The brilliant William Shakespeare also considered England s national poet, was an English actor, poet, and playwright who is considered to be the greatest writer in the English language during the Renaissance era. He wrote thirty eight plays, one hundred and fifty four sonnets, and two long narrative poems. Many of Shakespeare’s sonnets, poems, and plays focuses on the topic of love including the Sonnet 116 â€Å"Let me not to the marriage of true minds.† John DonneRead MoreWilliam Shakespeare s Romeo And Juliet1267 Words   |  6 PagesShakespeare s Romeo and Juliet variously links to the poetry; The Flea , by John Donne, Valentine , by Carol Ann Duffy, and Sonnet 116 , by Shakespeare. The first association is through theme, as Sonnet 116 demonstrates the importance of eternal love and through situation, such as how Valentine ends with violent imagery, so does the play. Another way in which the drama links to the poetry is by character, Romeo and the protagonist of The Flea convey characteristics of a courtlyRead MoreEssay on Amer. Lit2033 Words   |  9 Pagesassigned sonnets, Herrick’s â€Å"To the Virgins,† and Marvell’s â€Å"To His Coy Mistress.† Although their images differ, what do all these poets seem to be saying about time? Be specific when referring to the poems. The imagery is very different, but all of the poems and poets seem to be saying time is important in life. In Shakespeare’s Sonnet 18 he says, â€Å"And every fair from fair sometime declines,† when explaining the inevitable decline in appearance of his friend (Line 7). In Shakespeare’s Sonnet 29 heRead MoreThe Metaphysical And Victorian Concept Of Love Essay1308 Words   |  6 Pagesdefine its meaning. Plato once said At the touch of love everyone becomes a poet and that s why may be we have so many diverse poetry on the subject of love with so many different definitions of love that are available. Shakespeare wrote in his Sonnet 116 defining love, Love is not love which alters when alteration finds, or bends with the remover to remove, talking about the passion and loyalty, a belief unassailable, That look on tempests and is never shaken. Such intensity that ShakespeareRead MoreHow the Negative and Positive Impacts of Love Are Explored Using Various Main Char acters in the Play ‘Much Ado About Nothing’5155 Words   |  21 Pagesthink very much of Benedick yet it was the first line she ever said in this play so it conveys some interest. This is subtle as she disguises her concern with an insult. The idea links to the quote ‘My mistress’ eyes are nothing like the sun’ in ‘Sonnet 130’; he is saying that his mistress’ eyes have no light in them and nothing that would instantly draw him to her. The first time it is read, no concern can be spotted in his words as it sounds instantly insulting but he still actually loves her despite

Key Article On The Letter By Ryan Eliason - 1696 Words

Keys to Happiness - How to Conquer Depression By Ryan Eliason | Submitted On October 02, 2007 Recommend Article Article Comments Print Article Share this article on Facebook 1 Share this article on Twitter Share this article on Google+ Share this article on Linkedin Share this article on StumbleUpon Share this article on Delicious Share this article on Digg Share this article on Reddit Share this article on Pinterest Expert Author Ryan Eliason I haven t always been the happiest guy in the world. In fact, I ve been depressed several times. Some people are naturally happy, while others like myself have had to work hard for it. I m happy to say that I m pretty darn happy these days! I d say that I m a success story, and my struggles have led me to being an expert on the topic. Most people think happiness comes from certain conditions being met. For example, they think they will be happy when they find their soul mate and have that fairy tale relationship; or they believe happiness will find them when they are wealthy and no longer have to work for a living. Perhaps their standards aren t so high, and they think all it would take to be happy is a little more money, or a slightly sexier girlfriend/boyfriend, or a little more free time, or a more enjoyable job. Perhaps they will be happy when they finally own their own home, start their own business, or get a new car. Maybe they re waiting for retirement to be happy. Then there are those people who think happiness

Stereotypes in Poland free essay sample

There are a lot of stereotypes about polish people around the world. Many of them are putting Poles in a bad light, but not all of them are so negative. Have a closer look at some of them. First of all, Polish people are thought to be a sad nation. They never smile, but complain a lot. People on the streets do not smile, service workers also not. You expect store clerk to smile back to you? Forget about it. But if you ask them how is he/she doing you will probably get a lot of complaints and grouching because they are pessimists. That may be because of Polish village is constantly covered with snow and Polish farmers do not use any agricultural machines. My California born cousin ones asked me do I have a toilet inside my house. Poland is believed to be very poor country, especially by Americans. We will write a custom essay sample on Stereotypes in Poland or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page But for all that sadness â€Å"helps† one of the most famous stereotype which unfortunately became a kind of pervert is â€Å"to drink alcohol like Pole†. According to this Polish farmers are believed to work very hard on their farms because of cold climate they have to drink vodka to get warmer. But alcohol is not always putting them in bad light. Because Poles are well known celebrating everything with alcohol they are seen as sociable and just love to party and there are many drunken people around. With alcohol abuse comes good food which Europeans consider to be unique and healthy. The nicest stereotype is concerns kissing when Poles greet people. Poles are hospitable. Always take care about their guests, they are nice and kind. They like to say: â€Å"Guest at home- God at home†. Polish people are also taken as brave(love freedom), patriotic and nationalistic. Poland is home of Solidarity which had a great share in subverting the communistic system. It may be connected to nationalism that people in the whole world think that poles are prejudiced Jews and black people. Also in Poland there are hooligans who attacking foreigners. Talking about crime another stereotype is that Polish are thieves, especially in the area of theft cars. There is even a joke: if your car was stolen, you should go to Poland it surely would be there. Polish people also look up to other nationalities. Sociologists called Poland the most pro-American country in the world. Poles really love America. It has always been an opinion: USA- the country of dream, paradise, rich, beautiful land of people free of problems. Closer to Poland members of the European union think is their moral duty to add Poland which will improve its economical level in this way. All in all, there are many stereotypes about Poles which I mentioned from my own experience and observations. Also from the internet forums, articles and blogs. There is are numerous bad stereotypes but it goes in better way nowadays.

One Flew Over The Cuckooss Nest Essays - English-language Films

One Flew Over The Cuckoos's Nest One Flew Over the Cuckoo's Nest is a novel, which depicts the lives of the classified, mentally insane in a struggle against the authority of a hospital ward. Over the course of the novel, the hospital ward turns into a place of rebellion while the wise-guy hero, tries to reform the institution while dignifying the people within. The story is told in the first person point of view by Chief Bromden a huge patient who is sharing his mental hospital experience. He is a disturbed man who has fooled all of the other patients and the staff into believing that he is deaf and can't speak. He thinks of the hospital as a place of fear, rather than of a place of healing. This partly has to due with the head of the hospital ward, Nurse Ratched; a woman who believes in order at all times. She is viewed as the hospitals most powerful person, in turn, the least liked by the patients. In order to escape the Nurse, Chief Bromden thinks back to his childhood in an Indian village, but this also evokes the Combine force, which sends his mind into a deep fog. Early on in the story Kesey, introduces the character Randolph McMurphy, a newly admitted patient. He is a boisterous man with much self-confidence and a very friendly personality. He claims that he's only at the hospital to enjoy an easier life compared to the life he was living at a state farm. McMurphy quickly familiarizes himself with the people surrounding him and tells stories to all of the patients. His humorous personality enlightens the patients and the ward in general. However, Nurse Ratched doesn't like this change because she feels McMurphy is a manipulator. Her controlling personality clashes with his easy going personality and as expected she tries to enforce rules, while he is ready to rebel against them. Nurse Ratched has dealt with people similar to McMurphy by punishing them with electro-shock therapy or with lobotomies. Both are to degrade the"offender", the latter of the two makes the patients feel inferior to society on account of their sexuality. McMurphy is greatly disturbed by the Nurse's antics. He is dissatisfied by the way she treats the patients at the daily Group Meetings. She decrees the patients self esteem so greatly that she furthers them all into a state of depression. McMurphy decides that he's going to take a stand and he bets Harding, a patient who is intelligent, but is ashamed of his effeminacy, that he can make the Nurse loose control of the ward without getting in trouble. During his fight against the ward, McMurphy entertains the patients with his skirmishes with the Nurse. They all appear to be on his side, until an issue concerning watching the World Series on the television arises. McMurphy takes a stand, but only one man stands by his side, Cheswick. In order for the patients to watch the baseball game they would vote on it at the next Group Meeting. McMurphy needed one more vote to secure the game, so he turned to Chief Bromden, who was in a deep fog. McMurphy's personality forced the Chief back to reality. However, McMurphy still wasn't allowed to watch the game. Yet, he raised the spirits of the patients and he became somewhat of a hero to them. Soon, McMurphy comes to the realization that the only way he was going to get out of the ward is if Nurse Ratched releases him. Thus, he begins to obey the rules set forth by the Nurse. He also learns that the majority of the patients were sent voluntarily to the ward. This inspires him to destroy the fear that has entrapped the patients. McMurphy begins by planning a fishing trip that was successful and proved to the Nurse that these insane people were really capable of more than she gave them credit for. McMurphy is suspicious of Chief Bromden's deaf and dumb act and finally breaks through to him. The Chief describes to him the Combine, which consists of people like the Nurse, the government, and his mother. Generally anybody that destroyed tradition, nature, and freedom. After this talk that ended the years of silence, McMurphy makes a deal with Chief Bromden. If he grows strong enough to break the Nurse's control panel; McMurphy will let him go on the fishing trip for free. McMurphy at this point has helped nearly all of the patients by bringing them back to a

Acting Through the Ages Essay Essays

Acting Through the Ages Essay Essays Acting Through the Ages Essay Paper Acting Through the Ages Essay Paper The art of playing has evolved in many ways over its life-time and continues to germinate to this twenty-four hours. Acting foremost originated in Greece in the sixth century BC with the Grecian tragic histrion Thespis being widely regarded as the laminitis of the profession. This is why. to this twenty-four hours. histrions are frequently referred to as actors. Aristotle. the Grecian philosopher. defined moving as ‘the right direction of the voice to show assorted emotions ‘ and declared it to be a natural endowment that was unconditioned and could non be taught. There are a few antediluvian Greek dramas by Aeschylus. Euripides and Sophocles that survived all moving history and are still performed in the theaters. During the Christian regulation of Rome. moving began to worsen as an art and liturgical play began to be performed throughout the Middle Ages. The tradition was kept alive by jugglers. acrobats and mummers who entertained crowds at town carnivals and the gesture and modulation of histrions began to be mastered through spiritual play performed in church. Acting history so takes an tremendous leap to the sixteenth century. where modern professional playing began to emerge through Italian comedy. William Shakespeare is possibly the most adept of this peculiar manner of dramatist – and surely the best known. Many professional histrions during the Restoration period were famed for their natural endowment and manner but it was non until the eighteenth century that moving was considered a serious profession instead than an inexpert chase. In the mid-18th century. Charles Macklin and his student David Garrick began to present a new. realistic. manner of moving and new motions began to take topographic point across Europe. As moving history evolves. the old. declamatory. manner of moving did non decease out wholly until the beginning of the twentieth century with many popular histrions of this clip looking excessively melodramatic to many modern audiences. With the altering times. gustatory sensations and civilizations came a move off from the declamatory and intense moving manners of past ( with criterions set by the Meiningen Players in 1874 ) and the outgrowth of a new. realistic manner of moving whereby the histrion strives for absolute psychological designation with the character he is playing – the Stanislavski method introduced by Russian manager Konstantin Stanislavski. This method was adopted by the Group Theatre and subsequently by Lee Strasberg bring forthing a coevals of gifted realistic histrions such as Marlon Brando. The debut of gesture image and telecasting amusement began to offer a wealth of chances and associated stardom to draw a bead oning histrions and actresses and began to alter the art of moving forever. In the early twentieth century. the Academy Awards were launched and the profession of moving eventually began to be decently recognised as an admirable and reliable professional chase.

sexual consequences in adolesc essays

sexual consequences in adolesc essays Sexual activity hurts adolescents. Sadly, large numbers of children are placing themselves at risk by engaging in sexual activity early in their lives. Health risks are not the only consequences however. Sexually promiscuous lifestyles bring with them heavy responsibilities and commitments that young people cannot handle. Young adolescents do not have the capacity and maturing to endure the social, emotional, and psychological responsibilities that accompany their sexual choices. Sadly, the consequences include unwanted pregnancies, sexually transmitted diseases, and broken relationships, to name a few. The purpose of this essay is to investigate and discuss some of the research surrounding early sexual activity in adolescents. We will examine the findings of several academic journals, identify some of the current trends in sexual activity in adolescence, and examine the implications that follow. Lets begin by looking at some statistics regarding sexual promiscuity in adolescents. The statistics are frightening. According to the Alan Guttmacher Institute, about 80% of teenagers engage in sex by age 19 and most experience intercourse an average of 8 years before marriage. Roughly 1-in-4 sexually active teens acquires a sexually transmitted disease by age 20. Ten percent of all women become pregnant by their late teens, 78% of which are unwanted. For every ten teen pregnancies, four will be aborted. Of all rape victims, one in every two is a teenager. (Guttmacher, 1999). These statistics are overwhelming and frightening. Next, we will discuss 3 research articles that engage the teenage sexual crisis. Lets examine an article by Shaughnessy and Shakesby (1992). The authors were interested in the effects of sexual activity on the emotional and social development of adolescents. Their article comes from an academic journal entitled, Adolescence, Vol. 27, Issue 106. The conclusion drawn from their research in...

Who Benefits In Recession Essay Example | Topics and Well Written Essays - 3750 words

Who Benefits In Recession - Essay Example That would take care of the other factors in the economy and that would help to define the recession. (Brainard & Perry, 2001, Pp. 176-177). The recession has a severe effect on the economy as seen by the events during the recession. As the GDP decreases the country attracts less investment. There is a dearth of investment during the recession. There is decreased demand in the economy and the companies find it hard to make a commendable business. As a result, there is stock of unused goods and machinery. The consumption function of the economy decreases and this has a multiplier effect in the economy. As there is not a proper utilization of resources, there is a relatively higher production costs. As the production costs are high, therefore, it has an effect on the consumption. Though there is a rise in the production costs, the change in the wages is not uniform. In some cases the workers are thrown out of their jobs and the in the other5 cases there is a decrease in the wages of th e labor. In the case of the productivity, the volume of the production decreases. Therefore, the production of the companies decrease and the companies are on the verge of the extinction. From the typical recession scenario seen from the history of the world, it has been noted that the conditions of the economy needs some time to change. The economic conditions of the country are severe and the companies get closed. This effects the employment in the economy and the production. Most of the employees loose their jobs and experience a pay cut. This makes it hard for the survival of the people in the economy. The conditions are improved in the economy by the intervention strategies of the Government. The condition of the economy during the recession needs some thoughts put in by the Government and the economy needs financial support. In the modern world, most of the countries have minimum intervention strategies by the Government. But during the

Anorexia Nervosa in Today's Society Essay Example | Topics and Well Written Essays - 2250 words

Anorexia Nervosa in Today's Society - Essay Example Although Anorexia Nervosa mostly affects female population aged 15 - 30, girls under 15 and women above 30 can suffer from this disorder as well. Thus, the oldest patient reported was a woman of 68 without any prior history of eating disorders (Dally, 1984). Anorexia affects certain share of male population: estimated 10 to 15 percent of people with anorexia are men. The highest occurrence of anorexia among males is reported in the age group of young adolescents from 7 to 14 years: nearly 25 percent of anorexia cases in this age group are boys (Herman-Giddens et al, 1997). Experts identify two types of Anorexia Nervosa: food restricting type, and binge eating (purging). The most common characteristic of the restricting type is substantial reduction in calories intake (normally to 300 to 700 kcal per day) and intensive physical over-exercising. By contrast, in the binging type intake of calories may be either small or as high as several thousand followed by purging - self-induced or pharmacologically conditioned vomiting (Yager & Andersen, 2005: 1481). Health complications resulting from either type of this eating disorder affect practically all biological systems of human organism. Anorexia Nervosa poses a number of threats in terms of mental and physiological health. Similarly to other eating disorders Anorexia Nervosa frequently co-occur with depression, substance abuse and anxiety disorders (APAWGED, 2000). Physiologically Anorexia Nervosa causes a wide range of health complications some of which - cardiovascular conditions and kidney failure - are life threatening. However, despite the awareness of the risks associated with anorexia, it is on the rise these days, and a number of laymen and experts even believe that anorexia has already become a norm in modern society. A brief inquiry into the etiology of this eating disorder reveals the reasons for such seemingly strange point of view. MAIN DISCUSSION The cause of Anorexia Nervosa isn't fully understood at present. Possible causes of this eating disorder are: destructive influence of family and society, genetic (inherited) factors, brain dysfunction, neurotransmitter levels imbalances, etc. Yet, none of these factors has been proved to be the key determinant of developing Anorexia as well as no specific life experiences are linked to onset of this eating disorder. Several recent twin studies suggest that Anorexia Nervosa is more than other eating disorders associated with a genetic predisposition (Paris, 1999). Many recent studies associate the risk of developing Anorexia Nervosa with media influence. Evidences and arguments provided by these studies deserve particular attention: media influence may be one of the central factors in extremely high incidence of Anorexia Nervosa among female adolescents. Absolute majority of anorexia nervosa incidents occur in female population: according to estimations of American Psychiatric Association

What Are the Purposes of Prisons Essay Example for Free

What Are the Purposes of Prisons Essay

The Acid Rain Issue Essay -- essays research papers fc

Acid Rain is a serious problem with disastrous effects. Every day this problem increases. Many believe that this issue is too small to deal with, but if the acid rain problem is not met with head on, the effects on people, plants, animals, and the economy will only worsen. In the following paragraphs you will learn what acid rain is, the effects it has on human life, animals, the economy, the economic costs, and what is being done to help to stop this problem. This topic is very important because acid rain effects everyone everywhere all over the world.I. What is acid rain?Acid rain is the combination of two chemicals released into the atmosphere. These chemicals are sulphur dioxide (SO2) and nitrogen oxides (Nox). Natural sources such as volcanoes, sea spray, rotting vegetation and plankton are all contributors to acid rain, but burning fossil fuels, such as coal and oil which are referred to as dry emissions are largely to blame for more than half of the emissions into the world. 2 Nationally, one hundred and twenty tons of sulfur dioxide and nitrogen dioxide are emitted into the air each day.4A. How is acid rain formed?When the sulfur dioxide reaches the atmosphere, it oxidizes to first form a sulfate ion. It then becomes sulfuric acid when it joins with hydrogen atoms in the air and falls back down to earth, usually in the form of rain, snow, or fog. 1 Oxidation occurs the most in clouds and heavily polluted air where other compounds such as ammonia and ozone help to catalyze the reaction, converting more sulphur dioxide to sulphuric acid. The following are the stoichiometric equations for the formation of sulphuric acid:S (in coal) + O2 ? SO22 SO2 + O2 ? 2 SO3SO3 + H2O ? H2SO4Nitric oxide and nitric dioxide are also components of acid rain. Its sources are mainly from power stations and exhaust fumes. Like sulphur dioxide, these nitrogen dioxides also rise into the air and are oxidized in the clouds to form nitric acid. Through this diagram you can better understand how acid rain is formed and emitted into the earth:II. Effects of acid rainAcid rain causes problems in almost every aspect of the environment. Acid rain can have a devastating effect on aquatic life, crops, forests, buildings, and also human life. A. The human environmentAcid rain has a multiplicity of effects in the human environment. The corrosion of limestone buildings in towns ... ... Pennsylvania. These and thousands of other organizations strive to educate the community about the acid rain problem and would be more than happy to send you information about what you can do to help. BibliographyLeslie R. Alm, "Scientists and the Acid Rain policy in Canada and the US." Science, Technology, and Human Values, 1997, 349"Acid Rain: Bad News About The Good News" Business Week, 25 October 1999, 95Anne E. Smith, Jeremy Platt, A. Denny Ellerman, "The cost of reducing SO2: It’s (higher than you think)" Public Utilities Fortnightly, 15 May 1998, 22"Acid Rain-A Definition" <a href="http://www.qlink.queensu.ca">http://www.qlink.queensu.ca"Whats being done? What is Europe and the UN-ECE doing?" <a href="http://www.ec.gc.ca/acidrain">http://www.ec.gc.ca/acidrain"Acid Rain: The Facts" <a href="http://www.brixworth.demon.co.uk">http://www.brixworth.demon.co.ukDepartment od Enviormental Protection, "Acid Rain In Pennsylvania" <a href="http://www.dep.state.pa.us">http://www.dep.state.pa.usChuck, "Acid Rain" ChuckIII’s College Resources

Reflection paper on date rape for Human Sexuality Essay

There are many sad stories of girls who have been violated by someone that they know. They almost all begin with a wonderful night and eventually get taken advantage of. The woman in the situation may feel as though she asked for it. The male may feel as though she didn’t say no, so if I do this I am doing nothing wrong. It is horrifying to me how many times this has happened to a woman. The number of times it happens to women is the most significant thing about date rape to me, because I didn’t realize that it happened so much. I think knowing this will help me to watch out for things around me a little better and make my trust level go down even further. I think all women need to watch out for themselves in sketchy situations. If she or I feel uncomfortable then she or I should try to avoid the situation before it is too late, if possible. This isn’t always as easy as it sounds though. There have been quite a few times that I was in situations where potentially very bad things could have happened to me and out of pure luck they didn’t. I am usually a very trusting person, but the past couple of years I’ve been having to rethink that and become more of an untrusting person to try to protect myself. Men take their strong, masculine image and use it to their advantage. They may try to use guilt, lies, alcohol, and/or aggressiveness to get a girl to have sex with them. If she declines and he still continues to have sex with her, then he is committing a crime. The worst part is that girls don’t really know who to trust or not to trust. It’s a very scary world in which we live. I wish the world was different and it was ok to trust everyone especially the people you are close to, but since it’s not I have to be really careful when choosing who I will trust.

Medical Immunology

MEDICAL IMMUNOLOGY & SEROLOGY Terence L. Eday, RMT, MT(ASCPi), MPH College of Medical Technology / Medical Laboratory Science University of Perpetual Help System DALTA Historical Perspective †¢ 1773, Voltaire reported on an ancient Chinese custom where dried and powdered small pox scabs were inhaled †¢ 1798, Edward Anthony Jenner, Smallpox vaccination †¢ 1862, Ernst Haekel, Recognition of phagocytosis 1877, Paul Erlich, recognition of mast cells Historical Perspective †¢ 1879, Louis Pasteur, Attennuated chicken cholera vaccine development †¢ 1883, Ellie Metchnikoff developed the cellular theory of immunity through phagocytosis; phagocytic theory; cellular theory of vaccination †¢ 1885, Pasteur discovered therapeutic vaccination; first report of live â€Å"attenuated† vaccine for rabies Historical Perspective 1888, Pierre Roux & Alexander Yersin, Bacterial toxins (Yersinia pestis) †¢ 1888, George Nuttall, Bactericidal action of blood †¢ 1 890, Emil von Behring and Kitasata introduced passive immunization into modern medicine; humoral theory of immunity †¢ 1891, Robert Koch demonstrated the cutaneous (delayed-type) hypersensitivity †¢ 1894, Richard Pfeiffer, Bacteriolysis Historical Perspective (1 of 6 ) 1895, Jules Bordet, Complement and antibody activity in bacteriolysis †¢ 1900, Paul Ehrlich, responsible for the antibody formation theory †¢ 1901, Karl Landsteiner, A, B, and O †¢ 1901-8, Carl Jensen & Leo Loeb, Transplantable tumors †¢ 1902, Paul Portier & Charles Richet, Anaphylaxis Historical Perspective (1 of 6 ) †¢ 1903, Nicolas Maurice Arthus, discovered the Arthus reaction of intermediate hypersensitivity †¢ 1903, Almroth Wright and Stewart Douglas observed the humoral component, opsonin †¢ 1906, Clemens von Pirquet, coined the word allergy †¢ 1907, Svante Arrhenius, coined the term immunochemistryHistorical Perspective †¢ 1910, Emil von Dungern, & Ludwik Hirszfeld, Inheritance of ABO blood groups †¢ 1910, Peyton Rous, Viral immunology theory †¢ 1914, Clarence Little, Genetics theory of tumor transplantation †¢ 1915-20, Leonll Strong & Clarence Little, Inbred mouse strains Historical Perspective †¢ 1917, Karl Landsteiner, Haptens †¢ 1921, Carl Prausnitz & Heinz Kustner, Cutaneous reactions †¢ 1924, L. Aschoff, Reticuloendothelial system †¢ 1926, Loyd Felton & GH Bailey, Isolation of pure antibody preparation †¢ 1938, John Marrack, Antigen-antibody binding hypothesis Historical Perspective 1936, Peter Gorer, Identification of the H2 antigen in mice †¢ 1940, Karl Landsteiner & Alexander Weiner, Identification of the Rh Antigens †¢ 1941, Albert Coons, Immunofluorescence technique †¢ 1942, Jules Freund & Katherine McDermott, Adjuvants †¢ 1942, Karl Landsteiner & Merill Chase, Cellular transfer of sensitivity in guinea pigs (anaphylaxis) Historical Perspective †¢ 1944, Peter Medwar, Immunological hypothesis of allograft rejection †¢ 1948, Astrid Fagraeus, Demonstration of antibody production in plasma B cells †¢ 1948, George Snell, Congenic mouse lines †¢ 1949, Macfarlane Burnet & Frank Fenner, Immunological tolerance hypothesisHistorical Perspective †¢ 1950, Richard Gershon and K Kondo, Discovery of supressor T cells †¢ 1952, Ogden and Bruton, discovery of agammaglobulinemia (antibody immunodeficiency) †¢ 1953, Morton Simonsen and WJ Dempster, Graft-versus-host reaction †¢ 1953, James Riley & Geoffrey West, Discovery of histamine in mast cells Historical Perspective †¢ 1953, Rupert Billingham, Leslie Brent, Peter Medwar, & Milan Hasek, Immunological tolerance hypothesis †¢ 1955-1959, Niels Jerne, David Talmage, Macfarlane Burnet, Clonal Selection Theory †¢ 1957, Ernest Witebsky et all. Induction of autoimmunity in animals †¢ 1957, Alik Isaacs & Jean Lindemann, Discovery of interferon (cytokine) Hi storical Perspective †¢ 1958-62, Jean Dausset et al. , Human leukocyte antigens †¢ 1959-62, Rodney Porter et al. , Discovery of antibody structure †¢ 1959, James Gowans, Lympocyte circulation †¢ 1961-62, Jaques Miller et al. , Discovery of thymus involvement in cellular immunity †¢ 1961-62, Noel Warner et al. , Disctinction of cellular and humoral immune response Historical Perspective †¢ 1963, Jacques Oudin et al. Antibody isotypes †¢ 1964-68, Anthony Davis et al. , T and B cell cooperation in immune response †¢ 1965, Thomas Tomasi et al. , Secretory immunoglobulin antibodies †¢ 1967, Kimishige Ishizaka et al. , Identification of IgE as the reaginic antibody Historical Perspective †¢ 1971, Donald Bailey, Recombinant inbred mouse strains †¢ 1972, Gerald M. Edelman & Rodney Porter, Identification of antibody molecule †¢ 1974, Rolf Zinkernagel & Peter Doherty, MHC restriction †¢ 1975, Kohler and Milstein, First monoclona l antibodies used in genetic analysisHistorical Perspective †¢ 1984, Robert Good, Failed treatment of severe combined immunodeficiency (SCID, David the bubble boy) by bone marrow grafting †¢ 1985, Tonegawa, Hood et al. , Identification of immunoglobulin genes †¢ 1985-1987, Leroy Hood et al. , Identification of genes for the T cell receptor †¢ 1986, Monoclonal hepatitis B vaccine Historical Perspective †¢ 1986, Mosmann, Th1 versus Th2 model of T-helper-cell function †¢ 1990, Yamamoto et al. Molecular differences between the genes for blood groups O and A and between those for A and B †¢ 1990, NIH team, Gene therapy for SCID using cultured T cells †¢ 1993, NIH team, Treatment of SCID using genetically altered umbilical cord cells Historical Perspective †¢ 1996-1998, Identification of toll-like receptors †¢ 2001, FOXP3, the gene directing regulatory-T-cell development †¢ 2005, Frazer, Development of human papilloma-virus vaccine Th e IMMUNE SYTEM What is Immunology? †¢ Study of the molecules, cells, organs, and systems responsible for the recognition and disposal of foreign (nonself) material †¢ †¦ ow body components respond and interact †¢ †¦desirable and undesirable consequences of immune interactions †¢ †¦ways in which the immune system can be advantageously manipulated to protect against or treat disease What is Immunity? †¢ Latin word â€Å"immunitas†, freedom from †¢ It refers to all mechanisms used by the body as protection against environmental agents that are foreign to the body. †¢ Can be either natural (innate or inborn) or acquired (adaptive) Function of the Immune System †¢ Recognize â€Å"self† from â€Å"nonself† †¢ Defend the body against nonself Physiologic function is to prevent infection and to eradicate established infections (sterilizing immunity) Key Characteristics of the Immune System †¢ Innate immunit y †¢ Primary response †¢ Secondary response and immunologic memory †¢ Immune response is highly specific †¢ Immune system is tolerant of self-antigens †¢ Immune responses against self-antigens can result in autoimmune diseases †¢ Immune responses against infectious agents do not always lead to elimination of the pathogen (HIV/AIDS) Major Principles of Immunity (immune response): Elimination of many microbial agents through the nonspecific protective mechanisms of the innate immune system. †¢ Cues from the innate immune system inform the cells of the adaptive immune system as to whether it is appropriate to make a response and what type of response to make. Major Principles of Immunity (immune response): †¢ Cells of the adaptive immune system display exquisitely specific recognition of foreign antigens and mobilize potent mechanisms for elimination of microbes bearing such antigens. The immune system displays memory of its previous responses. à ¢â‚¬ ¢ Tolerance of self-antigens. Cells of the Immune System †¢ Lymphocytes – occupy the central stage; determines the specificity of immunity †¢ Dendritic cells (DCs) & Langerhan cells †¢ Monocyte/macrophages †¢ Natural killer (NK) cells †¢ Neutrophils †¢ Mast cells & Basophils †¢ Eosinophils †¢ Epithelial and stromal cells – provides anatomic environment (secretion of critical factors that regulate migration, growth and homeostasis) Lymphoid Tissues and Organs Primary Lymphoid Organs Sites where pre-B and pre-T lymphocytes mature into naive T and B cells in the absence of foreign antigen; †¢ Fetal Liver, Adult bone marrow, and thymus The INNATE IMMUNE SYTEM INNATE IMMUNE SYSTEM †¢ relies on germ line-encoded receptors to detect a limited set of microbial structures that are uniquely associated with microbial infection †¢ not a function of a single defined physiologic system; rather, it is a product of multiple a nd diverse defense mechanisms Modules of the Innate Immune System †¢ Surface epithelium The phagocyte system – critical for the defense against both intracellular and extracellular bacteria as well as fungal pathogens; aided by opsonins †¢ Acute phase response and complement – variety of secreted proteins that function in the circulation and in tissue fluids; secreted by the hepatocytes in response to the inflammatory cytokines IL1 and IL-6 Modules of the Innate Immune System †¢ Natural killer (NK) cells are specialized in the elimination of infected host cells and in aiding defense against viral and other intracellular infections through production of cytokines(IFN-? ; regulated by type I interferons (IFN-? /? ) †¢ Mast cells, eosinophils, and basophils are specialized in defense against multicellular parasites, such as helminthes; regulated by several cytokines, including IL-4, IL-5, IL-9, and IL-13 Strategies of Innate Immune Recognition 1. Recog nition of microbial nonself – referred to as pattern recognition, based on the recognition of molecular structures that are unique to microorganisms and not produced by the host 2.Recognition of missing self – based on the recognition of molecules expressed only on normal, uninfected cells of the host Targets of Innate Immune Recognition †¢ PAMPs (pathogen-associated molecular patterns) – molecular structures produced by microbial pathogens, but not by the host organism †¢ PRRs (pattern recognition receptors) – receptors of the innate immune system and represents targets of the innate immune system Targets of Innate Immune Recognition Examples of PAMPs include: (1) LPS of gram-negative bacteria (2) LTA of gram-positive bacteria (3) Peptidoglycans (4) Lipoproteins of bacteria (cell wall) (5) Lipoarabinomannan of mycobacteria (6) dsRNA produced by virus during the infection cycle (7) ? -glucans and mannans found in fungal cell wall Receptors of th e Innate Immune System †¢ Broad categories of PRRs: (1) PRRs that signal the presence of infection; expressed on the cell surface or intracellularly Categories of gene products: a. proteins and peptides that have direct antimicrobial effector functions (antimicrobial peptides and lysozyme) b. nflammatory cytokines and chemokines (TNF, IL-1, IL-8) c. gene products that control activation of the adaptive immune response (MHC, CD80/CD86, IL-12) Receptors of the Innate Immune System †¢ Broad categories of PRRs: (2) Phagocytic (or endocytic) PRRs; expressed on the surface of macrophages, neutrophils, and dendritic cells(DCs) (3) Secreted PRRs (mannan-binding lectin and peptidoglycan-recognition proteins Function: a. activate complement b. opsonize microbials cells to facilitate their phagocytosis c. ccessory proteins for PAMP recognition by transmembrane receptors (TLR) Receptors of the Innate Immune System †¢ Toll-like Receptors – comprise a family of type 1 transm embrane receptors characterized by leucine rich repeats (LRRs) in the extracellular portion and an intracellular TIR (Toll/IL-1 receptor) domain; grouped into two classes: (1) TLRs 1, 2, 4, 5, and 6 are expressed on the plasma membrane and detect bacterial and fungal cell wall components; (2) TLRs 3, 7, and 9 are expressed in endosomal compartments and recognize viral nucleic acidsToll-like receptor 4 (TLR4) †¢ expressed predominantly in the cells of the immune system, including macrophages, DC, neutrophils, mast cells, and B cells †¢ also expressed on endothelial cells, fibroblasts, surface epithelial cells, and muscle cell †¢ Signal transducing receptor for LPS, heat sensitive protein associated with the cell walls of MTB †¢ Together with CD14 shown to mediate responsiveness to the fusion (F) protein of RSVToll-like receptor 2 (TLR2) †¢ Involved in recognition of LTA and peptidoglycan from gram-positive bacteria, bacterial lipoproteins, mycoplasma lipoprot ein, mycobacterial lipoarabinomannan, a phenol-soluble modulin from S. epidermidis, zymosan of yeast cell walls, and lipoglycosylphosphotidylinositol T. cruzi †¢ Also shown to recognize two kinds of atypical LPS: L. interrogans and Porphyromonas gingivitis Toll-like receptor 3 (TLR3) Receptor for dsRNA †¢ Can mediate responses to poly(IC) †¢ Expressed on DCs, macrophages, and surface epithelial cells, including instestinal epithelium †¢ Also expressed in CD8+ DCs Toll-like receptor 7 (TLR7) †¢ Involved in viral recognition and both detect nucleic acids together with TLR9 †¢ Recognizes viral ssRNA (derived from RNA viruses); TLR9 (unmethylated DNA derived from DNA viruses) †¢ Expressed primarily on plasmacytoid dendritic cells †¢ Activated by small antiviral compunds, e. g. imiquinoid †¢TLR7-mediated recognition takes place inside the late lysosomes Toll-like receptor 9 (TLR9) †¢ Involved in the antiviral host defense; especially on r ecognition of DNA viruses (HSV) †¢ Expressed in type-I INF-producing plasmacytoid DCs Phagocytic Receptors †¢ Scavenger receptors – cell-surface glycoproteins that are defined by their ability to bind to modified LDL †¢ Macrophage Mannose Receptor (MR) – type I transmembrane protein expressed primarily in macrophages; involved in phagocytosis of bacterial (MTB, P. eruginosa, K. pneumonia), fungal (S. cerevisae, C. albicans), and protozoan pathogens (P. carinii) Cells of the Innate Immune System †¢ Macrophages – most central and essential functions and have multiple roles in host defense (e. i. â€Å"housekeeping functions†); in red pulp of the spleen, it phagocytose and remove from circulation senescent RBCs †¢ Neutrophils †¢ Mast Cells – best known effectors of allergic response; protective role is by rapid production of TNF-? nd leukotriene B4 (neutrophil recruitement) Cells of the Innate Immune System †¢ Eosino phils – found primarily in the respiratory, intestinal, and genitourinary tracts; contains cationic effector proteins toxic to parasitic worms; poor phagocytes †¢ Dendritic Cells – immature DCs reside in peripheral tissues and are highly active in macropinocytosis and receptor-mediated endocytosis; expresses PRRs and TLRs; have roles in the initiation of adaptive immune response Cells of the Innate Immune System Suface Epithelium – lines the mucosal surfaces of the intestinal, respiratory, and genitourinary tracts provide an important physical barrier The Effector Mechanisms of the Innate Immune System The Major Categories of Antimicrobial Effector Enzymes that hydrolyze components of microbial cell walls Antimicrobial proteins and petides that disrupt the integrity of microbial cell walls †¢ Lysozyme †¢ Chitinases †¢ Phospholipase A2 †¢ †¢ †¢ †¢ †¢ BPI Defensins Cathelicidins Complement Eosinophil cationic protein Mi crobicidal serine proteasesProteins that sequester iron and zinc Enzymes that generate toxic oxygen and nitrogen derivatives †¢ Seprocidins †¢ Lactoferrin †¢ NRAMP †¢ calprotein †¢ Phagocytic oxidase †¢ Nitric oxide synthase †¢ myeloperoxidase The Effector Mechanisms of the Innate Immune System †¢ Lysozyme – a. k. a. muramidase; degrades the peptidoglycan of some gram(+) bacteria; highly concentrated in secretions such as tears and saliva †¢ Chitinases – enzymes that degrade chitin; secreted by activated macrophages and presumably play a role in antifungal defenseThe Effector Mechanisms of the Innate Immune System †¢ Defensins – cationic peptides with a broad spectrum of antimicrobial activities against gram(+) and gram(-) bacteria, fungi, parasites, and some envelope viruses; kill microorganisms by forming pores in the membranes; divided into ? – and ? defensins †¢ ? -defensins – presynthesize d and stored in granules of neutrophils and Paneth cells of the small intestine †¢ ? -defensins – produced by epithelial cells and not stored in cytoplasmic granulesThe Effector Mechanisms of the Innate Immune System †¢ Cathelicidins – active against gram(+) and gram(-) bacteria and fungi; produced in neutrophils and stored as inactive proproteins in the secondary granules †¢ Serprocedins – comprise a family of cationic serine proteases with antimicrobial activity (neutrophil elastase, proteinase 3, cathepsin G, and azurocidin); exert its antimicrobial activity by either perturbation of microbial membranes or by proteolysisThe Effector Mechanisms of the Innate Immune System †¢ Lactoferrin, NRAMP, and Calprotectin – antimicrobial activities are due to the ability to sequester iron and zinc †¢ Lactoferrin – found in the secondary granules of neutrophils, in epithelial secretions (e. i. breast milk), in the intestinal epitheli um of infants, and in airway fluids; bacteriostatic (iron sequestration) and bacteriocidal (perturbation of microbial membranes) The Effector Mechanisms of the Innate Immune System NRAMP (natural resistance-associated macrophage protein) – integral membrane protein that functions as an ion pump in the phagocytic vacuoles of macrophage and neutrophils †¢ Calprotectin – member of the family of calciumbinding proteins; microbial activity is by chelation and sequestration of zinc ion ACUTE PHASE REACTANTS †¢ Soluble factors which are normal constituents that increase or decrease rapidly as produ †¢ Not a function of a single defined physiologic system; rather, it is a product of multiple and diverse defense mechanisms

Free Essays on Melatonin

MELATONIN Melatonin is a hormone made by the pineal gland, located within your brain. Every day, as it gets later, the pineal gland goes to work by releasing increasing amounts of melatonin into your bloodstream. This hormone may play a role in many body processes. Your blood vessels, ovaries, gastrointestinal system and brain all have cells that are specially equipped to utilize melatonin. The main influence it has involves sleep. The time period in which the pineal gland releases the hormones coincides with the hours you typically sleep. It doesn’t cause you to fall asleep, but it initiates changes throughout your body that make you feel ready for sleep. Several studies have shown that 1 to 2 milligrams a day may help improve the quality and duration of sleep in some people. However, it appears melatonin supplements may help only the small number of insomniacs who have a melatonin deficiency. Much remains unknown about this hormone and its effects on your body, particularly when it’s used long-term or with other medications. There also concerns about the quality and purity of the supplements. Because it is not a drug, the FDA doesn’t regulate its safety. No serious side effects have yet been attributed to taking melatonin supplements, but doctors and scientist believe it may cause hypothermia, reduced fertility, suppression of male sex drive, and damage to the retina of the eye.... Free Essays on Melatonin Free Essays on Melatonin MELATONIN Melatonin is a hormone made by the pineal gland, located within your brain. Every day, as it gets later, the pineal gland goes to work by releasing increasing amounts of melatonin into your bloodstream. This hormone may play a role in many body processes. Your blood vessels, ovaries, gastrointestinal system and brain all have cells that are specially equipped to utilize melatonin. The main influence it has involves sleep. The time period in which the pineal gland releases the hormones coincides with the hours you typically sleep. It doesn’t cause you to fall asleep, but it initiates changes throughout your body that make you feel ready for sleep. Several studies have shown that 1 to 2 milligrams a day may help improve the quality and duration of sleep in some people. However, it appears melatonin supplements may help only the small number of insomniacs who have a melatonin deficiency. Much remains unknown about this hormone and its effects on your body, particularly when it’s used long-term or with other medications. There also concerns about the quality and purity of the supplements. Because it is not a drug, the FDA doesn’t regulate its safety. No serious side effects have yet been attributed to taking melatonin supplements, but doctors and scientist believe it may cause hypothermia, reduced fertility, suppression of male sex drive, and damage to the retina of the eye....

25 Google Power Search Tips for Genealogists

25 Google Power Search Tips for Genealogists Google is the search engine of choice for most genealogists I know, due to its ability to return relevant search results for genealogy and surname queries and its huge index. Google is much more than just a tool for finding Web sites, however, and most people surfing for information on their ancestors barely scratch the surface of its full potential. If you know what you are doing, you can use Google to search within Web sites, locate photos of your ancestors, bring back dead sites, and track down missing relatives. Learn how to Google as youve never Googled before. Begin With the Basics 1. All Terms Count - Google automatically assumes an implied AND between each of your search terms. In other words, a basic search will only return pages that include all of your search terms. 2. Use Lower Case - Google is case insensitive, with the exception of the search operators AND and OR. All other search terms will return the same results, regardless of the combination of upper and lower case letters used in your search query. Google also ignores most common punctuation such as commas and periods. Thus a search for Archibald Powell Bristol, England will return the same results as archibald powell bristol england. 3. Search Order Matters - Google will return results that contain all of your search terms, but will give higher priority to the earlier terms in your query. Thus, a search for power wisconsin cemetery will return pages in a different ranked order than wisconsin power cemetery. Put your most important term first, and group your search terms in a way that makes sense. Search With a Focus 4. Search for a Phrase - Use quotation marks around any two word or greater phrase to find results where the words appear together exactly as you have entered them. This is especially useful when searching for proper names (i.e. a search for thomas jefferson will bring up pages with thomas smith and bill jefferson, while searching for thomas jefferson will only bring up pages with the name thomas jefferson included as a phrase. 5. Exclude Unwanted Results - Use a minus sign (-) before words that you want to be excluded from the search. This is especially useful when searching for a surname with a common usage such as rice or one which is shared with a famous celebrity such as Harrison Ford. Search for ford -harrison to exclude results with the word harrison. It also works well for cities that exist in more than one area such as shealy lexington south carolina OR sc -massachusetts -kentucky -virginia. You have to be careful when eliminating terms (especially place names), however, because this will exclude pages that have results including both your preferred location and the ones you eliminated. 6. Use OR to Combine Searches - Use the term OR between search terms to retrieve search results that match any one of a number of words. The default operation for Google is to return results that match ALL search terms, so by linking your terms with OR (note that you have to type OR in ALL CAPS) you can achieve a bit more flexibility (e.g. smith cemetery OR gravestone will return results for smith cemetery and smith gravestone). 7. Exactly What You Want - Google employs a number of algorithms to ensure accurate search results, including automatically considering searches for words that are common synonyms to be identical, or suggesting an alternate, more common spellings. A similar algorithm, called stemming, returns not only results with your keyword, but also with terms based on the keyword stem - such as powers, power and powered. Sometimes Google can be a little too helpful, however, and will return results for a synonym or word that you may not want. In these cases, use quotation marks around your search term to ensure that it is used exactly as you typed it (e.g. power surname genealogy) 8. Force Additional Synonyms - Although Google search automatically displays results for certain synonyms, the tilde symbol (~) will force Google to show additional synonyms (and related words) for your query. For example, a search for schellenberger ~vital records leads Google to return results including vital records, birth records, marriage records, and more. Similarly, ~obituaries will also include obits, death notices, newspaper obituaries, funeral, etc. Even a search for schellenberger ~genealogy will yield different search results than schellenberger genealogy. Search terms (including synonyms) are bolded in Google search results, so you can easily see what terms were found on each page. 9. Fill in the Blanks - Including an *, or wildcard, in your search query tells Google to treat the star as a placeholder for any unknown term(s) and then find the best matches. Use the wildcard (*) operator to end a question or phrase such as ​william crisp was born in * or as a proximity search to find terms located within two words of each other such as david * norton (good for middle names and initials). Note that the * operator works only on whole words, not parts of words. You cant, for example, search for owen* in Google to return results for Owen and Owens. 10. Use Googles Advanced Search Form - If the search options above are more than you want to know, try using Googles Advanced Search Form which simplifies most of the search options previously mentioned, such as using search phrases, as well as removing words you dont want included in your search results. Search Suggested Alternate Spellings Google has become one smart cookie and now suggests alternate spellings for search terms which appear to be misspelled. The search engines self-learning algorithm automatically detects misspellings and suggests corrections based on the most popular spelling of the word. You can get a basic idea of how it works by typing in geneology as a search term. While Google will return search results for pages on geneology, it will also ask you Did you mean genealogy? Click on the suggested alternate spelling for a whole new list of sites to browse! This feature comes in particularly handy when searching for cities and towns for which you arent sure of the correct spelling. Type in Bremehaven and Google will ask you if you meant Bremerhaven. Or type in Napels Italy, and Google will ask you if you meant Naples Italy. Watch out, however! Sometimes Google chooses to display the search results for the alternate spelling and youll need to select the correct spelling to find what you are really looki ng for. Bring Back Sites From the Dead How many times have you found what looks to be a very promising Web site, only to get a File Not Found error when clicking on the link? Genealogical Web sites seem to come and go every day as webmasters change file names, switch ISPs, or just decide to remove the site because they can no longer afford to maintain it. This doesnt mean the information is always gone forever, however. Hit the Back button and look for a link to a cached copy at the end of the Google description and page URL. Clicking on the cached link should bring up a copy of the page as it appeared at the time that Google indexed that page, with your search terms highlighted in yellow. You can also return Googles cached copy of a page, by preceding the pages URL with cache:. If you follow the URL with a space separated list of search words, they will be highlighted on the returned page. For example:  cache:genealogy.about.com surname  will return the cached version of this sites homepage with the term surname high lighted in yellow. Find Related Sites Found a site that you really like and want more? GoogleScout can help you find sites with similar content. Hit the Back button to return to your Google search results page and then click on the  Similar Pages  link. This will take you to a new page of search results with links to pages which contain similar content. The more specialized pages (such as a page for a specific surname) may not turn up many relevant results, but if you are researching a particular topic (i.e. adoption or immigration), GoogleScout can help you find a large number of resources very quickly, without having to worry about selecting the right keywords. You can also access this feature directly by using the related command with the URL of the site that you like (  related:genealogy.about.com). Follow the Trail Once youve found a valuable site, chances are that some of the sites which link to it may also be beneficial to you. Use the  link  command along with a URL to find pages which contain links pointing to that URL. Enter  link:familysearch.org  and youll find about 3,340 pages which link to the homepage of familysearch.org. You can also use this technique to find out who, if anyone, has linked to your personal genealogy site. Search Within a Site While many major sites have search boxes, this isnt always true of smaller, personal genealogy sites. Google comes to the rescue again, however, by allowing you to restrict search results to a specific site. Just enter your search term followed by the  site  command and the main URL for the site you wish to search in the Google search box on the main Google page. For example,  military site:www.familytreemagazine.com  pulls up 1600 pages with the search term  military  on the Family Tree Magazine Web site. This trick is especially useful for quickly finding surname information on genealogy sites without indexes or search capabilities. Cover Your Bases When you really want to make sure you havent missed a good genealogy site, enter  allinurl:genealogy  to return a list of sites with  genealogy  as part of their URL (can you believe that Google found more than 10 million?). As you can tell from this example, this is a better option to use for more focused searches, such as surnames or locality searches. You can combine multiple search terms, or use other operators such as OR to help focus your search (i.e.  allinurl:genealogy france  OR  french). A similar command is also available to search for terms contained within a title (i.e.  allintitle:genealogy france  OR  french). Find People, Maps and More If youre searching for U.S. information, Google can do so much more than just search Web pages. The lookup information they provide through their search box has been expanded to include street maps, street addresses, and phone numbers. Enter a first and last name, city, and state to find a phone number. You can also do a reverse lookup by entering a phone number to find a street address. To use Google to find street maps, just enter a street address, city, and state (i.e.  8601 Adelphi Road College Park MD), in the Google search box. You can also find business listings by entering the name of a business and its location or zip code (i.e.  tgn.com utah). Pictures From the Past Googles image search feature makes it easy to locate photos on the Web. Just click on the Images tab on Googles home page and type in a keyword or two to view a results page full of image thumbnails. To find photos of specific people try putting their first and last names within quotes (i.e.  laura ingalls wilder). If youve got a bit more time or a more unusual surname, then just entering the surname should be enough. This feature is also a great way to find photos of old buildings, tombstones, and even your ancestors hometown. Because Google doesnt crawl for images as often as it does for Web pages, you may find many pages/images have moved. If the page doesnt come up when you click on the thumbnail, then you may be able to find it by copying the URL from below the feature, pasting it into the Google search box, and using the cache feature. Glancing Through Google Groups If youve got a bit of time on your hands, then check out the Google Groups search tab available from the Google homepage. Find info on your surname, or learn from the questions of others by searching through an archive of over 700 million Usenet newsgroup messages going back as far as 1981. If youve got even more time on your hands, then check out this  historical Usenet timeline  for a fascinating diversion. Narrow Your Search by File Type Typically when you search the Web for information, you expect to pull up traditional Web pages in the form of HTML files. Google offers results in a variety of different formats, however, including .PDF (Adobe Portable Document Format), .DOC (Microsoft Word), .PS (Adobe Postscript), and .XLS (Microsoft Excel). These files appear among your regular search results listings where you can either view them in their original format, or use the  View as HTML  link (good for when you dont have the application that is needed for that particular file type, or for when computer viruses are a concern). You can also use the filetype command to narrow your search to find documents in particular formats (i.e. filetype:xls genealogy forms). You arent likely to use this Google feature often, but I have used it to find genealogy brochures in PDF format and family group sheets and other genealogy forms in Microsoft Excel format. If youre someone like me who uses Google quite a bit, then you may want to consider downloading and using the Google Toolbar (requires Internet Explorer Version 5 or later and Microsoft Windows 95 or later). When the Google Toolbar is installed, it automatically appears along with the Internet Explorer toolbar and makes it easy to use Google to search from any Web site location, without returning to the Google home page to begin another search. A variety of buttons and a drop-down menu make it easy to perform all of the searches described in this article with just a click or two. Best wishes for a successful search!

Fathers and Their Families Essay Example | Topics and Well Written Essays - 500 words - 24

Fathers and Their Families - Essay Example When fathers are not at home, the economic welfare of the family is adversely affected because mothers bear all the family financial burdens.a) When fathers are not at home, the economic welfare of the family is adversely affected because mothers bear all the family financial burdens.b) Fathers are usually a sense of security to their families, thus their absence exposes the family to potential risks of abuse among others.c) Fathers’ absence from the family breaks down the smallest unit of a family thus jeopardizes its functioning.Now that I have looked at the overall family welfare when fathers are away from home, I will proceed to discuss what happens to children when their fathers are not at home.II. Fathers’ absence from the family negatively affects the development and welfare of children) Children from families with more concerned and caring fathers encounter fewer behavioral challenges than their counterparts from fatherless families (Howard et al., 2006).b) Girl child usually needs the father for proper psychological development and absence of the father from home for a few hours or permanently servers the connection girls have with their fathers.c) Children are more likely to engage in early drug and substance abuse when their fathers are not at home. In conclusion, today, I have covered what happens to the family when fathers are away at home, which includes weakened social and economic strength as well as disturbed child development. When fathers are away from home, either for a short duration or permanently, their families are often adversely affected.  

The Proctor & Gamble Company Executive Financial Summary Research Paper

The Proctor & Gamble Company Executive Financial Summary - Research Paper Example The net sales for P&G remained at $79,029 million in the year 2009 whereas its net sales in 2008 were a bit high amounting to $81,748 million. The net sales for the year 2007 remained at $74,832 million. The net income for P&G remained at $13,436 million in the year 2009 whereas its net income in 2008 remained a bit low amounting to $12,075 million. For the year 2007, the net income for the year remained at $10,340 million. Cash generated by Operating Activities for P&G remained at $14,919 million in the year 2009 whereas its Cash generated by Operating Activities in 2008 remained a bit high amounting to $15,008 million. For the year 2007, Cash generated by Operating Activities for the year remained at $13,410 million. Cash used in Investing Activities for P&G remained at $(2,353) million in the year 2009 whereas its Cash used in Investing Activities in 2008 remained a bit high amounting to $(2,549) million. For the year 2007, Cash used in Investing Activities for the year remained at $(2,483) million. Cash generated by Financing Activities for P&G remained at $(10,814) million in the year 2009 whereas its Cash generated by Financing Activities in 2008 remained a bit high amounting to $(14,844) million. For the year 2007, Cash generated by Financing Activities for the year remained at $(12,453) million. P&G - A Company History - 1837-Today. (2012). P&G - A Company History - 1837-Today. Retrieved October 14, 2012, from P&G - A Company History - 1837-Today:

What is job analysis Essay Example | Topics and Well Written Essays - 500 words

What is job analysis - Essay Example Part of the reason for this is that managers feel that they have been familiar with the content of the social sciences, human nature, since their childhood as opposed to, say, the content of nuclear physics or microbiology. This leads managers to rely on what they perceive as their experience-based knowledge of human nature in personnel decision making. Job analysis is a systematic process for acquiring objective and detailed information about jobs. It is not a single methodology but a generic term representing a range of techniques. The data gathered may be in the form of information on job tasks, roles, and job holder attributes relevant to job performance (p. 9). In organization, the role of job analysis has encountered managers who do seem to have developed considerable insight into human behavior. As a result of long years of watching successful and unsuccessful performers in particular positions, they can now make well-informed guesses as to which employee will be successful in those positions. This discerning ability, however, is likely to be specific to the positions and could not be effectively applied to organizational development programs for employees in different occupational specialties and levels of organizational functioning. Job analysis is crucial for effective recruitment because it allows certain standardization of job description. To effect the standardization and control for which procedures are designed, they are presented in a specific format conveying information for a particular action to be taken. The achievement may be only one step in a series of steps or the entire series. Once formalized in this way, job analysis procedures need to be followed clearly to achieve their objectives. Sometimes exceptions in job analysis may be made to a formalized process, but in that case the manner of making an

Ocean to the Rivers of Story by Somadeva Essay Example for Free

Ocean to the Rivers of Story by Somadeva Essay Ocean to the Rivers of Story by Somadeva The Kathasaritsagara (Ocean to the Rivers of Story) is a famous compendium of Indian legends fairy tales and folk stories compiled by Somadeva. Somadeva lived in the 11th century. He was a court poet to King Ananta of Kashmir. Most likely he was asked to compose a cycle of stories for the Queen Suryamati to keep her mind away from the political crisis in the country. The poet knew a lot of ancient tales that contained many ancient Indian beliefs. As a basis for his book he took a much older Indian tale collection Brhat-katha (The Great Romance) by Gunadhya, the  original version of which had been lost. The structure of Kathasaritsagara is a collection of tales inside one main framing tale about the life and adventures of the son of the legendary King Udayana. It also includes the story about how The Great Romance was written and what happened to this book afterwards. As the title implies -Ocean to the Rivers of Story, Somadevas work united all the stories that were known at that time, just like an ocean unites all the rivers. Every story, big or small, written or told found its reflection in Somadevas collection. Thus, no wonder that the characters of this collection both, humans and all different creatures that humans believed in. Some stories reflected the life of Indian society, and their characters are desperate lovers, powerful kings, greedy bankers, smart merchants, shrewd and clever women, brave warriors and many others. Other stories reflect strange fantastic myths and the characters of them are goblins, vampires, witches, devils and all other imaginary creatures that were created by Indian folklore during the past centuries. This book is  sometimes called the mirror of Indian imagination. The story The Red Lotus of Chastity tell us about a live of a merchants family. The only son of a merchant got married to a smart and beautiful girl named Devasmita. The young man inherited his fathers business and had to take care of his familys prosperity. One day he decided to go to the island of Cathay to sell his goods. His wife was afraid that he would fall in love with another woman while being away. She went to the temple and asked God Siva for a piece of advise. God Siva gave a red lotuse to her  and her husband, saying that it any of them would be unfaithful, the lotus of the spouse would fade. On the trip the fellow merchants of the young man found out about this and decided to seduce the young merchants wife and humiliate Guhasena. However, all their attempts were in vain, as Devasmita understood their plan and could play a trick on all of them. At the end Devasmita travels to the island of Cathay to tell the story to her husband and to not be separated from him anymore. The three men who tried to seduce Devasmita admitted their plans and were turned into her slaves. This storys characters are regular people: a young merchant, who loves his wife and wants to give the best he can get to her; a young wife, who loves her husband and remains faithful to him all the time, three men- seducers, who represent the evil side; a witch- an old woman who help to make the plan of seduction. But at the end we see that the good characters celebrate the victory as it should always be. This story reminds me of the stories and tales of European troubadours who lived during the Medieval Ages. In contrast to the official sacred art, their tales and songs were  about real human lives, about human good and bad traits of character. The character of this story can be easily compared to the characters of Molieres plays and Shakespeares comedies. There have been many discussions about how Indian stories traveled around the world. According to some scientists Indian story-telling made the Persians learn the art of storytelling and pass it on to the Arabians. Then ancient Indian tales traveled from the Middle East to Constantinople and Venice. Later they were reflected in the works of the early representatives of the Renaissance Era. Some scientists believe that Western tales borrowed a lot from Indian ones. The discussion is still open nowadays. The researches could not prove anything yet. However, even on the example of this story we could see the similarity of character types and story development. But it would be not surprising that this type of a connection would be established as it is very likely that educated European people knew Indian tales and were fascinated by them. Obviously, they could have borrowed some motives and characters for their later works.

Equality Between Men and Women in Modern Society vs. Ancient Greek Soci

In today's society, women hold a position equal to that of a man. However, this has not always been the case especially in the Ancient Greek society. In the society there were many rules and regulations for all, but in particular the women had it the hardest. Women were seen as insignificant characters in the Ancient Greek society. While the men†¦.women attained the most difficult job of all, bearing children. These women in the society had very little freedom, actually no freedom at all. Can you imagine being locked inside a house all day with the windows locked? In the Ancient Greek society, women were actually very important to keeping the society together and functioning. Men did not give them the credit they deserved. Thus dominant role of women portrayed in Ancient Greek mythology and artwork is in direct contrast to the more subservient role of women during the classical era in Greece. In today's society, women hold a position equal to that of a man. However, this has not always been the case especially in the Ancient Greek society. In the society there were many rules and re...

My Alignment with the Values of the Bank Essay

According to Business Dictionary 2010, values can be defined as the important and enduring beliefs or ideals shared by the members of a culture about what is desirable and what is not. Each person has his or her own individual values and so does organizations. The values of organizations dictate its actions and behaviors. Corporate values can be said to play an important role in an organization and is imperative to success. And Access Bank PLC is known for its core values which are Excellence, Leadership, Empowered employees, Passion for customers, Professionalism, and Innovation. These values can be said to be responsible for its excellence and continuous strive to be the best both locally and globally. To attain a successful alignment between individual and organization values, there needs to be a synergy between the employee and the organization he or she works for. My alignment with these values are in no doubt because I as an individual always strive to be the best and these values should be cultivated by any individual or organization that strive to be the best. Firstly the value of Leadership, I as an individual that strive for excellence always want to be the leader. I strive to acquire all the necessary knowledge and expertise that makes me stand out as a leader that others look up to. So in this vein, contributing and believing in the Leadership value of Access Bank PLC is something that will come as second nature to me. Then there is excellence. This being part of my daily mantra is a value that aligning with will also come as second nature. I and Access Bank both believe in the value of excellence. As someone who strive to be the best and excel. Excellence is a watch word that applies to everything I do. I recognize the importance

Flight Control Systems

Flight Control Systems W. -H. Chen Department of Aeronautical and Automotive Engineering Loughborough University 2 Flight Control Systems by W. -H. Chen, AAE, Loughborough Contents 1 Introduction 1. 1 Overview of the Flight Envelope 1. 2 Flight control systems . . . . . . 1. 3 Modern Control . . . . . . . . . . 1. 4 Introduction to the course . . . . 1. 4. 1 Content . . . . . . . . . . 1. 4. 2 Tutorials and coursework 1. 4. 3 Assessment . . . . . . . . 1. 4. 4 Lecture plan . . . . . . . 1. 4. 5 References . . . . . . . . . 7 7 8 8 9 9 10 10 10 11 13 13 16 16 17 17 18 19 19 20 20 20 20 20 24 25 25 25 25 26 27 27 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Longitudinal response to the control 2. 1 Longitudinal dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2 State space description . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 1 State variables . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 2 General state space model . . . . . . . . . . . . . . . . . . . 2. 3 Longitudinal state space model . . . . . . . . . . . . . . . . . . . . 2. 3. 1 Numerical example . . . . . . . . . . . . . . . . . . . . . . . 2. 3. 2 The choice of state variables . . . . . . . . . . . . . . . . . . 2. 4 Aircraft dynamic behaviour simulation using state space models . 2. 4. 1 Aircraft response without control . . . . . . . . . . . . . . . 2. 4. 2 Aircraft response to controls . . . . . . . . . . . . . . . . . 2. 4. 3 Aircraft response under both initial conditions and controls 2. 5 Longitudinal response to the elevator . . . . . . . . . . . . . . . . 2. 6 Transfer of state space models into transfer functions . . . . . . . . 2. 6. 1 From a transfer function to a state space model . . . . . . . 2. 7 Block diagram representation of state space models . . . . . . . . . 2. 8 Static stability and dynamic modes . . . . . . . . . . . . . . . . . . 2. 8. 1 Aircraft stability . . . . . . . . . . . . . . . . . . . . . . . . 2. 8. 2 Stability with FCS augmentation . . . . . . . . . . . . . . . 2. 8. 3 Dynamic modes . . . . . . . . . . . . . . . . . . . . . . . . . 2. 9 Reduced models of longitudinal dynamics . . . . . . . . . . . . . . 2. 9. Phugoid approximation . . . . . . . . . . . . . . . . . . . . 2. 9. 2 Short period approximation . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Lateral response to the controls 3. 1 Lateral state space models . . . . . . . . . . . . 3. 2 Transient response to aileron and rudder . . . . 3. 2. 1 Numerical example . . . . . . . . . . . . 3 . 2. 2 Lateral response and transfer functions 3. 3 Reduced order models . . . . . . . . . . . . . . 3. 3. 1 Roll subsidence . . . . . . . . . . . . . . 3. 3. Spiral mode approximation . . . . . . . 3. 3. 3 Dutch roll . . . . . . . . . . . . . . . . . 3. 3. 4 Three degrees of freedom approximation 3. 3. 5 Re-formulation of the lateral dynamics . CONTENTS 31 31 33 33 33 35 38 38 39 39 40 43 43 46 46 46 46 48 49 49 55 55 55 58 58 60 60 61 62 65 66 66 67 68 68 68 69 69 69 70 70 71 71 73 73 73 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Stability Augmentation Systems 4. 1 State space design techniques . . . . . . . . . . . 4. 2 Longitudinal stability augmentation systems . . . 4. 2. 1 The choice of feedback variables . . . . 4. 2. 2 SAS for short period dynamics . . . . . . 4. 3 Lateral stability augmentation systems . . . . . . 4. 3. 1 Yaw rate feedback for rudder control . . . 4. 3. 2 Roll feedback for aileron control . . . . . 4. 3. 3 Integration of lateral directional feedback 5 Autopilots 5. 1 Pitch holding autopilot . . . . . . . . . . . . . . . . . . . . . . . 5. 1. 1 phugoid suppress . . . . . . . . . . . . . . . . . . . . . . 5. 1. 2 Eliminate the steady error with integration . . . . . . . 5. 1. 3 Improve transient performance with pitch rate feedback 5. 2 Height holding autopilot . . . . . . . . . . . . . . . . . . . . . . 5. . 1 An intuitive height holding autopilot . . . . . . . . . . . 5. 2. 2 Improved height holding systems . . . . . . . . . . . . . 5. 3 Actuator dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 6 Handling Qualities 6. 1 Handing qualities for aircraft . . . . . . . . . . . . 6. 2 Pilot-in-loop dynamics . . . . . . . . . . . . . . . . 6. 2. 1 Pilot as a controller . . . . . . . . . . . . . 6. 2. 2 Frequency response of a dynamic system . . 6. 2. 3 Pilot-in-loop . . . . . . . . . . . . . . . . . 6. 3 Flying qualities requirements . . . . . . . . . . . . 6. 4 Aircraft role . . . . . . . . . . . . . . . . . . . . . . 6. . 1 Aircraft classi? cation . . . . . . . . . . . . . 6. 4. 2 Flight phase . . . . . . . . . . . . . . . . . . 6. 4. 3 Levels of ? ying qualities . . . . . . . . . . . 6. 5 Pilot opinion rating . . . . . . . . . . . . . . . . . . 6. 6 Longitudinal ? ying qualities requirements . . . . . 6. 6. 1 Short perio d pitching oscillation . . . . . . 6. 6. 2 Phugoid . . . . . . . . . . . . . . . . . . . . 6. 6. 3 Flying qualities requirements on the s-plane 6. 7 Lateral-directional ? ying qualities requirements . . 6. 7. 1 Roll subsidence mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONTENTS 6. 7. 2 6. 7. 3 6. 7. 4 5 Spiral mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Dutch roll mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Lateral-directional mode in s-plane . . . . . . . . . . . . . . . . . 75 77 . . . . . . . . . . . control derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 79 79 79 79 79 7 Fly-by-Wire ? ight control 8 Appendices 8. Boeing 747-100 data . . . . . . . . . . . 8. 2 De? nitions of Aerodynamic stability and 8. 3 Root Locus . . . . . . . . . . . . . . . . 8. 4 Frequency response . . . . . . . . . . . . appendices 6 CONTENTS Chapter 1 Introduction 1. 1 Overview of the Flight Envelope †¢ Flight planing †¢ Aircraft checking †¢ Taxi †¢ Take-o? – Rotate, â€Å"select† an attitude – Clean up (gear, ? aps, etc) – Emergencies (engine failure, ? re, etc) †¢ Climb – Speed control – Procedure (manual, autopilot) †¢ Mission Tasks – Cruise – Combat (air to air) – Strike (air to earth) – General handling (stalling, spinning, aerobatics) – Formation ? ing (Navigation, procedure etc) – Emergencies – Con? guration (weapons, tanks, fuel load) †¢ Recovery – Descent – Instrument approach – Landing – Overshoot 7 8 CHAPTER 1. INTRODUCTION Stick – Linkage 6 Trim ? -? Servo Actuator – Aircraft dynam ics Figure 1. 1: Manual pilot control aircraft – Formation – Procedures – Emergencies †¢ Taxi Longitudinal and lateral dynamics thus Flight control systems are involved in Take o? , Climb, Mission tasks and Recovery. †¢ Di? erent aircraft (aircraft class) †¢ Di? erent ? ight phase Manual– handling qualities/? ight qualities Improve the handling qualities of airplane; Autopilot 1. 2Flight control systems Objectives †¢ To improve the handling qualities †¢ To release the operation burden of pilots partly or fully †¢ To increase the performance of aircraft or missiles Types of Flight Control Systems (FCS) 1. Open-loop control 2. Stability augmentation systems 3. Autopilot 4. Integrated Navigation systems and Autopilots (? ight management systems) 1. 3 Modern Control †¢ Classic control– transfer function – frequency domain †¢ Limitation of classic design method: single input, single output (SISO), only conc ern the output behaviour, linear systems (saturation) †¢ System description in state space form. 1. 4.INTRODUCTION TO THE COURSE 9 Stick Trim – Aircraft dynamics – + ? + -Linkage – ? – ? – Servo Actuator 6 6  Stability Aug. Systems  Sensor  ? Figure 1. 2: Stability Augmentation Systems Reference Command + -? Autopilot – 6 6 + -? 6 – SAS – Actuators – Aircraft dynamics – Sensor  6  Navigation Systems ? ? Figure 1. 3: Autopilot con? guration †¢ Describe aircraft or other dynamics systems in a set of ? rst order di? erential equations. Expressed in a matrix form †¢ State space analysis and design techniques– very powerful technique for control systems †¢ Matrix manipulation knowledge required 1. 4 1. 4. 1 Introduction to the courseContent This course will cover †¢ state space analysis and design techniques for aircraft †¢ simple ? ight control systems including stability aug mentation systems, and simple autopilots †¢ handling qualities 10 CHAPTER 1. INTRODUCTION Flight Management 6 Systems/Autopilot 6 + -? 6 – SAS – Actuators – Aircraft dynamics – Sensor  6 Navigation Systems ? ? Figure 1. 4: Autopilot con? guration †¢ Fly-By-Wire (FBW) 1. 4. 2 Tutorials and coursework †¢ Tutorials will start from Week 3 †¢ One tutorial section in each week †¢ One coursework based on MATLAB/Simulink simulation, must be handed in before 4:00 PM Thursday, Week 11 1. 4. 3Assessment †¢ Coursework: 20%; †¢ Examination: 2 hours; attempt 3 from 5 questions; 80% of the ? nal mark. 1. 4. 4 Lecture plan †¢ Overall ? ight envelope †¢ Flight control systems †¢ Modern control design methodology †¢ The introduction of the course– structure, assessment, exercises, references 1. Introduction 2. Response to the controls (a) State space analysis (b) Longitudinal response to elevator and throttle (c) Transient response to aileron and rudder 3. Aircraft stability augmentation systems 1. 4. INTRODUCTION TO THE COURSE (a) Performance evaluation †¢ †¢ †¢ †¢ stability Time domain requirements Frequency domain speci? ations Robustness 11 (b) Longitudinal Stability Augmentation Systems †¢ Choice of the feedback variables †¢ Root locus and gain determination †¢ Phugoid suppress (c) Lateral stability augmentation systems †¢ Roll feedback for aileron control †¢ Yaw rate feedback for rudder control 4. Simple autopilot design †¢ Augmented longitudinal dynamics †¢ Height hold systems 5. Handling Qualities (a) Time delay systems (b) Pilot-in-loop dynamics (c) Handling qualities (d) Frequency domain analysis (e) Pilot induced oscillation 6. Flight Control system implementation Fly-by-wire technique 1. 4. 5 References 1. Flight Dynamics Principles.M. V. Cook. 1997. Arnold. Chaps. 4,5,6,7,10,11 2. Automatic Flight Control Systems. D. McL ean. 1990. Prentice Hall International Ltd. Chaps. 2, 3,6,9. 3. Introduction to Avionics Systems. Second edition. R. P. G. Collinson. 2003. Kluwer Academic Publishers. Chap. 4 12 CHAPTER 1. INTRODUCTION Chapter 2 Longitudinal response to the control 2. 1 Longitudinal dynamics From Flight Dynamics course, we know that the linearised longitudinal dynamics can be written as mu ? ? ? X ? X ? X ? X u? w? ? w + (mWe ? )q + mg? cos ? e ? u ? w ? ?w ? q ? Z ? Z ? Z ? Z ? u + (m ? )w ? ? w ? (mUe + )q + mg? sin ? e ? u ? w ? ?w ? q ?M ? M ? M ? M u? w? ? w + Iy q ? ? q ? ?u ? w ? ?w ? q = = = ? X ? t ? Z ? t ? M ? t (2. 1) (2. 2) (2. 3) The physical meanings of the variables are de? ned as u: Perturbation about steady state velocity Ue w: Perturbation on steady state normal velocity We q: Pitch rate ? : Pitch angle Under the assumption that the aeroplane is in level straight ? ight and the reference axes are wind or stability axes, we have ? e = We = 0 (2. 4) The main controls in longitudina l dynamics are the elevator angle and the engine trust. The small perturbation terms in the right side of the above equations can be expressed as ? X ? t ?Z ? t ? M ? t where 13 = = = ? X ? X ? e + ? e ?Z ? Z ? e + ? e ?M ? M ? e + ? e (2. 5) (2. 6) (2. 7) 14 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL ? e : the elevator de? ection (Note ? is used in Appendix 1) ? : engine thrust perturbation Substituting the above expression into the longitudinal symmetric motion yields ? X ? X ? X ? X u? w? ? w? q + mg? ?u ? w ? ?w ? q ? Z ? Z ? Z ? Z ? u + (m ? )w ? ? w ? (mUe + )q ? u ? w ? ?w ? q ? M ? M ? M ? M u? w? ? w + Iy q ? ? q ? ?u ? w ? ?w ? q mu ? ? = = = ? X ? X ? e + ? e ?Z ? Z ? e + ? e ?M ? M ? ?e + e (2. 8) (2. 9) (2. 10)After adding the relationship ? ? = q, (2. 11) Eqs. (2. 8)- (2. 11) can be put in a more concise vector and matrix format. The longitudinal dynamics can be written as ? m ? 0 ? ? 0 0 ? ?X ? w ? ?Z m ? ?w ? ? ? M ? w ? 0 0 0 Iy 0 u ? 0 0 w ? ? 0 q ? ? 1 ? ? ? = ? ? ? ? ? ? ? ? ? ?X ? u ? Z ? u ? M ? u ? X ? w ? Z ? w ? M ? w ? Z ? q ? X ? q + mUe ?M ? q 0 0 ?X e ? Z e ? M e 0 ?X ?Z ?M ? ? ? ? 1 ?mg u 0 w 0 q ? 0 ? ? ?+ ? ?e ? (2. 12) 0 Put all variables in the longitudinal dynamics in a vector form as ? ? u ? w ? ? X=? ? q ? ? and let m ? ?X ? w ? ? 0 m ? ?Z ? ?w ? = ? 0 ? ?M ? w ? 0 ? ?X ? X ? = ? ? ? B ? = ? ? ? u ? Z ? u ? M ? u ? w ? Z ? w ? M ? w ? Z ? q (2. 13) ? M 0 0 Iy 0 ?X ? q ? 0 0 ? ? 0 ? 1 (2. 14) ? ?mg 0 ? ? 0 ? 0 A + mUe ?M ? q (2. 15) 0 0 ?X e ? Z e ? M e 0 ?X ?Z ?M ? ? ? ? 1 (2. 16) 0 U= ?e ? (2. 17) 2. 1. LONGITUDINAL DYNAMICS Equation (2. 12) becomes 15 ? MX = A X + B U (2. 18) It is custom to convert the above set of equations into a set of ? rst order di? erential equations by multiplying both sides of the above equation by the inverse of the matrix M , i. e. , M ? 1 . Eq. (2. 18) becomes ? ? ? ? ? ? u ? xu xw xq x? x? e x? u ? w ? ? zu zw zq z? ? ? w ? ? z? z? ? ? e ? ? ? =? ? ? ? ( 2. 19) ? q ? ? mu mw mq m? ? ? q ? + ? m? e m? ? ? ? ? ? 0 0 1 0 0 0 ? Let xu ? zu A = M ? 1 A = ? ? mu 0 ? ? xw zw mw 0 xq zq mq 1 ? x? z? ? ? m? ? 0 (2. 20) and x? e ? z? e B = M ? 1 B = ? ? m ? e 0 ? x? z? ? ? m? ? 0 (2. 21) It can be written in a concise format ? X = AX + BU (2. 22) Eq. (2. 22) with (2. 20) and (2. 21) is referred as the state space model of the linearised longitudinal dynamics of aircraft. Appendix 1 gives the relationship between the new stability and control derivatives in the matrix A and B, i. e. xu , so on, with the dimensional and non-dimensional derivatives, where ?X ? Xu = ? u (2. 23) denotes dimensional derivative and Xu its corresponding non-dimensional derivative. These relationships are derived based on the Cramer’s rule and hold for general body axes. In the case when the derivatives are referred to wind axes, as in this course, the following simpli? cations should be made Ue = Vo , We = 0, sin ? e = 0, cos ? e = 1 (2. 24) The description of the longitudinal dynamics in the matrix-vector format as in (2. 19) can be extended to represent all general dynamic systems. Consider a system with order n, i. e. , the system can be described by n order di? rential equation (as it will be explained later, this is the same as the highest order of the denominator polynomial in the transfer function is n). In the representation (2. 22), A ? Rn? n is the system matrix ; B ? Rn? m is the input matrix ; X ? Rn is the state vector or state variables and U ? Rm the input or input vector. The equation (2. 22) is called state equation. For the stability augmentation system, only the in? uence of the variation of the elevator angle, i. e. the primary aerodynamic control surface, is concerned. The above equations of motion can be simpli? ed. The state space representation remains the 6 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL same format as in eq. (2. 22) with the same matrix A and state variables but with a di? erent B and input U as given below ? ? x ? e ? z ? B = M ? 1 B = ? ?e ? (2. 25) ? m? e ? 0 and U = ? e (2. 26) Remark: It should be noticed that in di? erent textbooks, di? erent notations are used. For the state space representation of longitudinal dynamics, sometime widetilded derivatives are used as follows ? ? 1 ? X 1 ? X ? ? 1 ? X ? ? 0 ? g u ? u m ? u m ? w m e 1 ? Z 1 ? Z 1 ? Z ? w ? ? 0 ? ? w ? ? m e ? ?+? ? ? ? = ? m ? u m ? w Ue ? ? e (2. 27) ? q ? Mu ? Mw Mq 0 ? ? q ? ? M? e ? ? ? ? 0 0 1 0 0 where Mu = Mw = 1 ? M 1 ? Z 1 ? M + ? Iyy ? u m ? u Iyy ? w ? 1 ? M 1 ? Z 1 ? M + ? Iyy ? w m ? w Iyy ? w ? 1 ? M 1 ? M + Ue ? Iyy ? q Iyy ? w ? (2. 28) (2. 29) (2. 30) (2. 31) Mq = M? e = 1 ? M 1 ? Z 1 ? M + ? Iyy e m e Iyy ? w ? The widetilded derivatives and the other derivatives in the matrices are the same as the expression of the small letter derivatives under certain assumptions, i. e. using stability axis. 2. 2 2. 2. 1 State space description State variables A minimum set of variables which, when known at time t0 , together with the input, are su? ient to describe the behaviours of the system at any time t > t0 . State variables may have no any physical meanings and may be not measurable. For the longitudinal dynamic of aircraft, there are four state variables, i. e, ? ? u ? w ? ? X=? (2. 32) ? q ? ? and one input or control variable, the elevator de? ection, U = ? e (2. 33) 2. 3. LONGITUDINAL STATE SPACE MODEL Thus n=4 m=1 17 (2. 34) The system matrix and input matrix of the longitudinal dynamics are given by ? ? xu xw xq x? ? z zw zq z? ? ? A = M ? 1 A = ? u (2. 35) ? mu mw mq m? ? 0 0 1 0 and ? x? e ? z ? B = M ? 1 B = ? ?e ? ? m ? e ? 0 ? (2. 36) respectively. . 2. 2 General state space model w Ue When the angle of attack ? is of concern, it can be written as ? = which can be put into a general form as y = CX where y=? = and C= 0 1/Ue 0 0 (2. 40) Eq. (2. 38) is called Output equation; y the output variable and C the output matrix. For more general case where there are more than one output and has a direct path from input to output variable, the output equation can be written as Y = CX + DU (2. 41) w Ue (2. 38) (2. 39) (2. 37) where Y ? Rr ,C ? Rr? n and D ? Rr? m . For motion of aerospace vehicles including aircraft and missiles, there is no direct path between input and output.In this course only the case D = 0 is considered if not explicitly pointed out. Eq. (2. 22) and (2. 38) (or (2. 41)) together represent the state space description of a dynamic system, which is opposite to the transfer function representation of a dynamic system studied in Control Engineering course. 2. 3 Longitudinal state space model When the behaviours of all the state variables are concerned, all those variables can be chosen as output variables. In addition, there are other response quantities of interest including the ? ight path angle ? , the angle of attack ? and the normal acceleration az (nz ).Putting all variables together, the output vector can be written a s 18 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL ? ? ? ? ? Y =? ? ? ? ? Invoking the relationships ? = ? ? ? ? ? ? ? ? ? ? u w q ? ? ? az w Ue (2. 42) (2. 43) w Ue (2. 44) the ? ight path angle ? = = and the normal acceleration az (nz ) az = = = ?Z/m = ? (Zu u + Zw w + Zq q + Zw w + Z? e ? e )/m ? ? ? (w ? qUe ) ? ?zu u ? zw w ? zq q ? z? e ? e + Ue zq (2. 45) where the second equality substituting the expression matrix is given by ? ? ? u 1 ? w ? ? 0 ? ? ? ? q ? ? 0 ? ? ? Y =? ? ? =? 0 ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? 0 az ? zu ollows from (2. 9) and the last equality is obtained by of w in its concise derivative format. Hence the output ? 0 1 0 0 1/Ue ? 1/Ue ? zw 0 0 1 0 0 0 ? zq + Ue 0 0 0 1 0 1 0 ? ? ? ? ? ? ? ? ? ? u ? ? ? w ? ? +? q ? ? ? ? ? 0 0 0 0 0 0 ? z? e ? ? ? ? ? ? ? e ? ? ? ? (2. 46) There is a direct path between the output and input! The state space model of longitudinal dynamics consists of (2. 22) and (2. 46). 2. 3. 1 Numerical example Boeing 747 jet transpor t at ? ight condition cruising in horizontal ? ight at approximately 40,000 ft at Mach number 0. 8. Relevant data are given in Table 2. 1 and 2. 2.Using tables in Appendix 1, the concise small derivatives can be calculated and then the system matrix and input matrix can be derived as ? ? ? 0. 006868 0. 01395 0 ? 32. 2 ? ?0. 09055 ? ?0. 3151 774 0 ? A=? (2. 47) ? 0. 0001187 ? 0. 001026 ? 0. 4285 ? 0 0 0 1 0 ? ? ? 0. 000187 ? ?17. 85 ? ? B=? (2. 48) ? ?1. 158 ? 0 Similarly the parameters matrices in output equation (2. 46) can be determined. It should be noticed that English unit(s) is used in this example. 2. 4. AIRCRAFT DYNAMIC BEHAVIOUR SIMULATION USING STATE SPACE MODELS19 Table 2. 1: Boeing 747 transport data 636,636lb (2. 83176 ? 106 N) 5500 ft2 (511. m2 ) 27. 31 ft (8. 324 m) 195. 7 ft (59. 64 m) 0. 183 ? 108 slug ft2 (0. 247 ? 108 kg m2 ) 0. 331 ? 108 slug ft2 (0. 449 ? 108 kg m2 ) 0. 497 ? 108 slug ft2 (0. 673 ? 108 kg m2 ) -0. 156 ? 107 slug ft2 (-0. 212 ? 107 kg m2 ) 774 ft /s (235. 9m/s) 0 5. 909 ? 10? 4 slug/ft3 (0. 3045 kg/m3 ) 0. 654 0. 0430 W S c ? b Ix Iy Iz Izx Ue ? 0 ? CL0 CD Table 2. 2: Dimensional Derivatives– B747 jet X(lb) Z(lb) M(ft. lb) u(f t/s) ? 1. 358 ? 102 ? 1. 778 ? 103 3. 581 ? 103 w(f t/s) 2. 758 ? 102 ? 6. 188 ? 103 ? 3. 515 ? 104 q(rad/sec) 0 ? 1. 017 ? 105 ? 1. 122 ? 107 2 w(f t/s ) ? 0 1. 308 ? 102 -3. 826 ? 103 5 ? e (rad) -3. 17 ? 3. 551 ? 10 ? 3. 839 ? 107 2. 3. 2 The choice of state variables The state space representation of a dynamic system is not unique, which depends on the choice of state variables. For engineering application, state variables, in general, are chosen based on physical meanings, measurement, or easy to design and analysis. For the longitudinal dynamics, in additional to a set of the state variables in Eq. (2. 32), another widely used choice (in American) is ? u ? ? ? ? X=? ? q ? ? ? (2. 49) Certainly, when the logitudinal dynamics of the aircraft are represented in terms of the above state variab les, di? rent A, B and C are resulted (see Tutorial 1). 2. 4 Aircraft dynamic behaviour simulation using state space models State space model developed above provides a very powerful tool in investigate dynamic behavious of an aircraft under various condition. The idea of using state pace models for predicting aircraft dynamic behavious or numerical simulation can be explained by 20 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL the following expression X(t + ? t) = X(t) + dX(? ) ? |? =t ? t = X(t) + X(t)? t d? (2. 50) ? where X(t) is current state, ? t is step size and X(t) is the derivative calculated by the state space equation. . 4. 1 Aircraft response without control ? X = AX X(0) = X0 (2. 51) 2. 4. 2 Aircraft response to controls ? X = AX + BU ; X(0) = 0 (2. 52) where U is the pilot command 2. 4. 3 Aircraft response under both initial conditions and controls ? X = AX + BU ; X(0) = X0 (2. 53) 2. 5 Longitudinal response to the elevator After the longitudinal dynamics are descri bed by the state space model, the time histories of all the variables of interests can be calculated. For example, the time responses of the forward velocity u, normal velocity w (angle of attack) and ? ight path angle ? under the step movement of the levator are displayed in Fig 2. 1–2. 5 Discussion: If the reason for moving the elevator is to establish a new steady state ? ight condition, then this control action can hardly be viewed as successful. The long lightly damped oscillation has seriously interfered with it. A good operation performance cannot be achieved by simply changing the angle of elevator. Clearly, longitudinal control, whether by a human pilot or automatic pilot, demands a more sophisticated control activity than open-loop strategy. 2. 6 Transfer of state space models into transfer functions Taking Laplace transform on both sides of Eq. (2. 2) under the zero initial assumption yields sX(s) = Y (s) = where X(s) = L{X(t)}. AX(s) + BU (s) CX(s) (2. 54) (2. 55) 2. 6. TRANSFER OF STATE SPACE MODELS INTO TRANSFER FUNCTIONS21 Step response to elevator: Velocity 90 80 70 60 Velocity(fps) 50 40 30 20 10 0 0 1 2 3 4 5 Time(s) 6 7 8 9 10 Figure 2. 1: Longitudinal response to the elevator Step response to evelator: angle of attack 0 ?0. 005 ?0. 01 Angle of attack(rad) ?0. 015 ?0. 02 ?0. 025 ?0. 03 0 1 2 3 4 5 Time(s) 6 7 8 9 10 22 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Step respnse to elevator: Flight path angle 0. 1 0. 08 0. 06 0. 04 Flight path angle (rad) 0. 02 0 0. 02 ?0. 04 ?0. 06 ?0. 08 ?0. 1 0 1 2 3 4 5 Time(s) 6 7 8 9 10 Figure 2. 2: Longitudinal response to the elevator Step Response to elevator: long term 90 80 70 60 Velocity (fps) 50 40 30 20 10 0 0 100 200 300 Time (s) 400 500 600 Figure 2. 3: Longitudinal response to the elevator 2. 6. TRANSFER OF STATE SPACE MODELS INTO TRANSFER FUNCTIONS23 Step response to elevator: long term 0 ?0. 005 ?0. 01 Angle of attack (rad) ?0. 015 ?0. 02 ?0. 025 ?0. 03 0 100 200 300 Time (s) 400 50 0 600 Figure 2. 4: Longitudinal response to the elevator Step response to elevator: long term 0. 1 0. 08 0. 06 0. 04 Flight path angle (rad) 0. 02 0 ?0. 2 ?0. 04 ?0. 06 ?0. 08 ?0. 1 0 100 200 300 Time (s) 400 500 600 Figure 2. 5: Longitudinal response to the elevator 24 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Y (s) = C[sI ? A]? 1 BU (s) Hence the transfer function of the state space representation is given by G(s) = C[sI ? A]? 1 B = C(Adjoint(sI ? A))B det(sI ? A) (2. 56) (2. 57) Example 1: A short period motion of a aircraft is described by ? ? q ? = ? 0. 334 ? 2. 52 1. 0 ? 0. 387 ? q + ? 0. 027 ? 2. 6 ? e (2. 58) where ? e denotes the elevator de? ection. The transfer function from the elevator de? ection to the angle of attack is determined as follows: ? (s) ? 0. 27s ? 2. 6 = 2 ? e (s) s + 0. 721s + 2. 65 (2. 59) # The longitudinal dynamics of aircraft is a single-input and multi-output system with one input ? e and several outputs, u, w, q, ? , ? , az . Using the techniq ue in Section (2. 6), the transfer functions between each output variable and the input elevator can be derived. The notation u(s) Gue = (2. 60) ? ?e (s) is used in this course to denote the transfer function from input ? e to output u. For the longitudinal dynamics of Boeing 747-100, if the output of interest is the forward velocity, the transfer function can be determined using formula (2. 56) as u(s) ? e (s) ? 0. 00188s3 ? 0. 2491s2 + 24. 68s + 11. 6 s4 + 0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 0041959 (2. 61) Gue ? = = Similarly, all other transfer functions can be derived. For a system with low order like the second order system in Example 1, the derivation of the corresponding transfer function from its state space model can be completed manually. For complicated systems with high order, it can be done by computer software like MATLAB. It can be found that although the transfer functions from the elevator to di? erent outputs are di? erent but they have the same denominat or, i. e. s4 + 0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 041959 for Beoing 747-100. Only the numerators are di? erent. This is because all the denominators of the transfer functions are determined by det(sI ? A). 2. 6. 1 From a transfer function to a state space model The number of the state variable is equal to the order of the transfer function, i. e. , the order of the denominator of the transfer function. By choosing di? erent state variables, for the same transfer function, di? erent state space models are given. 2. 7. BLOCK DIAGRAM REPRESENTATION OF STATE SPACE MODELS 25 2. 7 Block diagram representation of state space models 2. 8 2. 8. 1 Static stability and dynamic modesAircraft stability Consider aircraft equations of motion represented as ? X = AX + BU (2. 62) The stability analysis of the original aircraft dynamics concerns if there is no any control e? ort,whether the uncontrolled motion is stable. It is also referred as openloop stability in general control engineeri ng. The aircraft stability is determined by the eigenvalues of the system matrix A. For a matrix A, its eigenvalues can be determined by the polynomial det(? I ? A) = 0 (2. 63) Eigenvalues of a state space model are equal to the roots of the characteristic equation of its corresponding transfer function.An aircraft is stable if all eigenvalues of its system matrix have negative real part. It is unstable if one or more eigenvalues of the system matrix has positive real part. Example for a second order system Example 1 revisited 2. 8. 2 Stability with FCS augmentation When a ? ight control system is installed on an aircraft. The command applied on the control surface is not purely generated by a pilot any more; it consists of both the pilot command and the control signal generated by the ? ight control system. It can be written as ? U = KX + U (2. 64) ? where K is the state feedback gain matrix and U is the reference signal or pilot command.The stability of an aircraft under ? ight co ntrol systems is refereed as closed-loop stability. 26 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Then the closed-loop system under the control law is given by ? ? X = (A + BK)X + B U (2. 65) Stability is also determined by the eigenvalues of the system matrix of the system (2. 65), i. e. , A + BK. Sometimes only part of the state variables are available, which are true for most of ? ight control systems, and only these measurable variables are fed back, i. e. output feedback control. It can be written as ? ? U = KY + U = KCX + B U where K is the output feedback gain matrix.Substituting the control U into the state equation yields ? ? X = (A + BKC)X + B U (2. 67) (2. 66) Then the closed-loop stability is determined by the eigenvalues of the matrix A+BKC. Boeing Example (cont. ) Open-loop stability: ? 0. 3719 + 0. 8875i ? 0. 3719 ? 0. 8875i eig(A) = ? 0. 0033 + 0. 0672i ? 0. 0033 ? 0. 0672i (2. 68) Hence the longitudinal dynamics are stable. The same conclusion can be drawn from the the transfer function approach. Since the stability of an open loop system is determined by its poles from denominator of its transfer function, i. e. , s4 +0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 041959=0. Its roots are given by s1,2 = ? 0. 3719  ± 0. 8875i s3,4 = ? 0. 0033  ± 0. 0672i (2. 69) (This example veri? es that the eigenvalues of the system matrix are the same as the roots of its characteristic equation! ) 2. 8. 3 Dynamic modes Not only stability but also the dynamic modes of an aircraft can be extracted from the stat space model, more speci? cally from the system matrix A. Essentially, the determinant of the matrix A is the same as the characteristic equation. Since there are two pairs of complex roots, the denominator can be written in the typical second order system’s format as 2 2 (s2 + 2? ? p s + ? p )(s2 + 2? s ? s s + ? s ) (2. 70) (2. 71) (2. 72) where ? p = 0. 0489 for Phugoid mode and ? s = 0. 3865 for the short period mode. ?s = 0. 9623 ? p = 0. 0673 2. 9. REDUCED MODELS OF LONGITUDINAL DYNAMICS B 747 Phugoid mode 1. 5 27 1 93. 4s 0. 5 Perturbation 0 ? 0. 5 ? 1 0 300 600 Time (s) Figure 2. 6: Phugoid mode of Beoing 747-100 The ? rst second order dynamics correspond to Phugoid mode. This is an oscillad d tion with period T = 1/? p = 1/(0. 0672/2? ) = 93. 4 second where ? p is the damped frequency of the Phugoid mode. The damping ratio for Phugoid mode is very small, i. e. , ? p = 0. 489. As shown in Figure 2. 6, Phugoid mode for Boeing 747-100 at this ? ight condition is a slow and poor damped oscillation. It takes a long time to die away. The second mode in the characteristic equation corresponds to the short period mode in aircraft longitudinal dynamics. As shown in Fig. 2. 7, this is a well damped response with fast period about T = 7. 08 sec. (Note the di? erent time scales in Phugoid and short period response). It dies away very quickly and only has the in? uence at the beginning of the response. 2. 9 Reduced mode ls of longitudinal dynamics Based on the above example, we can ? d Phugoid mode and short period mode have di? erent time scales. Actually all the aircraft have the similar response behaviour as Boeing 747. This makes it is possible to simplify the longitudinal dynamics under certain conditions. As a result, this will simplify following analysis and design. 2. 9. 1 Phugoid approximation The Phugoid mode can be obtained by simplifying the full 4th order longitudinal dynamics. Assumptions: †¢ w and q respond to disturbances in time scale associated with the short period 28 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Beoing 747 Short period mode From: U(1) 0. 7 0. 6 0. 5 0. 4Perturbation To: Y(1) 0. 3 0. 2 0. 1 0 ?0. 1 ?0. 2 0 5 10 15 Time (sec. ) Figure 2. 7: Short Period mode of Beoing 747-100 mode; it is reasonable to assume that q is quasi-steady in the longer time scale associated with Phugoid mode; q=0; ? †¢ Mq , Mw , Zq , Zw are neglected since both q and w are rel atively small. ? ? ? Then from the table in Appendix 1, we can ? nd the expression of the small concise derivatives under these assumptions. The longitudinal model reduces to ? ? ? Xu Xw ? ? X? e ? 0 ? g u ? u m m m Zw ? w ? ? Zu Ue 0 ? ? w ? ? Z? e ? m m ? ? ? =? M ? + ? M ? ?e (2. 73) ? m ? ? 0 ? ? u Mw 0 0 ? q ? ? ? e ? Iyy Iyy Iyy ? ? ? 0 0 1 0 0 This is not a standard state space model. However using the similar idea in Section 2. 6, by taking Laplace transform on the both sides of the equation under the assumption that X0 = 0, the transfer function from the control surface to any chosen output variable can be derived. The characteristic equation (the denominator polynomial of a transfer function) is given by ? (s) = As2 + Bs + C where A = ? Ue Mw Ue B = gMu + (Xu Mw ? Mu Xw ) m g C = (Zu Mw ? Mu Zw ) m (2. 75) (2. 76) (2. 77) (2. 74) 2. 9. REDUCED MODELS OF LONGITUDINAL DYNAMICS 29 This corresponds to the ? st mode (Phugoid mode) in the full longitudinal model. After substit uting data for Beoing 747 in the formula, the damping ratio and the natural frequency are given by ? = 0. 068, ? n = 0. 0712 (2. 78) which are slightly di? erent from the true values, ? p = 0. 049, ? p = 0. 0673, obtained from the full 4th longitudinal dynamic model. 2. 9. 2 Short period approximation In a short period after actuation of the elevator, the speed is substantially constant while the airplane pitches relatively rapidly. Assumptions: †¢ u=0 †¢ Zw (compared with m) and Zq (compared with mUe ) are neglected since they ? are relatively small. w ? q ? Zw m mw Ue mq w q + Z ? e m m ? e ?e (2. 79) The characteristic equation is given by s2 ? ( Zw 1 1 Mq Zw + (Mq + Mw Ue ))s ? (Ue Mw ? )=0 ? m Iyy Iyy m (2. 80) Using the data for B747-100, the result obtained is s2 + 0. 741s + 0. 9281 = 0 with roots s1,2 = ? 0. 371  ± 0. 889i The corresponding damping ratio and natural frequency are ? = 0. 385 wn = 0. 963 (2. 83) (2. 82) (2. 81) which are seen to be almost same as t hose obtained from the full longitudinal dynamics. Actually the short period approximation is very good for a wide range of vehicle characteristics and ? ight conditions. Tutorial 1 1. Using the small concise derivatives, ? d the state equations of longitudinal dynamics of an aircraft with state variables ? ? u ? ? ? ? X=? (2. 84) ? q ? ? 30 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Normal acceleration at the pilot seat is a very important quantity, de? ned as the normal acceleration response to an elevator measured at the pilot seat, i. e. aZx = w ? Ue q ? lx q ? ? (2. 85) where lx is the distance from c. g. to the pilot seat. When the outputs of interest are pitch angle ? and the normal acceleration at the pilot seat, ? nd the output equations and identify all the associated parameter matrices and dimension of variables (state, input and output). . The motion of a mass is governed by m? (t) = f (t) x (2. 86) where m is mass, f (t) the force acting on the mass and x(t) the di splacement. When the velocity x(t) and the velocity plus the position x(t) + x(t) are chosen ? ? as state variables, and the position is chosen as output variable, ? nd the state space model of the above mass system. Determine the transfer function from the state space model and compare it with the transfer function directly derived from the dynamic model in Eq. (2. 86). 3. Find the transfer function from elevator de? ection ? e to pitch rate q in Example 1.Determine the natural frequency and damping ratio of the short period dynamics. Is it possible to ? nd these information from a state space model directly, instead of using the transfer function approach? 4. Suppose that the control strategy ? ?e = ? + 0. 1q + ? e (2. 87) ? is used for the aircraft in Example 1 where ? e is the command for elevator de? ection from the pilot. Determine stability of the short period dynamics under the above control law using both state space method and Routh stability criterion in Control Engineeri ng (When Routh stability criterion is applied, you can study the stability using the transfer function from ? to q or that from ? e to ? (why? )). Compare and discuss the results achieved. Chapter 3 Lateral response to the controls 3. 1 Lateral state space models mv ? ?Y v ? ( ? Y + mWe )p ? ?v ? p ? mUe )r ? mg? cos ? e ? mg? sin ? e ? L ? L ? L ? v + Ix p ? ? p ? Ixz r ? ? r ? v ? p ? r ? N ? N ? N v ? Ixz p ? ? p + Iz r ? ? r ? ?v ? p ? r = = = ? Y ? A + A ? L ? A + A ? N ? A + A ? Y ? R R ? L ? R R ? N ? R R (3. 1) (3. 2) (3. 3) Referred to body axes, the small perturbed lateral dynamics are described by ? ( ? Y ? r where the physical meanings of the variables are de? ed as v: Lateral velocity perturbation p: Roll rate perturbation r: Yaw rate perturbation ? : Roll angle perturbation ? : Yaw angle perturbation ? A : Aileron angle (note that it is denoted by ? in Appendix 1) ? R : Rudder angle (note that it is denoted by ? in Appendix 1) Together with the relationships ? ?= p and ? ? = r, (3. 4) (3. 5) the lateral dynamics can be described by ? ve equations, (3. 1)-(3. 5). Treating them in the same way as in the longitudinal dynamics and after introducing the concise notation as in Appendix 1, these ? ve equations can be represented as ? ? ? ? ? ? v ? p ? r ? ? ? ? ? ? yv lv nv 0 0 yp lp np 1 0 yr lr nr 0 1 y? 0 0 0 0 y? 0 0 0 0 v p r ? ? ? ? y? A l? A n ? A 0 0 y? R l? R n ? R 0 0 ? ? ? ? ? ? ? A ? R (3. 6) ? ? ? ? ?=? ? ? ? ? ? ? ? ? ?+? ? ? ? ? 31 32 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS When the derivatives are referred to airplane wind axes, ? e = 0 (3. 7) from Appendix 1, it can be seen that y? = 0. Thus all the elements of the ? fth column in the system matrix are zero. This implies that ? has no in? uence on all other variables. To simplify analysis, in most of the cases, the following fourth order model is used ? ? ? ? ? v ? v y? A y? R yv yp yr y? ? p ? ? lv lp lr 0 ? ? p ? ? l? A l? R ? ?A ? ? ? ? ? ? =? (3. 8) ? r ? ? n v n p n r 0 ? ? r ? + ? n ? A n ? R ? ? R ? ? ? 0 1 0 0 0 0 ? (It should be noticed that the number of the states is still ? ve and this is just for the purpose of simplifying analysis). Obviously the above equation can also be put in the general state space equation ? X = AX + BU with the state variables ? v ? p ? ? X=? ? r ? , ? ?A ? R yp lp np 1 yr lr nr 0 ? (3. 9) (3. 10) the input/control variables U= the system matrix yv ? lv A=? ? nv 0 and the input matrix ? ? , ? y? 0 ? ? 0 ? (3. 11) (3. 12) y ? A ? l? A B=? ? n ? A 0 ? y? R l? R ? ? n ? R ? 0 (3. 13) For the lateral dynamics, another widely used choice of the state variables (American system) is to replace the lateral velocity v by the sideslip angle ? and keep all others. Remember that v (3. 14) Ue The relationships between these two representations are easy to identify. In some textbooks, primed derivatives, for example, Lp , Nr , so on, are used for state space representation of the lateral dynamics. The primed derivatives ar e the same as the concise small letter derivatives used in above and in Appendix 1.For stability augmentation systems, di? erent from the state space model of the longitudinal dynamics where only one input elevator is considered, there are two inputs in the lateral dynamic model, i. e. the aileron and rudder. 3. 2. TRANSIENT RESPONSE TO AILERON AND RUDDER Table 3. 1: Dimensional Derivatives– B747 jet Y(lb) L(ft. lb) N(ft. lb) v(ft/s) ? 1. 103 ? 103 ? 6. 885 ? 104 4. 790 ? 104 p(rad/s) 0 ? 7. 934 ? 106 ? 9. 809 ? 105 r(rad/sec) 0 7. 302 ? 106 ? 6. 590 ? 106 ? A (rad) 0 ? 2. 829 ? 103 7. 396 ? 101 ? R (rad) 1. 115 ? 105 2. 262 ? 103 ? 9. 607 ? 103 33 3. 2 3. 2. 1 Transient response to aileron and rudderNumerical example Consider the lateral dynamics of Boeing 747 under the same ? ight condition as in Section 2. 3. 1. The lateral aerodynamic derivatives are listed in Table 3. 1. Using the expression in Appendix 1, all the parameters in the state space model can be calculated, gi ven by ? ? ? 0. 0558 0. 0 ? 774 32. 2 ? ?0. 003865 ? 0. 4342 0. 4136 0 ? ? A=? (3. 15) ? 0. 001086 ? 0. 006112 ? 0. 1458 0 ? 0 1 0 0 and 0. 0 ? ?0. 1431 B=? ? 0. 003741 0. 0 ? ? 5. 642 0. 1144 ? ? ? 0. 4859 ? 0. 0 (3. 16) Stability Issue ? 0. 0330 + 0. 9465i ? 0. 0330 ? 0. 9465i eig(A) = ? 0. 5625 ? 0. 0073 (3. 17)All the eigenvalues have negative real part hence the lateral dynamics of the Boeing 747 jet transport is stable. 3. 2. 2 Lateral response and transfer functions ? v p ? ?+B r ? ? State space model of lateral dynamics ? ? ? v ? ? p ? ? ? ? ? = A? ? r ? ? ? ? ? ?A ? R (3. 18) This is a typical Multi-Input Multi-Output (MIMO) system. For an MIMO system like the lateral dynamics, similar to the longitudinal dynamics, its corresponding transfer function can be derived using the same technique introduced in Chapter 2. However, in this case the corresponding Laplace transform of the state space model, 34 CHAPTER 3.LATERAL RESPONSE TO THE CONTROLS G(s) ? Rr? m is a complex functi on matrix which is referred as a transfer function matrix where m is the number of the input variables and r is the number of the output variables. The ijth element in the transfer function matrix de? nes the transfer function between the ith output and jth input, that is, Gyij (s) = u yi (s) . uj (s) (3. 19) For example, GpA (s) denotes the transfer function from the aileron, ? A , to the roll ? rate, p. Its corresponding transfer function matrix is given by ? ? ? ? v G? A (s) GvR (s) v(s) ? ? p(s) ? ? Gp (s) Gp (s) ? ?A (s) ? R ? ? ? ? ?A (3. 20) ? r(s) ? ? Gr (s) Gr (s) ? ?R (s) ? A ? R ? p ? (s) G? A (s) G? R hi(s) With the data of Boeing 747 lateral dynamics, these transfer functions can be found as ? 2. 896s2 ? 6. 542s ? 0. 6209 GvA (s) = 4 fps/rad (3. 21) ? s + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 ? 0. 1431s3 ? 0. 02727s2 ? 0. 1101s rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 22) 0. 003741s3 + 0. 002708s2 + 0. 0001394s ? 0. 004534 GrA (s) = rad/s/rad, deg/s/deg ? s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 23) ? 0. 1431s2 ? 0. 02727s ? 0. 1101 ? rad/rad, or deg/deg (3. 24) G? A (s) = 4 s + 0. 6344s3 + 0. 9375s2 + 0. 097s + 0. 003658 and GpA (s) = ? GvR (s) = ? 5. 642s3 + 379. 4s2 + 167. 5s ? 5. 917 fps/rad s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 25) GpR (s) = ? 0. 1144s3 ? 0. 1991s2 ? 1. 365s rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 26) ? 0. 4859s3 ? 0. 2321s2 ? 0. 008994s ? 0. 05632 rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 27) 0. 1144s2 ? 0. 1991s ? 1. 365 rad/rad, or deg/deg (3. 28) s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 GrR (s) = ? G? R (s) = ? The denominator polynomial of the transfer functions can be factorised as (s + 0. 613)(s + 0. 007274)(s2 + 0. 06578s + 0. 896) (3. 29) 3. 3. REDUCED ORDER MODELS 35 It has one large real root, -0. 5613, one small real root, -0. 0073 (very close to origin) and a pair of complex roots (-0. 0330 + 0. 9465i, -0. 0330 – 0. 9465i). For most of the aircraft, the denominator polynomial of the lateral dynamics can be factorized as above, ie. , with two real roots and a pair of complex roots. That is, 2 (s + 1/Ts )(s + 1/Tr )(s2 + 2? d ? d s + ? d ) = 0 (3. 30) where Ts Tr is the spiral time constant (for spiral mode), Tr is the roll subsidence time constant (for roll subsidence), and ? d , ? are damping ratio and natural frequency of Dutch roll mode. For Boeing 747, from the eigenvalues or the roots, these parameters are calculated as: Spiral time constant Ts = 1/0. 007274 = 137(sec); (3. 31) Roll subsidence time constant Tr = 1/0. 5613 = 1. 78(sec) and Dutch roll natural frequency and damping ratio ? d = 0. 95(rad/sec), ? d = 0. 06578 = 0. 0347 2? d (3. 33) (3. 32) The basic ? ight condition is steady symmetric ? ight, in which all the lateral variables ? , p, r, ? are identically zero. Unlike the elevator, the lateral controls are not used individually to produce changes in steady state.That is because the steady state values of ? , p, r, ? that result from a constant ? A and ? R are not of interest as a useful ? ight condition. Successful movement in the lateral channel, in general, should be the combination of aileron and rudder. In view of this, the impulse response, rather than step response used in the lateral study, is employed in investigating the lateral response to the controls. This can be considered as an idealised situation that the control surface has a sudden move and then back to its normal position, or the recovering period of an airplane deviated from its steady ? ght state due to disturbances. The impulse lateral responses of Boeing 747 under unit aileron and rudder impulse action are shown in Figure 3. 1 and 3. 2 respectively. As seen in the response, the roll subsidence dies away very quickly and mainly has the in? uence at the beginning of the response. The spiral mode has a large time constant a nd takes quite long time to respond. The Dutch roll mode is quite poorly damped and the oscillation caused by the Dutch roll dominates the whole lateral response to the control surfaces. 3. 3 Reduced order models Although as shown in the above ? gures, there are di? rent modes in the lateral dynamics, these modes interact each other and have a strong coupling between them. In general, the approximation of these models is not as accuracy as that in the longitudinal dynamics. However to simplify analysis and design in Flight Control Systems, reduced order models are still useful in an initial stage. It is suggested that the full lateral dynamic model should be used to verify the design based on reduced order models. 36 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS Lateral response to impluse aileron deflection 0. 1 Lateral velocity (f/s) 0. 05 0 ? 0. 05 ? 0. 1 ? 0. 5 0 10 20 30 Time(s) 40 50 60 0. 05 Roll rate (deg/sec) 0 ? 0. 05 ? 0. 1 ? 0. 15 0 x 10 ?3 10 20 30 Time (s) 40 50 60 5 Yaw rate(deg/sec) 0 ? 5 ? 10 ? 15 0 10 20 30 Time (s) 40 50 60 0 Roll angle (deg) ? 0. 05 ? 0. 1 ? 0. 15 ? 0. 2 ? 0. 25 0 10 20 30 Time (s) 40 50 60 Figure 3. 1: Boeing 747-100 lateral response to aileron 3. 3. REDUCED ORDER MODELS 37 Lateral response to unit impluse rudder deflection 10 Lateral velocity (f/s) 5 0 ? 5 ? 10 0 10 20 30 Time (s) 40 50 60 2 Roll rate (deg) 1 0 ? 1 ? 2 0 10 20 30 Time (s) 40 50 60 0. 4 Yaw rate (deg) 0. 2 0 ? 0. 2 ? 0. 4 ? 0. 6 0 10 20 30 Time (s) 40 50 60 Roll angle (deg) 0 ? 1 ? 2 ? 3 ? 4 0 10 20 30 Time (s) 40 50 60 Figure 3. 2: Boeing 747-100 lateral response to Rudder 38 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS 3. 3. 1 Roll subsidence Provided that the perturbation is small, the roll subsidence mode is observed to involve almost pure rolling motion with little coupling into sideslip and yaw. A reduced order model of the lateral-directional dynamics retaining only roll subsidence mode follows by removing the side force and yaw moment equations to giv e p = lp p + l? A ? A + l? R ? R ? (3. 34) If only the in? uence from aileron de? ction is concerned and assume that ? R = 0, taking Laplace transform on Eq. (3. 34) obtains the transfer function p(s) l ? A kp = = ? A s ? lp s + 1/Tr where the gain kp = l? A and the time constant Tr = 1 Ix Iz ? Ixz =? lp Iz Lp + Ixz Np (3. 36) (3. 37) (3. 35) Since Ix Ixz and Iz Ixz , then equation (3. 37) can be further simpli? ed to give the classical approximation expression for the roll mode time constant Tr = ? Ix Lp (3. 38) For the Boeing 747, the roll subsidence estimated by the ? rst order roll subsidence approximation is 0. 183e + 8 Tr = ? = 2. 3sec. (3. 39) ? 7. 934e + 6 It is close to the real value, 1. sec, given by the full lateral model. 3. 3. 2 Spiral mode approximation As shown in the Boeing 747 lateral response to the control surface, the spiral mode is very slow to develop. It is usual to assume that the motion variables v, p, r are quasi-steady relative to the time scale of the mo de. Hence p = v = r = 0 and the ? ? ? lateral dynamics can be written as ? ? ? 0 yv ? 0 ? ? lv ? ? ? ? 0 ? = ? nv ? 0 ? yp lp np 1 yr lr nr 0 y? v 0 p 0 r 0 ? ? y? A ? ? l ? A ? +? ? ? n ? A 0 ? ? y ? R l? R ? ? n ? R ? 0 ?A ? R (3. 40) If only the spiral mode time constant is concerned, the unforced equation can be used.After solving the ? rst and third algebraic equations to yield v and r, Eq. (3. 40) reduces to lp nr ? l n l np ? lp n 0 p yv lr nv ? lr np + yp + yr lv nv ? lv nv y? v r r r (3. 41) ? = ? ? 1 0 3. 3. REDUCED ORDER MODELS 39 Since the terms involving in yv and yp are assumed to be insigni? cantly small compared to the term involving yr , the above expression for the spiral mode can be further simpli? ed as ? y? (lr nv ? lv nr ) ? = 0 ? + (3. 42) yr (lv np ? lp nv ) Therefore the time constant of the spiral mode can be estimated by Ts = yr (lv np ? lp nv ) y? (lr nv ? lv nr ) (3. 43)Using the aerodynamic derivatives of Boeing 747, the estimated spiral mode time c onstant is obtained as Ts = 105. 7(sec) (3. 44) 3. 3. 3 Dutch roll ? p=p=? =? =0 ? v ? r ? = yv nv yr nr v r + 0 n ? A y? R n ? R ? A ? R (3. 45) (3. 46) Assumptions: From the state space model (3. 46), the transfer functions from the aileron or rudder to the lateral velocity or roll rate can be derived. For Boeing 747, the relevant transfer functions are given by GvA (s) = ? GrA (s) = ? GvR (s) = ? GrR (s) = ? ?2. 8955 s2 + 0. 2013s + 0. 8477 0. 003741(s + 0. 05579) s2 + 0. 2013s + 0. 8477 s2 5. 642(s + 66. 8) + 0. 013s + 0. 8477 (3. 47) (3. 48) (3. 49) (3. 50) ?0. 4859(s + 0. 04319) s2 + 0. 2013s + 0. 8477 From this 2nd order reduced model, the damping ratio and natural frequency are estimated as 0. 1093 and 0. 92 rad/sec. 3. 3. 4 Three degrees of freedom approximation Assume that the following items are small and negligible: 1). The term due to gravity, g? 2). Rolling acceleration due to yaw rate, lr r 3). Yawing acceleration as a result of roll rate, np p Third order Dutch roll approximation is given by ? ? ? ? ? ? v ? yv yp yr v 0 y ? R ? p ? = ? lv lp 0 ? ? p ? + ? l? A l? R ? ? r ? nv 0 nr r n? A n?R ?A ? R (3. 51) 40 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS For Boeing 747, the corresponding transfer functions are obtained as GvA (s) = ? GpA (s) = ? GrA (s) = ? ?2. 8955(s + 0. 6681) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) ? 0. 1431(s2 + 0. 1905s + 0. 7691) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 0. 003741(s + 0. 6681)(s + 0. 05579) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 5. 642(s + 0. 4345)(s + 66. 8) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 0. 1144(s ? 4. 432)(s + 2. 691) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) ? 0. 4859(s + 0. 4351)(s + 0. 04254) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) (3. 52) 3. 53) (3. 54) and GvR (s) = ? GpR (s) = ? GrR (s) = ? (3. 55) (3. 56) (3. 57) The poles corresponding to the Dutch roll mode are given by the roots of s2 + 0. 1833s + 0. 8548 = 0. Its damping ratio and natural frequency are 0. 0995 and 0. 921 rad/sec. Compared wit h the values given by the second order Dutch roll approximation, i. e. , 0. 1093 and 0. 92 rad/sec, they are a little bit closer to the true damping ratio ? d = 0. 0347 and the natural frequency ? d = 0. 95 (rad/sec) but the estimation of the damping ratio still has quite poor accuracy. 3. 3. 5 Re-formulation of the lateral dynamicsThe lateral dynamic model can be re-formulated to emphasise the structure of the reduced order model. ? ? v ? yv ? r ? ? nv ? ? ? ? ? p ? = ? lv ? ? 0 ? ? yr nr lr 0 yp np lp 1 g v 0 r 0 p 0 ? ? 0 ? ? n ? A ? +? ? ? l? A 0 ? ? y? R n ? R ? ? l? R ? 0 ? A ? R (3. 58) The system matrix A can be partitioned as A= Directional e? ects Directional/roll coupling e? ects Roll/directional coupling e? ects Lateral or roll e? ects (3. 59) Tutorial 2 1. Using the data of Boeing 747-100 at Case II, form the state space model of the lateral dynamics of the aircraft at this ? ight condition.When the sideslip angle and roll angle are of interest, ? nd the output equa tion. 2. Find the second order Dutch roll reduced model of this airplane. Derive the transfer function from the rudder to the yaw rate based on this reduced order model. 3. 3. REDUCED ORDER MODELS 41 3. Using MATLAB, assess the approximation of this reduced order model based on time response, and the damping ratio and natural frequency of the Dutch roll mode. 4. Based on the third order reduced model in (3. 51), ? nd the transfer function from the aileron to the roll rate under the assumption y? A = yp = 0.